Quantum-Assisted Indoor Localization for Uplink mm-wave and Downlink Visible Light Communication Systems

Transcription

1 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 1 Quantum-Assisted Indoor Locaization for Upink mm-wave and Downink Visibe Light Communication Systems Panagiotis Botsinis, Member, IEEE, Dimitrios Aanis, Student Member, IEEE, Simeng Feng, Zunaira Babar, Hung Nguyen, Member, IEEE, Daryus Chandra, Soon Xin Ng, Senior Member, IEEE, Rong Zhang, Senior Member, IEEE, and Lajos Hanzo, Feow, IEEE Abstract With the proiferation of mm-wave systems and Visibe Light Communications VLC), indoor ocaization may find mutipe appications. When high ocaization accuracy is required and trianguation is not possibe due to the infrastracture and scenario imitations, the computationa compexity of searching on a virtua grid may become excessive. In this contribution, we amagamate upink mm-wave-based and downink VLC-based ocaization. We empoy quantum search agorithms for reducing the computationa compexity required for achieving the optima fu-search-based performance. Regarding the upink mm-wave-based ocaization, we empoy a singe anchor equipped with mutipe Antenna Eements AEs) and we expoit the specuar mutipath components created by the room s was. The proposed soutions outperform the stateof-the-art agorithms. Furthermore, various channe modes are considered, based on rea indoors mm-wave measurements. By using VLC-based trianguation for downink and the proposed mm-wave-based ocaization agorithm for upink, there was an average positioning error of 5.6 cm in the room considered, whie requiring 261 database queries on average. Index Terms Computationa Compexity, Dürr-Høyer Agorithm, Fingerprinting, Grover s Quantum Search Agorithm, Locaization, mm-wave, Quantum Computing, Visibe Light Communications I. INTRODUCTION Indoor ocaization is the process of estimating the position of an agent in an indoor environment, based on either the transmitted upink or the downink signas [1]. Given a singe or mutipe anchors, such as Access Points AP), a user with an unknown ocation in the room, has to estimate its position based on an upink of downink signa [2]. Accurate ocaization may improve the performance of diverse appications, such as beam-forming [3], where a narrow penci beam may be transmitted at high carrier frequencies, hence the receiver s position shoud be accuratey estimated. Other compeing appications incude network management and security [2], or assisted iving [4], where accurate ocaization wi aid activity recognition, movement pattern discoveries and it may The authors are with the Schoo of Eectronics and Computer Science, University of Southampton, Southampton, SO17 1BJ, UK emai: {pb1y14, da4g11, zb2g10, hvn08r, dc2n14, sxn, h}@ecs.soton.ac.uk). The financia support of the European Research Counci under the Advanced Feow Grant, that of the Roya Society s Wofson Research Merit Award and that of the Engineering and Physica Sciences Research Counci under Grant EP/L018659/1 is gratefuy acknowedged. The use of the IRIDIS High Performance Computing Faciity at the University of Southampton is aso acknowedged. detect anomaies. High-precision indoor ocaization may be used for creating new appications, such as accurate storage information in warehouses, improving coworking efficiency in office buidings by finding which meeting room is avaiabe, or where a coeague may be found, assigning the cosest downink Visibe Light Communication VLC) transmitter to the user, as we as improving the consumer s and traveer s experience in shopping mas and airports, by arranging ocation-oriented goods promotions and information deivery. Indoor ocaization may be performed by invoking various technoogies, such as wireess oca area networks [2], VLC systems [5] and wireess sensor networks [6], as ong as there are APs, whose positions are known. The next generations of wireess communications are expected to subsume an increasing number of heterogeneous network architectures [7]. For exampe, there may be femtoces, which amagamate the high bandwidth offered by the miimeter-wave mm-wave) technoogy [8] [12] for the upink and that of the VLC systems [5], [13] [15] for the downink. VLC systems have been shown to perform we in ocaizing users indoors [5], [16] [18], based on a combination of extracted characteristics, such as the Ange-of-Arriva AoA) or the Received Signa Strength Indicator RSSI), as ong as their imited coverage aows it. Due to the wide-spread use of Light Emitting Diodes LED), VLC-based techniques are promising for indoor ocaization. However, since the Fied Of View FOV) of the LEDs empoyed determine the coverage, there may be users whose presence may not be evident, when reying soey on VLC soutions. For this reason, we beieve that mm-wave systems, which may be used for the upink in the next-generation femtoces, may aso assist in the ocaization of indoor users. In highuser-density scenarios, the ocaization oad may be partitioned between the downink VLC and the upink mm-wave inks. Utra WideBand UWB) systems have often been used in the iterature for performing indoors ocaization [1], [4], [19] [22], mainy due to their short symbo duration, which aows a better resoution of the Time of Arrivas ToA) reying on the MutiPath Components MPC) in the Power Deay Profie PDP). In other words, the Inter-Symbo Interference ISI) is reduced, since the reception of a symbo has typicay been competed before a refected copy of it arrives at the receiver. By empoying UWB systems operating at mm-wave carrier frequencies, we may expoit the benefits This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

2 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 2 that UWB system offer in ocaization appications, whie aowing mutipe Antenna Eements AE) to be instaed at the anchors, due to their compact construction, for improving the estimation of the agents positions. Furthermore, the high avaiabe bandwidth of the mm-wave systems, as we as their beamforming capabiities, may aso increase the system s performance, once the users have been accuratey ocaized. As we demonstrate in this paper, the specific construction of the Antenna Array AA), which empoys mutipe AEs has to be harmonized with the symmetry of the room, as we as with the ocation of the anchor. The UWB-based indoor ocaization soutions [4], [21], [22] are based on both the Line Of Sight LOS) path, as we as on the specuar MPCs of the received signa, where a singe anchor equipped with a singe antenna is empoyed. We have aso adopted this approach for our investigations in mm-wave systems. The fingerprinting method [5] may be empoyed In both the VLC-based and the RF-based indoors ocaization categories, if high accuracy is required. The fingerprinting method assumes prior knowedge of the room s topoogy, which has been divided in a virtua grid. Additionay, it expoits that noiseess signas received or transmitted from the center of each virtua tie of the grid, depending on whether they correspond to downink or upink, respectivey, are avaiabe in a pre-buit database. A subset of that database is then searched based on the specific metric adopted for determining the most ikey tie that the agent transmitted from. Therefore, the computationa compexity of the search in the fingerprinting database may become excessive, especiay when the required accuracy is high, which means that the tie-size of the virtua grid is sma, hence the number of ties is high. Motivated by achieving a high precision, we empoy a Quantum Search Agorithm QSA), namey the Dürr-Høyer Agorithm DHA) [23], which find the minimum entry in an unsorted database having N eements, using as few as O N) Cost Function Evauations CFE). The DHA is based on Grover s QSA [24] [26], which is one of the eariest agorithms in quantum computing and forms the basic bock of various quantum agorithms. In fact, we have previousy empoyed Grover s QSA and the DHA for diverse appications, such as muti-user detection in the upink of Non- Orthogona Mutipe Access NOMA) systems [27] [31], for vector precoding in muti-user transmission in the downink of NOMA systems [32], for joint channe estimation and data detection [33] and for muti-objective routing in sef-organized networks [34], [35]. Even though the operation of Grover s QSA wi in practice be prone to quantum decoherence [36], in this contribution we assume perfect operation of both the quantum circuits, as we as of the cassica components. Against this background, our nove contributions are: 1) We conceive an indoor ocaization agorithm for mm- Wave communications systems in Section II, reying on a singe muti-antenna-aided anchor, which expoits both the LOS as we as the specuar MPCs [4], [22], based on practica indoor measurements of mm-wave systems [37]. The proposed agorithm initiay reduces the search space and subsequenty optimizes the estimated position based on a fingerprinting database, which is constructed with the aid of the room s foor pan, taking into account the required ocaization accuracy, as we as the affordabe compexity. The sma waveength of mm-wave communications aows an anchor to use mutipe antenna eements in a compact construction, which may be expoited for improving the ocaization estimation of the users. 2) We show that QSAs may be empoyed for reducing the computationa compexity of both the mm-wavebased and the VLC-based ocaization agorithms in Section IV, whie retaining the optima performance of a fu search, after we have briefy introduced the VLCbased ocaization mode of [5] in Section III. 3) We demonstrate the importance that the shape of the antenna array and various design parameters have on the performance of ocaization in Section V. In the spirit of contribution 1) and 2), we expoit the benefits of the high downink bandwidth of VLC [5] and that of its upink compement constituted by mm-wave communications in Section V, where their potentia coaboration may reduce both a user s estimated position deviation from its true position and the compexity of the ocaization. Furthermore, we argue that a potentia joint optimization of the anchors positions in the two systems is beneficia. 4) Throughout the paper, we have opted for presenting a step-by-step anaysis and tutoria both for the proposed mm-wave ocaization agorithm and for the VLC ocaization agorithm. Additionay, we quantify the effect of its features and parameters on the attainabe ocaization performance and compexity. Tabes I and II describe the parameters that wi be used in the mm-wave-based ocaization, whie Tabe III describes those empoyed in the VLC-based ocaization. Due to the pethora of different symbos and parameters in this manuscript, we request the reader to refer to these tabes as often as required. II. LOCALIZATION IN UPLINK MM-WAVE SYSTEMS Let us proceed by introducing the indoor environment that wi be considered for ocaization in both the anaysis and the simuations. Figure 1 presents a bird s eye view of a room. Assuming that the [0, 0] point is at the bottom eft corner of the room, et us insta a muti-antenna mm-wave anchor at the a i) = [a i) position. In a i), the superscript,x, ai),y, ai),z ]T i) determines the index of the N A physica anchors the positions refer to, where i = 1,..., N A, whie the subscript corresponds to the index of the Virtua Anchor VA) of the ith physica anchor, as defined beow. Hence, the position of a physica anchor has a subscript of = 0. The positions of a physica anchor s VAs may be found with high precision if the foor pan of the room is avaiabe, and they correspond to the imaginary anchors that woud have received a specuar MPC as a LOS path. Naturay, the VAs exist outside this room, since in our scenario a specuar MPCs are generated by the four was. Therefore, given that the ith physica anchor is ocated at a i) 0 = [a i) 0,x, ai) 0,y, ai) 0,z ]T in a room with foor dimensions W x and W y, the four VAs depicted in Fig. 1 woud be ocated This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

3 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access TABLE I: mm-wave System Parameters a 1) 1 3 Symbo N A M L a i) p r i) m t) h i) a m φ, θ) st) τ i) ν i) t) w i) m t) EIRP P L i) λ f c c n d i) Description Number of anchors Number of AEs per anchor Number of VAs, equa to the number of specuar paths Position of the ith physica anchor s th VA User s position Received signa at the ith physica anchor s mth AE at time t Channe state of the th path between the user and the ith physica anchor Phase rotation at the mth AE of the AA with respect to the center of the AA, when the anges of irradiance and incidence are φ and θ, respectivey Transmitted signa at time t Time of arriva of the th path between the user and the ith physica anchor Diffusion mutipath noise at the ith physica anchor at time t AWGN at the ith physica anchor s mth AE at time t Equivaent isotropic radiated power in dbm Path oss of the th path between the user and the ith physica anchor Waveength of the transmitted signa Carrier Frequency Speed of ight Path oss exponent of the th path Distance between the user and the th VA of the ith physica anchor χ,sh Shadowing coefficient of the LOS = 0) σ,sh BW XP D NLOS > 0) paths Standard deviation of the shadowing coefficient of the th path Bandwidth of the transmitted signa Cross-poarization discrimination coefficient a 1) 4 a 1) 0 a 1) 3 p a 1) 2 Fig. 1: Foor pan of the room, where the signa from the agent with the unknown position p = [p x, p y, p z ] T = [8.25, 4.25, 0.85] T back square) is received by the four AEs different circes) of the physica anchor s uniform inear array at a 1) 0 = [a 1) 0,x, a1) 0,y, a1) 0,z ]T = [2, 7.5, 2.5] T as a direct path and four specuar MPCs. since the carrier frequency is f c = 28 GHz, the four AEs are paced with a λ/2 = 5.4 mm spacing. The four specuar MPCs may be considered as having been received by VAs, in the same fashion as distributed MIMO. Note that the AEs of the physica anchor and the VAs are mirrored. at [ a i) 1 = a i) 0,x, 2 W y a i) 0,y, ai) [ a i) 2 = a i) 3 = a i) 4 = [ 2 W x a i) 0,x, ai) 0,y, ai) a i) 0,x, ai) 0,y, ai) 0,z] T 1) 0,z] T 2) 0,z] T 3) [ a i) 0,x, ai) 0,y, ai) 0,z] T 4) Pease note that we have assumed no specuar refection arrives at the physica anchor from the foor or the ceiing, therefore ony four VAs are considered. Furthermore, due to the high path oss of MPCs at mm-wave frequencies, we have ony considered the primary specuar MPCs due to a singe refection, since the power received from mutiperefection MPCs wi be under the noise eve. The user and the physica anchor are assumed to be synchronised. Furthermore, if the power received due to mutipe refected paths was above the noise eve and they were incuded in the proposed ocaization agorithm, the resutant ocaization accuracy woud be improved. However, more VAs shoud be considered, which woud resut in a increased computationa This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

4 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 4 TABLE II: mm-wave System Parameters continued) TABLE III: VLC System Parameters Symbo t m φ, θ) r β T f s P w, dbm SDN R ξ u y i) m t) r s t) z i) t) N p N s, LOS N s, NLOS Description Time difference of arriva between the mth AE and the center of the AA, when the anges of irradiance and impedence are φ and θ, respectivey Radius of the uniform circuar array Ro-off factor of the RRC fiter Symbo period Samping frequency AWGN power in dbm Signa to Diffusion Noise Ratio Exponentia decay constant of DM noise s exponentia decay process Uniformy distributed random number Matched fiter output at the mth AE of the ith physica anchor Impuse response of the raised cosine fiter at time t Tota power at the outputs of the MFs at the ith physica anchor Maximum number of seected peaks Maximum number of sampes difference between the actua ToA of the LOS path and that of a tie s LOS path, for that tie to be incuded in the reduced-size database Maximum number of sampes difference between the ToA of a tie s NLOS path and Symbo N AP P Tx,opt P n) R x h n) LOS h n) NLOS h n) ψ c m φ 1/2 d n d n, d,p A r T s ψ) gψ) n rfr ρ A wa α β I 0 N DB, V LC CF V LC Description Number of Access Points Transmitted optica power of each AP Optica power received by the user from the nth AP LOS path between the nth AP and the user NLOS path between the nth AP and the user Channe state of the nth AP s th refection Haf of user s Fied-Of-View Order of Lambertian emission Semi-ange at haf power Distance between the user and the nth AP Distance between the nth AP and the refection point on the wa Distance between the refection point on the wa and the user Physica area of the photodetector Optica fiter s gain Optica concentrator s gain Refraction index Refection efficiency of the wa s surface Wa s refective area Ange of irradiance at the refection point Ange of irradiance at the user Center uminous intensity per LED Size of searched database Cost function in VLC ocaization any estimated peak, for that tie to be N T N DB CF mmw p k ŷ i,k) m incuded in the reduced-size database Number of ties in the room Number of ties in the searched database Cost function in mm-wave ocaization Position of the center of the kth tie Reconstructed, noiseess MF output at the mth AE of the ith physica anchor, if the signa was transmitted from the center of the kth tie compexity. The specific PDP of the system depends on the appication scenario, i.e. on the positions of both the physica anchor and the user, as we as on the dimensions of the room. The positions of the VAs depend soey on the physica anchor s position, but not on that of the agents. Therefore, ony the foor pan s knowedge is required, but no prior knowedge of the users positions is necessitated. In Fig. 1, we have empoyed a Uniform Linear Array ULA) with four AEs, noting that in genera different formations of the AEs offer different advantages. Therefore, it is important during the signa combining stage to take into account the fact that the AEs of the VAs antenna arrays are at different positions, when compared to that of the physica array. More specificay, the antenna arrays of the VAs are mirrored with respect to This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

5 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 5 the four was used for creating them. This becomes evident in Fig. 1, where we have printed each AE using a different pattern. Let us now assume that a user, whose position has to be estimated, is at position p = [p x, p y, p z ] T, as iustrated in Fig. 1. In our systems, every user is assumed to use a singe antenna and since a user has no prior knowedge of the anchor s position in the room, an omnidirectiona signa is transmitted. The transmitted upink signa arrives at the physica anchor via five paths, hence the foowing signa is received: r i) m t) = L =0 h i) a m φ i) ) s t τ i) + st) ν i) t) + w i) m t), 5) where r m i) t) is the signa received by the ith physica anchor s mth AE at time instant t, with i = 1,..., N A and m = 1,..., M, whie = 0, 1,..., L is the index of the LOS and NLOS paths arriving at the anchor, with = 0 referring to the LOS path and L equa to the number of specuar MPCs L = 4 in our scenario). Sti referring to 5), h i) is the channe coefficient of the th path between the user and the ith physica anchor, which in our scenario ony incudes the effect of the path oss. In other words, no fading channes ) have been assumed in our systems. The function a m φ i) in 5) outputs the phase rotation of the signa received by the ith anchor s mth AE with respect to the signa that woud have been received at the center of the antenna array if an AE was there), based on the AoA of the signa that arrived on the th path. In the same equation, τ i) is the deay experienced by the signa received by the ith physica anchor from the th path, whie st) is the transmitted signa, which is the output of a root-raised cosine fiter and it is known to both the user, as we as to the anchors. The convoution st) ν i) t) describes the Diffused Mutipath DM) noise that arrives at the physica anchors. The diffused mutipath noise cannot be deterministicay estimated and it modes the signas received due to the diffusion that the transmitted signas experience by being scattered by non-deterministic or stationary objects in the room. The diffusion coefficient ν i) t) is different for every physica anchor i, and the associated diffused component appears after the arriva of the direct path, as we as after each specuar path and it decays exponentiay with time. Finay, w m t) N 0, N 0 ) describes the Additive White Gaussian Noise AWGN) experienced by the ith physica anchor s mth AE, which obeys a norma distribution with zero mean and a variance of N 0. In the foowing subsections, we wi further investigate the eements of 5), whie referring to our propagation scenario iustrated in Fig. 1. A. Path Loss The channe coefficient of the th path between the user and the ith physica anchor h i) of 5) may be described as ) h i) EIRP [dbm] P L = 10 i) [db] /20, 6) ) where the Equivaent Isotropicay Radiated Power EIRP) is the product of the transmitted power and of the transmit antenna gain, whie the Path Loss PL) of the th path received by the ith physica anchor is described in db as P L i) 4π [db] = 20 og 10 λ ) + 10 n og 10 d i) + χ,sh. 7) In 7), λ = c/f c is the waveength, c is the speed of ight and f c is the carrier frequency, d 0 = 1 m is a reference distance and d i) is the three-dimensiona distance traveed by the th path between the user and the ith physica anchor. In 7), n is the PL exponent of the th path, which depends both on the carrier frequency, as we as on whether the signa is received via a direct or a refected path and on the particuar nature of the room, where the atter is different for airports, empty warehouses and for office spaces in use. Finay, χ,sh in 7) represents the shadowing that the transmitted signa experiences for the th path, with the shadowing coefficient having a ognorma distribution associated with χ,sh [db] N 0, σ>0,sh 2 ), where σ2 >0,sh is the variance of the ognorma distribution, which aso depends on the carrier frequency and on whether the signa was received via a LOS or NLOS path, as we as on the room. In [37], the authors presented measurements performed in indoors office environments and proposed channe modes for generaizing the aforementioned measurements. The path oss mode described in 7) is termed as the Cose-In CI) free space reference distance mode. The CI path oss mode of 7) assumes that the transmit and receive antennas are co-poarized. In the scenarios, where the antennas are crosspoarized, it was proposed in [37] to incude a constant attenuation factor, termed as the Cross-Poarization Discrimination XPD), resuting in the Cose-In reference distance with XPD CIX) based PL mode, as encapsuated in ) P L i) 4π ) [db] = 20 og n og λ 10 d i) + χ,sh + XP D [db]. 8) As it may be observed in 8), the XP D factor was found to be different for the LOS and the NLOS paths. B. Phase Rotation at Antenna Arrays Each AE in an AA receives the transmitted signa with a different phase with respect to the other AEs, based on the inter-eement distance. 1) Uniform Linear Arrays: When a ULA of antenna eements is used, such as the one depicted in Fig. 1, and assuming that the ith physica anchor s position a i) 0 refers to the center of the ULA, the ULA output of the mth AE is equa to [38] ) ) φ a m φ i) = e j 2 π fc tm i), 9) ) where t m φ i) is the time difference between the arriva of the th path at the center of the ith physica anchor s ULA and at the mth eement of the ULA. Since the ULAs of the VAs have the same spacing between the AEs, even though their ) This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

6 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 6 m = 1 Panar { Wavefront m = 1 d AE m = 2 m = 3 m = 4 a 1) 0 φ 1) 0 m = 2 m = 3 m = 4 a 1) 3 φ 1) 3 Panar Wavefront Fig. 2: The arriva of the wavefront at the ULA of the physica anchor at a 1) 0 and at the south VA at a 1) 3. Knowedge of the ange of arriva φ 1) and of the distance between two AEs d AE are sufficient for reconstructing the phase difference of the signa arriving at the center of the ULA and the AEs. Note that the indexing of the AEs is performed from top to bottom, resuting in different physica AEs having the same index, depending on the VA. position on the ULA is mirrored with respect to the was, et us initiay investigate the phase rotation experienced by the direct path. Based on Fig. 2, when there is an even ) number of AEs M in the ULA, the time difference t m φ i) between the mth AE of the ith ULA and the center of that ULA is stated in 10) top of the next page). In 10), m = 1 refers to the top AE and m = M to the bottom AE in Fig. 2, d AE is the spacing between two neighbouring AEs, φ i) is the AoA of the direct signa to the ith physica anchor and c is the speed of ight. The ange between the user and the physica anchor is where φ i) = µ i) sign µ i) ) π µ i) p x > a i),x p x < a i),x 0 p x = a i),x µ i) = tan 1, 11) i) a,y p ) y a i),x p. 12) x As far as the VAs are concerned, the AEs of the physica anchor s ULA are refected with respect to the VA s associated wa, and the same procedure appies for finding the AoA based on 11) and 12). Afterwards, the arriva time difference with respect to the center of the ULA is cacuated based on 10) and the ULA output is found by evauating 9). Pease note that the anges cacuated based on 11) are with respect to the VAs positions. 2) Uniform Circuar Arrays: We aso empoy Uniform Circuar Arrays UCA), since the vertica symmetry of the ULA with respect to the AoAs wi cause a probem in the ocaization, as we wi see in the foowing sections. A UCA with four AEs is iustrated in Fig. 3. The UCA output is the same as that of the ULA, which is given in 9). Nonetheess, there is a difference in the cacuation of the time difference between the arriva of the signa at an AE, compared to its arriva at the center of the UCA, since the m = 3 m = 3 y y r m = 4 r m = 4 m = 2 z z a 1) 0 a 1) 3 m = 2 φ 2 θ 1) 0 φ 1) 3 θ 1) 3 φ 1) 0 m = 1 x m = 1 Fig. 3: Signa reception at the UCA of the physica anchor at position a 1) 0 and at the south VA at position a 1) 3. Knowedge of the azimuthan and eevation anges of arriva φ 1) and θ 1), as we as of the UCA s radius r and number of AEs M are sufficient for reconstructing the phase difference of the signa arriving at the center of the UCA and that which arrives at the AEs. Note that the indexing of the AEs is performed in a counter cockwise direction starting from the x axis, resuting in different physica AEs having the same index, depending on the VA. AEs have different positions. Furthermore, both the azimutha ange φ i) and the eevation ange θ i) affect the resutant phase difference, as exempified in Fig. 3. More specificay, we have ) t m φ i), θ i) = r ) ) c sin θ i) cos φ i) φ m, 13) where r is the radius of the UCA and φ m is the ange of the mth AE with respect to the horizonta axis that passes through the center of the UCA. Pease note that again, the indexing of a UCA s AE wi begin counter-cockwise from the righthand side of the horizonta axis that passes throught the UCA s center, which resuts in the same AE having a different index, when it beongs to a VA s UCA, due to the refection with respect to the was, as iustrated in Fig. 3 for the South- VA at position a 1) 3. The azimuthan ange of the mth AE is cacuated as φ m = 2 π m 1, m = 1, 2,..., M. 14) M x This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

7 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access t m φ i) ) = sign sign φ i) φ i) ) ) [ dae 2 + M 2 m) d AE [ dae 2 +m M 2 1) d AE ] sin φ i) ) c, m < M 2 ] sin φ i) ) c, m > M ) The azimuthan ange between the th received path and the UCA φ i) may be found as described in 11), whie the eevation ange θ i) is cacuated as in i) a,z p ) z θ i) = cos 1 d i), 15) where d i) is the distance traveed by the th path before reaching the ith physica anchor. Pease note that none of these parameters are known at the anchors, hence they cannot be expoited for finding the user s position. However, the equations may be used for reconstructing a noiseess signa as if it was transmitted from a position ˆp in order to determine how simiar the received signa is to the noiseess reconstructed one. The ocaization agorithm wi be investigated in detai in the foowing section, but we beieve that the motivation of our anaysis in this section shoud be made expicit. The radius of the UCA is r = λ, in order for the distance between two neighbouring AEs to be equa to λ/2. C. Puse Shaping The user transmits a singe Binary Phase Shift Keying BPSK) moduated symbo +1, puse shaped with the aid of a Root Raised Cosine RRC) fiter having a ro-off factor of β. The impuse response of the RRC, which is the transmitted signa in 5), is equa to [39] st) = 4β cos π T 1+β)πt T ) 1 β)πt sin T ) + T 4βt 1 ) 4πt 2, 16) T where T is the symbo period. At the receiver, the signa r m i) t) of 5) received by the mth AE of the ith physica anchor passes through a matched RRC fiter. Since different AEs wi experience different noise contamination, the diversity provided by anayzing the summation of the received powers at the outputs of the MF operations may improve the abiity to distinguish the usefu signa and the AWGN. D. Diffused Mutipath The diffused mutipath noise νt) in 5) modes the MPCs, which cannot be deterministicay estimated and they are physicay caused by refections due to sma or moving objects [40] [43]. In our systems we have opted for modeing the DM noise power as an exponentiay decaying process triggered by each reception of a deterministic specuar MPC, incuding the direct path. This woud resut in an ampitude of [43] h 1) >0 νt) = t) e t ξ e j 2 π u, 17) 10 SDNR/10 Received Signas Matched Fiter Find the Peaks Reduce the Search Space Search the Search Space Estimated Position Fig. 4: Fow chart of the fingerprinting method using AAs in mm-wave Systems. where u is a random number obeying the uniform distribution u U0, 1), and ξ is the exponentia decay constant of the exponentia decay process. Sti referring to 17), we have chosen the peak power of the DM noise to be a scaed version of the power received by the specuar MPC at that same time, since h 1) >0 t) is the channe state of a NLOS path at time t, received by the first physica anchor. By introducing in 17) the Signa to Diffusion Noise Ratio SDNR), measured in db, we are abe to scae the received DM noise power in our simuations. Pease note that the SDNR is assumed to be constant in time. The resutant DM noise that arrives at the receiver is the convoution of the noise in 17) with the transmitted signa of 16) as stated in 5) and it passes through the matched RRC fiter, as described in Section II-C. The DM noise is a coored noise process, in contrast to the AWGN of 5), since it does not have uniform power at a frequencies. The DM noise may degrade the accuracy of the ocaization process due to its random phase rotation imposed on the received signa, as stated in 17). E. Fingerprinting using AAs in mm-wave Systems Let us now commence with the fingerprinting-based ocaization agorithm that makes use of both the AAs and of the specuar MPCs. The agorithm may be divided in four processes, as iustrated in Fig. 4. Appication Scenario: After presenting each step of the agorithm, we wi demonstrate it in a specific appication This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

8 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 8 TABLE IV: Path Loss Parameters for f c = 28 GHz PLE σ sh db) XP D db) LOS = 0) NLOS > 0) exampe, in order to provide deeper intuition to the process of the proposed agorithm. As an appication scenario, et us consider the 15m) 15m) = 225m 2 room seen in Fig. 1. Assuming that the [0, 0] point is at the bottom eft corner of the room, et us insta a singe N A = 1) mutiantenna mm-wave anchor at the position a 1) 0 = [2, 7.5, 2.5] T, which is on the ceiing cose to the eft wa. Since the foor pan is avaiabe, we may find the positions of the VAs that correspond to the physica anchor by finding the symmetrica positions of the physica anchor with respect to the four was, resuting in a 1) 1 = [2, 22.5, 2.5] T, a 1) 2 = [28, 7.5, 2.5] T, a 1) 3 = [2, 7.5, 2.5] T and a 3) 2 = [ 2, 7.5, 2.5] T, as iustrated in Fig. 1. In our scenario, a user is at the unknown position p = [8.25, ] T. The carrier frequency is set to f c = 28 GHz, hence we have λ 1 cm. The anchor is a ULA having M = 4 AEs, which have a spacing of d AE = λ/2 = 5 mm, in a formation parae to the west wa. The CIX PL mode of 8) has been assumed. For a carrier frequency of f c = 28 GHz as we as for a two-sided bandwidth of BW = 800 MHz, the authors of [37] estimated the LOS PL exponent to be equa to n 0 = 1.1, whie that of the NLOS paths equa to n >0 = 2.7. Simiary, the shadowing standard deviation was estimated as σ 0,sh = 1.8 db for the direct path and σ >0,sh = 9.6 db for the specuar MPCs. Furthermore, in [37] it was estimated that XP D 0 = 14 db for the direct path and XP D >0 = 10.4 db for the specuar MPCs. The aforementioned parameters of the PL cacuation for f c = 28 GHz are gathered in Tabe IV. The samping frequency is equa to f s = 2/T = 1600 MHz, where T = 1/BW = 1.25 ns is the symbo period. Regarding the noise in our scenario, an AWGN foor of P w,dbm = 174 dbm / Hz has been incuded, as we as DM noise having a negative-exponentia decay parameter equa to the symbo period of ξ = T = 1/BW = 1.25 ns. Finay, we have SDNR = 3 db and the ro-off factor of the RRC fiters is β = ) Matched Fiter: As mentioned in the previous section, the signas received by each AE initiay pass through an RRC MF. The output of the RRC MF at the mth AE of the ith physica anchor is y i) m t) = L =0 h i) a m φ i) ) r s ) t τ i) + r s t) ν i) t) + ŵ i) m t), 18) where ŵ i) m t) is sti an AWGN process with zero mean and a variance of N 0, whie r s t) is the impuse response of the raised cosine fiter essentiay formed by the sequentia use of Received MF Output Power db) Direct Path Refection at West Wa Refection at South Wa Refection at North Wa Refection at East Wa e-08 4e-08 6e-08 8e-08 1e e e-07 Time s) Fig. 5: Combined MF outputs at the physica anchor s ULA in the scenario of Fig. 1, when both DM and AWGN noise are incuded. Two matching RRC fiters with β = 0.5 were used at the user and the physica anchor, whie the samping period is equa to haf the symbo period. two root raised cosine fiters, which is described as ) ) t cos πβt T r s t) = sinc. 19) T 1 4β 2 t 2 T 2 The outputs of the MFs are then combined as encapsuated in z i) t) = M m=1 y m i) t) 2, 20) which describes the tota power received by a AEs at the ith physica anchor at time instance t. Appication Scenario: In our scenario, the combined MF output, which incudes the usefu signa, the DM noise and the AWGN at a AEs of the physica anchor is depicted in Fig. 5. Even though the additiona power that the DM noise constitutes may not be substantia for a paths, the associated phase rotation may prove catastrophic for the success of the ocaization agorithm. The combined MF output of our scenario, which is depicted in Fig. 5, was cacuated based on 20). Each of the MF outputs is found based on 18). More specificay, 18) depends on the path oss of 8), the phase rotation of the ULA anchor of Section II-B1, the impuse response of the pair of RRC fiters given in 19) and the diffusion mutipath noise process of 17) convoved with the transmitted signa of 16). 2) Finding the Peaks: Based on the received combined power received at the output of the MF stage of Fig. 4, we may estimate the ToAs of the five paths one direct path and four specuar paths), by detecting the peaks in its PDP. Since in ow-snr scenarios some of the paths may be cose ot the noise eve, if we just seect the specific five peaks, where the maximum received power was recorded, we may be ed to wrong decisions, when peaks corresponding to noise are This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

9 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 9 Received MF Output Power db) Direct Path Refection at West Wa Received Power at MF Outputs Top 5 Peaks Refection at South Wa Refection at North Wa Refection at East Wa Received MF Output Power db) Direct Path Refection at West Wa Received Power at MF Outputs Top 30 Peaks Refection at South Wa Refection at North Wa Refection at East Wa e-08 4e-08 6e-08 8e-08 1e e e-07 Time s) Fig. 6: The top five peaks, with respect to the received power, at the output of the MFs e-08 4e-08 6e-08 8e-08 1e e e-07 Time s) Fig. 7: The top thirty peaks, with respect to the peak persistence, at the output of the MFs. seected. This is expected to cause issues in the next stage of Fig. 4, where the search space is shrunk, since there is a high probabiity that the correct position of the user woud be eiminated from the search space. In order to avoid missing the peaks that correspond to the actua received paths, we may keep the N p number of preeminent peaks, which woud be forwarded to the next stage of the agorithm. The number of peaks N p is a design parameter and we may vary it based on the channe conditions, or on the number of VAs. As it wi be anayzed in more detai in the foowing stage of the agorithm, the ony peak that we may identify with a confidence is the first peak that exceeds a specific power threshod, which corresponds to the direct path. Therefore, there is no need to search for peaks before the ToA of the direct path. The power threshod shoud take into consideration both the DM noise and the AWGN, as we as the fact that the samping may not take pace exacty at the peak of the transmitted signa. Therefore, the heuristic power threshod we used in our investigations is ) 1 r s T hr LOS t) = M h 1) 2f s 0. 21) 2 The first peak, with respect to time, that is higher than the corresponding threshod vaue is considered to be the LOS path. Appication Scenario: In our scenario of Fig. 5, if ony the top five peaks were seected, with respect to power, the second highest peak, which is caused by the DM noise, woud be erroneousy seected instead of the desired peak, which corresponds to the East wa s refection, as depicted in Fig. 6. Therefore, et us set in our exampe N p = 30, which resuts in finding and saving the peaks iustrated in Fig. 7. 3) Reducing the Search Space: During the shrinking stage of Fig. 4, we scan the virtua grid, generated by the fingerprinting methodoogy, by checking whether transmission from the center of a specific tie is capabe of identifying the peaks. More specificay, transmission from the center of a tie resuts in the reception of five peaks at known deays, since the position of each tie in the room is known. If a these five paths match five of the peaks identified during the previous stage, then that tie is termed as a egitimate tie and it remains in the search space. By contrast, if no peak has been found at a specific deay, where a peak shoud have been found according to a specific tie, that tie is removed from the search space. Pease note that the ampitude of the peak is not checked at this stage, ony the ToA of each path. Pease note that other techniques, such as Time Difference of Arriva TDoA), or AoA may aso be used at this stage of the agorithm, if the required infrastructure is avaiabe in order to reduce the search space. It shoud be noted that even though the ToA of each path may be readiy estimated from the received signas, we are not abe to estimate, which specific path corresponds to which particuar wa s refection, or in other words, which path corresponds to which VA. Therefore, search spaces that are symmetric with respect to the physica anchor are expected to appear, due to the symmetry of the room considered in our scenario. Let us now define, when there is a match between the deays expected by transmitting from the center of a tie and the estimated peaks of the previous stage. Initiay, the direct path is sought, since this is the ony path that is known with certainty from the MF outputs. If the expected ToA of the direct path of a tie is within N s, LOS sampes from the ToA of the actuay received direct path, then it is considered a match. Simiary, if there is at east one estimated peak within N s, NLOS sampes from the ToA of a specuar path of a tie, then it is aso considered a match. Pease note that a the expected ToAs of a tie shoud have a match in the estimated peak-database, whie N s, LOS and N s, NLOS may differ. The reason that N s, LOS and N s, NLOS are greater than zero is that due to DM noise and AWGN, as we as due to the samping times, the true peak due to a specific path may not resut in an observabe peak, when the This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

10 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 10 Fig. 8: The search space after the shrinking stage, where the tie size is 0.5 m 0.5 m) and hence N T = 900 ties are considered, with N s, LOS = 1 and N s, NLOS = 3. The N DB, mmw = 126 ties incuded in the search space are potted with gray coor. The correct tie, which incudes the true position of the user, is shown with back coor. The ties that are not incuded in the search space are iustrated with white coor. Fig. 9: The search space after the shrinking stage, where the tie size is 0.5 m 0.5 m) and hence N T = 900 ties are considered, with N s, LOS = 1 and N s, NLOS = 1. The N DB, mmw = 26 ties incuded in the search space are potted with gray coor. The correct tie, which incudes the true position of the user, is shown with back coor. The ties that are not incuded in the search space are iustrated with white coor. signas are received. In that case, if N s, LOS and N s, NLOS were equa to zero, the correct tie woud not even be incuded in the reduced-size database. However, the above-mentioned observed peak wi not have moved far away from the true peak. The reason that N s, LOS and N s, NLOS may be different is due to design considerations, where we may want the match of the direct path to be stricter than that of the specuar paths. The objective of the shrinking stage of Fig. 4 is to reduce the size of the search space, so that the compexity of the actua search, which takes pace in the foowing stage of Fig. 4, becomes ower. Naturay, the performance wi not be improved by shrinking the search space. On the contrary, if the shrinking procedure is not performed carefuy, the ocaization performance may degrade. Therefore, the current stage describes a performance versus compexity trade-off in the ocaization agorithm. Appication Scenario: Figure 8 depicts the reduced search space in our scenario, when the tie size of the grid is 0.5 m 0.5 m), resuting in N T = 900 ties in the room and when we have opted for N s, LOS = 1 and N s, NLOS = 3 sampes. The resutant search space consists of N DB, mmw = 126 ties, which constitutes the database that wi be searched. The peaks found in Fig. 7 have been used for shrinking the search space. We may observe that the distance estimated by the ToA of the direct path determines the shape of the search space. If we used N s, LOS = 1 and N s, NLOS = 1 instead, the resutant search space woud ony incude N DB, mmw = 26 ties, as iustrated in Fig. 9. As expected, the ower the vaues of N s, LOS and N s, NLOS are, the stricter the eigibiity of a tie is judged and hence the smaer the shrunk search space becomes. However, this comes at the risk of excuding the Fig. 10: The search space after the shrinking stage, where the tie size is 0.25 m 0.25 m) and hence N T = 3600 ties are considered, with N s, LOS = 1 and N s, NLOS = 3. The N DB, mmw = 484 ties incuded in the search space are potted with gray coor. The correct tie, which incudes the true position of the user, is shown with back coor. The ties that are not incuded in the search space are iustrated with white coor. correct tie from the resutant search space, due to the noise imposed on the received signas. Moreover, if the virtua grid was separated into N T = 3600 ties of size 0.25 m 0.25 m) each, then the resutant search space woud be the one shown in Fig. 10, where we have N s, LOS = 1 and N s, NLOS = 3 and the estimated peaks of This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

11 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 11 Fig. 11: The search space after the shrinking stage, where the tie size is 0.25 m 0.25 m) and hence N T = 3600 ties are considered, with N s, LOS = 1 and N s, NLOS = 1. The N DB, mmw = 100 ties incuded in the search space are potted with gray coor. The correct tie, which incudes the true position of the user, is shown with back coor. The ties that are not incuded in the search space are iustrated with white coor. Fig. 7 were used. By using a smaer tie size, the precision of the ocaization wi be increased, but at the cost of increased compexity, since N DB, mmw = 484 ties woud have to be searched in contrast to the N DB, mmw = 126 ties in the case, where each tie had a size of 0.5 m 0.5 m). By changing the design parameter of N s, NLOS = 1, the search space is reduced even further, as shown in Fig. 11, but the agorithm becomes more sensitive to noise. By comparing Fig. 9 and Fig. 11, which use the same design parameters of N s, LOS = 1 and N s, NLOS = 1, but different tie sizes, we may observe that when the tie size is smaer, more ties are incuded in the resutant search space. Therefore, based on both the avaiabe compexity budget and on the target ocaization precision, the tie size and the design parameters N s, LOS and N s, NLOS may be tuned accordingy. 4) Exporing the Search Space: This stage of Fig. 4 determines, which particuar tie in the resutant database is the most ikey to incude the true position of the user. In order to achieve that the noiseess received signas, which woud have been received at the outputs of the RRC MFs, if the signa was transmitted from the kth tie are compared to the actua outputs of the MF of each AE according to the Cost Function CF), of N I p M y m i) t p ) ŷ i,k) m t p ) 2 CF mmw p k ) =, 22) N i N p M i=1 p=1 m=1 where p k = [p k,x, p k,y, p k,z ] T is the center position of the kth tie, N A is the number of physica anchors in the systems, N p is the number of peaks estimated by the Finding the peaks stage of Fig. 4, M is the number of AEs instaed at each physica anchor, t p is the pth peak s time of arriva, and ŷ m i,k) t p ) is the noiseess version of 18), if the transmitted signa had originated from the center of the kth tie, as formuated in L ) ) ŷ m i,k) t) = h i,k) a m φ i,k) r s t τ i,k), 23) =0 where h i,k) is the channe state, which may be reconstructed based on h i,k) EIRP [dbm] P L = 10 [db] ) /20, 24) where P L i,k) is based on 7) or 8), with the difference that d i,k) is substituted in those equations, determining the distance between the ith physica anchor and the kth tie, as in d i,k) = a i) p k. 25) Sti referring to 23), φ i,k) is the AoA of the th path between the ith physica anchor as we as the kth tie and it is cacuated according to 11), where µ i) is repaced by µ i,k), which in turn is described by i) a µ i,k) = tan 1,y p ) k,y a i),x p. 26) k,x Finay, τ i,k) describes the deay of the th path between the ith physica anchor and the kth tie, and it is cacuated as in τ i,k) = di,k), 27) c where d i,k) is given in 25) and c is the speed of ight. Therefore, it may be concuded that the cost function in 22) is a function of the position of a tie s center. Hence, the optima tie, with respect to its center being the cosest to the user s true position, is the one that minimizes the cost function of 22). In other words, the user s estimated position is the center of the tie that minimizes 22), as encapsuated in ˆp mmw = arg min CF mmw p). 28) p A fu search of a ties woud resut in an excessive search. By reducing the search space according to the previous stage s procedure, the compexity is reduced, but a high compexity may sti be required. The reason we opted for the CF of 22) is that by comparing a N p peaks that were estimated in the corresponding stage of the agorithm, we ensure that a five peaks, which were originated by the different paths of the received signas are taken into consideration. The remaining peaks, which appear due to the DM noise, as we as to the AWGN, wi inevitaby increase the CF vaue. Therefore, a tie whose power deay profie matches the more dominant peaks, wi be associated with a ower CF vaue. Finay, the computationa compexity of the mm-wave ocaization agorithm may be quantified by the number of CFEs of 22). Therefore, the fu search woud require C mmw = N DB, mmw CFEs, where N DB, mmw < This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

12 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 12 1e-05 1e-05 9e-06 8e-06 8e-06 7e-06 6e-06 6e-06 5e-06 4e-06 4e-06 3e-06 2e-06 2e-06 Fig. 12: The CF vaues of the reduced search space, where N DB, mmw = 126 ties participate, with N s, LOS = 1 and N s, NLOS = 1. The tie positioned at ˆp mmw = [8.25, 4.25] T exhibits the minimum CF vaue of 22) and it perfecty matches the user s position p = [8.25, 4.25] T. N T due to the reduction of the search space during the corresponding stage of Fig. 4. Appication Scenario: In our scenario, when the tie size is 0.5 m 0.5 m) and the design parameters are N p = 30, N s, LOS = 1 and N s, NLOS = 3, we have a database size of 126 ties, as iustrated in Fig. 8. The cost function vaues of each egitimate tie are depicted in Fig. 12. As expected, the specific ties which are cose to the user s true position p = [8.25, 4.25] have a ower CF vaue, whie the tie ocated at position p = [8.25, 4.25] T has the minimum CF vaue of Fig. 13: The CF vaues of the reduced search space, where N DB, mmw = 484 ties participate, with N s, LOS = 1 and N s, NLOS = 1. The tie positioned at ˆp mmw = [8.125, 4.375] T exhibits the minimum CF vaue of 22) and it is 0.18 m away from the user s position p = [8.25, 4.25] T, due to the grid s quantization Therefore, a fu search woud correcty estimate the user s position. If the tie size is 0.25 m 0.25 m), again with N s, LOS = 1 and N s, NLOS = 3, the resutant CF vaues of the 484 ties of Fig. 10 are iustrated in Fig. 13. The best estimated position after a fu search is ˆp = [8.125, 4.375] T, which is 0.18 m away from the user s true position, due to the quantization of the grid. In genera, since a user wi be aowed to occupy any position in the room, smaer ties wi resut in an improved average precision, as we wi This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

13 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 13 Room Width m) Access Point User Room Length m) Fig. 14: Foor pan of the room, where the N AP = 8 8 = 64 APs transmit to the user at the unknown position p = [8.25, 4.25, 2.5] T. time domain. Since the user receives a different power eve from each AP, there are N AP power sampes for estimating that user s position. Let us commence by defining the RSSI at the user s position, when transmitting from the nth AP, n = 1, 2,..., N AP, as [5] ) P n) R x p) = h n) LOS p) + hn) NLOS p) P Tx, opt, 29) where P Tx, opt is the transmitted optica power of each AP, h n) LOS is the LOS path between the nth AP and the user, whie h n) NLOS is a NLOS path between the nth AP and the user, originated by refections from the four was. Naturay, the transmitted ight wi be received by the users via mutipe NLOS paths due to the mutipe refections, but as in the case of the mm-wave mode and ocaization agorithm of Section II, we wi ony consider the deterministic refections from the four was, which are aso the most dominant NLOS paths. In more detai, the LOS VLC channe coefficient may be described as [5] demonstrate in the foowing sections. Since in our scenario the user s true position is exacty the same as the center of a tie of size 0.5 m 0.5 m), the positioning error is zero. III. LOCALIZATION IN DOWNLINK VISIBLE LIGHT COMMUNICATION SYSTEMS Let us now try to ocaize the same user of our scenario in Section II with the aid of a downink VLC system. In our downink scenario, N AP APs, or physica anchors, are instaed cose to the ceiing of the room, as iustrated in Fig. 14. The APs may be considered as LEDs that are aso used to iuminate the room. The user is ocated at the unknown position p = [p x, p y, p z ] T as in the upink mm- Wave scenario. Mutipe ocaization methodoogies designed for VLC systems have been investigated in great detai in [5]. In this paper we wi use the fingerprinting methodoogy described in [5]. Since we wi not introduce additiona novety in the ocaization agorithm of a downink VLC system, but rather ony in the search agorithm that wi be empoyed, the anaysis in this section wi focus on presenting the hoistic picture of the VLC downink and it wi not be as detaied as that of the upink mm-wave system of the previous section. The motivated reader may refer to [5] for a tutoria-paced description of this downink VLC ocaization agorithm. The main concept of the downink VLC ocaization agorithm, when the fingerprinting methodoogy is adopted is to determine, which specific tie woud have the most simiar power received by each of the N AP APs. As in [5], this means that the APs are assumed to transmit in an orthogona manner with respect to each other, so that the user can distinguish the received power eves that correspond to each individua AP. In order to reate it to the upink mm-wave ocaization agorithm, the N AP APs may be reated to the N p number of peaks that were estimated during the Finding the Peaks stage of Fig. 4, which are naturay separated from each other in the h n) LOS p) = m + 1) A r 2 π d 2 cos m φ) T s ψ) gψ) cosψ), n 30) where ψ is the ange of incidence, with 0 ψ ψ c, where ψ c is haf of the user s FOV. Moreover, φ is the ange of irradiance, m is the order of Lambertian emission, which is described as m = n2)/ n [ cos )] φ 1/2, where φ1/2 is the semi-ange at haf power, and d n is the distance between the user and the nth AP. Sti referring to 30), A r is the physica area of a photodetector, T s ψ) is the optica fiter s gain and gψ) is the optica concentrator s gain, which is given by gψ) = n 2 rfr / sin2 ψ c ), where n rfr is the refractive index. The tota power received due to a NLOS paths is a fraction of the transmitted optica power, as encapsuated in h n) NLOS p) = L =1 h n) p), 31) where h n) p) is the channe response of the th refection, which is modeed as h n) p) = m + 1) A r 2 π 2 d 2 n, ρ A wa cos m φ) d2,p cosα) cosβ) T s ψ) gψ) cosψ), 32) where d n, is the distance between the nth AP and the point on the specific wa that refected the th NLOS path, d,p is the distance between that same point on the wa and the user, who is at position p, ρ is the refection efficiency of the wa s surface, A wa is the refective area, α is the ange of irradiance at the refection point and β is the ange of irradiance at the user. In our scenarios, we assume a refection efficiency of ρ = 0.75 and once again, 32) is vaid when the ange of incidence is within haf of the user s FOV ψ c. A. Fingerprinting-Based Locaization The fingerprinting-based ocaization agorithm partitions the room into a grid of N T ties, the potentia RSS at the This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

14 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 14 Simiary, 30), 31), and 32) are used in conjunction with p k. During the ocaization process, the actua RSS of 29) is compared to that of 33) for a ties. The tie center which has the cosest RSS vaue to that of the actua one is seected as the user s estimated position. This may be described according to the foowing CF CF V LC p k ) = N AP n=1 P n) R x p) P n) R x p k ) 2. 34) Therefore, simiary to 28), the user s estimated position is ˆp V LC = arg min p CF V LC p). 35) 5e-09 4e-09 3e-09 2e-09 Appication Scenario: Let us consider a scenario based on Fig. 14, where the user is positioned at p = [8.25, 4.25, 0.85] T and there are N AP = 8 8 = 64 APs at a height 2.5 m from the foor, at the positions depicted in Fig. 14. Each AP consists of = 3600 LEDs [44]. Each LED has an optica power of 5.55 mw. Therefore, the transmitted optica power of each AP in our scenario is equa to P Tx,opt = = 20 W. The semi-ange at haf power is φ 1/2 = 60 o and the FOV is 100 o. Furthermore, the physica area of the user s photodetector is A r = 1 cm 2, the optica fiter s gain is T s ψ) = 1 and the refractive index is n rfr = 1.5. The CF vaues of our scenario are iustrated in Fig. 15. We may observe that the tie with center ˆp V LC = [8.25, 4.25, 0.25] T exhibits the minimum CF vaue of CF V LC p k ) = 0, since it perfecty matches the true position and ony deterministic contributions to the RSS have been considered. The compexity of the fu search in this scenario is N DB, V LC = 900 CFEs reying on 34). 1e-09 Fig. 15: The CF vaues of the search space in the VLC fingerprinting ocaization agorithm, where a N DB, V LC = 900 ties participate. The tie positioned at ˆp V LC = [8.25, 4.25] T exhibits the minimum CF vaue of 34) and it perfecty matches the user s position p = [8.25, 4.25] T. center of which has aready been cacuated and is stored in a database. Since a ties participate in the search, the size of the resutant database is N DB, V LC = N T. The cacuation of the RSS at the center of the kth tie, k = 1, 2,..., N DB, V LC, is based on 29), where the unknown position of the user p is now repaced by the known position of the center of the kth tie p k, as encapsuated in P n) R x p k ) = ) h n) LOS p k ) + hn) NLOS p k ) P Tx, opt. 33) 0 IV. QUANTUM SEARCH ALGORITHMS IN LOCALIZATION In this section rudimentary famiiarity with quantum information processing is assumed. For the associated basics pease refer to [45] [47], but beow we provide a brief introduction to the required basics. In quantum computing, the basic unit of information is the quantum bit, or qubit, which can be found in the quantum states 0 or 1, or any superposition of the two, as in q = a 0 + b 1, 36) where a 2 and b 2 are the probabiities of obtaining the quantum states 0 or 1, when we measure or observe the qubit q of 36), whie a, b C. When a measurement or observation takes pace, the superposition of states wi coapse to the measured state of the cassic domain. When using mutipe qubits, quantum registers may be created, essentiay increasing the number of egitimate quantum states exponentiay. By appying quantum operators or quantum gates to the qubits, we are abe to change, or evove, their state. Furthermore, when a quantum state of two or more qubits cannot be described separatey by its qubits states, then it is said to be entanged. For exampe, et the foowing two qubits be in the state x = q 1 q 2 = a 00 + b ) This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

15 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 15 If it was possibe to describe the state x using the individua states of the two qubits q 1 and q 2, then we woud have x = q 1 q 2 = a b 1 1 )a b 2 1 ) = a 1 a a 1 b b 1 a b 1 b ) However, since either a 1 or b 2 shoud be equa to 0, based on 37), this means that 38) cannot describe 37). Therefore, 37) describes an entanged state. For an extended tutoria on quantum computing and QSAs, the motivated reader might aso ike to consut [27]. A. Grover s Quantum Search Agorithm QSAs expoit these postuates of quantum computing for finding the position of an eement in a database. Grover s QSA finds the index of an entry δ in a database of size N with 100% probabiity of success, by ony requiring O N) queries to the database. However, in order to achieve this, the desired entry δ, the size of the database N and the number of times that δ appears in the database S have to be known prior to Grover s search. From a high-eve perspective, Grover s QSA [24], [25] is initiaized by having an equiprobabe superposition of a N egitimate quantum states, where each quantum state corresponds to the index of a singe entry in the database. Therefore, og 2 N) qubits are required in order to index a N egitimate states. The goa is then to appy a specific quantum circuit L opt number of times, so that when we measure the resutant state of the quantum register, the quantum state that corresponds to the index of the desired entry in the database is obtained. This is achieved by the activation of the appropriate quantum gates in Grover s quantum circuit, which change the ampitudes of the quantum register s state, so that eventuay the quantum state that corresponds to the desired entry in the database has a probabiity to be observed cose to 100%. The number of iterations of Grover s quantum circuit, or Grover s quantum operator, L opt is equa to [24], [25] L opt = π 4 N S. 39) Naturay, Grover s QSA shines in unsorted databases. The most important quantum gate empoyed in Grover s quantum circuit is the Orace, which is capabe of querying a entries in the database simutaneousy in parae, with the aid of the superimposed qubits and a few auxiiary ones. The Orace ony manipuates the specific quantum states that correspond to the indices of those particuar entries in the database, which contain δ, whie eaving the rest of the quantum states unatered. Therefore, the Orace is tasked with marking the so-caed soutions of the search. B. Boyer - Brassard - Høyer - Tapp Quantum Search Agorithm When, however, the number of occurrences S of a desired entry δ in a database of ength N is not known prior to the search, and ony δ and N are known, then Grover s QSA is not appicabe, because according to 39) it wi not be possibe to determine the optima number of Grover iterations L opt. To circumvent this imitation, Boyer, Brassard, Høyer and Tapp BBHT) proposed the BBHT QSA [26] for such search probems by reying on Grover s QSA. Again, from a bird s eye perspective, since the number of soutions S is not known and we are unabe to determine how many times Grover s quantum circuit shoud be appied to the initiay equiprobabe superposition of states, the BBHT QSA pseudo-randomy chooses the number of Grover iterations. Even though it is highy ikey that the state observed is not the desired one after the first few trias, a fact that can be checked by cassicay querying the database with the obtained state, the BBHT QSA has been formay proven to obtain the desired state, provided that it exists, after at most 4.5 N/S database queries. Since S is unknown, the agorithm can be terminated after 4.5 N Grover iterations, which is the highest-compexity scenario of S = 1. In other words, the BBHT QSA invokes Grover s QSA mutipe times for a different number of Grover iterations, unti the index of the desired entry is acquired. The probabiity of success remains at 100%, as in Grover s QSA. Since the BBHT QSA is a probabiistic agorithm, its compexity may vary even between different search instances in the same database. However, even though the maximum required compexity is 4.5 N/S, before we manuay terminate the agorithm and concude that there is no soution to this the search probem, when at east one soution exists, the maximum actuay encountered and recorded compexity is usuay much ower than 4.5 N/S. C. Dürr - Høyer Agorithm Naturay, when the goa of a search is to find the minimum entry in an unsorted database, then δ is aso unknown prior to the search. Therefore, neither Grover s nor the BBHT QSA are abe to find that minimum entry, since they both require a priori knowedge of δ. The Dürr-Høyer Agorithm manages to find the index of the minimum entry in a database of size N with 100% success probabiity after at east 4.5 N and at most 22.5 N database queries. In [28], we showed that the compexity of the DHA may be further reduced without sacrificing the success probabiity, provided that appropriate search statistics about the database are avaiabe. Initiay, the DHA randomy chooses one of the entries of the database. If there is a way of seecting an entry, the vaue of which is coser to the minimum one in the database, the compexity of the DHA is further reduced [28]. For exampe, in the signa detection fied, if a ow-compexity Minimum Mean Square Error MMSE) detector is empoyed before the DHA, then the output of the MMSE detector may be used as the initia input to the DHA for reducing its compexity [28], [31]. After the initia input entry to the DHA δ has been seected, the BBHT QSA is empoyed, as described in Section IV-B, but with the difference that the Orace now marks as soutions a the quantum states that correspond to the specific indices of those entries in the database that are smaer than δ. Naturay, there wi be mutipe entries in the database that have a ower vaue than δ. Since it is impossibe to know the exact numbers of entries that are smaer than δ prior to the This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

16 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 16 9e-06 8e-06 7e-06 6e-06 5e-06 4e-06 3e-06 2e-06 Fig. 16: The ties that were obtained by the DHA, when used in the mm-wave ocaization agorithm for N DB = 900 ties. The CF vaue of each evauated tie is aso potted. The entries of the database that were not obtained during the DHA search have been fixed to a CF vaue of , just for the sake of presentation, without meaning that their true CF vaue, presented in Fig. 12, has changed. The fina output of each BBHT search during the DHA s process is numbered, in the sequence of the BBHT QSA occurrences. The circed tie is the cosest to true position of the user. The ast output of the ast BBHT QSA s ca, indicated by the number 1 is the output of the DHA and it is the correct tie. The unnumbered ties denote the ties that were measured by the BBHT QSAs but were not soutions, as expected by the tria-and-error procedure of the BBHT QSA. Fig. 17: The ties that were obtained by the DHA, when used in the VLC fingerprinting ocaization agorithm for N DB = 900 ties. The CF vaue of each evauated tie is aso potted. The entries of the database that were not obtained during the DHA search have been fixed to a CF vaue of , just for the sake of presentation, without meaning that their true CF vaue, presented in Fig. 15, has changed. The fina output of each BBHT search during the DHA s process is numbered, in the sequence of the BBHT QSA occurrences. The circed tie is the cosest to true position of the user. The ast output of the ast BBHT QSA s ca, indicated by the number 3 is the output of the DHA and it is the correct tie. The unnumbered ties denote the ties that were measured by the BBHT QSAs but were not soutions, as expected by the tria-and-error procedure of the BBHT QSA. search, ony the BBHT QSA can be used. However, when we measure the fina quantum state at the end of the BBHT QSA, ony one of the candidate quantum states wi be obtained. By cassicay checking, whether the entry that corresponds to the index of the quantum state observed has a ower vaue than δ, we are abe to determine whether there is an entry ower than δ or not. If there is, then that entry becomes the new δ and the same process is repeated, unti the BBHT QSA is terminated without yieding an entry ower than δ. At that point we may concude that the ast δ we used is the minimum entry of the database and the DHA is concuded. Since DHA empoys the BBHT QSA, it aso has a probabiistic compexity. The average compexity found for randomy constructed, unsorted databases was around 7 N database queries. The minimum compexity of 4.5 N is equa to the maximum compexity of the BBHT QSA and it corresponds to the particuar scenario, where the minimum entry of the database was seected to be the initia input entry of the DHA. The maximum compexity of the database given by 22.5 N is rarey approached. In [28], we proposed an eary termination criterion for the DHA. With the aid of this criterion we are abe to tune its compexity, based on striking a trade-off between the affordabe compexity budget and the success probabiity desired. Due to the methodoogy foowed by the DHA, with the continuous updates of δ, even if the true minimum entry of the database is not found, an entry with a vaue cose to that of the true minimum entry wi have been obtained. D. Locaization Using Quantum Search Agorithms In the ocaization probem, the search aims for finding the minimum entry in an unsorted database. Hence, the DHA may be empoyed for reducing the search compexity quantified in terms of the number of CFEs, whie having a success probabiity of 100%. In both the mm-wave and in the VLC ocaization agorithms, the average compexity of the DHA depends on the size of the database N DB, mmw and N DB, V LC. For the same tie size, the database size in the mm-wave ocaization agorithm is ower than that in the VLC ocaization agorithm N DB, mmw < N DB, V LC, due to the search space shrinking stage of Section II-E3. In the mm-wave ocaization agorithm, the DHA performs a search for the minimum entry in the database consisting of N DB, mmw entries, which are constructed based on the CF This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

17 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 17 of 22). Simiary, in the VLC ocaization agorithm the DHA is empoyed for finding the minimum entry in a database of size N DB, V LC = N T, the entries of which are cacuated based on 34). When we empoyed the DHA in the scenario of Fig. 1 and the database of Fig. 12, where the database size is N DB, mmw = 126, the resutant compexity was 52 CFEs. Ony a certain fraction of the search space was retained after the measurements of the BBHT QSAs empoyed by the DHA, as iustrated in Fig. 16. For the same scenario, when using the VLC ocaization agorithm in the database of Fig. 15, 247 CFEs were required for identifying the specific tie that minimized the CF of 34). The ties observed during the DHA search in the VLC ocaization agorithm are shown in Fig. 17. We may observe that in both ocaization agorithms, the required computationa compexity is reduced, when the DHA is used instead of a fu search. At the same time, the DHA succeeds in finding the correct tie in both the mm-wave and the VLC ocaization agorithms. When the DHA is used, the compexity reduction, quantified in terms of the percentage of the database size is improved when the database size is higher. This is the reason why in the mm-wave ocaization agorithm the DHA requires 41.37% of the compexity needed by a fu search in a database size of 126 entries, whie it requires ony 27.4% of the compexity imposed by the fu search in a database size of 247 entries. Since the DHA s compexity is proportiona to N DB, where N DF is the size of the database, the higher the size of the database is, the higher the compexity reduction achieved by the DHA becomes. Due to the nature of the mm-wave-based ocaization agorithm, the database size differs, depending on the position of the user. At the same time, for the DHA to require a ower compexity than the fu search, the database size shoud be higher than 2 6 = 64 entries [28]. Therefore, in the mm-wave ocaization methodoogy we wi empoy a hybrid quantum search for the Exporing the Search Space stage of Fig. 4, where a fu search is performed if the size of the database is ower than 64 entries, whie if the database size is higher than 64 entries, the DHA is used for finding the tie that corresponds to the minimum entry. V. SIMULATION RESULTS & DISCUSSIONS Let us now evauate the ocaization methodoogies and search agorithms investigated. Tabes V and VI gather the vaues of a the parameters invoked by the mm-wave-based and VLC-based ocaization agorithms, respectivey. These remain unatered in a the simuations. In a the simuations, we have moved a user to different positions in the room, essentiay moving a user on a grid with a step of 5 cm. We have empoyed a ocaization agorithm for each of these positions for 100 independent trias. We have aso investigated the performance that different tie sizes offer, as we as different transmit power and antenna arrays. We have opted for using the maximum and average positioning error distance as our prime performance metric. For the mm- Wave-based ocaization agorithm, in contrast to the previous TABLE V: mm-wave Scenario Parameters Number of anchors N A = 1 Anchor s position a 1) 0 = [7.5, 7.5, 2.5] T Height of Users 0.85 m Number of AEs M = 8 Number of VAs L = 4 Carrier frequency Bandwidth Samping frequency f c = 28 GHz Ro-off factor of RRC β = 0.5 Path oss parameters AE spacing in ULA Radius of the UCA AWGN power SDNR Exponentia decay constant BW = 800 MHz f s = 1600 MHz See Tabe IV d AE = 5 mm r = 3.8 mm P w,dbm = 174 dbm/hz 6 db ξ = 1.25 ns Locaization agorithm s N p = 30 design parameters N s, LOS = 1 N s, NLOS = 5 sections, an antenna array is instaed on the ceiing in the center of the room, whie for the VLC-based system, 64 APs are instaed uniformy in the room. The reason we opted for a carrier frequency of f c = 28 GHz with a bandwidth of 800 MHz, was both the avaiabiity of actua measurements of that system in [37], as we as the fact that in even higher frequencies, the associated high PLE for the NLOS paths increases the difficuty of detecting them. Nevertheess, the presented agorithm is appicabe for a range of carrier frequencies. Figure 18 presents both the maximum and average positioning error for each of the user positions, when the mm- Wave-based ocaization reied on the hybrid quantum search and a tie size of 0.5 m 0.5 m), EIRP = 25 dbm. The resutant error pattern depends on the number of AEs instaed on the UCA, as we as on the position of the UCA in the room. Based on the maximum positioning error recorded in Fig. 18a, the maximum error observed among a positions was 1.64 m, even though the reative frequency of observing such a high positioning error is very ow, as it wi be shown with the aid of probabiity density functions in our forthcoming anaysis. A gimpse of this may be observed in Fig. 18b, which depicts the average positioning error for the same system, demonstrating that the average positioning error among a positions is 0.27 m. It shoud be noted that both Fig. 18a and Fig. 18b have been obtained using the same simuation instances and hence depend on the same random variabe This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

18 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 18 a) Tie size: 0.5 m 0.5 m). Average error: 0.27 m. Average compexity: 80 CFEs. b) Tie size: 0.3 m 0.3 m). Average error: 0.18 m. Average compexity: 146 CFEs. c) Tie size: 0.1 m 0.1 m). Average error: 0.07 m. Average compexity: 490 CFEs. Fig. 20: Maximum positioning error, when using the mm-wave ocaization methodoogy with hybrid quantum search for user positions, three different tie sizes, EIRP = 25 dbm. The rest of the parameters are stated in Tabe V. a) Tie size: 0.5 m 0.5 m). Positions Lost: 1.12% 1010 positions). Average error for found positions: 0.44 m. Average compexity: 208 CFEs. Average tota error, assuming max error for ost positions: 0.67 m. b) Tie size: 0.3 m 0.3 m). Positions ost: 1.12% 1010 users). Average error for found positions: 0.24 m. Average compexity: 436 CFEs. Average tota error, assuming max error for ost positions: 0.46 m. c) Tie size: 0.1 m 0.1 m). Positions ost: 1.12% 1010 users). Average error for found positions: 0.09 m. Average compexity: 1293 CFEs. Average tota error, assuming max error for ost positions: 0.32 m. Fig. 21: Maximum positioning error, when using the VLC ocaization methodoogy with DHA for user positions and three different tie sizes. The rest of the parameters are stated in Tabe VI. vaues. We may aso concude that the positioning error pattern is symmetric with respect to the center of the room, where the UCA is instaed. Sti referring to Fig. 18, the average number of CFEs required for a ties over a independent simuation instances by the hybrid quantum search was 80 CFEs. At the same time, if ony a fu search was performed for the databases, the average compexity woud have been 139 CFEs, whie the positioning error performance woud be the same. In other words, the hybrid quantum search achieves the same performance as the fu search, whie requiring 57.5% of the CFEs. As we wi show in a subsequent figure, this percentage wi be even ower, when the tie size is reduced and hence the database size is increased. Even though we used a ULA for our tutoria exampe, Fig. 19 suggests that a ULA shoud not be used in the mm-wave-based ocaization agorithm, due to the inherent symmetry of the antenna array with respect to an axis. Hence, when a ULA is instaed in the center of a symmetric room, the mm-wave-based ocaization agorithm becomes unabe to distinguish, whether the user is positioned on the eft or on the right side of the ULA, since in both cases a AEs woud have received exacty the same signas. A parameters vaues in Fig. 19 are the same as those in Fig. 18. Therefore, in the foowing simuations we wi empoy a UCA for the mmwave-based ocaization. When reducing the tie size, the positioning accuracy is expected to improve, since the grid s resoution is enhanced. This is evident in Fig. 20, where the maximum positioning error has been potted for three different tie sizes, namey for 0.5 m 0.5 m), 0.3 m 0.3 m) and 0.1 m 0.1 m), resuting in an average positioning error across a user positions of 27 cm, 18 cm and 7 cm, respectivey. When the penci-wide beams of mm-wave technoogy are used for communication, the more precise the ocaization, the ess interference wi be imposed on the adjacent users. Naturay, this comes at the price of an increased compexity, since by increasing the number of ties, more CFEs are required by This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

19 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 19 TABLE VI: VLC Scenario Parameters Number of APs N AP = 64 Height of APs 2.5 m Height of users 0.85 m Number of LEDs per AP = 3600 Center uminous intensity per LED I 0 = 350 mcd Transmitted optica power per LED 5.5 mw Transmitted optica power per AP P Tx,opt = 20 W Haf of user s FOV ψ c = 45 o Semi-ange at haf power φ 1/2 = 60 o Physica area of photodetector A r = 1 cm 2 Optica fiter s gain T s ψ) = 1 Refraction index n rfr = 1.5 Wa s refection efficiency ρ = 0.75 Wa s refective area A wa = m 2 a) Maximum Positioning Error both the fu search and by the hybrid quantum search. More specificay, in order to achieve a 20 cm reduction in the average positioning error, from 27 cm to 7 cm, six times the number of CFEs is required on average. When the 64 APs are empoyed for performing a VLCbased ocaization, the positioning accuracy aso depends on the tie size and on the affordabe compexity, as portrayed in Fig. 21, where the maximum recorded positioning error is iustrated for three different tie sizes. The main difference between the mm-wave-based ocaization s performance of Fig. 20 and that of the VLC-based ocaization in Fig. 21, is that in the atter some user positions may never be found by the methodoogy, due to the visibe ight s imited coverage. As it may be seen cose to the was of the room, and especiay at its four corners, there are 1010 positions, which are never found by the VLC-based ocaization. In other words, 1.12% of the positions cannot be identified by the current system setup. By assigning the maximum possibe positioning error of 15 2 = m to them for our anaysis, the average positioning error is 51 cm, 37 cm and 30 cm for the tie sizes of 0.5 m 0.5 m), 0.3 m 0.3 m) and 0.1 m 0.1 m), respectivey. If we ony consider the specific positions that were in the coverage area, their average positioning error becomes 28 cm, 14 cm and 6 cm, respectivey, for the three aforementioned tie sizes. Since in the VLC-based ocaization of Fig. 21 ony the perturbations due to wa-refections are assumed, if the user s position happens to be exacty at the center of a tie, its associated ocaization error may be equa to zero. None of the three tie sizes we used in Fig. 21 have a tie center exacty at a user s positions, in order to guarantee a fair comparison between the different tie sizes. Sti referring to Fig. 21, the average compexity required by the VLC-based ocaization using the DHA is 208 CFEs, b) Average Positioning Error Fig. 18: Maximum and average positioning error of the mm- Wave-based ocaization, when a user is ocated in different positions in the room and a UCA is instaed at the center of the room, whie the tie size is 0.5 m 0.5 m). Furthermore, we have EIRP = 25 dbm. The rest of the parameters are gathered in Tabes IV and V. The search compexity, averaged on a positions, when the hybrid quantum search is empoyed is 80 CFEs, whie that of the fu search was 139 CFEs on average. 436 CFEs and 1293 CFEs, respectivey, for the three tie sizes used. Comparing the compexities of the VLC-based ocaization for the three different tie sizes to the respective ones of the mm-wave-based ocaization in Fig. 20, we may concude that the mm-wave-based ocaization achieves a simiar performance in terms of the average positioning error over a the positions, whie requiring fewer CFEs. Since the This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

20 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 20 Average Position Error m) Hybrid Quantum Search in mm-wave Locaization Fu Search in mm-wave Locaization Quantum Search in VLC Locaization Fu Search in VLC Locaization a) Maximum Positioning Error Compexity CFEs) Fig. 22: Average positioning error among a user positions, with respect to the required computationa compexity, in terms of the number of CFEs, for the mm-wave-based and VLCbased ocaization methodoogies, when a quantum search or a fu search is performed. For the mm-wave-based ocaization methodoogy, we have EIRP = 25 dbm. The rest of the parameters are gathered in Tabes V and VI. b) Average Positioning Error Fig. 19: Maximum and average error of the mm-wave-based ocaization, when a user is ocated in different positions in the room and a ULA is instaed at the center of the room, whie the tie size is 0.5 m 0.5 m). Furthermore, we have EIRP = 25 dbm. The search compexity, averaged on a positions, when the hybrid quantum search is empoyed is 80 CFEs, whie that of the fu search was 139 CFEs on average. cost functions of the mm-wave-based and the VLC-based ocaization methodoogies are different, it may not be fair to compare them, but they both represent a singe query of a database formed by the same tie arguments. Furthermore, in contrast to the VLC-based ocaization, the mm-wave-based ocaization succeeds in ocaizing a user positions in the room. The average positioning error s reation to the number of CFEs required for both ocaization techniques may be better understood by observing Fig. 22. The compexity of both the mm-wave-based and of the VLC-based ocaization methodoogies was varied by ony changing the tie size and the search agorithm. In both techniques, when a quantum search is used, we achieve a compexity reduction, which becomes even higher, when the compexity required by the fu search is higher. In other words, the smaer the tie size of both ocaization methodoogies, the higher the compexity reduction achieved by the quantum search becomes. For exampe, in order to achieve an average positioning error of 7 cm, the mm- Wave-based ocaization agorithm using the hybrid quantum search requires 14% of the number of CFEs required by a fu search. Simiary, the VLC-based ocaization agorithm using the DHA requires 5.75% of the number of CFEs required by a fu search for achieving an average positioning error of 9 cm. From another point of view, by investing the same compexity, a more precise ocaization can be achieved, when quantum search is used. For exampe, in the mm-wave-based ocaization scenarios of Fig. 22, if the affordabe compexity budget was 490 CFEs, by using a fu search the average positioning error woud be 16.9 cm, whie the same error woud be reduced to 7 cm, if the hybrid quantum search was used. By comparing the quantum-search-aided mm-wave-based and VLC-based ocaization methodoogies in Fig. 22, assuming that their CFEs are equivaent in terms of power consumption, we may concude that the mm-wave based ocaization may achieve a simiar average positioning error by requiring fewer CFEs than the VLC-based ocaization. This is due to the Shrinking the Search Space stage of the mm- Wave-based ocaization methodoogy of Section II-E3, which reduces the resutant search space. At the same time, the VLC- This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

21 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access Average Position Error m) Fig. 23: Number of required CFEs among a user positions, when the mm-wave-based ocaization is empoyed, with hybrid quantum search, EIRP = 25 dbm, and a tie size of 0.1 m 0.1 m). The rest of the parameters are stated in Tabe V. based ocaization methodoogy aways performs a search right across the entire room. It shoud be noted that in Fig. 22, we have not taken into consideration during the cacuation of the VLC-based ocaization s average positioning error, those specific user positions, which are out of coverage. Reca that the Shrinking the Search Space stage of the mm-wave-based ocaization methodoogy of Section II-E3 is based on the peaks estimated in the received power deay profie, as described in Section II-E2. In other words, it reies on the distance traveed by the received signas, without taking into consideration, which refection caused which specuar path. This is aso iustrated in Fig. 23, which quantifies the computationa compexity in terms of the number of CFEs, which is required at each user s position for the mm-wavebased ocaization methodoogy, when the hybrid quantum search is used for a tie size of 0.1 m 0.1 m). The compexity foows the trend of the number of ties in the resutant database. If the shrinking stage was omitted, then the number of CFEs required woud have been the same at a user positions. Figure 24 depicts the effect of different EIRP eves on the average positioning error, when the mm-wave-based ocaization reying on the hybrid quantum search is used and the tie size is 0.1 m 0.1 m). As expected, by increasing the transmitted power, a ower average positioning error is achieved, which eventuay reaches the minimum error foor, governed by the imited resoution of the room imposed by the seected tie size. Viewing Fig. 24 from another ange, by using a ower tie size and ower EIRP, we may achieve a simiar performance to those scenarios, where a higher tie size combined with a higher EIRP was used. Therefore, depending on the ocaization precision required, on the power budgets EIRP dbm) Fig. 24: Average positioning error among a user positions, with respect to the EIRP from the user, when the mm-wavebased ocaization with hybrid quantum search, and a tie size of 0.1 m 0.1 m) are empoyed. The rest of the parameters are stated in Tabe V. Probabiity of Occurrence Tie Size 0.5 m) 0.5 m)) Tie Size 0.3 m) 0.3 m)) Tie Size 0.1 m) 0.1 m)) Position Error m) Fig. 25: Probabiity density function of the position error among a positions in the room for three different tie sizes in the mm-wave based ocaization agorithm, where the hybrid quantum search was empoyed, EIRP = 25 dbm. The rest of the parameters are stated in Tabe V. of the users and on that of the physica anchor, a suitabe aocation of transmission power and search compexity may be performed. Figure 25 iustrates the probabiity density functions of the positioning error recorded for a positions in the room for three different tie sizes in the mm-wave-based ocaization methodoogy using the hybrid quantum search. As expected, the probabiity of having a ow position error is higher, when the tie size is sma. The tais of the three probabiity distributions show that even though reativey high errors may be encountered, the probabiity of their occurrence is very ow. For exampe, the probabiity of having an error cose to 1.45 m is , and for the tie size of 0.1 m 0.1), This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

22 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access Fig. 26: Maximum positioning error of the VLC-based trianguation method, when a user is ocated in different positions in the room, 64 APs for VLC are instaed in the room. The system parameters are stated in Tabe VI. 0.3 m 0.3) and ), respectivey. Therefore, even though Fig. 20 depicts the highest recorded positioning error for the three tie sizes, the probabiity distribution of the errors observed in Fig. 25 provides a more compete perspective on the mm-wave-based ocaization s performance. Fig. 27: Maximum positioning error of the joint VLC-based and mm-wave-based ocaization, when a user is ocated in different positions in the room, 64 APs for VLC are instaed in the room and a UCA is instaed at the center of the room. The VLC-based ocaization agorithm is empoyed first using the trianguation method. When a user is not found, the mm-wave-based ocaization is used with hybrid quantum search, a tie size of 0.1 m 0.1 m), EIRP = 25 dbm. The rest of the parameters are stated in Tabe V and Tabe VI. The average positioning error is m and the average compexity is 261 CFEs. A. Joint VLC-based and mm-wave-based Locaization Let us now join the forces between the downink VLCbased and upink mm-wave-based ocaization, by empoying the VLC-based ocaization using trianguation, as discussed in [5], and subsequenty invoke mm-wave-based ocaization, if the user happens to be out of the VLC coverage range. The presence of a user wi be known due to its upink transmissions. Hence, it is viabe to assume that the system wi know, when a user is present in the room, but he / she has not been ocaized by the VLC-based methodoogy. The trianguation method requires three APs in order to estimate the position of the user, simiary to the Goba Positioning System GPS). In our system, when the user receives signas from three APs, then VLC-based trianguation is performed, whie in any other cases, the mm-wave-based ocaization methodoogy using the hybrid quantum search and a tie size of 0.1 m 0.1 m) is used. The performance of the VLC-based trianguation aone is shown in Fig. 26. Naturay, since three APs are required for ocaizing the user, the number of positions, where the user is estimated by the VLC-based methodoogy is ow. On the other hand, when trianguation is performed, the positioning error is cose to zero, with the exception of the positions cose to the four was, where we have assumed in our simuations that the ight is refected, which aows trianguation to be used, abeit with a degraded resut. Nevertheess, trianguation requires the overap of coverage areas from different APs, therefore its success highy depends on the architecture of the room and on the density of the APs, as we as on the fied of view. When we aow the mm-wave-based ocaization methodoogy to foow the VLC-based ocaization, by empoying a UCA at the center of the room as in the previous scenarios, using hybrid quantum search and a tie size of 0.1 m 0.1 m), the resutant performance is iustrated in Fig. 27. Since we empoy both investigated systems sequentiay, their maximum positioning error is reated to the combination of Fig. 20c and Fig. 26. However, the average positioning error in the joint VLC-based and mm-wave-based ocaization is 5.6 cm, which is ower than that of Fig. 20c, due to the improved ocaization precision offerred by the VLC-based trianguation in some parts of the room. At the same time, assuming that the trianguation s compexity is much ower, than that of the fingerprinting method, we have assumed that no CFEs were required, when trianguation was empoyed. Therefore, the average number of CFEs required in Fig. 27 is 261 CFEs and a beong to the mm- Wave-based ocaization using the hybrid quantum search. VI. CONCLUSIONS In this contribution, we have proposed indoor ocaization agorithms for the upink of mm-wave communication systems, which rey on a singe muti-antenna anchor and expoit the specuar paths. In Section II we presented a tutoria on the This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

23 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 23 operation of this ocaization agorithm, whie in Section IV we investigated the empoyment of quantum search agorithms for it, in order to reduce the number of CFEs required. Furthermore, we have used quantum search agorithms in the VLC-based ocaization methodoogy of Section III for achieving the same performance as the fu search, whie requiring ower compexity. As iustrated in Fig. 18 and Fig. 19, we concuded that ony the UCA, or two-dimensiona antenna arrays, are suitabe for the upink mm-wave ocaization methodoogy. In Fig. 20, we observed that by decreasing the size of the ties in a fingerprinting method, the average positioning error diminishes, whie the associated search compexity increases. The positioning error pattern in the room depends on a number of factors, such as the position of the anchor, the transmitted power and the number of AEs on the UCA. Simiar concusions were drawn for the VLC-based ocaization methodoogy in Fig. 21, which shows the positioning error for mutipe tie sizes, when the DHA was used for conducting the search. The same figure shows that the VLC-based ocaization agorithm may be bind to specific user positions, due to its imited coverage. Therefore, the position of the APs is crucia for the performance of the VLC-based ocaization. In Fig. 22 we compared the ocaization performance of both the upink and downink agorithms, when a quantum search agorithm is used and when ony a cassica fu search is empoyed. We observed that when a quantum search agorithm is used for improving the ocaization, fewer CFEs are required for achieving the same performance as the fu search. At the same time, assuming for the sake of comparison that the compexity of a singe CFE in the mm-wave-based ocaization methodoogy is equivaent to a singe CFE in the VLC-based ocaization methodoogy, the upink mm-wavebased ocaization agorithm is abe to offer a ower average positioning error across the room at a ower compexity, as observed in Fig. 22 for the two setups that we investigated. For exampe, if more APs were instaed on the ceiing and especiay cose to the four was, we expect the downink VLCbased ocaization to outperform the upink mm-wave-based ocaization. Simiary, if more mm-wave-enabed physica anchors are instaed in the room, the ocaization estimation woud improve. As expected, based on Fig. 23, in the mm-wave-based ocaization methodoogy, the required compexity depends on the user s position in the room due to the shrinking stage of the agorithm, as stated in Section II-E3. Furthermore, Fig. 24 iustrated the effect of different radiated powers on the average positioning error of the mm-wave-based ocaization methodoogy. Since in Figs. 18, 19, 20 and 21 we referred to both the maximum observed and the average positioning error at each user s position, in Fig. 25, we potted the probabiity distributions of the position error obtained by the mm-wave-based ocaization methodoogy. More specificay, the maximum positioning error shown in Figs. 18, 19, 20 and 21 describes the worst-case scenario, but it has a very ow probabiity of occurrence. At the same time, as expected, the position error probabiity distribution is shifted towards ower positioning errors, when the tie size is smaer. However, this comes with the cost of increased compexity. Since the mm-wave and VLC technoogies are capabe of operating at the same time in a given room the for upink and downink, respectivey, we opted for joining their forces, instead of simpy comparing their individua performances. Therefore, in Fig. 27 we presented the maximum positioning error observed, when the VLC-based trianguation of [5] is empoyed and if the user was not found, the mm-wavebased ocaization methodoogy of Section II was activated. By empoying this combined VLC and mm-wave scheme, we were abe to achieve a reduced average positioning error across a user positions in the room, whie requiring fewer CFEs. The reason was that even though the downink VLC-based trianguation achieves an infinitesimay ow positioning error, it has a very imited coverage. This probem was eiminated, by using the upink mm-wave-based ocaization methodoogy. Our future work incudes the empoyment of mutipe physica anchors in the mm-wave-based ocaization methodoogy in order to further improve the ocaization accuracy. Moreover, we are aiming for expoiting the mutipe AEs in the physica anchor of the mm-wave-based ocaization methodoogy for further reducing the search space, before actuay searching through it. This may aow us to achieve an even ower positioning error at the same compexity. Furthermore, in our treatise we ony considered rooms, where there was no bockage. In reaity, piars and was may bock the LOS path, resuting in degraded ocaization accuracy. In our future work, we are panning to circumvent this probem by either empoying mutipe anchors, or expoiting the VAs in a different way. At the same time, we aim to use the estimated position as an initia step for a quantum-assisted tracking agorithm, which woud foow the trajectory of each user. Finay, a joint VLC and mm-wave ocaization agorithm, which woud aow the exchange of information between the upink and the downink may prove beneficia. REFERENCES [1] S. Gezici, Z. Tian, G. B. Giannakis, H. Kobayashi, A. F. Moisch, H. V. Poor, and Z. Sahinogu, Locaization Via Utra-Wideband Radios: A Look at Positioning Aspects for Future Sensor Networks, IEEE Signa Processing Magazine, vo. 22, pp , Juy [2] A. Khaajmehrabadi, N. Gatsis, and D. Akopian, Modern WLAN Fingerprinting Indoor Positioning Methods and Depoyment Chaenges, IEEE Communications Surveys Tutorias, vo. PP, no. 99, pp. 1 1, [3] V. Degi-Esposti, F. Fuschini, E. M. Vitucci, M. Barbiroi, M. Zoi, L. Tian, X. Yin, D. A. Dupeich, R. Mer, C. Schneider, and R. S. Thom, Ray-Tracing-Based mm-wave Beamforming Assessment, IEEE Access, vo. 2, pp , [4] K. Witrisa, P. Meissner, E. Leitinger, Y. Shen, C. Gustafson, F. Tufvesson, K. Haneda, D. Dardari, A. F. Moisch, A. Conti, and M. Z. Win, High-Accuracy Locaization for Assisted Living: 5G systems wi turn mutipath channes from foe to friend, IEEE Signa Processing Magazine, vo. 33, pp , March [5] S. Feng, X. Li, R. Zhang, M. Jiang, and L. Hanzo, Hybrid Positioning Aided Amorphous-Ce Assisted User-Centric Visibe Light Downink Techniques, IEEE Access, vo. 4, pp , [6] T. Lv, H. Gao, X. Li, S. Yang, and L. Hanzo, Space-Time Hierarchica- Graph Based Cooperative Locaization in Wireess Sensor Networks, IEEE Transactions on Signa Processing, vo. 64, pp , Jan [7] L. Hanzo, H. Haas, S. Imre, D. O Brien, M. Rupp, and L. Gyongyosi, Wireess Myths, Reaities, and Futures: From 3G/4G to Optica and Quantum Wireess, Proceedings of the IEEE, vo. 100, no. Specia Centennia Issue, pp , This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

24 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 24 [8] F. Khan and Z. Pi, mmwave Mobie Broadband MMB): Uneashing the 3 300GHz Spectrum, in IEEE Sarnoff Symposium, pp. 1 6, May [9] Z. Pi and F. Khan, System Design and Network Architecture for a Miimeter-Wave Mobie Broadband MMB) System, in IEEE Sarnoff Symposium, pp. 1 6, May [10] T. Rappaport, S. Sun, R. Mayzus, H. Zhao, Y. Azar, K. Wang, G. Wong, J. Schuz, M. Samimi, and F. Gutierrez, Miimeter Wave Mobie Communications for 5G Ceuar: It Wi Work!, IEEE Access, vo. 1, pp , [11] W. Roh, J. Y. Seo, J. Park, B. Lee, J. Lee, Y. Kim, J. Cho, K. Cheun, and F. Aryanfar, Miimeter-Wave Beamforming as an Enabing Technoogy for 5G Ceuar Communications: Theoretica Feasibiity and Prototype Resuts, IEEE Communications Magazine, vo. 52, pp , February [12] I. A. Hemadeh, M. E-Hajjar, S. Won, and L. Hanzo, Layered Muti- Group Steered Space-Time Shift-Keying for Miimeter-Wave Communications, IEEE Access, vo. 4, pp , [13] S. Rajagopa, R. D. Roberts, and S. K. Lim, IEEE Visibe Light Communication: Moduation Schemes and Dimming Support, IEEE Communications Magazine, vo. 50, pp , March [14] C. X. Wang, F. Haider, X. Gao, X. H. You, Y. Yang, D. Yuan, H. M. Aggoune, H. Haas, S. Fetcher, and E. Hepsaydir, Ceuar Architecture and Key Technoogies for 5G Wireess Communication Networks, IEEE Communications Magazine, vo. 52, pp , February [15] P. H. Pathak, X. Feng, P. Hu, and P. Mohapatra, Visibe Light Communication, Networking, and Sensing: A Survey, Potentia and Chaenges, IEEE Communications Surveys Tutorias, vo. 17, pp , Fourthquarter [16] A. ahin, Y. S. Erou,. Gven, N. Paa, and M. Ykse, Hybrid 3-D Locaization for Visibe Light Communication Systems, Journa of Lightwave Technoogy, vo. 33, pp , Nov [17] M. Biagi, S. Pergooni, and A. M. Vegni, LAST: A Framework to Locaize, Access, Schedue, and Transmit in Indoor VLC Systems, Journa of Lightwave Technoogy, vo. 33, pp , May [18] K. Qiu, F. Zhang, and M. Liu, Let the Light Guide Us: VLC-Based Locaization, IEEE Robotics Automation Magazine, vo. 23, pp , Dec [19] A. Conti, M. Guerra, D. Dardari, N. Decari, and M. Z. Win, Network Experimentation for Cooperative Locaization, IEEE Journa on Seected Areas in Communications, vo. 30, pp , February [20] H. Wymeersch, S. Marano, W. M. Gifford, and M. Z. Win, A Machine Learning Approach to Ranging Error Mitigation for UWB Locaization, IEEE Transactions on Communications, vo. 60, pp , June [21] P. Meissner and K. Witrisa, Mutipath-assisted singe-anchor indoor ocaization in an office environment, in Internationa Conference on Systems, Signas and Image Processing IWSSIP), pp , Apri [22] E. Leitinger, P. Meissner, C. Rdisser, G. Dumphart, and K. Witrisa, Evauation of Position-Reated Information in Mutipath Components for Indoor Positioning, IEEE Journa on Seected Areas in Communications, vo. 33, pp , Nov [23] C. Durr and P. Høyer, A Quantum Agorithm for Finding the Minimum, eprint arxiv:quant-ph/ , Juy [24] L. K. Grover, A Fast Quantum Mechanica Agorithm for Database Search, Proceedings, 28th Annua ACM Symposium on the Theory of Computing, pp , May [25] L. K. Grover, Quantum Mechanics Heps in Searching for a Neede in a Haystack, Physica Review Letters, vo. 79, pp , Juy [26] M. Boyer, G. Brassard, P. Høyer, and A. Tapp, Tight Bounds on Quantum Searching, Fortschritte der Physik, vo. 46, pp , [27] P. Botsinis, S. X. Ng, and L. Hanzo, Quantum Search Agorithms, Quantum Wireess, and a Low-Compexity Maximum Likeihood Iterative Quantum Muti-User Detector Design, IEEE Access, vo. 1, pp , [28] P. Botsinis, S. X. Ng, and L. Hanzo, Fixed-Compexity Quantum- Assisted Muti-User Detection for CDMA and SDMA, IEEE Transactions on Communications, vo. 62, pp , March [29] P. Botsinis, D. Aanis, S. X. Ng, and L. Hanzo, Low-Compexity Soft-Output Quantum-Assisted Mutiuser Detection for Direct-Sequence Spreading and Sow Subcarrier-Hopping Aided SDMA-OFDM Systems, IEEE Access, vo. 2, pp , May [30] P. Botsinis, D. Aanis, Z. Babar, S. X. Ng, and L. Hanzo, Noncoherent Quantum Mutipe Symbo Differentia Detection for Wireess Systems, IEEE Access, vo. 3, pp , May [31] P. Botsinis, D. Aanis, Z. Babar, S. Ng, and L. Hanzo, Iterative Quantum-Assisted Muti-User Detection for Muti-Carrier Intereave Division Mutipe Access Systems, IEEE Transactions on Communications, vo. 63, pp , Juy [32] P. Botsinis, D. Aanis, Z. Babar, H. V. Nguyen, D. Chandra, S. X. Ng, and L. Hanzo, Quantum-Aided Muti-User Transmission in Non- Orthogona Mutipe Access Systems, IEEE Access, vo. 4, pp , [33] P. Botsinis, D. Aanis, Z. Babar, S. X. Ng, and L. Hanzo, Joint Quantum-Assisted Channe Estimation and Data Detection, IEEE Access, vo. 4, pp , [34] D. Aanis, P. Botsinis, Z. Babar, S. X. Ng, and L. Hanzo, Non- Dominated Quantum Iterative Routing Optimization for Wireess Mutihop Networks, IEEE Access, vo. 3, pp , [35] D. Aanis, J. Hu, P. Botsinis, Z. Babar, S. X. Ng, and L. Hanzo, Quantum-Assisted Joint Muti-Objective Routing and Load Baancing for Sociay-Aware Networks, IEEE Access, vo. 4, pp , [36] P. Botsinis, Z. Babar, D. Aanis, D. Chandra, H. Nguyen, S. X. Ng, and L. Hanzo, Quantum error correction protects quantum search agorithms against decoherence, Scientific Reports, vo. 6, no , [37] G. R. Maccartney, T. S. Rappaport, S. Sun, and S. Deng, Indoor Office Wideband Miimeter-Wave Propagation Measurements and Channe Modes at 28 and 73 GHz for Utra-Dense 5G Wireess Networks, IEEE Access, vo. 3, pp , [38] P. Ioannides and C. A. Baanis, Uniform Circuar Arrays for Smart Antennas, IEEE Antennas and Propagation Magazine, vo. 47, pp , Aug [39] J. G. Proakis, Digita Communications. McGraw-Hi, [40] J. Pascua-Garca, J. M. Moina-Garca-Pardo, M. T. Martnez-Ings, J. V. Rodrguez, and N. Saurn-Serrano, On the Importance of Diffuse Scattering Mode Parameterization in Indoor Wireess Channes at mm- Wave Frequencies, IEEE Access, vo. 4, pp , [41] K. Haneda, J. Jrveinen, A. Karttunen, M. Kyr, and J. Putkonen, A Statistica Spatio-Tempora Radio Channe Mode for Large Indoor Environments at 60 and 70 GHz, IEEE Transactions on Antennas and Propagation, vo. 63, pp , June [42] N. Micheusi, U. Mitra, A. F. Moisch, and M. Zorzi, UWB Sparse/Diffuse Channes, Part I: Channe Modes and Bayesian Estimators, IEEE Transactions on Signa Processing, vo. 60, pp , Oct [43] N. Czink, A. Richter, E. Bonek, J. P. Nuutinen, and J. Yitao, Incuding Diffuse Mutipath Parameters in MIMO Channe Modes, in IEEE Vehicuar Technoogy Conference, pp , Sept [44] T. Komine and M. Nakagawa, Fundamenta Anaysis for Visibe-Light Communication System Using LED Lights, IEEE Transactions on Consumer Eectronics, vo. 50, pp , Feb [45] M. A. Niesen and I. L. Chuang, Quantum Computation and Quantum Information. Cambridge University Press, [46] S. Imre and F. Baázs, Quantum Computing and Communications: An Engineering Approach. John Wiey & Sons, [47] S. Imre and L. Gyongyosi, Advanced Quantum Communications: An Engineering Approach. John Wiey & Sons, Panagiotis Botsinis S 12-M 15) received the M.Eng. degree from the Schoo of Eectrica and Computer Engineering of the Nationa Technica University of Athens NTUA), Greece, in 2010, as we as the M.Sc. degree with distinction and the Ph.D. degree in Wireess Communications from the University of Southampton, UK, in 2011 and 2015, respectivey. He is currenty working as a Research Feow in the Southampton Wireess group at the Schoo of Eectronics and Computer Science of the University of Southampton, UK. Since October 2010, he has been a member of the Technica Chamber of Greece. His research interests incude quantum-assisted communications, quantum computation, iterative detection, OFDM, MIMO, mutipe access systems, coded moduation, channe coding, cooperative communications, as we as combinatoria optimization. This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

25 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 25 Dimitrios Aanis S 13) received the M.Eng. degree in Eectrica and Computer Engineering from the Aristote University of Thessaoniki in 2011 and the M.Sc. degree in Wireess Communications from the University of Southampton in He is currenty working towards the PhD degree with the Southampton Wireess SW) Group, Schoo of Eectronics and Computer Science of the University of Southampton. His research interests incude quantum computation and quantum information theory, quantum search agorithms, cooperative communications, resource aocation for seforganizing networks, bio-inspired optimization agorithms and cassica and quantum game theory. Simeng Feng received her B.Eng degree in Eectronic Information Science and Technoogy from Ocean University of China and received her Master degree in Wireess Communications from University of Southampton, UK. Now, she is working towards her Ph.D. degree with Southampton Wireess, University of Southampton, UK. Her research interests incude visibe ight communications, optica moduations, indoor positioning, amorphous ces, heterogeneous networks and energy efficiency. Zunaira Babar received her B.Eng. degree in eectrica engineering from the Nationa University of Science & Technoogy NUST), Isamabad, Pakistan, in 2008, and the M.Sc. degree Distinction) and the Ph.D degree in wireess communications from the University of Southampton, UK, in 2011 and 2015, respectivey. She is currenty working as a Research Feow in the Southampton Wireess group at the University of Southampton. Her research interests incude quantum error correction codes, channe coding, coded moduation, iterative detection and cooperative communications. Hung Viet Nguyen received the B.Eng. degree in Eectronics & Teecommunications from Hanoi University of Science and Technoogy HUST), Hanoi, Vietnam, in 1999, the M.Eng. in Teecommunications from Asian Institute of Technoogy AIT), Bangkok, Thaiand, in 2002 and the Ph.D. degree in wireess communications from the University of Southampton, Southampton, U.K., in Since 1999 he has been a ecturer at the Post & Teecommunications Institute of Technoogy PTIT), Vietnam. He is invoved in the OPTIMIX and CONCERTO European projects. He is currenty a postdoctora researcher at Southampton Wireess SW) group, University of Southampton, UK. His research interests incude cooperative communications, channe coding, network coding and quantum communications. Daryus Chandra S 13) received the M.Eng. degree in eectrica engineering from Universitas Gadjah Mada UGM), Indonesia, in He is currenty pursuing the Ph.D degree with the Southampton Wireess group, Schoo of Eectronics and Computer Science, University of Southampton. He is a recipient of schoarship award from Indonesia Endowment Fund for Education LPDP). His research interests incudes channe codes, quantum error correction codes, and quantum communications. Soon Xin Ng S 99-M 03-SM 08) received the B.Eng. degree First cass) in eectronics engineering and the Ph.D. degree in wireess communications from the University of Southampton, Southampton, U.K., in 1999 and 2002, respectivey. From 2003 to 2006, he was a postdoctora research feow working on coaborative European research projects known as SCOUT, NEWCOM and PHOENIX. Since August 2006, he has been a member of academic staff in the Schoo of Eectronics and Computer Science, University of Southampton. He is invoved in the OPTIMIX and CONCERTO European projects as we as the IUATC and UC4G projects. He is currenty an Associate Professor of Teecommunications with the University of Southampton. He has authored over 180 papers and co-authored two John Wiey/IEEE Press books in his research fied. His research interests incude adaptive coded moduation, coded moduation, channe coding, space-time coding, joint source and channe coding, iterative detection, OFDM, MIMO, cooperative communications, distributed coding, quantum error correction codes and joint wireess-and-optica-fiber communications. He is a a Chartered Engineer and a Feow of the Higher Education Academy in the UK. Rong Zhang M 09-SM 16) is an assistant professor in Southampton Wireess group within the schoo of ECS at University of Southampton UoS). He received his PhD in wireess communications from UoS in 2009, where he was a research assistant during that period with Mobie Virtua Centre of Exceence, one of UK s argest industria-academic partnership in ICT. During his post-doctora period in ECS, he contributed as the UoS ead researcher on a number of internationa projects. After that, he took his industria consuting eave for Huawei EU R& D as a System Agorithms Expert. He has a tota of 80+ IEEE/OSA pubications, incuding 55+ journas 20+ of which as first author). Owing to his outstanding academic achievements, he is the recipient of the prestigious Dean s Pubication Award. He is aso the recipient of the prestigious RAEng industria feowship. He reguary serves as reviewer for IEEE/OSA journas and funding bodies and has been severa times as TPC member/invited session chair of major conferences. He is a RAEng industria feow, a senior member of the IEEE, a member of the OSA. This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

26 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI /ACCESS , IEEE Access 26 Lajos Hanzo M 91-SM 92-F 04) received his degree in eectronics in 1976 and his doctorate in In 2009 he was awarded the honorary doctorate Doctor Honoris Causa by the Technica University of Budapest. During his 38-year career in teecommunications he has hed various research and academic posts in Hungary, Germany and the UK. Since 1986 he has been with the Schoo of Eectronics and Computer Science, University of Southampton, UK, where he hods the chair in teecommunications. He has successfuy supervised about 100 PhD students, co-authored 20 John Wiey/IEEE Press books on mobie radio communications totaing in excess of 10,000 pages, pubished 1,500+ research entries at IEEE Xpore, acted both as TPC and Genera Chair of IEEE conferences, presented keynote ectures and has been awarded a number of distinctions. Currenty he is directing a 100-strong academic research team, working on a range of research projects in the fied of wireess mutimedia communications sponsored by industry, the Engineering and Physica Sciences Research Counci EPSRC) UK, the European Research Counci s Advanced Feow Grant and the Roya Society s Wofson Research Merit Award. He is an enthusiastic supporter of industria and academic iaison and he offers a range of industria courses. Lajos is a Feow of the Roya Academy of Engineering, of the Institution of Engineering and Technoogy, and of the European Association for Signa Processing. He is aso a Governor of the IEEE VTS. During he was the Editor-in-Chief of the IEEE Press and a Chaired Professor aso at Tsinghua University, Beijing. He has 22,000+ citations. For further information on research in progress and associated pubications pease refer to This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see