Coverage and Rate Analysis for Massive MIMO-enabled Heterogeneous etworks with Millimeter wave Small Cells Anum Umer, Syed Ali Hassan, Haris Pervaiz, Qiang i and eila Musavian School of Electrical Engineering & Computer Science SEECS, ational University of Sciences & Technology UST, Islamabad, Pakistan 44, {aumermsee5seecs, alihassan}@seecsedupk School of Computing & Communications, ancaster University, UK {hpervaiz, qni}@lancasteracuk School of Computer Science and Electronics Engineering, University of Esse, UK leilamusavian@esseacuk Abstract The eisting cellular networks are being modified under the umbrella of fifth generation 5G networks to provide high data rates with optimum coverage Current cellular systems operating in ultra high frequency UHF bands suffer from severe bandwidth congestion hence 5G enabling technologies such as millimeter wave mmwave networks focus on significantly higher data rates In this paper, we eplore the impact of coeistance of massive Multiple-Input Multiple-Output MIMO that provides large array gains and mmwave small cells on coverage We investigate the downlink performance in terms of coverage and rate of a three tier network where a massive MIMO macro base stations MBSs are overlaid with small cells operating at sub-6ghz and mmwave frequency bands Based on the eisting stochastic models, we investigate user association, coverage probability and data rate of the network umerical results clearly show that massive MIMO enabled MBSs alongside mmwave small cells enhance the performance of heterogeneous networks Hetets significantly Inde Terms Heterogeneous networks, 5G cellular networks, Millimeter wave, sub-6ghz bands, massive MIMO, stochastic geometry I ITRODUCTIO Over the years, the data rate demands have increased immensely and the eponential growth in traffic calls for making use of higher frequency bands in addition to conventional sub-6ghz bands The upcoming 5G technology is thought of, by researchers, as a miture of multiple network tiers of variable sizes, transmit powers, range, operating frequencies, making a heterogeneous network Hetet 5G promises wide range of applications alongside high data rates but eisting cellular infrastructure works on sub-6ghz bands, which is unable to meet the 5G data demands However, millimeter wave mmwave communication base stations BSs operating at to 3 GHz frequency bands with bandwidths up to GHz and multiple antenna arrays at sub-6ghz BSs providing high array gains are seen as key enablers of 5G communication providing high coverage and data rates The Hetets, massive Multiple-Input Multiple-Output MIMO and mmwave cells have gathered researchers attention and a lot of work is being done on their performance For instance, proposed stochastic geometry-based model for mmwave network to analyse coverage and rate trends, effects of antenna pattern and blockages by deploying BSs using a Poisson point process PPP model Authors in analysed performance of mmwave hybrid networks based on simulation models The massive MIMO has been investigated in 3, it presents results for achievable rate in uplink network scenario for MIMO at BSs, the authors investigated user association for massive MIMO Hetets in 4 and 5 stochastically modelled user association and coverage for K-tier Hetet with massive MIMO in macro tier Though the aforementioned literature clearly eplains the efficiency of mmwave networks in providing better coverage than UHF networks and that of massive MIMO in providing large array gains, an analytical approach to investigating the impact of co-eistence of massive MIMO and mmwave cells on user association, coverage and rate in a Hetet has not been eplored yet This paper deals with etending eisting stochastic geometry models for analysis of 3-tier network composed of massive MIMO enabled sub 6-GHz macro cells overlaid with mmwave and sub 6-GHz small cells We analyse network performance in terms of user association, network coverage and data rate To the best of our knowledge, no prior work has investigated network performance of mmwave small cells coeisting with traditional heterogeneous networks while assuming akagami fading model for mmwave communication and massive MIMO enabled macro BSs MBSs We deploy antennas at each macro cell BS which simultaneously transmit data streams to S users using linear zero-forcing beamforming The mmwave and sub-6ghz small cells BS are deployed at higher density than MBSs and user association, coverage and rate trends are discussed II SYSTEM MODE We consider the downlink transmission scenario of a threetier Hetet comprising of sub-6ghz macro cells overlaid with small cells operating at sub-6ghz and mmwave frequency band The BSs of k th tier are uniformly distributed as Homogeneous Poisson Point Process HPPP Φ k with density λ k where k = {,, 3} The users are also assumed to be uniformly distributed as HPPP Φ u with density λ u The sub- 6GHz small cells constitute tier while tier 3 constitutes
small cells operating at mmwave frequency band Massive MIMO is implemented at the macro cells where antennas are installed at each MBS which simultaneously transmit to S users such that S 6 The sub-6ghz small cell BSs, mmwave BSs and users are single antenna nodes Zero forcing beamforming is used by each MBS for transmitting S data streams with equal power assignment Transmission is taken to be time-division duple TDD and it is assumed that downlink channel state information is known at the MBS 5 Analysis is performed for a typical user located at the origin, in accordance with Slivnyak s Theorem The mmwave small cells can have either line of sight os or on-line of sight os link to the typical user Hence we split Φ 3, by applying independent thinning theorem, to Φ 3 and Φ 3 as point processes of os and os mmwave small cells, using os probability function pr, to evaluate that a link of length R is os or os Thus, Φ 3 and Φ 3 have the densities prλ 3 and prλ 3, respectively, while pr is discussed in Section II-C A Downlink User Association An open access scheme has been assumed such that user is allowed to connect to any tier BS We assume user association is based on maimum average received power The average received power at a user associated with MBS jj φ is P r, = G M S j,m, where is MBS s transmit power, j,m = α is path loss function where α is path loss eponent and G M = S + is the array gain for zero forcing beamforming transmission 6 It is evident from that the array gain of massive MIMO macro cell tier has a prominent impact on user cell association The average received power in case the user is associated with small cell tier i BS is, P r,i = P i i, where i = {, 3}, where P i is small cell BS transmit power in the i th tier and i = αi i is small cell path loss function with path loss eponent α i B Channel Model We assume independent and identically distributed iid Rayleigh fading channel for sub-6ghz links and independent akagami fading for mmwave links The SIR of a typical user located at a distance associated with the MBS is represented as SIR u M = S h o,m o,m σ + j Φ \b o,m S h j,m j,m j + I S, 3 such that I S = q Φ P q h q q q is inter cell interference from the small cell operating in sub-6ghz band ecept the serving BS b o,m, while h q es the small scale fading gain from the interfering channel Similarly, q is distance between the typical user and small cell BS q, h o,m Γ S +, is the small scale fading gain of the typical user at the distance from the serving BS and h j,m ΓS, 6, j is distance between typical user and MBS j, q q = α q and σ is the noise power Similarly, the SIR of a typical user located at the distance associated with the sub-6ghz small cell is represented as SIR u S = P h o,s o,s σ + I M + q Φ \b o,s P h q,s q,s q, 4 P j where I M = j Φ S h j j j is intercell interference from macro cells, q,s q = α q and o,s = α Here, h q es the small scale fading gain from the interfering channel and q is the distance of the typical user from small cell BS q Similarly, h o,s es the small scale fading gain of the typical user at the distance from the serving BS while h j is small scale fading power gain such that h j ΓS, Here, j is distance of the user from MBS j The SIR for the typical user associated with mmwave small cell is represented as P 3 M r M t h o,m o,m SIR m = σ + P 3 j, i Φ 3\b o,m G l h i,m i,m i, 5 where o,s = α3, h o,m is small scale fading gain where different akagami fading parameters are taken for os and os links, M r and M t are the main lobe gains of the transmit and receive antennas, j {, } identifies the interfering link as either os or os and G l is the directivity gain of interfering BSs It is assumed that both the BSs and the users are in perfect alignment with each other so the directivity gain of the desired link signal is given by M r M t Beam direction is assumed to be independently and uniformly distributed between, π Hence G l for l = {,, 3, 4} is a i = M r M t with prob = θr θ t π π a G l = i = M r m t with prob = θr θt π π a i = m r M t with prob = θr π θt π a i = m r m t with prob = θr θt π π C Blockage Model A stochastic blockage model is assumed for mmwave small cells, where blockages are modeled as a rectangle Boolean scheme, based on random shape theory On the basis of this scheme, os probability function pr is given by, pr = e βr where R is the link distance and β is dependent on statistics of blockages The os probabilities for various links are assumed to be independent III PERFORMACE AAYSIS In this section, we perform stochastic modeling of typical user association probability for each tier followed by coverage and rate analysis of proposed network scenario
A Association Probability per Tier Sub-6GHz Macro Cell tier: The association probability that a user is connected to MBS is given by, P S A = πλ ep πλ α /α S + /α3 6 πλ P 3 S πλ 3 d, S + where is given by, = tptdt + t ptdt, 7 where = α /α and = α /α is based on the independent thinning of φ 3 with os probability function pr, as described in section II The probability density function of users distance to serving MBS, f X,is f X = πλ P S ep πλ α /α A S + /α3 8 πλ P 3 S πλ 3 S + Sub-6 GHz Small Cell tier: The association probability that a user is connected to sub-6ghz small cell BS is given by, A = πλ ep πλ πλ 3 πλ P S + α P S /α d, where is given by 8 The probability density function of users distance to serving sub-6ghz small cell BS, f X,is f X = πλ ep A πλ πλ 3 πλ P S + α P S /α 9 3 mmwave Small Cell tier: The association probability that a user is connected to mmwave small cell BS is given as A 3 = A k k, The probability of associating with os link is given by, { } A = Λ ep πλ 3 tptdt f d Thus, the probability of associating with os link is A = A Here, f is probability density function of the distance of the typical user to the os BS given by, f = πλ 3 pep πλ 3 t ptdt/λ and for os link, f = πλ 3 pep πλ 3 tptdt/λ Eq 4 of, where Λ = ep { πλ 3 t ptdt } is probability of user having at least one os link, likewise, Λ = ep { πλ 3 tptdt } for os link PDF of the distance of user to serving BS given it is associated with os BS is ˆf = { Λ f A ep } πλ 3 t ptdt link ˆf = Λ f A ep B Coverage Probability { πλ 3 tptdt and for } os Coverage probability is the measure that the received SIR at a typical user is higher than a certain threshold, Mathematically P k CΓ = PrSIR k > Γ = = PrSIR k > Γ X k = f Xk d P k Γ, f Xk d where k = {, } The total SIR coverage probability, P C, is calculated using law of total probability as 3 P C = PCA r r 3 r= The coverage probability for a user associated with MBS is given by, Γ, = S l= ep Γσ S α ΓS α Ξ B q S α α l l! l! l l j= n j!j! nj l Ψ j α nj, j= where Ξ and Ψ j is S z S P q Ξq = πλ q z S z+ α z S α z= z J α α, S + πλ qp α α α F, ; ; qp J, α α 4 5 Ψ i = Γσ S α πλ SΓ α α α F, S + ; ΓS ; iγ α πλ α α J α α α F α α, ; α ; iγs P J Ψ j i = πλ Γ S + j! α S! B Γi α j α, S j ΓSP where J = i j+ α α + πλ j! i j+ α α α B α j, j ΓSi P P J α α P S α S+, 6, 7
The coverage probability for a user associated with sub- 6GHz small cell tier is P Γ, = ep Γσ S z α S P Γ α πλ P z SP z= α Γ P SP z+ α B α Γ α SP H z, S α α α πλ Γ α α F, ; ; Γ, α α 8 S+ where H = SP α The proof can be found on similar lines as mentioned in 5 and is omitted here due to the space limitation The coverage probability for a user associated with mmwave small cell is given by, P 3 CΓ = A P 3, Γ + A P 3, Γ, 9 where P 3, and P 3, are and where P 3, j+ j j= jη α Γσ ep C j Γ, D j Γ, ˆf d, M r M t P 3, j+ j j= jη α Γσ ep E j Γ, V j Γ, ˆf d M r M t C j Γ, = πλ 3 i= D j Γ, = πλ 3 E j Γ, = πλ 3 V j Γ, = πλ 3 i= F, jη â i Γ α t α pttdt, i= i= F, jη â i Γ α t α pttdt, F, jη â i Γ α t α pttdt, F, jη â i Γ α t α pttdt, and F, = / + Here η =! and η =! Parameter â i = a i /M r M t, a i and are defined in Section II The proof can be found on similar lines as mentioned in and is omitted here due to the space limitation Association Probability 9 8 7 6 5 4 3 sub-6 GHz macro cell sub-6ghz small cell mmwave small cell 3 4 5 6 7 8 9 Fig Association probability verses with λ = λ 3 = 3λ and S = 5 C Rate Coverage Probability We define the instantaneous downlink coverage rate for typical user such that the rate is higher than a certain threshold for an associated tier k defined as R k C = PrRate k > ρ = PrW log + SIR k > ρ = PrSIR k > ρ W = P k C ρ W, where W is the total available bandwidth at the BS IV SIMUATIO AD UMERICA RESUTS A 3-tier Hetet is taken with MBS density λ = 5 π, λ and λ 3 are taken multiples of MBS density The sub-6ghz tiers are assumed to be operating at GHz carrier frequency, W = MHz, path loss eponents α = 35, α = 4 and transmit power = 46dBm and P = 3dBm, respectively ikewise for mmwave tier, the operating frequency is 8GHz, W = MHz, path loss eponent for os α = and for os α = 4 and transmit power P 3 = 3dBm akagami fading parameters for mmwave tier, and, are assumed to be positive integers, and 3, respectively Array gains for all angles in main lobe are taken M r = db, M t = db and for the side lobes m r = db, m t = db Main lobe beamwidth is taken to be θ r = 9 and θ t = 3 oise σ = 9dBm is taken with noise figure of db For the os probability function pr = e βr, β is takes as /β = 44 meters In Fig we observe the effect of increasing the number of antennas on association probability of each tier and see that association with macro BSs is directly proportional to the number of antennas on each BS and it prominently effects the user association with other tiers This can be attributed to the higher array gains because of higher antenna density at macro BSs Other reason is that macro BSs have greater transmit power than small cell BSs After macro BSs most of the load is managed by mmwave BSs due to their favourable SIR distribution and larger available bandwidth compared to the sub-6ghz small cell BSs
9 9 SIR Coverage Probability 8 7 6 Simulation λ =3λ Analytical λ =3λ Rate coverage probability 8 7 6 λ =3λ λ =5λ Simulation λ =5λ 5 Analytical λ =5λ 5 4 - -5 - -5 5 5 SIR Threshold Fig SIR coverage probability P C Γ verses SIR threshold Γ for = 4 and S = 4 5 5 5 3 Acheivable rate in Mbps Fig 4 Rate coverage probability R C verses rate threshold ρ for = 4 and S = SIR Coverage Probability 9 8 7 6 5 4 3 Simulation λ =3λ Analytical λ =3λ Simulation λ =3λ Analytical λ =3λ - -5 - -5 5 5 5 3 SIR Threshold Fig 3 SIR coverage probability P C Γ verses SIR threshold Γ for = 4 and S = Fig shows the network coverage probability P C for different small cell BS densities and we observe that as small cell BS density increases, more users are offloaded to small cells and it significantly improves the SIR coverage of the network Since small cells operate at lower power this may lead to power efficient network where high power macro BS have lower traffic but it comes at the cost of high small cell BS deployment The macro cells may serve to provide better coverage at cell edges but within them small cells provide better coverage Moreover, it can be observed that simulation results and analytical results are tightly bound to each other that validates the model Fig 3 compares network coverage probability of -tier network with sub-6ghz macro and small cells and 3-tier network We see that the mmwave tier has significant contribution to SIR coverage probability This can be attributed to the favourable SIR distribution, larger available bandwidth and higher density of mmwave cells Macro cells may serve to provide better coverage at cell edges but within them small cells provide better coverage Moreover, it can be observed that simulation results and analytical results are tightly bound to each other that validates the model In Fig 4 we observe that as the small cell BS density increases, rate increases drastically This is due to the fact that small cell BSs form better links to the users when their deployment density is high and users associated with mmwave small cells have greater allocated bandwidth V COCUSIO In this paper, 3-tier Hetet coverage and rate is analysed with massive MIMO at macro tier User association is performed based on maimum received power and effect of massive MIMO and mmwave BS density on the user cell association is investigated It has been observed that the implementation of massive MIMO on macro tier and deployment of high density of mmwave small cells leads to significant enhancement of rate and coverage Moreover, numerical results showed that on increasing number of antennas at macro BS, user association is biased towards macro tier, leading to low demand of small cells that simplifies the network REFERECES R W Heath and T Bai, Coverage and rate analysis for millimeter-wave cellular networks, IEEE Trans Wireless Commun, vol 4, no, pp -4, 5 M S Omar, M A Anjum, S A Hassan, H Pervaiz and Q i, Performance analysis of hybrid 5G cellular networks eploiting mmwave capabilities in suburban areas, IEEE Int Conf Commun ICC, pp -6, 6 3 E G arsson, H Q go and T Marzetta, The multicell multiuser mimo uplink with very large antenna arrays and a finite-dimensional channel, IEEE Trans Commun, vol 6, no 6, pp 35-36, 3 4 H C Papadopoulos, D Bethanabhotla, O Y Bursalioglu and G Caire, Optimal user-cell association for massive mimo wireless networks, IEEE Trans Wireless Commun, Vol5, pp 835-85, 6 5 Y Chen, M Elkashlan, AHe, Wang and K-KWong, Massive mimo in k-tier heterogeneous cellular networks: Coverage and rate, Proc IEEE Global Telecommun Conf GOBECOM, pp -6, 5 6 W Yu, K Hosseini and R S Adve, arge-scale mimo versus network mimo for multicell interference mitigation, IEEE J Sel Areas Commun, vol 8, no 5, pp 93-94, Oct 4