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1 Onireti, O., Heliot, F., and Imran,. A. 3 On the energy efficiency-spectral efficiency trade-off of distributed IO systems. IEEE ransactions on Communications, 69, pp here may be differences between this version and the published version. You are advised to consult the publisher s version if you wish to cite from it. Deposited on: February 7 Enlighten Research publications by members of the University of Glasgow

2 On the Energy Efficiency-Spectral Efficiency rade-off of Distributed IO Systems Oluwakayode Onireti, ember, IEEE, Fabien Héliot, ember, IEEE, and uhammad Ali Imran Senior ember, IEEE Abstract In this paper, the trade-off between energy efficiency EE and spectral efficiency SE is analyzed for both the uplink and downlink of the distributed multiple-input multiple-output DIO system over the Rayleigh fading channel while considering different types of power consumption models PCs. A novel tight closed-form approximation of the DIO EE- SE trade-off is presented and a detailed analysis is provided for the scenario with practical antenna configurations. Furthermore, generic and accurate low and high-se approximations of this trade-off are derived for any number of radio access units RAUs in both the uplink and downlink channels. Our expressions have been utilized for assessing both the EE gain of DIO over co-located IO CIO and the incremental EE gain of DIO in the downlink channel. Our results reveal that DIO is more energy efficient than CIO for cell edge users in both the idealistic and realistic PCs; whereas in terms of the incremental EE gain, connecting the user terminal to only one RAU is the most energy efficient approach when a realistic PC is considered. Index erms Energy efficiency, spectral efficiency, trade-off, distributed IO, Rayleigh channels. I. INRODUCION INCREASING global energy demand and soaring energy related operating cost is currently steering research in communications towards the design of energy efficient networks. Up to now, the spectral efficiency SE metric has been the main performance indicator for designing and optimizing wireless communication networks. he SE metric measures how efficiently a limited frequency resource is utilized but fails to give insights on how efficiently the energy is consumed and, thus, this has recently led to the introduction of the energy efficiency EE as a performance metric. he EE of a communication network can be measured in terms of the bit-per-joule capacity [], which is the maximum amount of bits that can be delivered by the network per joule it consumed to do so, or by using energy consumption metric such as the traditional energy-per-bit to noise spectral density []. Accurate evaluation of the EE of a network indeed requires that its power consumption must be adequately modelled. In the literature, two forms of power consumption models PCs can be identified for characterizing the EE of a communication network: the idealistic PC which only considers transmit power [] [5] and; the realistic PC which accounts for the total power consumed in the network by including in addition he authors are with the Centre for Communication Systems Research, Faculty of Engineering & Physical Sciences, University of Surrey, Guildford GU 7XH, UK F.Heliot@Surrey.ac.uk. his work has been done within joint project, supported by Huawei ech. Co., Ltd, China. to the transmit power, the amplifier inefficiency, processing and backhauling powers, cooling loss, etc., in its model [6] []. he Shannon information theoretic capacity for point-topoint additive white Gaussian noise AWGN channel has established the existence of a fundamental trade-off between EE and SE, such that an explicit expression for this AWGN EE- SE trade-off can be found in [] and []. However, except for the AWGN channel and deterministic channel with coloured Gaussian noise, explicit expressions of the EE-SE trade-off for most other common communication channels does not yet exist. Instead, closed-form approximations CFAs such as Verdú low-power approximation of [], has been extensively utilized in the literature for mathematically characterizing this trade-off [3] [5]. In general, explicit expressions and CFAs are not only useful for swiftly assessing the performance of complicated communication systems, but they are also useful for analyzing them and getting valuable insights on how to improve them. oreover, their importance and usage is expected to grow rapidly with the advent of future cellular networks such as self-organizing networks, where machines will rely on such mathematical formulations for keeping the system optimized at any time. We have recently proposed an approach for deriving CFAs of the EE-SE trade-off for the point-to-point multiple-input multiple-output IO over the Rayleigh fading channel in [], [] and for uplink of the symmetric coordinated multi-point CoP system in [3]. Contrarily to the Verdú s approach, which is only accurate in the low-se regime, our novel approach is highly accurate in any SE regime. Bearing in mind that new generations of communication networks such as Long erm evolution LE and LE-advanced LE-A are designed to operate in the midhigh SE region, there is a need for developing EE-SE trade-off CFAs that are very accurate in these regimes. he distributed multiple-input multiple-output system DIO was originally proposed to cover dead spots in indoor wireless communications [4]. However, the range of applications for DIO has recently been broadened due to the increasing demand for high data rate and limited power resource in wireless networks. Indeed, DIO can prove useful for improving the network capacity by shortening the transmission distance [5] [7]. In the DIO system, the antenna units, which is usually referred to as radio access units RAUs, are geographically distributed contrarily to the traditional colocated IO CIO system where the antennas are just a few wavelength apart. he capacity gain and improved power efficiency of the DIO system over the CIO

3 Fig.. Distributed IO system model. scheme results from its ability to exploit both the macro and micro diversities [5] []. he channel capacity of DIO has been extensively studied and its asymptotic closed-form expression can be found in [], [] while its high signalto-noise ratio SNR approximation has been derived in [], [3]. As far as the uplink of the DIO EE-SE trade-off is concerned, its lower and upper bounds at high SNR have been obtained in [4] by using the high SNR approximation of [], but only for some limited antenna configurations. Furthermore, an energy-efficient resource allocation for the downlink of the DIO system has been recently proposed in [5]. In this paper, we propose a framework for comprehensively analyzing the DIO system from both an EE and SE perspective by means of a tight CFA of its EE-SE trade-off. Relying on our novel approach, we go beyond [4] and propose an accurate CFA of the DIO EE-SE trade-off for any SE regime and wider range of antenna configurations. Section II presents the system model for the DIO system and reviews its capacity expression which serves as a basis for our own derivation. We then briefly present the realistic PC of DIO system and formulate the actual DIO EE-SE trade-off expression. In Section III, we derive our CFA of the DIO EE-SE trade-off for any number of RAUs; we obtain this CFA for the case with a practical antenna setting by designing a parametric function and using a heuristic curve fitting method [], [6], [7]. Numerical results show the accuracy of our approximation for several RAUs, a wide range of SE values and numerous antenna configurations. However, obtaining the CFA of the DIO EE-SE trade-off is too intricate for a large number of RAUs. Consequently, we derive in Section IV generic low and high-se approximations of the DIO EE-SE trade-off for both the uplink and downlink scenarios. On the one hand, results show that our novel low- SE approximation is as accurate as the approximation of [], but it has the advantage of a simplified formulation. On the other hand, our novel high-se approximation is very tight with the actual EE-SE trade-off results in both the mid as well as high SE regimes, and is far more accurate than the approximation in [4]. his is due to the fact that the derivation of the approximations in [4] is based on lower and upper bounds instead of an exact formulation. As an application for our novel and accurate approximations, we study in Section V, both analytically and numerically, the effects of connecting additional RAUs to the user terminal U on the system EE and how DIO compares with CIO in terms of EE, for both idealistic and realistic PCs. Results show that some of the SE gain that is obtained by using DIO system can be traded-off with power to achieve EE gain over the CIO system. In addition, connecting the U to the RAU, which has the strongest channel gain to the U, is the most energy efficient approach when a realistic PC is considered. Finally, conclusions are drawn in Section VI. A preliminary version of this work has been reported in [8]. Herein, our DIO EE-SE trade-off expression has been made more generic and its low and high-se approximations have also been derived. Furthermore, a detailed analysis of the EE gain of DIO over CIO systems and incremental EE gain of DIO system have been conducted. II. SYSE ODEL A. DIO System odel and Channel Capacity We consider a DIO communication system which consists of RAUs, each equipped with L antennas and a U equipped with antennas, as it is illustrated in Fig. for the case of = 7. he main processing is performed at the central unit CU which itself is connected to the RAUs via a high-speed delay-less error-free channel such as optical fibre links. he RAUs and CU exchange signalling information, and they are assumed to be perfectly synchronized. We define the total number of transmit and receive antennas in the DIO system as N t and N r, respectively, where N t = and N r = L in the uplink direction, while N t = L and N r = in the downlink case. As a result of the large distance separating each RAU and the U, each corresponding channel matrix is formed of independent microscopic and macroscopic fading components. he matrices Ω i and G i represent the deterministic distance dependent pathloss/shadowing macroscopic fading component and the IO Rayleigh fading channel microscopic fading component, respectively, between the i th RAU and the U, where i {,..., }. he channel model of the DIO system can then be defined as H = Ω G, where G = [G, G,..., G ],. is the complex conjugate transpose, denotes the Hadamard product, H C Nr Nt, G C Nr Nt and Ω R Nr Nt + with R + = {x R x }. oreover, due to the multiple antennas at the U and RAUs, the matrix Ω is such that Ω = Λ [α D,... α D ] L in the uplink and Ω = Λ in the downlink, where denotes the Kronecker product, L is a L matrix of ones. Furthermore, α id is obtained from a power-law pathloss function such as α id = L + D/D η, where L is the power loss at reference distance D and η is the pathloss exponent. We assume that G is a random matrix having i.i.d. complex circular Gaussian entries with zero-mean and unit variance. DIO Channel Capacity : In the case that the channel state information CSI is unknown at the transmitting node and perfectly known at the receiver, equal power allocation is adopted at the transmitter. hus, the ergodic channel capacity

4 3 per unit bandwidth of the DIO system in both the uplink and downlink channels can then be expressed according to [5], [] as { INr C = fγ = E H log + γ } n HH, where. is the determinant of a matrix, I Nr is a N r N r identity matrix, E is the expectation, γ P N B is the average SNR, P is the average transmit power per node, B is the bandwidth, N is the noise spectral density and n is the number of transmit antenna per node. Note that n = in the uplink and n = L in the downlink. Asymptotic Approximation of the DIO System Capacity: It has been shown in [], [] that the mutual information of the DIO system is asymptotically equivalent to a Gaussian random variable such that both the uplink and downlink ergodic capacity per unit bandwidth can be approximated as [ fγ fγ= n ln κ +ln + d αi + ρ +d αi /ρ i= ] + + ln + g + +g bit/s/hz for large values of N t and N r, where g = κ i= α i ρ + d αi ρ, ρ = / γ, κ = L and = in the uplink while κ = and = L in the downlink. In addition, d is the unique positive real root of the + th degree polynomial equation P m d = dρ d + ρv i +dκ d + ρv k, 3 i= i= k= k i where v i = /αi. In order to simplify the analysis, d i can be defined as d i = d αi /ρ in and, hence, the capacity per unit bandwidth of DIO given in can be re-expressed as fγ = S + S Li, 4 ln i= where S and S Li are given by S = + + g +ln+g and S Li = L + +ln+d i, i {,..., }, 5 + d i respectively, for both the uplink and downlink channels. B. DIO Power odel and EE-SE rade-off Formulation DIO Power Consumption odel: he EE of a communication system is closely related to its total power consumption. In a realistic DIO setting, power components such as the signal processing, DC-DC/AC-DC converter as well as backhaul powers and power losses from cooling, main supply as well as amplifier inefficiency must be taken into account in addition to the transmit power when evaluating the actual EE of such a system. In order to model the power consumption of DIO system, we assume that each RAU Fig.. Distributed IO power model. is a remote radio head RRH, such that the power amplifier PA and radio frequency RF units are mounted at the same physical location as the RAU, whereas the baseband BB processing unit is located at the CU, as it is illustrated in Fig.. In comparison with the usual base station BS transceiver, a RRH transceiver does not require feeder cables such that feeder loss is mitigated; furthermore, its PAs are naturally cooled by air circulation and, hence, cooling unit is not necessary. By utilizing the realistic PC for RRH in [8], the total consumed powers in the uplink and downlink of the DIO system are given by P u = Γ U P + P ct + LP u + P bh and, 6 P d = Γ BS P + LP d + P bh + P cr, 7 respectively, where P ct and P cr are the U s transmit and receive circuit power, respectively, Γ U quantifies the U amplifier efficiency, and P bh is the backhauling induced power. Furthermore, P u and P d are the uplink and downlink power consumptions of the BS at minimum non-zero output power, and Γ BS is the slope of the load-dependent power consumption. In addition, P [, P max ], with P max being the maximum transmit power. We assume that the backhauling architecture is based on fibre optic and that all switches and interfaces are identical as in [9]. oreover, an optical smallform factor pluggable SFP interface is used to transmit data from each RAU over the backhauling fibre and it has a power consumption of c Watts, hence, the total backhauling induced power P bh per RAU can be expressed according to [9] as P bh C= φp b + φ Ag switchc p b +p dl +c, 8 max dl Ag max where max dl is the number of interfaces per aggregation switch, p dl is the power consumed by one interface in the aggregation switch that is used to receive the backhauled traffic at the CU, p b is the maximum power consumption of the switch, i.e. when all the interfaces are utilized, φ [, ] represents a weighting factor. In addition, Ag max and Ag switch denote the maximum and actual amounts of traffic passing through the switch, respectively, where Ag switch is linearly dependent on the capacity per unit bandwidth of the system.

5 4 DIO EE-SE rade-off: According to [], the bit-per- Joule capacity of an energy limited wireless network is the maximum amount of bits that can be delivered per joule of consumed energy in the network, i.e. the ratio of the capacity of the system to the total consumed power, such that C J = C P in the general case, where C = CB is the capacity of the system in bit/s and P is the total consumed power of the system. Consequently, the EE-SE trade-off for the uplink and downlink of DIO system can simply be expressed as C Ju = C [ Γ U f C+ P ] ct+ LP u +P bh C 9 N N and [ C Jd = C Γ BS f C+ LP d +P bh C+ P ] cr, N N respectively, based on the realistic uplink and downlink total power consumptions given in 6 and 7. In 9 and, f : C [, + ] γ [, + ] is the inverse function of f and N = N B is the noise power. Note that in the idealistic PC, P u = P and P d = P such that C Ju and C Jd are expressed as in 9 and for the uplink and downlink scenarios, respectively, but with P d = P u = P ct = P cr = P bh = and Γ BS = Γ U =. III. CLOSED-FOR APPROXIAION OF HE DIO EE-SE RADE-OFF he EE-SE trade-off expressions of the DIO system given in 9 and require the knowledge of f C, however, obtaining an explicit solution of f C from the ergodic capacity expression in is hardly feasible. eanwhile, fγ in 4 can be inverted, as it is explained in the following theorem, and since fγ is an accurate approximation of fγ, f C is very likely to be an accurate approximation of f C. heorem III.: An accurate CFA of the inverse function, f C, used in evaluating the EE-SE trade-off for both the uplink and downlink of the DIO system over the Rayleigh fading channel can be expressed as f C= [+W g S ] i= [ +W g L S Li ] Δ i Δ i + κ, i= α i xi+α where g S = exp S + + ln, g L S Li = SLi exp L + + ln, x i = Wg LS Li W g L S L and Δ i = α i. In addition, W α x is the real branch of the Lambert function. he Lambert W function is the inverse function of fw = w expw and is such that W ze W z = z, where w, z C [9]. Proof: See Section A of the Appendix. Note that S and S Li in 5 are functions of γ. hus, in order to use we first need to express S and S Li as a function of C. We know from 4 that C ln S + S Li, then if we could define S S Li and S Li /S L, i {,..., }, as a function of C, we could easily express independently S φ L, C bit/s/hz κ = κ = 3/ κ = 3 κ = 4/3 κ = 4 κ = 5/3 -RAUs 3-RAUs 5-RAUs S i= exp SL i q φ L, C 3 φ L, C--RAU Spectral efficiency per RAU-receive antenna bit/s/hz S i= S L i Fig. 3. Comparison of e with the parametric function φ L, C obtained from 3 and 8 as a function of the spectral efficiency per RAU -receive antenna for various number of RAUs, receive/transmit antenna ratios with κ = > and Δ i = i db. and S Li, i {,..., }, as a function of C by solving a set of + equations. Approximation of S S Li : In the following, we propose to find a parametric function φ L, that accurately approximate S S Li by means of an heuristic curve fitting method [6] such that S φ L, C e S Li = / + g i= + d, i L since it can be easily proved by direct substitution that L + +g + i= +d i = in 5. Note that such a method has been successfully applied in [], [] for defining the point-to-point IO EE-SE trade-off. In the heuristic curve fitting method proposed in [6], a parametric function is designed in terms of elementary functions and three independent parameters for solving a curve fitting problem. In this paper, we use this method to design the parametric function φ L, C that tightly fits e S S Li for L >. We first numerically evaluated e S S Li as a function of C for a fixed channel gain offset, i.e. Δ i = αi /α, i {,..., }, and also for various values of, L and, as it is shown in Fig. 3. Similar to the IO case in [], [], e S S Li presents the feature of a logarithmic function at low C and linear function at high C. he function is also monotonic and its value at C = is zero. In order to define the function that best fits the curves of Fig. 3, the curve fitting method leads us to the following parametric function φ L, C = cosh C ln/ η η 3 which provides a satisfying approximation for e S S Li, as it is shown in Fig. 3. hen, we obtain S as S.5 C ln + η ln cosh C ln / η, 4

6 5 Parameter η κ = / = 4 κ = / = 3 κ = / = κ = / = 3/ κ = / = 4/3 κ = / = 5/3 η 3 η 8 ABLE II PARAEERS FOR HE SYSE AND POWER ODELS Realistic PC [8] [] System Parameters Parameter Value Parameter Value P u 4.8 W B Hz P d 59. W N 69 dbm/hz Γ BS.8 L 34.5 db P cr. W η 3.5 P ct. W D m Γ U % P max Uplink 7 dbm φ.5 P max downlink 46 dbm max dl 4 Fading Rayleigh flat fading p dl W c W p b 3W Ag max 4 Gb/s Channel gain offset, Δ db Fig. 4. Comparison of the parameter η obtained from 3 with η obtained via our interpolation approach of 8 as a function of the channel gain offset Δ in db for the -RAUs scenario. by solving equations 3 and C ln S + i= S L i. Approximation of S Li : Furthermore, by solving equations 3 and C ln S + i= S L i, we also obtain that S Li.5 i= C ln η ln cosh C ln η. 5 In our scenario of interest where L >, then S S Li and, hence, it is sufficient to evaluate any S Li i {,..., } based on its low-se approximation. oreover, from the proof of the DIO EE-SE trade-off in the low-se regime of Proposition IV., we know that the ratio S L i S L = Δ i at low SE. Consequently, any S Li can be approximated as S Li α i i= α i C ln η ln cosh C ln η A. DIO System with = -RAU, i {,... }.6 he case in which only one RAU is active, i.e. the -RAU DIO case is a very important scenario since it is equivalent to the CIO scenario. It can easily be shown that the inverse function, f C, in simplifies into f C = [ + W g S ] [ ] + W g L S L α κ + 7 in both the uplink and downlink channels, since x = Δ = when only one RAU is active, i.e. when =. he functions S and S L can be obtained from 4 and 5, respectively, where η ς in able I. Note that 7 is equivalent to of [] which is utilized in obtaining the EE-SE trade-off closedform expression of the point-to-point IO over the Rayleigh fading channel. B. DIO System with = -RAUs he parameter η, varies with the ratio of the channel gain offset between the links, i.e. Δ i. In the case where only - RAUs are active, the absolute value of the log of Δ varies from, i.e. the two channel gains α and α are equal, to +, i.e. one of the links is far stronger than the other one such that α α or α α, which corresponds to a L and L IO systems, respectively. Consequently, η [ς, ς ], where ς and ς are the respective values of η for the L and L IO cases. According to Fig. 4, where η is plotted as a function of Δ for Δ ranging from to 4 db and various antenna configurations, η presents the feature of a tangent hyperbolic function, where η = ς at Δ = db and η converges to ς as Δ. Consequently, a tight approximation of η can be defined by means of a curve fitting method as η ς + ς ς tanh log Δ λ λ 8 where the tightness of this approximation is shown in Fig. 4. We then obtain an accurate approximation of S S L +S L via φ L, C by inserting 8 into 3, as it is illustrated in Fig. 3. Note that the parameters ς, ς, λ and λ are given in able I for some selected antenna settings. Inserting η in 8 into 4 and 6, we easily obtain, S, S Li i {, } and x i i {, } solely as a function of the variable C and for various parameters. Finally, our CFA of the EE-SE trade-off for the uplink and downlink of the -RAUs DIO system is then formulated by substituting S, S Li i {, } and x i i {, } into f C in and inserting f C f C in 9 and, respectively. C. Numerical Results and Discussions In order to present some numerical results, we consider the scenario where only RAU and RAU are active in the DIO architecture of Fig. resulting in a linear array and the U is assumed to be positioned at points E and F, which are.6r and.4r, respectively from RAU with R = m while the rest of the system parameters are given in able II. In Figs. 5 and 6, we compare our CFA of the DIO EE-SE trade-off with the nearly-exact EE in the uplink and downlink, respectively, for an idealistic PC and some specific values of κ =, i.e. κ = {,.5,.6,.5} which corresponds to the following antenna configurations L ={, 3, 5 3, 6 4}. We can easily obtain fc for a given C by using and, hence, we can numerically obtain the nearly-exact f C and EE by using a linear search algorithm on such that the target C differs from the actual C by less than 4

7 6 ABLE I PARAEERS δ, δ, λ AND λ VALUES FOR VARIOUS VALUES OF κ OR κ / ς ς λ λ κ / ς ς λ λ κ / ς ς λ λ / / / / / / / / / / / / / / / / / / / / / Energy efficiency, CJu bit/j 5 3 Nearly-exact C Ju CFA approx. Point E Point F Spectral efficiency, C bit/s/hz Fig. 5. Comparison of the EE-SE trade-off for the uplink of a -RAUs DIO system obtained via the nearly-exact approach and by our CFA when the U is at position E and F, based on the idealistic PC. Energy efficiency, CJd bit/j 9 8 Nearly-exact C Jd CFA approx. Point E Point F Spectral efficiency, C bit/s/hz Fig. 6. Comparison of the EE-SE trade-off for the downlink of a - RAUs DIO system obtained via the nearly-exact approach and by our CFA when the U is at position E and F, based on the idealistic PC. bit/s/hz. Results clearly show the tight fitness of our CFA with the nearly-exact EE, hence, it is a graphical illustration of the accuracy of our CFA for both the uplink and downlink channels. In addition, these results reveal that the most energy efficient point occurs at C when an idealistic PC is assumed. Finally, moving the U from E to F, i.e. closer to its serving RAU RAU, obviously improves the EE. As we earlier mentioned, the parameter η varies with the channel offset between the links when more than one RAU is active. For the case of -RAUs, a simple approach for obtaining η has been defined in 8, regardless of any channel offset. However, such an approach is hardly feasible when more than -RAUs are active. Instead, we derive a generic and accurate approximations of the DIO EE-SE trade-off at low and high SE in Section IV, which we utilize in Section V for getting insights on the EE of DIO systems when >. IV. LOW & HIGH-SE APPROXIAIONS OF HE DIO EE-SE RADE-OFF A. Low-SE Approximation he results that have been obtained in Figs. 5 and 6, clearly indicate that the low-se regime is the energy efficient regime in the DIO system when considering the idealistic PC. According to [, eq. 3 and 6] the inverse function, f C, used in evaluating the DIO EE-SE trade-off in the low-se regime can be expressed as f C C = N tc ln E H tr [H H], 9 where N t = and N t = L in the uplink and downlink cases, [ respectively. his formulation implies the evaluation of E H tr H H ], which is tedious for large values of N t and N r. A simplified version of 9 can easily be obtained by assuming that C in our CFA of the DIO trade-off in, as it is explained in the following proposition. Proposition IV.: In the low-se regime, C, such that can be simplified and, hence, the low-se approximation of the inverse function, f C, which is utilized in characterizing the DIO EE-SE trade-off over the Rayleigh fading channel is simply given by f C = C ln l L, i= α i where L = L in the uplink and L = in downlink. Proof: See Section B of the Appendix It can be observed from that the low-se approximation of the EE-SE trade-off is independent of the number of

8 7 transmit antennas which is in line with the results in [], [3] for the point-to-point IO Rayleigh fading channel. In addition, increasing the number of receive antennas, L, increases the EE as a result of an improved diversity gain. B. High-SE Approximation In general, high-snr/se approximations are of practical interest for accurately assessing the SE or EE of communication networks which operate in the mid-high SNR/SE regime. he high-se approximation of the DIO EE-SE trade-off can be obtained via the high-snr approximation of the unique real positive root of the + th degree polynomial given in 3, i.e. d. According to [3], the formulation of the asymptotic approximation of this root is dependent on the relationship between the total number of antennas at the RAUs and the total number of antennas at the U, i.e. L > or L = or L <. Using the same categorization as in [3, Lemma ], we formulate the high-se approximation of the DIO f h EE-SE trade-off, i.e. C, for both the uplink and downlink channels in the following propositions. L > : Proposition IV.: he high-se approximation of the inverse function, f C, used in evaluating the DIO EE-SE trade-off when L > is given by f C= h V + W C + e where V = κ i= α i i= S L i κ α k k= x α k κ k= α k x α k α i α, In addition, x i and i= S L i, which are independent of C, are given in 4 and 4, respectively. Proof: See Section C of the Appendix L = : he high-se approximation of the inverse function, f C, used in expressing the DIO EE-SE trade-off when L = can be obtained by utilizing the asymptotic high-se approximation of the unique positive real root of the + th degree polynomial in 3, which can be approximated as [3] d α i= i. Hence, we formulate the following proposition. Proposition IV.3: When L =, the inverse function, f C, used in the DIO EE-SE trade-off expression can be approximated in the high SE regime as follows f h C = where Q = C + e κ+ 4 κ + i= 4W Q α i α i= κ Proof: See Section D of the Appendix α i κ+, 3 α α i= i. 4 3 L < : he asymptotic high-se approximation of the unique positive real root of the + th degree polynomial in 3 when L < can be expressed from [3] as d γ κ. 5 Based on the latter result, we propose the following. Proposition IV.4: When L <, the high-se approximation of the inverse function, f C, used in the DIO EE-SE trade-off can be expressed as where f h C = Q = C L e κ i= α i κ W Q κ i= α i= α i i 6 7 Proof: See Section E of the Appendix It can be seen from equations 3 and 6 that the high-se approximation of the EE-SE trade-off is dependent on the capacity, C, the number of antennas at the U and RAU, i.e. and L, respectively, the channel gain between the U and the RAU, i.e. αi and the number of active RAU. Furthermore, by using the properties of the Lambert function, f C increases linearly log scale with linear increase in h C when all other variables are fixed in, 3 and 6. Consequently, the idealistic EE decreases linearly log scale as C increases. In addition, it can be observed in, while L >, that increasing leads a greater improvement in the diversity gain than increasing either or L. Whereas, the contrary is observed in 6, where increasing either or L, while L <, results in a much significant improvement in the diversity gain as compared with when is increased. his f h improvement in diversity gain results in a reduction in C and consequently an improvement in the idealistic EE, as it is depicted in Figs. 8 and 9. C. Numerical Results and Discussion In order to present some results on the low and high-se approximations of the DIO EE-SE trade-off, we consider the scenario where only RAUs, and 7 are active in the DIO architecture of Fig., i.e. = 3, while the U is positioned at point E with R = 5m. In Fig. 7, we present some numerical results on the EE of the DIO system at low SE for both the uplink and downlink scenarios. We compare our EE approximation at low SE in with Verdú s low-se approximation of [], which is given in 9, for both the uplink and downlink channels in the upper and lower of Fig. 7, respectively. he results show a tight match between these two approximations. In line with the insights drawn earlier on the low-se regime approximation, Fig. 7 show that the EE of DIO system is independent of the number of transmit antenna at low SE, i.e. in the uplink channel and L in the downlink channel, while increasing the number of receive antennas, i.e. L and in the uplink and downlink channel, respectively, improves the EE, when an idealistic PC is considered. In Figs. 8 and 9, we compare our high SE approximations of the DIO EE-SE trade-off obtained from Propositions

9 8 Energy efficiency, CJu bit/j Energy efficiency, CJd bit/j 3 3 Low-SE approx. in [] Our low-se approx. in, m =, L = Our low-se approx. in, m = L, = Number of antenna elements m uplink Low-SE approx. in [] Our low-se approx. in, m =, L = Our low-se approx. in, m = L, = Number of antenna elements m downlink Fig. 7. Comparison of our low-se approximation of the EE CFA for the uplink and downlink of DIO with the approximation in [] when the U is at position E, based on the idealistic PC. Energy efficiency, CJu bit/j L > L = L < Nearly-exact C Ju 8 3 Novel high-se approx. High-SE approx. in [4] Spectral efficiency, C bit/s/hz Fig. 8. Comparison of the EE-SE trade-off for the uplink of a 3-RAUs DIO system obtained via the nearly-exact approach with its high- SE approximations when the U is at E, based on the idealistic PC. IV., IV.3 and IV.4 for L >, L = and L <, respectively, with the nearly-exact DIO EE-SE trade-off and the high SE approximation of [4] when considering the idealistic PC and = 3. In Fig. 8, we consider the uplink of DIO system with the following antenna configurations L = {3 }, { 3} and { 8} which ensure that L >, L = and L <, respectively, since = 3. Whereas in Fig. 9, we consider the downlink of DIO system and utilize the antenna configurations L = {,, 4, 4 }, { 3, 6} and {,, } which ensure that L >, L = and L <, respectively. Note that the high-se approximation of [4] has only been plotted for the uplink, since it is by design only valid for the uplink. he results in Fig. 8 indicates that even for the uplink scenario this Energy efficiency, CJd bit/j L > L = L < Nearly-exact C Jd Novel high-se approx Spectral efficiency, C bit/s/hz 6 4 Fig. 9. Comparison of the EE-SE trade-off for the downlink of a 3-RAUs DIO system obtained via the nearly-exact approach with its high-se approximations when the U is at E, based on the idealistic PC. method is not very accurate, especially when > L. On the contrary, our high-se approximations are valid for both uplink and downlink and the results in Figs. 8 and 9 both indicate their great accuracy for any antenna settings, since they tightly match the nearly-exact EE results in any case. oreover, not only our high-se approximations are very accurate at high SE, but they are also accurate at mid-se, i.e. for C > bit/s/hz in Figs. 8 and 9. In Fig 9 we also investigate the impact of increasing the number of antennas elements at the U, i.e., and each RAU, i.e. L, on the idealistic EE. For the case where L >, i.e. L = {, 4, 4}, increasing L, has a less significant impact on improving the idealistic EE as compared with increasing. As it can be seen in, is dividing C, such that it directly affects the diversity and modify the slope of the trade-off curves, as it is clearly depicted in Fig. 9. Whereas L acts as an EE multiplicative gain, since curves with different L values are parallel to each other s. Note that, the contrary is observed for the case where L <, i.e. L = {,, }. hese results are in line with the insights previously drawn on equations and 6. In Fig., we further demonstrate the accuracy of our high SE approximation for various number of active RAUs and a variable U position. We plot the idealistic EE against the normalized distance : U collocated at RAU and : U collocated at RAU while 3 sets of RAUs are active and the U is moving from point X to Y in the DIO architecture of Fig., for the antenna configurations L = {, } and C =, 3 bit/s/hz. he RAUs set are: -RAUs DIO with RAUs and active, 3-RAUs DIO with RAUs, and 7 active, and 5-RAUs DIO with RAUs,, 5, 6 and 7 active. 3 4 V. ENERGY EFFICIENCY ANALYSIS OF DIO SYSE As an application for our CFAs of Section III and IV, we study in this Section the impact of increasing the number

10 9 high-se regimes can be approximated as Energy efficiency, CJd bit/j RAUs 3-RAUs 5-RAUs Nearly-exact C Jd, C = bit/s/hz Nearly-exact C Jd, C = 3 bit/s/hz Novel high-se approx Normalized distance Fig.. Comparison of the EE-SE trade-off for the downlink of the -RAUs, 3-RAUs and 5-RAUs DIO systems obtained via the nearly-exact approach with its high-se when the U is moving from point X to Y, based on the idealistic PC. of RAUs on the DIO EE, i.e. capacity improvement, additional processing as well as power consumption, and compare the EE performance of DIO with CIO, for the downlink scenario and both idealistic as well as realistic PCs. In this regards, we derive the incremental EE gain and EE gain of DIO over CIO in the two following subsections, respectively. A. Incremental Energy Efficiency Gain of DIO System We define here the incremental EE gain of DIO as the variation of EE when an additional RAU is connected to the U. Note that the same type of analysis has been undertaken in [7] but to quantify the SE instead of the EE variations. Contrary to [7], we assume a target SE, i.e. a fixed channel capacity, and evaluate how the total power consumption is affected when extra RAUs are added. We consider as in [7] that the RAU connection order to the U is from the closest RAU to the furthest one and define the incremental EE gain according to as IG E = Γ BS f C + ˉP /N + Γ BS f + C + ˉP /N 8 where ˉP pp d + P bh C since U receive circuit power, P cr, is negligible. In addition, f C and f+ C are approximated in for the initial DIO system and when an additional RAU is connected to the U, respectively. Since obtaining the exact closed-form expressions for f and f+ is not straightforward when the number of RAUs is greater than two, we utilize their low and high-se approximations given in Propositions IV. and IV.-IV.4, respectively. Consequently, the idealistic incremental EE gains of the DIO system when considering the idealistic PC in the low and IG E,Id IG E,Id i= α i i= α i f h, C f h,+ C and, 9 f respectively, when ˉP = and Γ BS = while h, C and f h,+ C are the high-se approximation of f C and f + C. Notice that in the symmetric channel case, i.e. all αi are equal, IG E,Id in 9. Furthermore, the maximum value of IG E,Id occurs when the links are symmetrical, hence, no EE gain can be achieved by having additional RAUs in the low-se regime. By using 9, the realistic incremental EE gains of the DIO system when considering the realistic PC in the low and high-se regimes can be expressed as IG Γ BS f l, E,Re C+ ˉP /N Γ BS f l, C/IG E,Id+ ˉP and /N+ IG Γ BS f h, E,Re C+ ˉP /N, 3 respectively, where Γ BS f h, C/IG E,Id+ ˉP /N+ f l, C is given in. B. EE Gain of DIO System Over Co-located IO CIO System he power efficiency gain of the DIO system over CIO system where all the antenna elements are separated by a few wavelengths has been analyzed in [7] while considering the idealistic PC. In order to evaluate how the DIO system compares with the CIO system in terms of EE over the downlink channel, we express the EE gain of DIO over CIO according to and [8] as G E = G Id,SE Γ BS f C C + LP d /N Γ BS f C + ˉP /N, 3 where G Id,SE = C C C is the idealistic SE gain, C C and C are the capacities of the CIO and DIO systems, respectively, and f C C and f C are approximated in 7 and, respectively. From a PC perspective, we consider that CIO utilizes a RRH. his EE gain can result from DIO transmit power reduction capability when both systems are required to achieve the same SE, i.e. C=C C. he idealistic EE gain due to power reduction, which is denoted by G Id,PR, is then simply G Id,PR = f C C since G f Id,SE=, C C while its realistic value, i.e. G Re,P R, is simply a ratio of the total consumed power in the two systems as observed in 3. he EE gain of DIO over CIO can also be approached via its SE improvement capability when a fixed total transmit power is assumed for both systems, i.e. f C = f C C. Hence, this EE gain is simply equivalent to the SE gain, i.e. G Id,SE in the idealistic setting. Note that the DIO system incorporates an additional backhauling induced power in comparison with the CIO system, hence the realistic EE gain as a result of its SE improvement capability, denoted as G Re,SE, is always lower than G Id,SE, as it can be seen in Fig. 3.

11 Incremental DIO energy efficiency gain IG E,Id, C = bit/s/hz IG E,Id IG E,Id, C = 4 bit/s/hz IG E,Id IG E,Id IG E,Id 3 L =, = L =, = Normalized distance Fig.. Incremental EE gain of DIO when the U is moving from point X to Y, based on the idealistic PC. DIO vs CIO EE gain DIO vs CIO EE gain G Re,SE G Re,P R G Re,P R G Id,SE CIO DIO DIO P R G Id,SE DIO P R G Id,P R G Id,P R Normalized distance Normalized distance Fig. 3. EE gain of DIO over CIO when the U is moving from point X to Y, based on both the idealistic and realistic PCs. 5 5 Pd W Spectral efficiency bit/s/hz Incremental DIO energy efficiency gain IG E,Re IG E,Re 3 L =, = L =, = IG E,Re, C = bit/s/hz IG E,Re IG E,Re, C = 4 bit/s/hz IG E,Re Normalized distance Fig.. Incremental EE gain of DIO when the U is moving from point X to Y, based on a realistic PC. C. Numerical Results and Discussions In order to understand the EE behaviour of DIO system, we present some results on both the incremental EE gain of DIO and EE gain of DIO over CIO for both the idealistic and realistic PCs over the downlink channel. We consider the DIO architecture of Fig. with R = m and where the U is moving from point X to Y, and rely on the realistic power consumption parameters given in able II for plotting our results. In Figs. and, we evaluate the idealistic and realistic incremental EE gains of DIO, respectively, as a function of the normalized distance : U collocated at RAU and : U collocated at RAU, for the antenna configurations L = {, }, C/ = 4 and bit/s/hz. We consider that only RAUs, and 7 can be active and that the connection order to the RAU is from the closest RAU to the furthest one. We can obtain f C by using the numerical search approach and its low and high-se approximations from Propositions IV. and IV.-IV.4, respectively. he result in Fig. confirms that at low SE, IG E,Id = for the symmetric case, when the number of RAUs connected to the U increases from to. oreover, the incremental EE gain is independent of the number of antennas at the U at low-se, which is in line with the insight previously drawn. Furthermore, increasing the number of RAUs connected to the U from one to two is only beneficial in terms of EE when the average channel gains are fairly equal and when considering the idealistic PC. Whereas, connecting a third RAU is not beneficial in terms of EE when compared to the two RAUs scenario due to the reduced impact of the macro diversity. In Fig., we consider that the maximum transmit power per RAU does not exceed 43 dbm. he result clearly indicates that when considering the realistic PC, no EE gain is achieved by using an additional RAU in the system. Indeed, the RAU connection order entails that the closest RAU is connected to the U, hence the reduction in transmit power as a result of the additional RAU is minimal except when the channel gains of the two links are fairly equal. However, since other power consumptions increase linearly as the number of RAUs increase and since this increase cannot be compensated by transmit power reduction, hence a loss in EE occurs. It can also be observed that the incremental EE is nearly constant with the user positioning at very low SE. his is due to the fact that P as C, and that the part of the backhauling power depending on the traffic also tends to zero. Consequently, IG E,Re + as C. Figure 3 compares the DIO with CIO system in terms of EE for various normalized U positions and for the antenna configuration L = { }. We consider that all RAUs are active in the DIO system, i.e. = 7, and that all RAUs are co-located at RAU in the CIO case. In

12 the lower-right graph, we plot the SE of both the DIO and CIO systems when the total transmit power is set to 46 dbm. As it is expected, CIO system has a higher SE than DIO when the U is within its range, since the CIO has L collocated antennas giving micro-diversity gain. Whereas, in the DIO system, each distributed RAU is equipped with L antennas and the combination of macro and micro-diversity gains results in a higher SE when the U is close to the cell edge RAU. In the upper-left graph, we plot the idealistic and realistic EE gains of DIO system over CIO system i.e. G Id,SE and G Re,SE, which are obtained from 3. As it can be observed, the SE improvement capability of DIO when the U is in close proximity with RAU, results into EE gain. Furthermore, in line with our analysis, the idealistic EE gain as a result of the SE improvement ability of DIO, i.e. G Id,SE is always greater than the realistic EE gain, i.e. G Re,SE. In order to demonstrate the EE gain of DIO over CIO as a result of power reduction, we utilize our high-se approximation from Proposition IV.-IV.4 to plot this EE gain for both the idealistic and realistic PCs, i.e. G Id,P R and G Re,P R, respectively, when the total transmit power of the CIO is fixed to 46 dbm and the DIO system achieves the same SE as the CIO system. We also plot the EE gains, G Id,P R and G Re,P R based on a numerical search approach to further demonstrate the accuracy of our high-se approximations. Hereafter, we plot in the upper-right graph, the total power consumption of the CIO and DIO systems when the total transmit power is fixed at 46 dbm. We also plot the total power consumption of the DIO system as a result of the EE gains G Re,P R and G Re,P R i.e. DIO P R and DIO P R, respectively. he results indicate that a reduction in the total power consumption in the DIO system can be achieved by sacrificing the SE gain of DIO while transmitting at a lower power for cell edge users. VI. CONCLUSION In this paper, an accurate CFA of the EE-SE trade-off for both the uplink and downlink of the DIO system over a Rayleigh fading channel has been derived by considering both an idealistic and realistic PCs. In addition, simplified tight approximations of this trade-off have also been derived at low and high SE for any number of RAUs and antennas. We first proposed a formal proof of our approach for obtaining the generic CFA of the EE-SE trade-off for the DIO system. We then obtained this CFA by designing a parametric function and using a heuristic curve fitting method. he accuracy of our CFA has been shown graphically for various practical antenna configurations and a wide range of SE values. Since obtaining the CFA of the DIO EE-SE trade-off is more intricate for a large number of RAUs, we have resorted to low and high- SE approximations of the EE-SE trade-off for the generic - RAUs DIO scenario. Our approximations have proved to be very accurate, far more accurate than the existing ones for the high SE case and as accurate as the one in the literature for the low SE regime but with a simplified formulation. he EE gain of DIO over CIO and the incremental EE gain of DIO in the downlink channel has been investigated by using our low and high-se approximations for both the idealistic and realistic PCs. he realistic incremental EE gain indicated that the optimal approach in terms of EE is to connect the U to the RAU with the strongest channel gain. In terms of the EE gain of DIO over CIO, DIO is more energy efficient than CIO for cell edge Us in both PCs. Furthermore, the SE gain that is obtained by using DIO system can be traded-off with power to achieve EE gain over the CIO system. Note that the DIO system model presented in this paper is based on the single cell scenario with an orthogonal multiple access scheme implemented within the cell and is therefore noise limited. Since interference is a key limiting factor in cellular communication, hence the CFA of the EE-SE trade-off for the interference limited DIO deserves much attention in future study. APPENDIX A. Proof of heorem III. Let u i = γ in, hence g κ i= α i ρ + d αi ρ = κγ i= α i u i and the + th degree polynomial equation in 3 is equivalent to +d α i /ρ = +d α i d d γ = + g 3 d γ = Furthermore, γ can be expressed as A+ A +4α γ α γ, by substituting u into g, where A = κγ i= α i x i + αγ and x i = u i u. oreover, d i d α i γ = Δi A+ A +4α γ and g can easily be expressed from 3 as g γ d, which is equivalent to g = + A+ A +4α γ. Consequently, by defining ḡ and ˉd i as ḡ = g + and ˉd i = d i +, hence, we have ḡ = A + ˉd i Δ i Δ i + = A + A + 4α γ and A + 4α γ Furthermore, by substituting the value of A = κγ i= α i x i+ αγ into 33, it can be easily shown that ˉdi ḡ + = γ κ αi x i +α Δ i Δ + 34 i i= i= and, hence, the CFA of the inverse function, f C, used in the DIO EE-SE trade-off formulation can be expressed as γ f ḡ ˉdi i= Δ i Δ i + C = κ. 35 i= α i x i + α he first equation in 5 is equivalent to S + + ln = [ + ḡ] + ln + ḡ hence g S = + ḡ exp, 36 + ḡ which can be re-formulated by using the Lambert W function [9] as

13 + ḡ = W g S [ + ḡ = W g S ], 37 where g S = exp S + + ln. Similarly, ˉdi [ ] = + W g L S Li and, moreover, x i can be easily expressed as x i = Wg LS Li W g L S L, i {,..., }, by noting that u i = / + ˉd i. Finally, is obtained by inserting ḡ in 37 and ˉd i into 35. B. Proof of Proposition IV. In the low-se regime, C and, hence, S = i= S L i. oreover, by applying the following approximations of the functions ln + x x and x to 5, the S L i +x ratio S L = Δ i, i {,..., }, such that S Li is directly proportional to αi in this regime. Consequently, S L i α can be expressed as S Li = i i= S L i and g S, i= α i which is utilized in our CFA of, can be re-expressed C ln as g S = e + +ln. In turn, the latter further simplifies to g S C ln e e C ln C ln e C ln 38 since e x + x and, hence, W g S C ln. Similarly, W g L S Li α i C ln L i= α i and x i L i= α i α i C ln L i= α i α C ln. By inserting the approximations of W g S and W g L S Li into ḡ and ˉd i, respectively, in addition with x i into, we obtain upon simplification that f l C C ln L i= α i +α κl C ln L i= α i +α L κ i= α i i= α i C ln i= α i +α /κ i= α i +α 39 when C. Note that κ = L/, = and κ =, = /L, in the uplink and downlink channels, respectively. Hence we can simplify 39 and express it in the generic form of. C. Proof of Proposition IV. At high-se, it can be easily proved that κ u i k= Δ kx k Δ ix i κ k= Δ kx k d γ =, i {,..., }, κ k= α k x k α, 4 and the ratio of ui u, i.e. x i, converges to a fixed value which can be obtained by solving a series of equation given by x i = u i = κ k= Δ kx k Δ ix i u κ k= Δ kx k, i {,..., }. 4 Note that for the case of =, x = and x = U+ U +4κ Δ κδ, where U = κ Δ. A useful observation is that by utilizing the approximation of d γ and x i at the high-se regime, the explicit expression of S Li can be expressed as from 5 as [ SL i = L κ k= + Δ kx k κ k= Δ kx k Δ i + ln κ ] k= Δ kx k Δ i κ k= Δ kx k. 4 hus, we can obtain i= S L i with 4 and S = C ln i= S L i according to 4, which is also equivalent to S = ln + + ln + ḡ ḡ oreover, ḡ = g + and ḡ = + W, where Q Q = exp S + + ln, hence, we can express g as g = W Q In addition, note that g can also be defined as g = κγu i= α i x i which is equivalent to αi κ k= g = κγ Δ kx k κ k= Δ kx k Δ 45 i i= at high SE. Consequently, we obtain the closed-form approximation of the inverse function, f C, in the high-se regime when L > in by equating 44 to 45. D. Proof of Proposition IV.3 d Relying on and knowing that γ = γ i= v i, g + = γ, d = α γ i= vi i= v i as well as d i = Δ i d, where v i = /αi, the asymptotic approximation of the capacity per unit bandwidth can be expressed as C ln L i= Δ +ln α γ i= vi i= v i γ +ln i= Δ i γ i= vi +ln α γ i= v i, 46 which can be further simplified as A = L i= vi γ + i= vi γ +L ln α γ i= v i + ln γ 47 v i i= where A C ln + L ln i= Δ i +. Since in the uplink and downlink scenarios, /L =, equation 47 can be re-expressed as A ln α = A + ln γ 48 γ i= v i. Hence, by expressing γ in terms where A = κ+ of a dummy variable D such that γ = A / D, equation 48 simplifies to A 4 + ln α + ln A = ln D such that D +

14 exp A 4 + ln α +ln A = exp D. 49 D Using the real branch of the Lambert W function [9], equation 49 can be reformulated as = W Q 5 D where Q is expressed in equation 4. Hence, the high- SE approximation of the inverse function, f C, used in expressing the DIO EE-SE trade-off is obtained when L = in 3 by replacing the dummy variable D with γ C. f h E. Proof of Proposition IV.4 Since the high-se approximation of the unique positive real root of the + th degree polynomial in 3 is such that γ d = + g = κ, it implies that the high-se approximation of S in 5, i.e. S, is independent of γ and can be expressed as S = + κ + ln κ = L ln κ. 5 Furthermore, we know from 4 that sum of S Li at high-se can be expressed in terms of the capacity per unit bandwidth C which simplifies to SL i = C ln S 5 i= = L + d i= Δ i + ln Δ i + ln d. 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15 4 Oluwakayode Onireti S - 3 received his B.Eng. degree in Elecrical Engineering from University of Ilorin, Nigeria, in 5. he.sc. in obile & Satellite Communications and Ph.D. degrees in Electronics Engineering from University of Surrey, UK, in 9 and, respectively. He secured a first class grade in his B.Eng. and a distinction in his.sc. degree. He is currently a research fellow at the Centre for Communication Systems Research CCSR at the University of Surrey, UK. He has been actively involved in European Commission funded projects such as ROCKE and EARH. His main research interests include energy efficiency, IO and cooperative communications Fabien He liot S 5-7 received the.sc. degree in elecommunications from the Institut Supe rieur de l Electronique et du Nume rique ISEN, oulon, France, and the Ph.D. degree in obile elecommunications from King s College London, in and 6, respectively. He is currently a research fellow at the Centre for Communication Systems Research CCSR of the University of Surrey. He has been actively involved in European Commission funded projects such as FIREWORKS, ROCKE, SAR-Net projects and more recently in the award-winning EARH project. He is currently involved in the LexNet project, a project investigating human exposure to electromagnetic fields induced by wireless telecommunication networks. His main research interests are energy efficiency, cooperative communication, IO, and radio resource management. He received an Exemplary Reviewer Award from IEEE COUNICAIONS LEERS in. uhammad Ali Imran 3-S received his B.Sc. degree in Electrical Engineering from University of Engineering and echnology Lahore, Pakistan, in 999, and the.sc. and Ph.D. degrees from Imperial College London, UK, in and 7, respectively. He secured first rank in his BSc and a distinction in his Sc degree along with an award of excellence in recognition of his academic achievements, conferred by the President of Pakistan. He is currently a Reader in the Centre for Communication Systems Research CCSR at the University of Surrey, UK. He has been actively involved in European Commission funded research projects ROCKE, EARH, LexNet and ijoin; obile VCE funded project on fundamental capacity limits; EPSRC funded India-UK AC and REDUCE projects. He is chairing the work area on the air interface design under the 5G innovation centre. His main research interests include the analysis and modelling of the physical layer, optimization for the energy efficient wireless communication networks and the evaluation of the fundamental capacity limits of wireless networks.