Massive MIMO or Small Cell Network: Who is More Energy Efficient?

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1 or Small Cell Network: Who is More Energy Efficient? Wenjia Liu, Shengqian Han, Chenyang Yang Beihang University, Beijing, China {liuwenjia, Chengjun Sun Beijing Samsung Telecom R&D Center, China Abstract Energy efficiency (EE) is becoming an important design goal for wireless communication systems providing high spectral efficiency (SE). Both massive multi-input multi-output (MIMO) and small cell network (SCN) are expected to achieve high EE for high throughput cellular networks, though using different mechanisms. improves EE by exploiting a large array gain, while SCN improves EE by deploying a large number of low-power base stations (BSs) to reduce the propagation loss and increase the opportunity of BS sleep. In this paper, we compare the EEs as well as the SEs of Massive MIMO and SCN. For a fair comparison, we consider a multi-cell network with the same user density, antenna density and average cell-edge signal-to-noise-ratio (SNR). Perfect channel information is assumed, and three BS sleep strategies are considered. Our analysis shows that the EE of SCN increases with the cell size shrinking, and the achievable SEs of SCN and increase with the cell-edge SNR. When the number of cells is large, SCN is always more energy efficient than. On the other hand, when the number of cells is small, Massive MIMO achieves higher EE than SCN when the circuit power consumptions of are much lower than SCN. I. INTRODUCTION Wireless communication systems have been being designed toward high spectral efficiency (SE) to support the explosively growing traffics. Among various advanced technologies for improving the SE, the approaches to exploit spatial resources have been explored extensively, e.g., frequency reuse and spatial multiplexing. Both small cell network (SCN) [1] and Massive multi-input multi-output (MIMO) [2] have been recognized as promising ways to provide high SE, which actually are two extreme ways to use the spatial resources. SCN consists of densely deployed low-cost and low-power base stations (BSs). With the shrinking of the cell size, SCN benefits from the cell-splitting gain. employs a large number of antennas to serve a much smaller number of users, which enjoys a high array gain [3]. Except for improving the SE, both SCN and Massive MIMO are expected to improve energy efficiency (EE), which is becoming an important design goal for high throughput networks [4]. SCN brings transmitters and receivers closer and reduces the required transmit power to overcome path loss [1]. This work was supported in part by the National Natural Science Foundation of China (No ), the National Basic Research Program of China (No. 2012CB316003) and Beijing Samsung Telecom R&D Center. Moreover, the resulting small cell size provides much more opportunities of closing the BSs with low traffics for energy saving. By contrast, exploits giant antenna arrays to achieve high array gain and high spatial multiplexing gain. It can also reduce the transmit power to support a given throughput. Recently, the performance of SCN and on energy saving has drawn significant attention. The effects of cell size shrinking on energy saving were investigated in [5], where only transmit power consumption was considered. The required transmit powers of SCN and to achieve the same SE requirement were compared in [6], where only a single-user scenario was considered without intercell interference (ICI) and multi-user interference (MUI). In practical systems, the circuit power consumption cannot be ignored, especially for cellular systems where the BS occupies a large portion of the overall power consumption in the network [7]. When the circuit power consumed at the BSs are taken into account, it is still unclear whether SCN or Massive MIMO will be more energy efficient, especially for the multicell multi-user systems where both ICI and MUI exist. In this paper, we compare the EEs as well as the achievable SEs of SCN and, toward the goal to reveal how we should employ spatial resources to provide high SE and high EE. For a fair comparison, we consider identical number of users and identical number of antennas in the same area of a multi-cell network, and the cell-edge signalto-noise-ratio (SNR) is equal. Note that pilot contamination was identified as a bottleneck on improving performance of [3] and the training and signalling overhead will reduce both the SE and EE of SCN. Nonetheless, as a first attempt to compare the two different architectures, we assume that perfect channel information is available at the BSs. We consider three BS sleep strategies, and analyze the impact of various levels of circuit power consumptions and cell sizes on the performance of and SCN. The remainder of this paper is organized as follows. Section II introduces the system model. The EEs of and SCN are analyzed in Section III. The SE-EE relationships of the two systems are compared In Section IV through simulations, and conclusion remarks are given in Section V /13/$ IEEE 24

2 2013 IEEE WCNC Workshop on Future green End-to-End wireless Network area within a cell that has received power above a given minimum [8]. Under the assumptions of no random shadowing and identical receiver noises, the same cell-edge SNR should be ensured for the two systems with different cell sizes and different number of antennas to obtain 100% cell coverage area. Therefore, the maximal transmit power of the BS, Pmax, is set to ensure a given cell-edge SNR, which is defined as the average receive SNR for a user located at the cell boundary when the BS transmits with single antenna and with Pmax [8]. B. Downlink Transmission Consider that BSb serves Kb single antenna users with zeroforcing beamforming (ZFBF). For, Kb = K M. For SCN, we assume that Kb Ms.3 Denote Hb = [α1,b h1,b αkb,b hkb,b ] as the downlink channel matrix from BSb to the Kb users it serves, where αk,b and hk,b denote the large-scale fading gain and the small-scale fading channel from BSb to the k-th user (denoted by MSk ), respectively. Assume that perfect channel state information (CSI) is available at the BSs. Then the ZFBF at BSb can be computed as (1) Wb = [ p1,b g1,b pkb,b gkb,b ], Fig. 1. Illustration of the system settings. The cluster includes seven macrocells, each including one macro-bs and seven small-bss, i.e., L = 7, N = 7. II. S YSTEM M ODEL where gk,b = g k,b / g k,b, g k,b denotes the k-th column vector of (HH b ), pk,b is the power allocated to MSk, ( ) denotes the H Moore-Penrose inverse, ( ) is the conjugate transpose, and denotes the Euclidean norm. The received signal of MSk can be expressed as Nc H (2) yk = pk,b hh k,b gk,b sk + j=1,j =b hk,j Wj sj +nk, {z } A. System Settings of and SCN We consider a cellular network consisting of multiple noncoordinated hexagonal cells. The cell and the BS in the system are called macro-cell and macro-bs. Each macro-bs is equipped with a large number of co-located antennas, which is much larger than the number of users in its serving cell. The SCN system consists of a large number of small cells, each with a BS called small-bs. In this paper, user density and antenna density are respectively defined as the number of BS antennas and users per unit area. To ensure an approximately identical user density and antenna density in the two systems, we consider a reference area as illustrated in Fig. 1, which is a cluster of seven macrocells. Denote L as the number of macro-cells in the cluster, then L = 7 in Fig. 1. To unify the model and analysis of and SCN systems, we use N to denote the number of BSs deployed in one macro-cell. When N = 1, the system is, and the macro-bs equipped with M antennas serves K users in the macro-cell, where M K [3]. When N > 1, the system is SCN, and each small-bs is equipped with Ms antennas.1 Since we consider the same antenna density for the two systems, the total number of antennas of and SCN in one macro-cell should be the same, i.e., N Ms = M. For notational simplicity, we assume that M is an integer multiple of Ms.2 We consider the same cell coverage of the two systems for a fair comparison, i.e., the same expected percentage of Inter-cell interference where sk is the data symbol transmitted from BSb to MSk, sj is the data symbol vector for all Kj users served by BSj, nk is the additive white Gaussian noise (AWGN) with zero mean and variance σ 2, and Nc denotes the number of BSs in the cluster. According to the system settings, Nc = L for Massive MIMO, and Nc = LN for SCN. With ZFBF and perfect CSI, the intra-cell MUI can be eliminated. Hence only ICI exists as shown in (2). The signal-to-interference-plus-noise ratio (SINR) of MSk can be obtained as 2 pk,b hh k,b gk,b SINRk = Nc j=1,j =b. (3) 2 2 hh k,j Wj +σ {z } Ik III. EE A NALYSIS OF M ASSIVE MIMO AND SCN A. Problem Formulation The EE of the network is defined as the ratio of the total number of transmitted bits to the total energy consumption in the cluster. Let Rk,b denote the data rate of MSk supported 1 The homogeneous SCN system is considered in this paper, where the small-bss are uniformly deployed to avoid coverage hole. 2 More general cases can be easily included by first setting M = M s N and then randomly allocating the remaining M Ms N antennas to the N small-bss, where is floor operator. 3 If the number of users closest to BS exceeds M, BS will select M s s b b nearest users and the other users will be served by their closest adjacent BSs. 25

3 by BS b, and P b denote the total power consumption of BS b. Then the EE can be expressed as EE = Nc b=1 Kb k=1 R k,b Nc b=1 P b R sum P sum, (4) where R sum and P sum are the sum data rate of all users and the overall power consumption at all BSs in the cluster, respectively. Based on the result in [7], the total power consumption at BS b can be modeled as ( ) Pt,b P b = λ ρ + P c,b, (5) where P t,b, P c,b and ρ denote the transmit power consumption, circuit power consumption and power amplifier efficiency, respectively, and λ reflects the impacts of cooling, DC-DC and main supply. The values of these parameters depend on the type of the BS [9]. Switching the BSs with low traffic loads into sleep mode is an essential approach for saving energy in SCN. We consider three BS sleep strategies, which will be introduced in detail in next section. Let P ca and P ci denote the circuit power consumed at the RF chain of each antenna in active mode and sleep mode, respectively [7]. Then, the circuit power consumption of BS b can be expressed as follows, P c,b = N t (P ci + δ b (P ca P ci )), (6) where δ b = sign (P t,b ) denotes the operating modes of BS b, and sign ( ) denotes the sign function. If BS b is in sleep mode, then P t,b = 0 and δ b equals to zero. If BS b is in active mode, P t,b > 0 and δ b = 1. N t is the number of antennas at BS b. If BS b is a macro-bs, N t = M. If BS b is a small BS, N t = M s. To provide a whole picture of the SE-EE relationship of and SCN, we maximize the EE of each system for a given data rate requirement of each user. Let Rk,b 0 denote the data rate requirement of MS k, which is served by BS b. By setting R k,b = Rk,b 0, it is not hard to see from (4) that to maximize the EE is equivalent to minimize the overall power consumption P sum, which includes both transmit power consumption and circuit power consumption. According to (6), the circuit power consumption depends on the operating modes of the BSs. For a given BS sleep strategy, the circuit power consumption will be a constant. Therefore, we only need to minimize the overall transmit power consumption. Then, the problem that maximizes the EE by allocating transmit powers to multiple users under the data rate requirement of each user and the maximal transmit power constraint of each BS for a given BS sleep strategy can be formulated as min {p 1,b,...,p Kb,b} N c K b p k,b b=1 k=1 s.t. log 2 ( K b k=1 1 + p k,b h H k,b g k,b 2 I k + σ 2 p k,b P max, b p k,b 0, k, b, ) (7a) = R 0 k,b, k, b (7b) (7c) (7d) where I k is the ICI power defined in (3). Since there is no cooperation among the BSs, BS b has no knowledge of I k, which depends on the power allocation results of the interfering BSs. The problem (7) is similar to a conventional multi-cell power allocation problem, which can be solved by BS-wise iteration power allocation, and the convergence of the iterations was proven in [10]. However, when the cell number is large, the iteration algorithm is not applicable due to the prohibitive complexity. To circumvent this problem, we consider two extreme cases when calculating I k in the following. The performance of practical systems will lie between these two extreme cases. 1) Average Maximal Interference Power: In this case, we assume that all interfering BSs transmit with P max regardless of the data rate requirements of the users. Since the precoding vectors at each BS are independent of the interfering channels, the average interference power experienced at MS k, which is served by BS b, can be obtained as Ī k = E{ N c = N c Kj j=1,j b Kj j=1,j b = N c j=1,j b i=1 p i,j h H k,j g i,j 2 } i=1 p i,jgi,j H E{h k,jh H k,j }g i,j Kj i=1 p i,jα(d k,j ) g i,j 2 = N c j=1,j b δ jp max α(d k,j ) where d k,j is the distance between BS j and MS k, α(d k,j ) is the corresponding large-scale fading gain of MS k, and δ j is defined in (6) denoting the operating mode of BS j. By replacing I k with Īk, (7b) can be expressed as ) p k,b h log 2 (1 H k,b + g k,b 2 Nc j=1,j b δ jp max α(d k,j ) + σ 2 (8) = R 0 k,b. (9) Then problem (7) can be solved independently at each BS. It is not hard to find the optimal power allocation at BS b as ( Nc ) r k,b p j=1,j b δ jp max α(d k,j ) + σ 2 k,b = h H k,b g, (10) k,b 2 where r k,b = 2 R0 k,b 1. If the sum of the optimal powers allocated to all the K b users exceeds the maximal transmit power of each BS, i.e., they do not meet the constraints in (7c), an outage will occur. 26

4 2) Instantaneous Minimal Interference Power: The above average maximal interference power model assumes maximal transmit power of the interfering BSs, which can be regarded as the worst-case average ICI power. Next, we consider the case where all the BSs cooperatively allocate the powers based on the instantaneous CSI of all the users in the cluster, which corresponds to the best-case ICI power. With (1) and (2), the constraints in (7b) can be equivalently expressed as p k,b h H k,bg k,b 2 r k,b N c K j j=1,j b i=1 p i,j h H k,jg i,j 2 = r k,b σ 2 (11) for k = 1,..., K b and b = 1,..., N c. The N c b=1 K b linear constraints in (11) can be rewritten in a compact form as Ap = b, (12) where A, p and b are respectively defined as r k,b h H k,j g i,j 2 j b, i k [A] k+ b 1 l=1 K l,i+ j 1 l=1 K = 0, j = b, i k l h H k,b g k,b 2 j = b, i = k [p] k+ b 1 l=1 K l = p k,b, and [b] k+ b 1 l=1 K l = r k,bσ 2. By replacing the constraints in (7b) with (12), the joint power allocation problem can be formulated as min {p 1,1...p K1,1,...,p 1,Nc...p KNc,Nc } s.t. (12), (7c), (7d) N c K b p k,b b=1 k=1 (13a) (13b) This is a linear programming problem, which can be numerically solved with efficient algorithms [11]. When the matrix A has full rank, then the problem (7) has the unique solution, p = A 1 b. If p does not satisfy the constraints (7c) and (7d), then the problem is infeasible and an outage occurs. The solution of this problem maximizes the EE of the multicell network under the data rate requirement of each user and the maximal transmit power constraint of each BS for a given BS sleep strategy, where the instantaneous ICI power is minimal. IV. SIMULATION RESULTS In this section, we evaluate the EEs of and SCN systems, when the same number of users in the same area are served with identical antenna density and with identical cell-edge SNR. In the simulations, 10 users are uniformly distributed in each macro-cell with the radius of 1000 m. Overall 300 antennas are either all equipped at the macro-bs of a system or distributed over multiple small-bss of the SCN systems. The network layout is shown in Fig. 1, where L = 7 macro-cells are considered. The numbers of hexagonal smallcells within each hexagonal macro-cell are respectively set as 7, 61, 150 and 300, and the corresponding radiuses are 378 m, 128 m, 82 m, and 58 m. The cell-edge SNR is set to 10 db Transmit Power (W) Circuit Power (W) Min Interference Max Interference Fig. 2. Transmit power and circuit power versus the data rate requirement per user with the cell-edge SNR of 10 db. for all cells with various sizes unless otherwise specified. In the simulations, we consider a data rate requirement (i.e., SE requirement) achievable if the outage probability is less than 10%. Without otherwise specified, the BS sleep strategy for the SCN is set as follows: the BSs are turned into sleep mode when they have no users to serve. Since the propagation model depends on the cell size, both the short-range and long-range models are considered in the simulations. We define the transition distance as 10 m and 35 m respectively for SCN and systems, after which the propagation model switches from the short-range model to the long-range model. For the short-range model, the line-of-sight (LOS) channel exists with large probability and the large-scale fading gain follows log d in db [8], where d is the distance between the user and the BS. For the long-range model [12], the large-scale fading gain follows log d in db for, and follows log d in db for SCN. The EEs of and SCN largely depend on the circuit power consumption model, whose parameters depend on the BS types, and change with the cell size. The power consumption parameters of four typical BSs in prevalent cellular systems are summarized in [9], which are given in Table I. The four types of BSs have the coverage of 1000 m, 250 m, 100 m and 30 m, respectively. A. EE comparison Figure 2 shows the overall transmit power and circuit power of the BSs in and SCN systems in the centric macro cell. 4 Due to the limit of acceptable outage probability and maximal transmit power, and SCN systems have different maximum achievable SEs. As expected, the required overall transmit power in maximal interference case is larger than that in minimal interference case. The required transmit power in practical cases of interference power will lie between these two extreme cases. 4 In this way the cell-edge effects will be removed. 27

5 Fig. 3. The EE versus the required SE per user. The cell-edge SNR is 10 db. Fig. 4. The EE versus the required SE per user. The cell-edge SNR is 30 db. For conciseness, we only analyze the performance of Massive MIMO and SCN in the minimal interference case in the sequel. With the cell-edge SNR of 10 db, the achievable SE of is higher than SCN, and the achievable SE of SCN decreases as the number of cells increases. To achieve the same SE, needs more transmit power than SCN and the transmit power of SCN decreases with cell shrinking. This is because when the cell size reduces, the users will be closer to the BS. Although reducing cell size will reduce the array gain for a given antenna density, Fig. 2 shows that the benefit of high large-scale fading gain exceeds the loss of array gain, which results in a lower transmit power for a smaller cell size. On the other hand, when the cell number of SCN is small, e.g. N = 7, nearly all BSs will be active. Hence, the circuit power of SCN is close to that of. When the cell number of SCN is large, e.g. N = 300, most BSs will be in sleep mode. Therefore, the circuit power of SCN is much smaller than that of and decreases as the cell number increases. Fig. 3 shows the EEs of and SCN as a function of the required SE per user. It is shown that the EE of SCN to achieve the same SE requirement is much higher than that of. The gain increases as the cell size reduces, because the transmit power is much lower than the circuit power for SCN such that the EE is dominated by the circuit power. B. Impact of cell-edge SNR By comparing Fig. 3 with Fig. 4, we can observe the impact of the cell-edge SNR on the performance of and SCN. Similar relationship between the EEs of Massive MIMO and SCN can be observed from the two figures. For the SE, however, when the cell-edge SNR is 30 db, SCN can achieve higher SE than. This can be explained as follows. With high cell-edge SNR, the system operates in an ICI-limited scenario. In SCN, the reduction of cell size increases the number of sleep BSs and hence reduces the number of interfering BSs, which leads to the improvement of the SE. On the other hand, since the antenna density is given, N=7 UEthre=0 N=7 UEthre=1 N=7 UEthre=2 Fig. 5. The EE versus the required SE per user with different BS sleep strategies. reducing the cell size will decrease the array gain. Therefore, the achievable SE decreases when the cell size is too small as shown in Fig. 4. C. Impact of BS sleep strategy In Fig. 5, we analyze the impact of BS sleep strategies on the EE and the SE. In particular, we consider that a BS will turn into sleep mode when there are no users, one user, and two users in its coverage, respectively, corresponding to increasing values of the sleep threshold, where the SCN with seven cells is considered. It can be observed that when the sleep threshold is higher, more BSs will be in sleep mode and the system will consume less circuit power. Since the users in the cells covered by the sleep BSs will be served by adjacent active BSs, the increased propagation distance leads to more transmit power consumption. Because circuit power dominates the total power consumption, the EE of SCN improves as the sleep threshold increases. However, the increased transmit power leads to lower achievable SE because of the maximal transmit power constraint. D. Impact of the power consumption parameters All previous simulation results have shown that Massive MIMO achieves a lower EE than SCN, where the power 28

6 TABLE I PARAMETERS FOR ENERGY CONSUMPTION [9] η Fig. 6. The EE versus η for with the SE per user of 1.5bps/Hz. consumption parameters of are identical to the Macro BS currently deployed in cellular systems since the was set to have the same coverage as the Macro BS. In Fig. 6, we show with what power consumption parameters the can achieve a comparable EE to SCN. To this end, we adjust the power consumption of by using the Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) with different η, where R 1000 η = represents the relative cell size. The four different cell radiuses in Table I correspond to four breakpoints of η, i.e., η 4 = 1, η 3 = 0.25, η 2 = 0.1, η 1 = The interpolating function for parameter ρ can be expressed as ρ 1 (η), η [η 1, η 2 ] ρ(η) = ρ 2 (η), η [η 2, η 3 ] ρ 3 (η), η [η 3, η 4 ] (14) where ρ i (η), i = 1, 2, 3 are the corresponding Hermit cubic interpolant. Other power consumption parameters in Table I can be similarly obtained by the interpolating functions. In the simulations above, the values of η of SCN with 7, 61, 150 and 300 cells are 0.378, 0.128, and 0.058, respectively. It can be seen that when the cell number of SCN is small, e.g. N = 7, can achieve a higher EE than SCN when η is less than 0.25, which is smaller than that of SCN with 7 small-cells. This indicates that to achieve the same EE, should be designed with lower power consumption than SCN. However, when the cell number of SCN is large, e.g. N c > 61, the EE of is always lower than SCN regardless of the power parameters. This is because SCN can enjoy more BS sleep opportunity to save the circuit power consumption. V. CONCLUSIONS In this paper, we compared the energy efficiencies (EEs) of and small cell network (SCN), given the same user density, antenna density and cell-edge SNR. To this end, we employed a unified model to analyze and optimize the two systems. We formulated the optimization problem for cell radius λ ρ P ca P ci 1000 m W 10.9 W 250 m W 5.4 W 100 m W 0.8 W 30 m W 0.4 W power allocation to multiple users that maximizes the EE under the constraint of data rate requirement of each user and the constraint of the maximal transmit power of each BS, where a best and worst case of interference power were considered. With the optimal solution of the problem, we analyzed the impacts of cell-edge SNR, BS sleep strategies and circuit power consumption on their performance. Our results showed that more transmit power is required by Massive MIMO than SCN to achieve the same spectral efficiency (SE) requirement. With typical circuit power consumption parameters, the EE of SCN is larger than that of Massive MIMO, because in SCN the BSs with low traffic loads can be turned into sleep mode. The achievable SE increases with the cell-edge SNR for both and SCN. When the BS sleep threshold becomes higher, SCN can achieve higher EE but lower achievable SE. When the number of cells in SCN is small, can achieve higher EE than SCN only with very low circuit power consumption. When the number of cells in SCN is large, is always less energy efficient than SCN regardless of the power consumptions. REFERENCES [1] J. Hoydis, M. Kobayashi, and M. Debbah, Green small-cell networks, IEEE Vehicular Tech. Mag., vol. 6, no. 1, pp , Mar [2] J. Hoydis, S. ten Brink, and M. Debbah, : How many antennas do we need? in Proc. Allerton Conf., [3] F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta, O. Edfors, and F. Tufvesson, Scaling up MIMO: Opportunities and challenges with very large arrays, IEEE Signal Process. Mag., [4] G. Li, Z. Xu, C. Xiong, and C. Yang, Energy-efficient wireless communications: tutorial, survey, and open issues, IEEE Wireless Commun. Mag., vol. 18, no. 6, pp , Dec [5] H. Leem, S. Y. Baek, and D. K. Sung, The effects of cell size on energy saving, system capacity, and per-energy capacity, in Proc. IEEE WCNC, [6] E. Kurniawan and A. Goldsmith, Optimizing cellular network architectures to minimize energy consumption, in Proc. IEEE ICC, [7] G. Auer, V. Giannini, C. Desset, I. Godor, P. Skillermark, M. Olsson, M. Imran, D. Sabella, M. Gonzalez, O. Blume, and A. Fehske, How much energy is needed to run a wireless network? IEEE Wireless Commun. Mag., vol. 18, no. 5, pp , Oct [8] A. Goldsmith, Wireless Communications. Cambridge, U.K.: Cambridge Univ. Press, [9] M. A. Imran and P. Partners, Energy efficiency analysis of the reference systems, areas of improvements and target breakdown, Tech. Rep., [10] R. Yates, A framework for uplink power control in cellular radio systems, IEEE J. Select. Areas Commun., vol. 13, no. 7, pp , Sep [11] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, [12] TR V1.2.0, Further Advancements for E-UTRA Physical Layer Aspects (Release 9), 3rd Generation Partnership Project, Jun