Improved Water-Filling Power Allocation for Energy-Efficient Massive MIMO Downlink Transmissions

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1 INTL JOUNAL OF ELECTONICS AND TELECOMMUNICATIONS, 17, VOL. 63, NO. 1, Manuscrit received October 7, 16; revised December, 16. DOI: /eletel Imroved Water-Filling ower Allocation for Energy-Efficient Massive MIMO Downlin Transmissions Noor Shahida M., osdiadee Nordin and Mahamod Ismail Abstract Energy Efficiency (EE) is becoming increasingly imortant for wireless communications and has caught more attention due to steadily rising energy costs and environmental concerns. ecently, a new networ architecture nown as Massive Multile-Inut Multile-Outut (MIMO) has been roosed with the remarable otential to achieve huge gains in EE with simle linear rocessing. In this aer, a ower allocation algorithm is roosed for EE to achieve the otimal EE in Massive MIMO. Based on the simlified exression, we develo a new algorithm to comute the otimal ower allocation algorithm and it has been comared with the existing scheme from the revious literature. An imroved water filling algorithm is roosed and embedded in the ower allocation algorithm to maximize EE and Sectral Efficiency (SE). The numerical analysis of the simulation results indicates an imrovement of 4% in EE and 5% in SE at the downlin transmission, comared to the other existing schemes. Furthermore, the results revealed that SE does not influence the EE enhancement after using the roosed algorithm as the number of Massive MIMO antenna at the Base Station () increases. eywords energy efficiency, Massive MIMO, ower allocation, sectral efficiency O I. INTODUCTION NE romising technology for achieving the future bandwidth requirements of the next-generation wireless communication system is Massive MIMO that has attracted lots of research attention recently [1]-[5]. Massive MIMO is based on the use of a large number of antennas to accommodate more mobile users and is allowed to imrove sectrum efficiency (SE) and energy efficiency (EE) by installing massive antennas at the [6]. When used with suitable recoding schemes, Massive MIMO systems exerience small inter-user and intercell interference, and consequently achieve significant higher throughut than the earlier multiuser-mimo systems. This wor suorted from Grant ef. No: FGS/1/15/ICT4/UM// (Malaysia s Ministry of Higher Education) and Universiti Tenial Malaysia Melaa (UTeM). Noor Shahida M. is with Faculty of Electronic and Comuter Engineering, Universiti Tenial Malaysia Melaa, Hang Tuah Jaya, 761 Durian Tunggal, Melaa, Malaysia ( noorshahida@utem.edu.my). osdiadee Nordin and Mahamod Ismail are with Deartment of Electrical, Electronic and Systems Engineering, Faculty of Engineering and Built Environment, Universiti ebangsaan Malaysia, 436 UM Bangi, Selangor, Malaysia ( {adee,mahamod}@um.edu.my). EE has drawn lots of attention and has been considered as an imortant metric for evaluating a communication system, where, it focuses on maximizing EE that can reduce the total energy consumtion. In existing wors, there are various designs of wireless that aim for achieving energy efficient communications. In [7], the authors rovide insights on the otimal design of the number of antennas, active users and transmit ower for maximizing EE in multiuser MIMO systems, whose results show that the maximal EE is achieved by a Massive MIMO setu with hundreds of antennas deloyed. Moreover, by installing a large number of antennas and with the low transmit ower er-antenna, inexensive comonents can be used to build the system [8]. In the ast several years, valuable research results have been obtained by analyzing the EE of Massive MIMO systems. For instance, in [9] and [1], equal ilot and data ower assignment for all users have been assumed in a single-cell analysis to imrove the system EE. The Massive MIMO with hundreds of antennas designed in [9] has assumed erfect CSI. esource allocation is focused in [1] to maximize EE in OFDMA systems with massive antennas, which taes imerfect CSI and inter-carrier interference into consideration. However, there is no ower allocation scheme considered in both studies. Therefore, the authors in [11]-[16] introduced ower allocation strategies to imrove EE that can be described as the successfully delivered information bits er unit energy consumtion. Authors [11] investigated the imact of circuit ower consumtion on the EE in Massive MIMO. However, the simulation results show that either the average channel gain is large or the circuit ower consumtion is high, the energy efficiency of the Massive MIMO system is not increasing consistently. In [1], the tradeoff between EE and SE were designed to maximize the EE of systems with distributed antennas. Then, the SE-EE relationshi of Massive MIMO systems was investigated in [13], which showed that the EE will increase exonentially with a linear SE loss by reducing the circuit ower. This result can also be interreted as the Massive MIMO is not energy efficient to achieve very high SE because a linear increase of SE leads to an exonential decrease of EE. The wor resented in [14] develoed a resource allocation of EE to maximize the EE for a multi-user OFDMA. However, an energy consumtion is increasing, even though the authors in [15] showed that MIMO techniques are effective in imroving caacity and SE of wireless systems. In [16], an EE ower allocation has been roosed for the Massive MIMO system with Maximum atio Transmission (MT) recoding and the EE and SE are imroved when the number of antennas at

2 8 NOO SHAHIDA M., OSDIADEE NODIN AND MAHAMOD ISMAIL increases and hence reduce ower consumtion. However, the recoding can not eliminate inter-user interference at each User Terminal (UT). Authors in [17] investigated on QoS-aware EE ower allocation in downlin large-scale MIMO systems by extending the wor described in [18] to overcome the roblem of an EE maximization and reformulate the objective function under er-antenna transmit ower and er-user rate constraints. However, the system can only achieve maximum EE when serves almost users and 1 number of antennas. ecently, [19] roosed an otimal antenna selection, users and transmit ower for the single-cell Massive MIMO system with zeroforcing beamforming (ZFBF), which imrove the EE Massive MIMO systems. Contrary to [], the authors focused on otimizing the transmit ower at the base station for the multicell Massive MIMO system, where the maximal ratio transmission (MT) and ZFBF with equal ower allocation are used. The simulation results resented the imrovement of EE by otimizing transmit ower increases with the number of antennas. However, [19] and [] otimized the total transmit ower at the base station (), which is subotimal for the system EE. In [1], the authors roosed a water-filling algorithm to achieve a balance between EE and SE with reduced comlexity. However, the allocation is based on a fixed otimization model, in which each user has its water level. In this aer, we develo an EE ower allocation using an imroved water filling algorithm (IWF) for Massive MIMO and comare against the wor reorted in [16], [] and [1] because to determine the ower allocation algorithm with different ower levels for the users. w s h Table I Some notations and symbols used in this aer recoding weighting vector data symbol of the -th (cooeratively served by the sector s) channel matrix from the n-th and the -th user n noise vector of the -th user transmit ower for each UT r distance between the user and the base station B sectrum bandwidth c distance between the user and the base station σ noise ower H channel matrix total the overall ower consumtion t total transmission ower consumtion c the total of circuit ower consumtion cx ower consumtion at uc ower consumtion at UTs η ower amlifier efficiency min the minimum rate threshold required by user g the effective channel ower gain to the -th user µ a water level The contributions of this aer are listed as follows: (i) both the number of antenna arrays at and the transmit ower at the user are adjusted to maximize the EE, and (ii) we roosed a novel ower allocation algorithm and comared with the another ower allocation scheme from the revious wors in [16], [] and [1]. The simulation results show that it is ossible to maximize EE by using the roosed ower allocation comared with the wor roosed in [], [1]. The rest of the aer is organized as follows: In Section, the system model for the Massive MIMO system is introduced. The EE of Massive MIMO is analyzed in Section 3. Followed by the energy efficiency ower allocation scheme in Section 4. In Section 5, simulation results and analysis are reorted. Finally, conclusions are resented in Section 6. For convenience, some notations and symbols used throughout the aer are listed in Table I. II. SYSTEM MODEL Consider a hexagonal cell system with the Massive MIMO systems at as illustrated in Fig. 1, where the systems consist of one with N antennas and user terminals (UTs) each with M antennas which are randomly and uniformly distributed in the cell with the radius c. User terminal User terminal Base Station User terminal Base Station n =1 n = n =N Base Station with N transmit antenna H Channel User terminal User terminal user terminals with a receive antenna Fig. 1. Single-cell system with Massive MIMO systems at Based on channel estimates, the forms recoding vectors to transmit data to the intended terminals. We adot the zeroforcing (ZF) recoding scheme in the system to reduce interuser interference. The transmitted signal vector of the system can be stated as w1,1 w1, s1 x Ws = 1,., w,1 w, s (1) Then, the received signal of -th UT can be written as h x y i i i1, i h x h x n i i i1, i = () indicates the existing inter-user interference. Therefore, the signal-to-interference-lus-noise ratio (SIN) that is achieved by UT can be reresented as SIN i h xi i1, i Then, the achievable sum rate of the -th user is 1 h x (3) B log (1 SIN ) (4)

3 IMOVED WATE-FILLING OWE ALLOCATION FO ENEGY-EFFICIENT MASSIVE MIMO DOWNLIN TANSMISSIONS 81 Because of the simlest form, the ZF recoding is adoted at the and the SIN can be written as ZF SIN H 1 tr( H H ) (5) The equation below is based on the large number of antennas at and then the theory of random matrix in [15] 1 N, N H 1 E tr H H (6) Then, the achievable sum rate of the system in the downlin transmission can be obtained as sum SIN B log 1 III. EE FO MASSIVE MIMO We define the EE as EE where total can be written as sum total 1 1 total t c t uc cx uc cx (9) 1 1 According to equation (8) and equation (9), the EE of the lin can then be measured in (b/j/hz) EE sum total B 1 1 log 1 SIN uc cx (7) (8) (1) IV. ENEGY EFFICIENCY OWE ALLOCATION SCHEME FO MASSIVE MIMO EE is an imortant metric that reresent transmit information bits er Joule by measuring the ratio of caacity and transmit ower. Noticeably, the EE will not be very high when the transmission ower is uncontrolled even though it brings much higher data rate. Hence, an aroriate transmission ower allocation should be develoed to achieve the best EE. In this section, the aroximation of otimal ower allocation is given and EE ower allocation algorithm will be develoed to maximize the EE. Based on equation (1), the design of an energy-efficient ower allocation scheme, which includes ower allocation algorithm for the multi-objective otimization roblem can be summarized as: subject to 1 max EE max, (11) (1) log SIN (13) 1 The allocated transmission ower has been formulated in constraint (1), where each subchannel ower have a range within - max, and (13) reresents the normalized rate requirement. min A. Energy Efficiency Water Filling ower allocation algorithm In this subsection, we allocate each UE using the Water-Filling algorithm. The overall ower allocated to an active user by WF is written as where the function 1 g max, 1 max, (14) confines the range of as er (14). Using (3), the SIN of ZF can be written as follows SIN (15) h w 1, i the achievable rate for UT is given by B log (1 SIN ) (16) Hence, the EE is exressed as below sum EE c (17) Finally, the EE WF ower allocation algorithm is shown in Fig.. Inut:, Outut: max, min,, EE, i 1: Initialization: Set max, : Calculate ower allocated:.1) Calculate WF().) Calculate in (14) 3: Calculate the minimum rate: 3.1) If min, go to 4.). If not, continue 3.) If max,, the roblem is unworable. If not, calculate max log (1 g max, ).If min max, the roblem is unworable. 1 4: Calculate the total ower: 4.1) If max,, the roblem is unworable. If not, calculate EE and exit 4.) If max,, Calculate EE and exit. If not, calculate WF () and. 4.3) If min, the roblem is unworable. If not, calculate EE and exit. Fig.. Algorithm 1: Energy Efficient WF ower Allocation Algorithm [] B. Energy Efficiency roosed ower allocation algorithm In the following, a roosed ower allocation is develoed based on an imroved water filling (IWF) algorithm by extending the idea of authors [] to solve the EE otimization roblems. Contrary to [], our roosed ower allocation roduces simler structure and allows the differentiability of the system rate function towards the total of ower transmitted. Based on the above WF algorithm, an IWF ower allocation algorithm is introduced by using the Lagrange Multilier technique as below

4 8 NOO SHAHIDA M., OSDIADEE NODIN AND MAHAMOD ISMAIL SIN max, max, (,, ) log 1 (18) the vector of the Lagrange Multiliers reresents µ and λ, resectively. From equation (17), we formulate following otimization roblem, aiming to maximize the EE with constraint (1). An IWF ower allocation algorithm is roosed by using the maximum of total squared weights among all the s is given by n S max w n1,..., N Therefore, max log 1 g 1 subject to 1 S max, (19) () By introducing the Lagrange Multilier technique, the IWF is defined as below. log 1 g S (1) max, 1 1 Hence, the new otimal ower allocated can be written as follows: where (1 ) B (1 ) ln() N max, max, () reresents the maximum between zero and the max,, while [,1] reresents each user riority. In a certain case of equal riority, = 1/, for all. This corresonds to an IWF distribution with variable water levels that can be changed only by the user riorities. Using (5), the SIN of user can be obtained as: g SIN The seudo-code for an IWF is summarized in Fig. 3. 1: Inut: Set of N, λ, µ, B and max, = 1,., : Outut: { } and 3: if μ = and B B ln ln 4: = 5: else if μ > and B ln(1 ) 6: then, (1 ) B (1 ) ln() 7: B log 1 g 1 max, 8: Chec convergence: the algorithm stos when λ + 1 < (3) Fig. 3. Algorithm IWF The allocates each UT with different amounts of ower and the ower allocation should be allocated. The SIN of UT is given by SIN g (4) where is the transmit ower for UT. Then, we can obtain the value of SIN and the achievable rate for UT as below SIN ZF H 1 (5) B 1 tr ( H H) log (1 g ) (6) Let g is received signal to noise ratio. Then, the otimization roblem is formulated as follows Subject to max 1 cx 1 1 ( ) max, min uc (7) Based on the above IWF algorithm, we can roose an EE ower allocation algorithm by introducing the Lagrange Multilier technique is defined as below (,, ) 1 ( ) ( ) EE cx 1 1 ( ) min max, 1 Hence, the EE ower allocated can be written as follows: max, uc (8) (1 ) B EE ( EE ) ln() N (9) The roosed ower allocation scheme is more roer and can bring considerable gains over the equal ower allocation. The EE an IWF algorithm as shown below. Inut: max,, min, (small constant for error tolerance) Outut: total, EE, EE 1: Initialization: Set total max, : Calculate ower allocated:.1) Calculate IWF( ) (see Fig. 3).) Calculate EE in (9).3)If[ EE max, ], set EE max, and go to.1). If not, calculate the Shanon caacity and go to the next ste. 3: Calculate the minimum rate: 3.1) If min, go to 4.). If not, continue 3.) If EE max,, the roblem is unworable. If not, calculate max log (1 g max, ).If min max, the roblem is unworable. 1 4: Calculate the total ower: 4.1) If EE max,, the roblem is unworable. If not, calculate EE and exit 4.) If EE max,, Calculate EE and exit. If not, calculate IWF ( )and. 4.3) If min, the roblem is unworable. If not, calculate EE and exit. Fig. 4. Energy efficient ower allocation with the ZF recoding

5 Energy Efficiency [bit/joule] Energy Efficiency [bit/joule] SE [bits/hz/s] IMOVED WATE-FILLING OWE ALLOCATION FO ENEGY-EFFICIENT MASSIVE MIMO DOWNLIN TANSMISSIONS 83 V. SIMULATION AND ANALYSIS In this section, we simulate the EE ower allocation scheme for Massive MIMO. The roosed ower allocation is comared with the existing scheme reorted in [16], [] and [1]. The main arameters used in the simulation are listed in Table II. Table II arameters For The Massive MIMO System [16] arameter Cell adius, System Bandwidth Circuit ower at UT Circuit ower at Value 5 m MHz.1 mw/hz 1 mw/hz roosed-iwf- [ZF] WF [1] - [ZF] MT [16] E [] ower amlifier efficiency, ξ ath loss exonent, α Noise ower sectrum density σ min / th max, dbm/hz Mbs [1] 1.5 mw Fig. 5 comares the effect of antenna number N with different ower allocation algorithm. In this case, increasing N can cause a linear increasing of dynamic and static ower. It can be observed that the roosed algorithm outerforms the other schemes [16], [] and [1]. As seen from this figure, the ower allocation algorithm with the ZF, is better than MT. The reason comes from the effect of the ractical dynamic ower. Besides, ZF can remove intra-cell interference while maximizing the signal at the desired terminal whereas MT cannot remove intra-cell interference. In other words, the structure of the Massive MIMO systems has benefited from the use of ower efficiently. For that reason, the Massive MIMO systems with a large number of transmit antennas have been develoed to transmit data efficiently with low ower usage. This verifies the effectiveness of our roosed aroach Number of Antennas () Fig. 6. SE vs the number of antennas at In Fig. 6, SE values of the roosed algorithm are achieved by increasing the number of antennas at. The SE erformance is reduced when the number of antennas at is very small. However, the erformance of SE can be imroved when the number of users increases and the number of antennas is large enough. The inter-cell interference can be cancelled, when using more transmit antennas. So, EE can get the benefits of the existing inter-cell interference at s in the downlin communication system with the Massive MIMO systems. 3 5 roosed-iwf - [ZF] WF [1] - [ZF] MT [16 E [] roosed-iwf -[ZF] WF [1] - [ZF] MT [16] E [] Number of Antennas () Fig. 5. EE vs the number of antennas at Number of Users Fig. 7. EE vs the number of users Fig. 7 comares the otimal EE when the has 1 antennas. The number of users is varied to observe its imact on EE. Fig. 7 shows that the erformance of EE with the IWF algorithm is better comared with the existing scheme. The otimal EE increases with the increasing of a number of users. This is because more multiuser diversity gain can be obtained by oortunistic scheduling. Besides, the number of users and transmit antenna number N affect the EE in a comlicated manner, adjusting these arameters adatively is imortant for imroving the EE.

6 SE [bits/hz/s] 84 NOO SHAHIDA M., OSDIADEE NODIN AND MAHAMOD ISMAIL Number of Users Fig. 8. SE vs the number of users In Fig. 8, we comare the SE as a function of the number of users. The results indicate that an IWF algorithm is again really effective for enhancing the SE. In our roosed scheme, SE increases as the number of users increases due to the obtainable various multiuser diversity gain. That means when the s suort increasing number of users, a higher number of antennas s are activated, causing the interference and increment of networ ower consumtion. By activating the ower allocation strategy, the SIN and average throughut can be increased while reducing the ower. Therefore, the systems can achieve maximum SE when serving a higher number of users and the number of antennas at MS. It can be observed that by using ower allocation strategy, the system erformance has imroved not only EE but also SE due to the reduction of the cell interference. VI. CONCLUSION In this aer, the energy-efficient ower allocation for Massive MIMO was investigated. The energy efficient ower allocation was designed based on the IWF algorithm with ZF recoding. The simulation results shown that the IWF outerforms the revious studies by achieving the maximum EE erformance. At the same time, the erformance of SE also can be imroved with Massive MIMO. Based on the roosed ower allocation algorithm, we also simulate and analyze the tendency of the EE with the different number of antennas at, MS and the number of users. EFEENCES roosed - IWF [ZF] WF [1] - [ZF] MT [16] E[] [1] V. Jungnicel,. Manolais, W. Zirwas, B. anzner, V. Braun, M. Lossow, M. Sternad,. Aelfrojd, and T. Svensson, The role of small cells, coordinated multioint, and Massive MIMO in 5G. IEEE Communications Magazine, vol. 5, no., , 14. [] Mohammed H. 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