Trade-off Energy and Spectral Efficiency in 5G Massive MIMO System

Adeb Salh 1*, Nor Shahida Mohd Shah2*, Lukman Audah1, Qazwan Abdullah1, Norsaliza Abdullah3, Shipun A. Hamzah1, Abdu Saif1 1Faculty of Electrical and Electronic Engineering, Universiti Tun Hussein Onn Malaysia, Parit Raja, Batu Pahat, Johor, Malaysia. 2Faculty of Engineering Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Muar, Johor, Malaysia. 3Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Muar, Johor, Malaysia. *Corresponding authors’ e-mail: [email protected], [email protected]

to multiple single active users (UEs) in same time-frequency resource. The EE and SE cannot be simultaneously optimized. ABSTRACT It is still quasi-concave due to noise amplifier, a large number of antennas, and cost of hardware, which decreases the radio A massive multiple-input multiple-output (MIMO) system is frequency chains (RF) [7]-[15]. A large number of antennas in very important to optimize the trade-off energy-efficiency both linear precoder and decoder are needed to select the (EE) and spectral-efficiency (SE) in fifth-generation cellular optimal antenna to limit the noise with uncorrelated networks (5G). The challenges for the next generation depend interference. In addition, deploying more antennas causes on increasing the high data traffic in the wireless higher circuit power consumption. From the perspective of communication system for both EE and SE. In this paper, the energy-efficiency, the increasing base stations in the cellular trade-off EE and SE based on the first derivative of transmit networks reported that the total consumed energy in the whole antennas and transmit power in downlink massive MIMO network approximately 60-80% [16]-[20]. Adopted power system has been investigated. The trade-off EE-SE by using scaling at transmitting signal from BS to users depends on multi-objective optimization problem to decrease transmit reducing the interference. It takes into account the constraints power has been analyzed. The EE and SE based on constraint of the transmit power allocation. Massive MIMO system helps maximum transmits power allocation and a number of to reduce transmit power created from high power gain and antennas by computing the first derivative of transmit power provides the higher EE. Moreover, distributed users in every to maximize the trade-off EE – SE has been improved. From cell and spectrum allocation are needed to improve spectral the simulation results, the optimum trade-off between EE and efficiency. From [21]-[26], the user association is optimized SE can be obtained based on the first derivative by selecting to enhance the EE by decreasing the transmit power the optimal antennas with low cost of transmit power. consumption, while the area of spectral efficiency is linear Therefore, based on an optimal optimization problem is based on a fixed number of users and an optimal number of flexible to make trade-offs between EE-SE for distinct antennas according to [27]. The degree of freedom in a preferences massive MIMO system maximizes the SE by utilizing all available resources such as an available antenna that Key words : Massive MIMO, energy efficiency, spectral maximizes high data rate and transmit power. The area of SE efficiency, 5G. growths linearly with a large number of transmit antennas, while with respect to user’s association, the SE becomes a 1. INTRODUCTION concave function. The future cellular networks must collect the explosive demand to increase the high data rate with low Growing demand to achieve high data traffic, high-resolution complexity of energy consumption. video streams and smart communication in cellular networks From the existing works, the author in [28] studied the depends on a promising candidate massive MIMO system. maximizing trade-off EE and SE based on user’s association, The massive MIMO technique is a key to improve the energy- number of antennas, power coordination and takes into efficiency (EE) and spectral-efficiency (SE) in the fifth- account backhaul capacity to improve the performance EE- generation (5G) wireless communication networks. The SE. Ensuring good rate fairness, lower-level power with user’s deployment of cellular networks has a great potential to association improves the performance of EE and SE in the improve the low power base station (BS) and enhance the EE [29]. Meanwhile, the author in [30] investigated the EE and in a cellular network [1]-[6]. Due to the increasing attention in SE based on K-tier heterogeneous networks by offloading data cellular networks, the performance of 5G depends on traffic to small cell massive MIMO system. The improving evaluating the EE in the massive MIMO system. A massive trade-off EE and SE with Rayleigh fading channel is based on antenna array at the BS is able to provide the high connection using the different types of theoretical power consumption

model and realistic power consumption model accordingly The received signal 푦푘 of users 퐾푡ℎ inside 푗푡ℎ cell can be [31]. Another author investigated that the maximization of written as EE-SE in downlink massive MIMO system depends on 퐾 analyzing the signal to interference noise ratio and optimum 휌 휌 transmission power in each cell when the number of BSs for 푦 = √ 푑 횑 퓋 푥 + √ 푑 ∑ 횑 퓋 푥 + 퓃 푘 퐾₣ 푘 푘 푘 퐾₣ 푘 푗 푗 푘 SE is high [32]. Achieving high sum-rates by using many 푗=1,푗≠푘 transmit antennas, the balancing of EE-SE depends on admitting an optimal number of distributed users and active 휌 푦 = √ 푑 푥 + 퓃 (2) transmit antenna with low cost of power consumption [33]. 푘 퐾₣ 푘 푘 The author in [34] focused on reducing the high complexity hybrid beamforming and power consumption for radio where 횑푘 is the Hermitian transpose channel matrix, and 휌푑 frequency chains by utilizing Butler phase shifter to enhance is the transmit power in the downlink. The transmit signal energy efficiency. From [35], the optimal design of EE-SE vector 휙 ∈ ∁푀×1 from BS 푗 a 푀 × 1 preceded vector 휙 = improved by employing the uplink and downlink high data 푗 푘 rates under imperfect channel state information (CSI) 퓋푘푥푘, where each UE receives the signal vector from each 푀×퐾 combined with maximum ratio, matched filter and zero- BS, 퓋푘 ∈ ∁ is the linear precoding matrix, 푥푘 ∈ 퐾 forcing. Maximum EE-SE trade-off in massive MIMO system ∁ ~풞풩(0, 퐼퐾) is the data transmitted from BS to UEs. ₣ is is achieved by equipping a great number of active users with the normalization factor of 퐾푡ℎ UEs, which is expressed as 2 2 less power and pilot training signal. ₣ = ‖혝‖푓⁄퐾, ‖. ‖푓 represents the Frobenius norm and 퓃푘 is In this paper, accurate CSI depend on used time-division the received noise with zero mean and variance. duplexing (TDD). Also, the goal of solving multi-objectivity problems is to find a set of trade-off solutions, by derivation 2.1 Power Consumption of the EE-SE trade-off in closed form. To decrease the complexity based on computing, the essential derivative of EE Reducing the transmit power depends on improving transmit and SE are in terms of power. antenna in a massive MIMO system. The circuit power consumption is established depend on selecting the optimal 2. SYSTEM MODEL antennas at the BSs created due to antenna architectures considered not only from a power amplifier, but also from Considering a downlink multiuser massive MIMO system, it power consumption such as baseband processing, DAC, and is assumed that every cell contains one base station, every BS filter. The total power consumption can be written as contains many transmit antenna 푀and 퐾 single users. It is assumed that 푀 ≫ 퐾. The channel matrix between BS and 푄푚푎푥 = 휌푑 + 푄퐶 (3) 푇 푇 푇 푇 1×푀 users ℋ = [횑1 , 횑2 , . . . . . 횑퐾] ∈ ∁ , as shown in Fig.1, with the assumption that the BS has perfect channel state The circuit power consumption in cellular networks is information. continuously increasing based on a large distributed UEs and . higher traffic demands. The circuit power consumption in 횑 11 [23]-[27],[36] is used and modeled as

푥 횑12 푦 1 1 푄퐶 ≈ 푁(푄퐷퐴퐶 + 푄푚푖푥 + 푄푓푖푙푡푒푟) + 2푄푠푦푛 + 푄퐿푁퐴 + 푄퐼퐹퐴 +

K- 푄푓푖푙푡푒푟 + 푄푚푖푥 + 푄퐴퐷퐶 (4) 푥2 푦2 BS with . . UEs 푀 . . data where 푄퐷퐴퐶 , 푄푚푖푥, 푄푓푖푙푡푒푟, 푄푠푦푛, 푄퐿푁퐴 + 푄퐴퐷퐶 , 푄푓푖푙푡푒푟 and antennas 푥푀 Channel 푦푀 Matrix 푄퐼퐹퐴 are the power consumption value for the DAC, the ℋ mixer, the filter in the transmitter, frequency synthesizer, the power consumption for soft noise amplifier, the power for the transitional frequency amplifier, and power consumed due to analog to digital converter, respectively. To simplify the Transmitted Received power consumption, 푄퐶 = 푄1 + 푀푡푄2, where 푄1 = 2푄푠푦푛 + vector 푦 vector 푥 푄퐿푁퐴 + 푄퐼퐹퐴 + 푄푓푖푙푡푒푟 + 푄푚푖푥 + 푄퐴퐷퐶 and 푄2 = 푄퐷퐴퐶 + 푄푚푖푥 + 푄푓푖푙푡푒푟 . Then, the total power consumption can be Figure 1: System model for multi-user massive MIMO system. simplified as

According to the increase in Shannon capacity, high data rate 푄 = 휌 + 푄 = 휌 + 푄 + 푁푄 (5) can be achieved by increasing the transmit power of channel 푚푎푥 푑 퐶 푑 1 2 to users. The zero-forcing beamforming precoding is used to 2.2 Trade-off Energy Efficiency and Spectral Efficiency mitigate the inter-user interference. The zero-forcing beamforming혝 = [퓋1, 퓋2, … … . . 퓋퐾] can be written as In this section, the objectives are to optimize EE-SE of multi- 혝 = ℋ퐻(ℋℋ퐻)−1 (1) user in terms of transmitting a huge number of antennas and

transmit power. From (2), it is assumed that the capacity of transmitting antennas 푁 is fixed [26]-[29],[38]. In addition, 퐾푡ℎ UEs is multiplied by a bandwidth written as from (11) the performance of SE is obtained with a small and constant number of selected antennas 푁. The derivative of SE 휌푑 according to downlink transmit power 휌푑 풞푘 = 훽 log2 (1 + 2) (6) ‖혝‖푓 푀 푁 휌 푀 푆퐸 휕(퐾 log (1+(1+ln 푡) 푑)) (1+ln 푡)푁 휕휂 푘 2 푁 퐾 푁 2 = = 푀 푁 휌 ≥ where 훽 is the bandwidth. From (6), ‖혝‖푓 can be equivalent 휕휌푑 휕휌푑 (1+(1+ln 푡) 푑) ln 2 푁 퐾 2 퐾 1 as ‖혝‖푓 ≈ ∑푘=1 2 at the number of antennas to serve a 0 (13) ‖횑푘‖ number of UEs 푀 ≫ 퐾 , where The performance SE in terms a number of transmit antennas 1 1 1 1 ≈ ≤ ∑퐾 ‖횑 ‖2 = ∑푀푡 ∑퐾 ‖횑 ‖2 (7) can be expressed as ‖ ‖2 퐾 1 2 푘=1 푘 2 푗=1 푘=1 푘 혝 푓 ∑푘=1 2 퐾 퐾 ‖횑푘‖

푀푡 푁 휌푑 푀 휕휂푆퐸 휕(퐾 log (1+(1+ln ) )) 휌 ln 푡 The maximal SE is equivalent to limit the transmit power and 푘 = 2 푁 퐾 = 푑 푁 ≥ 휕푁 휕푁 푁 휌 푀 ln 2(1+( 푑)(1+ln 푡)) a large number of transmit antennas for equivalent quality of 퐾 푁 the channel. From the Chi-square distribution for an 0 (14) increasing number of antennas 푀푡 , where 훾푗 = 2 ∑퐾 ‖횑 ‖ , 푗 = 1, . . . . . , 푀 and 훾 ≥ 훾 ≥...... ≥ 훾 . 휕휂푆퐸 푘=1 푗,푘 푡 1 2 푀 From (14), the 푘 strictly increases depending on There are large numbers of antennas that are equipped in a 휕푁 selecting the optimal antenna from available antenna massive MIMO system which requires selecting the optimal 퐸퐸 antenna with low cost of transmit power. According to [24], transmission, while the 휂 푘 firstly increases after the capacity of transmit antennas selection is expressed as decreasing with transmit power 휌푑 and fixed a number of transmit antennas 푁 in a massive MIMO system. 휌 The performance constraints of the trade-off EE-SE for 풞 = 퐾훽 log (1 + 푑 ∑푁 훾 ) (8) 푘 2 퐾2 푗=1 푁 transmitting power may not be enough to maximize spectral efficiency or energy efficiency to obtain a comprehensive where 푁 is the selection of optimal antennas from available insight for both transmit antennas 푁 and power 휌푑 for EE transmit antennas. From [25],[37], the mutual information for [39]. In this case, the trade-off EE-SE by using multi-objective a channel with multiple receive antenna selection is optimization problem to decrease transmit power is analyzed as follows: 푁 푀푡 피{∑푗=1 훾푁} = 퐾푁 (1 + ln ( )) (9) 푁 푆퐸 푚푎푥 퐸퐸 푚푎푥 max {휂 푘(휌푑 , 푁), 휂 푘(휌푑 , 푁)} (15) 푄푚푎푥,푁 From (8) and (9), the average capacity can be written as S.t 퐾 ≤ 푁 ≤ 풩 (16) 휌푑푁 푀푡 피{풞푘} = 퐾훽 log2 (1 + ) (1 + ln ( )) (10) 퐾 푁 푚푎푥 0 ≤ 휌푑 ≤ 휌푑 (17) A high achievable SE in per unit of bandwidth can be obtained by taking into account interference between users in a massive where 풩 is the number of available transmit antennas and 푚푎푥 MIMO system. Distributing more than one user is scheduled 휌푑 is the maximum transmit power. The trade-off EE-SE 푚푎푥 푆퐸 in every cell to eliminate the inter-cell interference, and can during transmit power 휌푑 = [0 , 휌푑 ] the 휂 푘(휌푑) > 푆퐸 푚푎푥 퐸퐸 퐸퐸 푚푎푥 be expressed as 휂 푘(휌푑 ) and 휂 푘(휌푑) > 휂 푘(휌푑 ) the performance 퐸퐸 푚푎푥 푚푎푥 of 휂 푘(휌푑) increases when 휌푑 ≥ 휌푑 during[0 , 휌푑 ]. 푆퐸 푀푡 휌푑푁 A large number of transmit antennas provide more transmit 휂 푘 = 퐾 log2 (1 + (1 + ln ) ) (11) 푁 퐾 power which causes a decreasing in EE according to (16). From (14) the 휂푆퐸 strictly increases with 푁 and 휌 , while From (5) and (11) the maximal EE can be written as 푘 푑 퐸퐸 the 휂 푘 become concave shape when number of 푁 and 휌푑 푀푡 휌푑푁 휂푆퐸 퐾 log (1+(1+ln ) ) increases. Also, from (17) the EE decreases when the 휂퐸퐸 = 푘 = 2 푁 퐾 (12) 푚푎푥 푘 푄 휌 +푄 +푁푄 transmitted power 휌푑 ≤ 휌푑 equals maximum transmit 푚푎푥 푑 1 2 푚푎푥 circuit power 푄푑 2.3 Trade-off the EE-SE With Multi-Objective 푀푡 푁 휌푑 Optimization Problem 휕(휂퐸퐸 ) 휕(퐾 log2(1+(1+ln ) )) 푘 = 푁 퐾 (18) 휕휌푑 휌푑+푄1+푁푄2 푆퐸 The better EE-SE trade-off depends on achieving 휂 푘 for every UE and limits the transmit power at an increasing We assume some of samples to simplify the following 푆퐸 equations number of antennas 휂 (휌푑, 푁). From (11), the SE increases 푘 푀 푁 휌 (휌 + 푄 + 푁푄 ) = 푄 , (1 + (1 + ln 푡) 푑) ln 2 = 훺 proportionally with transmitted power when the number of 푑 1 2 푚푎푥 푁 퐾

퐸퐸 푄1 + 푁푄2 in (5). The 휂 푘 becomes concave shape when number of 푁 and 휌푑 increases. From Fig. 2, the maximum 푀 (1+ln 푡)푁 푁 2 EE = 32 Mbit/J,when the number of evaluable antennas 푁 = [ ] (푄푚푎푥 ) − [퐾 log2(훺)]⁄[((푄푚푎푥, )) ] (19) 훺 20, at fixed transmit power 휌푑 = 30 dBm and number of distributed users 퐾 = 8 , while increasing the number of 푀 [(1+ln 푡)푁](푄 ,)−(훺)[퐾 log (훺)] 2 served users 퐾 = 15, and fixed number of transmit power 푁 푚푎푥 2 ⁄[((푄 , )) ] (20) (훺) ln 2 푚푎푥 휌푑 = 30 dBm, the EE becomes small and equal to EE = 26 Mbit/J when the number of antennas 푁 = 18.

휌 푀 40 푁2 푑((1+ln 푡))  =30dBm,K=8 휕(휂퐸퐸 ) 퐾 푁 k 푘 = < 0 (21) 휕휌 푀 푁 휌 2 35  =30dBm,K=15 푑 (1+(1+ln 푡) 푑) ln 2 k 푁 퐾 30 From the first derivative in (19), the EE increases and then 25 decreases when the transmit power increases 휌푑. In addition, from the second term in the numerator lim ((1 + (1 + 20 휌푑→∞ 푀 푁 휌 푀 푁 휌 ln 푡) 푑) ln 2) [퐾 log (1 + (1 + ln 푡) 푑)] < 0 , while 15 푁 퐾 2 푁 퐾 푀 the first term lim [(1 + ln 푡) 푁] ((휌 + 푄 + 푁푄 )) > 0, 10

푑 1 2 Efficiency[Mbit/joule] Energy 휌푑→0 푁 the EE starts increasing and after that starts decreasing due to 5 large cost for every antenna that contains the radio frequency chains and power amplifier. From (21) maximizing EE 0 0 50 100 150 depends on obtaining the optimal antenna selection and Number of Base Station Antennas (N) optimal transmit power allocation. Figure 2: EE versus number of transmit antennas 푁 푆퐸 푆퐸 In case of 휂 푘 = min 휂 푘: from (15) the relation of EE strict decreases with SE, while the EE become maximized Figure 3 presents the trade-off between EE and SE. The 푆퐸 푆퐸 transmit power and an available number of antennas are able when the SE is small 휂 푘 = min 휂 푘 to maximize the trade-off EE-SE by setting multi-objective 퐸퐸 푆퐸 optimization problem. 휕휂 푘( 휂 푘) 푆퐸 | ≤ 0 (22) 휕휂 푘 푆퐸 푆퐸 30 휂 푘= 휂 푘(min)  =30dBm, K=8 k  =30dBm, K=15 From (22) the EE firstly increases with minimum SE based 25 k on available antenna selection and transmits power. 푆퐸 푆퐸 퐸퐸 In another case, when 휂 푘 = 휂 푘(max) , the EE 휂 푘 20 firstly increases with SE and can be a performance to be maximized when the power allocation become allocated to 15 every UE at a fixed number of transmit antennas as follows;

휕휂퐸퐸 ( 휂푆퐸 ) 푘 푘 | ≥ 0 (23) 10 휕휂푆퐸 푘 휂푆퐸 = 휂푆퐸 (푚푎푥)

푘 푘 (Mbit/Joule) EfficiencyEnergy 5

3. NUMERICAL RESULTS 0 0 5 10 15 20 25 Spectral Efficiency (bit/s/Hz) In this section, the numerical results are presented by using MATLAB based on the Monte Carlo simulations to verify the Figure 3: Trade of EE-SE in terms of power allocation and theoretical analysis. distributed a number of users. From Fig. 2, there is a trade-off between EE and the number of antennas 푁 , the use of different circuits power, the The achievements of optimizing values for EE and SE is based hardware cost of circuit power created from noise amplifier, on the number of distributed users with fixed transmit power. DAC and radio frequency chains that impact of 푄퐶 that limit The trade-off between EE and SE increases simultaneously the EE. The maximum value of EE is obtained by distributing with a first corresponding minimum SE to the number of EE a number of users and fixing the transmit power. The EE employed antennas with less transmit power. The η k starts increasing when the number of available antennas is becomes quasi-concave in the region small, while a large number of transmit antennas makes the SE SE [ η k(min), η k(max)] according to (22) and (23). The EE start decreasing due to the large number of RF chains and EE max performance of η k(ρd) increases when ρd ≤ ρd . consumption of circuit power according to 푄푚푎푥 = 휌푑 + Selecting the optimal transmit power ρd = 30 dBm, and

a number of the employed active users K = 8, the EE wireless networks. International Journal of Advanced increases with the SE and gives the value EE = 28 Mbit/J, at Trends in Computer Science and Engineering, vol.9. no. SE = 12 bit/s/Hz. Meanwhile, when the optimal transmit 1, pp.315-321, 2020. power ρd = 30 dBm, at a distributed number of active users 7. Z. Liu, W. Du, and D. Sun, Energy and spectral increases to K = 15, the EE = 23 Mbit/J with SE = 8bit/s/Hz efficiency tradeoff for massive MIMO systems with and become small values due to a large transmit power. After transmit antenna selection. IEEE Transactions on this value, the EE starts to decrease with SE due to the Vehicular Technology, vol. 66, no. 5, pp.4453-4457, complex processing complexity and high operation cost for 2016. radio frequency chains at the employed antenna in a massive 8. T. L. Marzetta, Noncooperative cellular wireless with MIMO system. unlimited numbers of base station antennas. 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