Performance Analysis and Comparison of ZF and MRT Based Downlink Massive MIMO Systems

Transcription

1 Performance Analysis an Comparison of ZF an MRT Base Downlink Massive MIMO Systems Tebe Parfait, Yujun uang, 1,2 ponyo Jerry 1 Mobilelink Lab Univ of Electronic Sci an Tech of China, UESTC Chengu, China 2 Department of Electrical Engineering wame Nkrumah Univ of Sci an Tech, NUST umasi, Ghana pariteb@yahoo.fr, kyj@uestc.eu.cn, jjkponyo.soe@knust.eu.gh, Abstract In this paper the performances of zero-forcing (ZF) an maximum ratio transmission (MRT) are analyze an compare in a ownlink massive multiple-input multipleoutput system. The system employs a large number of base station antennas serving multiple user terminals within the same cell. The achievable sum rate an the require ownlink transmit power using each of the precoing schemes are erive, analyze an compare uner the same conitions an assumptions. Simulation results are foun to coincie with the theoretical results, an show that ZF performs better than MRT uner the same conitions. eywors-massive MIMO, zero-forcing(zf), maximum ratio transmission(mrt), achievable sum rate, ownlink transmit power. I. INTRODUCTION With toays avances in mobile communication systems, the nee for ata services has never been greater. The banwith of wireless communication systems is often limite by the cost of the raio spectrum require. Any increase in ata rate, which can be realize without increasing the banwith, but with a reuction in power consumption, makes the system more spectrally an power efficient an less costly [1]. In orer to meet the nee, multiple-input multiple-output (MIMO) communication systems have been a hot topic of research over the past several years, ue to its ability to greatly increase spectral an energy efficiencies[2]. With the avancement of technology comes an increase in eman for spectral capacity, an massive MIMO technique has been propose to improve the performance of MIMO. Massive MIMO is essentially a multiuser MIMO technique with lots of base station antennas in which a large number of antennas are serve simultaneously [2]. Massive MIMO reaps all the benefits of conventional MIMO in a much greater scale in terms of spectral efficiency, energy efficiency, reliability, an interference minimization [3]. In aition to these benefits, it also takes avantage of the large number of antennas to simplify multiuser processing, an makes thermal noise an fast faing vanish [3]. The huge potential of massive MIMO has attracte the interest of many researchers with much focus on spectral efficiency an power efficiency in cellular communication systems [2]-[4]-[5]. Linear precoing/beamforming schemes play an important role in massive MIMO signal processing. In [6], the authors analyze the performance of the ownlink massive MIMO in terms of spectral efficiency, energy efficiency an link reliability using ZF precoing. The authors in [7] compare the matrix an vector normalization for ownlink ZF an MRT precoing an analyze the ergoic performance of such precoing in a cell-bounary users scenario. In [8], the authors compare the eigen beamforming (BF) an regularize zero-forcing (RZF) performance in terms of achievable ata rate in a multi-cell ownlink scenario. The author in [9] analyze the spectral efficiency of a single-cell ownlink massive MIMO system with ZF, MRT an MMSE (minimum mean-square error). Although the above works provie goo results about the performances of the linear precoing schemes, they i not provie the comparison of ZF an MRT performances in terms of achievable ata rate an transmit power at the same time, uner the same conitions an in a single-cell ownlink scenario. The author in [9], who analyze the performance of such precoing schemes in terms of spectral efficiency in a single-cell ownlink scenario, fixe the same value of signal-to-interference-to-noise ratio for both precoers; which shoul not be one for a goo analysis. This is because accoring to equation (3) the signal-to-interferenceto-noise ratio is a function of the transmit beamforming vector, an ZF an MRT have ifferent beamforming vectors accoring to equations (4) an (6). This paper analyzes an compares the performance; in terms of achievable ata rate an total transmit power, of ZF an MRT precoing schemes in a single-cell ownlink massive MIMO system, uner the same assumptions. A fixe number of mobile users are assume to be uniformly istribute in the cell with equal power allocation. After formulating the system moel, the achievable ata rate is erive for each of the linear precoing schemes uner the same assumptions. The total ownlink transmit power is also erive for each of them. Simulations for both ata rate an transmit power are one for both schemes. The various /14/$ IEEE 383 ICUFN 2014

2 Figure 1. A single-cell ownlink massive MIMO system results are analyze in orer to compare the performance of the techniques in the given system. The remaining parts of this paper are organize as follows. Section II looks at the system moel an ZF an MRT transmit beamforming. The achievable ata rate with each of the precoing schemes is presente in section III. The total ownlink transmit power for each scheme is erive in section IV. Section V provies numerical results an analysis. Conclusion an future work are ealt with in VI. II. SYSTEM MODEL A. Channel Moel As shown in Figure 1, the system is a single-cell ownlink where one base station (BS) equippe with M antennas serves single-antenna mobile users with the same timefrequency resource. The channel is a Rayleigh faing MIMO channel with the assumption of perfect channel state information. Let h k enote the channel vector between the BS an the k th user. The system channel vector between the BS an all the users is h with H as channel matrix. The elements of H are inepenent an ientically istribute (ii) complex Gaussian variables with zero mean an unit variance. The linear precoing or beamforming vector of kth user is enote by w k, an the system beamforming matrix is W. The receiver vector is given by: y = P Hx + n = P HWS + n (1) Where P is the total ownlink transmit power, x is the transmitter vector, S is the receiver signal matrix, an n is the aitive Gaussian white noise (AGWN). H is a M matrix, an W is an M matrix. The signal receive by the k th user after using the linear precoing/ beamforming scheme is given by y k = P h k w k s k + P k h k w i s i + n (2) i=1 where P h k w k s k is the esire signal, k P i=1 h kw i s i is the interference, an n is the noise. The receive signal-to-interference-plus-noise ratio of the kth user can then be expresse as [10] P h k w k 2 SINR = k P i=1 h (3) kw i 2 +1 which is a function of the transmit beamforming vector. B. Transmit beamforming Two conventional linear precoing/beamforming schemes are use in this work: the Zero-Forcing beamformer (ZF) an the Maximum Ratio Transmission (MRT). The two beamformers have ifferent SINR accoring to equation (3). C. Zero-forcing (ZF) precoing ZF is one technique of linear precoing in which the interuser interference can be cancelle out at each user [9]. The ZF precoing employe by the BS is written as W = H H (HH H ) 1 (4) For large values of M an, the relate signal-tointerference-plus-noise ratio of the kth user is given as [10] SINR zf = P ( M ) (5) D. Maximum ratio transmission (MRT) precoing MRT is one technique of linear precoing which maximizes the signal gain at the intene user [9]. The MRT precoing employe by the BS is written as W = H H (6) For large values of M an, the relate signal-tointerference-plus-noise ratio of the kth user is given as [10] SINR mrt P M = (7) (P + 1) From equations (5) an (7), it is obvious that for the same available ownlink transmit power an same value of M an in ZF an MRT cases, the two schemes have ifferent signal-to-interference-to-noise ratio. Therefore, the same value shoul not be assigne to it (SINR) for both precoers for a goo performance comparison. III. ACHIEVABLE DATA RATE One of the methos to quantify the system performance is the achievable ata rate. The achievable ata rate follows the Shannon theorem. This theorem gives the maximum rate at which the transmitter can transmit over the channel. In this section, we escribe the achievable ata rate with ZF an MRT accoring to the system uner consieration, with the assumption that the total ownlink power is fixe an equally ivie among all the users. From Shannon theorem, the channel capacity over Aitive White Gaussian Noise channel is erive by [10] as R = log 2 (1 + SNR)(bits/s/Hz) (8) 384

3 Where SNR is the signal-to-noise ratio. Channel state information (CSI) is an important issue in multiuser communication systems. Typically, the transmitter transmits multiple ata streams to each user simultaneously an selectively with CSI [11]. All the receivers sen the channel estimation feeback to the transmitter on the reverse link, so the transmitter obtains CSI. Hence, the transmitter communicates with all the receivers with perfect CSI [9]. An as shown in equation (2), the signal receive by the each user consists of aitive noise an interference between the users themselves. Then, the achievable ata rate per user in a single-cell ownlink massive MIMO system, with perfect channel state information is given as R k = log 2 (1 + SINR k ) (9) an for number of users, the achievable sum rate is given as R sum = log 2 (1 + SINR k ) (10) A. The Achievable Data Rate with ZF From (10), the achievable ata rate with ZF can be euce as Rsum zf = log 2 (1 + SINR zf k ) (11) Substituting (5) into (11), gives Rsum zf = log 2 [1 + P ( M )] (12) B. The Achievable Data Rate with MRT Similarly, the achievable ata rate with MRT can be euce from (10) as Rsum mrt = log 2 (1 + SINRk mrt ) (13) Substituting (7) into (13) gives Rsum mrt = log 2 [1 + P M (P + 1) ] (14) Equations (12) an (14) show that for the same available ownlink transmit power an a fixe number of mobile users; as the number of transmit antennas increases with M, ZF achieves higher ata rate than MRT. IV. REQUIRED DOWNLIN TRANSMIT POWER The energy efficiency of a communication system epens on the require transmit power. The system is more energy efficient when less transmit power is require to achieve the targete information rate on conition that the quality of service is satisfie. In this section, we erive the total ownlink transmit power require by ZF an MRT to achieve the same ata sum rate accoring to the system uner consieration. For the erivations we enote α = M (15) An then α 1= M (16) A. Total Downlink Transmit Power with ZF Substituting (16) into (12) an consiering the fact that the targete ata rate is the same for both precoing schemes, we can write R sum = log 2 [1 + P zf (α 1)] ln[1 + P zf Rsum (α 1)] = ln2( ) Taking exponential of both sies we have P zf = e k 1 α 1 Substituting (16) into (17) gives P zf (17) = [ e ln2r sum k 1 M ] (18) which is the total ownlink transmit power require with ZF. B. Total Downlink Transmit Power with MRT With the same analogy as for ZF, we substitute (15) into (14) an we can write R sum = log 2 (1 + P mrt α +1 ) (19) Taking exponential of both sies we have = [e α [e Substituting (15) into (20) gives = = [e M [e [e M [e (20) (21) (22) Since the total ownlink transmit power is assume to be equally ivie among all the users, we also assume that the total achievable ata rate is equally share among the users; an three ifferent cases are stuie for our analysis, consiering Equations (18) an (22). Case 1: the total power is require to achieve 1 bit per secon per Hertz for each user. That is R sum = an for R sum =,e = e ln2 =2 M [e = M (23) Base on this analysis an from equations (18), (22) an (23), we can conclue that P zf = P mrt. For the total achievable ata rate equally share among the users, as the 385

4 Figure 2. Performance comparison of achievable sum rate versus the number of transmit antennas, with =10 users an the total available transmit power P = 15B Figure 3. Performance comparison of total ownlink transmit power require to achieve more than 1bit per secon per Hertz for each user, with the number of users =10 an the targete sum rate R sum = 15bits/s/Hz number of transmit antennas increases with M, the same total ownlink transmit power is require with ZF an MRT to achieve 1 bit per secon per Hertz for each user. Similarly: Case 2: the total power is require to achieve more than 1 bit per secon per Hertz for each user. That is R sum > which gives >P zf Base on this analysis, we conclue that, for the total achievable ata rate equally share among the users, as the number of transmit antennas increases with M>>, MRT requires more power than ZF to achieve more than 1 bit per secon per Hertz for each user. It means that ZF is more power efficient to achieve higher ata rate. Case 3: the total power is require to achieve less than 1 bit per secon per Hertz for each user.that is: R sum < which gives <P zf Base on this analysis, we conclue that, for the total achievable ata rate equally share among the users, as the number of transmit antennas increases with M>>, MRT requires less power than ZF to achieve less than 1 bit per secon per Hertz for each user. It means that MRT is more power efficient to achieve lower ata rate. V. NUMERICAL RESULTS AND ANALYSIS In orer to valiate the theoretical results in sections III an IV, numerical results are provie by simulations in this section. With available BS ownlink transmit power equal to 15B after all losses, an the number of mobile users fixe to 10, Figure 2 epicts the achievable sum rate versus the number of transmit antennas for both precoing schemes. It shows that as the number of BS antennas increases, the achievable sum rate for each of the schemes also increases. Furthermore, a comparison of the two performances shows Figure 4. Performance comparison of total ownlink transmit power require to achieve less than 1bit per secon per Hertz for each user, with the number of users =10 an the targete sum rate R sum = 5bits/s/Hz Figure 5. Performance comparison of total ownlink transmit power require to achieve 1bit per secon per Hertz for each user, with the number of users =10 an the targete sum rate R sum = 10bits/s/Hz 386

5 that for the same available ownlink transmit power ranging from 0 B to 20 B, ZF achieves higher ata rate than MRT. The achievable rate is higher than the number of mobile users; which means that more than 1 bit per secon per Hertz is achieve for each user. This also valiates the theoretical results obtaine in section IV. Therefore, we conclue that ZF is more power efficient than MRT to achieve high ata rate. Figure 6. Power efficiency comparison of ZF an MRT, with =10 users an M=200 base station antennas that ZF achieves much higher sum rate than MRT. The average sum rate achieve with ZF can be estimate to be more than a ouble of that achieve with MRT for 20 to 200 base station antennas. This valiates the theoretical results obtaine in section III. Therefore, we conclue that ZF achieves higher ata rate than MRT in a single-cell ownlink massive MIMO system where the available BS transmit power is assume to be equally ivie among all the users. Figures 3, 4 an 5 show the require ownlink transmit power versus the number of transmit antennas for both precoing schemes. In figure 3 the power is require to achieve more than 1 bit per secon per Hertz for each user an the targete sum rate is 15 bits/s/hz an is assume to be equally share among 10 mobile users. In figure 4 the power is require to achieve less than 1 bit per secon per Hertz for each user an the targete sum rate is 5 bits/s/hz an is assume to be equally share among 10 mobile users. In figure 5 the power is require to achieve 1 bit per secon per Hertz for each user an the targete sum rate is 10 bits/s/hz an is assume to be equally share among 10 mobile users. The results in the three figures show that as the number of BS antennas increases, the require ownlink transmit power for each of the schemes ecreases. Furthermore, a comparison of the performances of both schemes for 20 to 200 BS antennas shows that ZF requires less power than MRT in figure 3, MRT requires less power than ZF in figure 4, an both schemes require the same power in figure 5. This also valiates the theoretical results obtaine in section IV. Therefore, we conclue that ZF requires less power than MRT to achieve higher ata rate, MRT requires less power than ZF to achieve lower ata rate, an both require the same power to achieve 1 bit per secon per Hertz for each user in a single-cell ownlink massive MIMO system where the sum rate is assume to be equally share among all the users. Figure 6 shows the achievable sum rate versus the require ownlink transmit power for both schemes. The results show VI. CONCLUSION This paper provies the performance analysis an comparison of ZF an MRT precoing schemes in a singlecell ownlink massive MIMO system. The key performance parameters stuie are the achievable sum rate an the total ownlink transmit powers which are theoretically erive for both schemes uner the same assumptions an accoring to the system. Simulation an theoretical results show that ZF achieves higher ata rates than MRT. ZF is more power efficient than MRT to achieve high ata rate. Therefore, we conclue that ZF is the best choice in a single-cell ownlink massive MIMO system. In future work we will consier multi-cells an both own an up links for more performance analysis. ACNOWLEDGMENT This work was supporte by the National Natural Science Founation of China (NSFC) (No ) REFERENCES [1] John Fitzpatrick, Simulation of a Multiple Input Multiple Output Wireless System, A thesis of Dublin City University, April 2004 [2] Erik G. Larsson, Frerik Tufvesson, Ove Efors an Thomas L. Marzetta, Massive MIMO for next Generation Wireless Systems, IEEE Communication Magazine, Vol.52, no. 2, 2014, pp [3] Robert W. Heath Jr., What is the Role of MIMO in Future Cellular Networks:Massive? Coorinate?mmWave?, A lecture Presentation on massive MIMO, The University of Texas at Austin, 2013 [4] Hien Quoc Ngo, Erik G. Larsson, an Thomas L. Marzetta, Energy an Spectral Efficiency of Very Large Multiuser MIMO Systems, IEEE Transactions on Communications, Vol.61, no.4, 2013, pp [5] Jinkyu ang, Joonhyuk ang, Namjeong Lee, Byung Moo Lee an Jongho Bang, Minimizing Transmit Power for Cooperative Multicell System with Massive MIMO, The 10th Annual IEEE Cosumer Communications an Networking Conference (CCNC), 2013, pp [6] Long Zhao, an Zheng, Hang Long Hui Zhao an Wenbo Wang, Performance Analysis for Downlink Massive MIMO System with ZF precoing, Transactions on Emerging Telecommunications Technologies, Vol.8, no.3, 2014, pp [7] Yeon-Geun Lim, Chan-Byoung Chae, an Giuseppe Caire, Performance Analysis of Massive MIMO for Cell-Bounary Users, IEEE Communication Magazine, In Press, Available at: http//arxiv: v1 [cs.it], 30 September 2013 [8] Jakob Hoyis, Stephan Ten Brink, an Merouane Debbah, Comparison of Linear Precoing Schemes for Downlink Massive MIMO, IEEE ICC - Communications Theory, 2012, pp [9] Eakkamol Pakeejit, Linear Precoing Performance of Massive MU-MIMO Downlink System, A thesis of Linkopeng University, May 2013 [10] Sooyong Choi, Special Topics: Massive MIMO, A lecture presentation on Massive MIMO, Yonsei University, June

6 [11] T. Marzetta an B. Hochwal, Fast Transfer of Channel State Information in Wireless Systems, IEEE Transactions on Signal Processing, Vol. 54, no. 4, 2006, pp