LOS Component-Based Equal Gain Combining for Ricean Links in Uplink Massive MIMO

Transcription

1 016 Sixth International Conference on Instrmentation & Measrement Compter Commnication and Control LOS Component-Based Eqal Gain Combining for Ricean Lins in plin Massive MIMO Dian-W Ye College of Information Science and Technology Dalian Maritime niversity Dalian China Ziqi Meng College of Information Science and Technology Dalian Maritime niversity Dalian China Abstract This paper is concerned with a mltiser plin massive MIMO system in Ricean flat fading. To avoid the pilot contamination isse we firstly propose a simple eqal gain combining scheme based only on the line-of-sight (LOS) component for a Ricean lin in the plin scenario with a single cell or mltiple cells. Then we investigate the powerscaling law for the Ricean lin when the transmit power is scaled down by the nmber of antennas at the base station (BS). We show by analytical reslts that when the nmber of BS antennas goes to infinity the Ricean lin can asymptotically achieve the same achievable rate as in the case with a single ser and the achievable rate is also asymptotically eqal to that of the conventional maximal-ratio combining scheme based on both the LOS component and the imperfect scattered component. Finally we provide several simlation examples throgh which we corroborate these analytical reslts. eywords massive-mimo Ricean fading eqal gain combining line-of-sight plin I. INTRODCTION In wireless commnications massive MIMO is an emerging technology that can considerably improve spectral and energy efficiencies of celllar systems by deploying a very large nmber of antennas at each BS and ths has been a promising soltion to meet the reqirements of 5 G[1-4]. Frthermore the benefits of massive MIMO can be reaped by sing a simple linear processing sch as maximm ratio combining (MRC) for the plin and maximm ratio transmission(mrt) for the downlin [1] [5-7]. So far there have appeared a lot theoretical contribtions that provide varios asymptotic performance with the MRC/MRT for massive MIMO systems. In particlar several power scaling laws for plin massive MIMO have been given in order to qantify the potential of transmit energy savings. In Rayleigh fading environments it is shown from [7] that if perfect channel state information (CSI) is available the average (ergodic) achievable plin rate can converge to a constant when the nmber of BS antennas M grows large and the transmit power of each ser is scaled down proportionally to 1/ M. However when only imperfect CSI is available the corresponding transmit power can only be scaled down by a factor of 1/ M. The power scaling analysis in [7] has been extended to Ricean fading channels in [9-10]. It is shown in [9] that with imperfect CSI at the BS the plin rate also converges to a constant vale when M goes to infinity and the transmit power of each ser is scaled down proportionally to 1/ M. Moreover power scaling properties for a mlti-pair relaying system have been also presented in [11]. In order to acqire the needed CSI however we mst carry on channel estimation. The conventional way to perform channel estimation is sing plin pilots. The nmber of different orthogonal pilot seqences depends on its length which is constrained by the coherence time of wireless channels. As a reslt the same or correlated pilot seqences will be resed at different cells. The estimated CSI for the cells with the same or correlated pilot seqence interfere each other which is called pilot contamination and is a fndamental challenge in massive- MIMO systems [1-4]. In Ricean fading environments it is mch easier to estimate only channel information corresponding to the lineof-sight (LOS) component. Therefore the pilot contamination isse wold be completely avoided if we cold ignore the scattered component and perform signal processing only based on the LOS component. Motivated by this reason we have treated the scattered component as interference and investigated a beamforming scheme with eqal gain combining (EGC) and eqal gain transmission (EGT) only based on the LOS component for a single-ser massive MIMO system where the transmitter and the receiver are eqipped with a very large of antennas [1]. Or analytical reslt has shown that if the transmit power is scaled down by the mltiplication of the two nmbers of antennas at the transmitter and the receiver the ergodic achievable rate of the novel EGC/EGT scheme can be asymptotically eqal to that of the conventional MRC/MRT scheme based on the perfect CSI when both of the nmbers of antennas go to infinity with a fixed ratio. Inspired by the reslt in this paper we contine to stdy the linear transmission scheme only based on LOS-component for the plin massive MIMO where each mobile ser is eqipped with one antenna and give several power scaling properties with EGC. II. PLIN SYSTEM MODEL Consider an plin single-cell MIMO system where the BS is eqipped with M antennas and serves sers simltaneosly at the same freqency each ser is with a /16 $ IEEE DOI /IMCCC

2 single antenna. Then M 1 received signal vector at the BS is represented as y p g x z 1 where p is the average transmitted power of each ser g is the M 1 channel vector between the BS and the th - ser x is the signal transmitted by the th - ser and z is the vector of zero-mean additive white Gassian noise (AWGN) with covariance matrix I M. As discssed in [7] and [9] the channel vector g can be given by g h 1 h T M where h h h h h m represents the fast fading coefficient from the transmit antenna of the th - ser to the mth - receive antenna of the BS and models the path loss and shadow fading. In Ricean flat fading h can be frther decomposed into a sm of a LOS vector and a scattered vector as h h h where h is the LOS (deterministic) vector h is the 1 scattered (random) vector and is the Ricean factor that represents the power ratio of LOS and scattered components for the th - ser. Note that 0 corresponds to a Rayleigh fading while corresponds to non-fading channels. Throgh the paper or analysis always focses on a general Ricean lin with 0. The entries in the scattered vector h are independent and identically distribted (i.i.d) circlar complex Gassian random variables with zero mean and nit variance. From [13] the LOS vector h can be expressed as T jdsin j M1dsin h 1 e e e where is the angle of arrival at the BS and d is the antenna spacing normalized by wavelength at the BS. We assme that the angles of arrival for any two sers are different ie. i when i. The LOS component h depends only on the angle of arrival and the spacing between antennas and is very easy to estimate. Ths it is assmed to be available at the BS for EGC detection. III. LOS COMPONENT-BASED EGC DETECTION AND POWER-SCALING LAW Eqation (1) can be rewritten in matrix forms as y p Gxz where x x x x 1 and G g g g 1 g 1 g 1 g g g g g g g g g g g GG where G and G correspond to the LOS and scattered components respectively. Obviosly for detection we can employ well-nown linear detectors sch as MRC ZF and MMSE even nder the constraint that the BS only nows the LOS component of channel matrix G. Now let A denote an M linear detecting matrix that depends only on G. After sing the linear detector A the received vector y becomes v A p Gx z Denote a as the th - colmn of A. Then the th - element of v is written in detail as g i i i1 i v p agx p agx p agx az MRC detection may be preferable to ZF or MMSE detection de to its low implement complexity and decentralized signal processing. To this end we pay or attention to the MRC detection which is really the EGC detection in this wor. For the EGC detector a g. Then the effective otpt signal-to-interference-pls-noise (SINR) for the th - ser is given by p 4 p g g p gi g i1 i Throgh the derivation given in Appendix A the individal ergodic achievable rate denoted as R E log 1 are pper and lower bonded by the following. Proposition 1: R L where log 1 log 1 477

3 p 1 M pm L 1 i i i p i i i1 i i and p M jmi 1 e i ji 1 e i d sin sini 4 Note that in (13) the parameter i is still j i 1 e 1 finite as M grows large. Conseqently lim i 0 M M ths we have the following power-scaling law. Corollary 1: Let E Mp be fixed when M. Then lim lim 1 where M R R R M R E log 1 log 1E From Corollary 1 the plin system with mlti-sers has the same rate limit as the one with a single-ser when the nmber of the antennas at the BS grows withot bond. In other words the very large antenna array deployed at the BS can eliminate intra-cell LOS interference and fast fading (FF) impact. For the plin system with mltiple sers athors in [8] investigated the conventional MRC scheme based on FF and MMSE channel estimation. By MMSE channel estimation the channel matrix G in (5) can be expressed as GGˆ E where Ĝ is the MMSE estimate of G and E is the channel estimation error independent of Ĝ. Frthermore we can write the channel estimation error as E e M 1 m m 1 e e e From [9] and [7] it is nown that e m is a random variable with zero mean and its variance is given by 1 p with denoting the nmber of symbols sed as pilots for the MMSE channel estimation. Ths the ergodic achievable rate with the MRC scheme for the th - ser can be given by Rˆ ˆ log 1 where ˆ E denotes the receive SINR at the BS for the thser - and can be expressed as ˆ 4 p ˆ g p ˆ ˆ 1 gˆ 1 i p i i i1 i As proved in Appendix B we have the following theorem. Theorem 1: Let E Mp be fixed when M. Then lim lim ˆ M R R R M This theorem reveals that for a Ricean lin in the plin scenario its individal ergodic achievable rate nder the LOS component-based EGC scheme will have the same asymptotical rate as that with the FF-based MRC scheme when the nmber of BS antennas goes to infinity. IV. EGC ANALYSIS FOR THE MLTICELL SCENARIO We can extend the mentioned-above analysis for a single cell system to the scenario with mlticell. To this end we need to modify the model in Section II. Assming that there are a total of I interfering single antenna sers from other cells [13] then the M 1 received vector at the BS can be rewritten as where y pgx pgx z T p GG xx z I I xi x 1 x x I and GI g 1 g g I Note that g i i1 I are modeled as in Section II. 478

4 lim lim M R R I M I V. NMERICAL RESLTS In this section we present some nmerical reslts to verify or analytical reslts. For the single-cell scenario we consider a hexagonal cell with a radis of rm 1000 meters and sers distribted randomly and niformly over it. We assme that there is no ser closer to the BS than rh 100 meters. Then the largescale fading coefficient for the th - ser is modeled as [7]: Fig. 1. Average sm rate verss the nmber of BS antennas for maing a comparison between the LOS- and FF-based schemes when several vales of are sed. Fig.. Average sm rate verss the nmber of BS antennas for maing a comparison between the LOS- and FF-based schemes when several vales of ϑ are sed. The received vector y in (3) is sed to detect the signal x transmitted by the th - ser. By comparing (5) and (3) we can view the EGC system of detecting x in mltiple cells as the one in a single cell with I sers. Therefore the ergodic achievable rate for the th - ser in the mlti-cell case denoted as I has the following similar power scaling law. Corollary : Let E Mp be fixed when M. Then v z r r h where the log-normal shadowing z is with standard deviation 8 db the path loss exponent v is eqal to 3.8 and r denotes the random distance between the th - ser and the BS. In this case when 10 ths we mae se of the same set of large-scale fading coefficients 1 as given in [14]. In addition we assme that a half of the lins are Ricean lins while the other half are Rayleigh lins and all of these Ricean lins have the identical Ricean factor denoted as. For simplicity all of these spacings between adjacent antennas at BS are assmed to be 0.5 and the angle of arrival for the th - ser is set to 1 be 1. In the case with E 0 db and 5 db we firstly consider to validate Theorem 1 by comparing the sm rate of the LOS-based EGC scheme with that of the FF-based MRC scheme. We let all for simplicity. For the nmber of sers 3010 Figre 1 plots the two sm rates R 1 and ˆ R 1 as M increases from 0 to 500. For comparison three crves by sing the corresponding limit reslts R are also inclded in 1 Figre 1. From Figre 1 it can be observed that the two LOSand FF-based schemes perform similarly and their sm rates tend to the corresponding limit reslts for the three different vales of. However as increases inter-ser interference becomes stronger and stronger and ths the speed of convergence becomes slower and slower even when M is very large. When E 0 db and 10 then we consider to compare the sm rate of the LOS-based EGC scheme with that of the FF-based MRC scheme for different Ricean factors. For the Ricean factor db Figre plots R 1 and ˆ R 1 as M increases from 0 to 500. From Figre it can be fond that the sm rate 479

5 with the LOS-based EGC scheme is closer to that with the FF-based MRC scheme as or M increases. In particlar the two LOS and FF-based schemes perform similarly when 5 db. Fig. 3. Average sm rate verss the nmber of BS antennas for maing a comparison among EGC and ZF linear detectors when several vales of E are sed. performance tends to the ZF with increasing M or decreasing E. In particlar when E 10 db the EGC and the ZF perform similarly. Moreover for comparison Figre 3 also plots the EGC lower bond based on Proposition 1. It can be seen that the lower bond for the sm rate is qite tight for any M when E 0. Finally we consider the mlticell scenario where each cell serves 10 sers. The large-scale fading coefficients are set according to the realization of large-scale fading chosen in [14] and the intercell interference factor is fixed to be 5 in or simlation. We assme that all interfering lins from each interfering cell are Rayleigh. In order to corroborate Corollary Figre 4 plots the average sm rate with the LOS-based EGC scheme when L Note that I 0 when L 1 I 0 when L 3 and I 60 when L 7. It can be seen that the average sm rate increases as M increases from 0 to 500. The average sm rate with L 7 is obviosly less than the one with L 1 and the average sm rate with L 3 is very close to the one with L 1. VI. CONCLSIONS In this article we have investigated the LOS component based EGC scheme for plin massive-mimo systems over Ricean fading channels derived the individal achievable rates for the Ricean lins and presented several power scaling properties for them. Or discssion can be easily extended to the downlin scenario and the corresponding reslts are similar. By comparison with pre Rayleigh fading environments massive MIMO systems are more sitable to be deployed in Ricean fading environments especially when the LOS component is strong. APPENDIX A. The proof of Proposition 1 Proof: By sing Jensen s ineqality we obtain the following lower bond on the ergodic achievable rate of the th - ser R 1 log 1 E 1 Fig. 4. Average sm rate verss the nmber of BS antennas for different nmbers of cells. For the ZF detector the detecting matrix becomes A GG G 1. After that we consider to compare among the EGC and ZF linear detection schemes. When 10 and 5 db Figre 3 plots six crves abot the average sm rate for E db. As expected simlation reslts show that the ZF scheme otperforms the EGC scheme in the terms of the sm rate. However the EGC rate L Now define L p 1 E 1. Then 4 p g E g p E i1 i gi g Frthermore (11) is easily derived by sing the following expressions g M 480

6 and when i i i g i E E g i M i i E M i i ihh i 1 e 1 e i i i jmi i i ji On the other hand it is obvios that p g Frthermore (1) is easily derived by sing the mentioned-above expressions. B. The proof of Theorem 1 From Corollary 1 it follows that [8] Q. Zhang Z. L S. Jin. -. Wong H. Zh M. Mattaio Power scaling of massive MIMO systems with arbitrary -ran channel means and imperfect CSI in proc. IEEE Global Telecommn. Conf. (GLOBECOM) Dec.013 pp [9] Q. Zhang S. Jin. -. Wong H. Zh M. Mattaio Power scaling of plin massive MIMO systems with arbitrary -ran channel means IEEE J. Sel. Topics Signal Process. vol.6 no.5 pp Oct [10] Q. Zhang S. Jin Y. Hang and H. Zh plin Rate Analysis of Mlticell Massive MIMO Systems in Ricean Fading in Proc. IEEE Global Commnications Conf. (GLOBECOM) Astin TX S Dec. 014 pp [11] H. A. Sraweera H. Q. Ngo T. Q. Dong C. Yen and E. G. Larsson Mlti-Pair Amplify-and-Forward Relaying with Very Large Antenna Arrays in in Proc. IEEE Int. Conf. on Commn.(ICC) Bdapest Hngary Jne 013. [1] D.-W. Ye Y. Zhang and Y.-N. Jia Beamforming based on speclar component for massive MIMO systems in Ricean fading IEEE Wireless Commnications Letters vol.4 no. pp Apr [13] G. Taricco and E. Riegler On the ergodic capacity of correlated Ricean fading MIMO channels with interference IEEE Trans. Inf. Theory vol. 57 no. 7 pp Jly 011. [14] H. Q. Ngo M. Matthaio and E. G. Larsson Performance Analysis of Large Scale M-MIMO with Optimal Linear Receivers in Proc. Swedish Commnication Technologies Worshop (Swe-CTW) LndSweden Oct. 01 pp lim M R R On the other hand we have from Corollary 6 of [9] lim ˆ M R R Therefore we obtain the desired reslt. REFERENCES [1] T. L. Marzetta Noncooperative celllar wireless with nlimited nmbers of base station antennas IEEE Trans. Wireless Commn. vol. 9no. 11 pp Nov [] F. Rse D. Persson B.. La E. G. Larsson T. L. Marzetta O. Edfors and F. Tfvesson Scaling p MIMO: Opportnities and challenges with very large arrays IEEE Signal Process. Mag. vol. 30 no. 1 pp Jan [3] E. G. Larsson F. Tfvesson O. Edfors and T. L. Marzetta Massive MIMO for next generation wireless systems IEEE Commn. Mag. vol. 5 no. pp Feb [4] L. L G. Y. Li A. L. Swindlehrst A. Ashihmin and R. Zhang An overview of massive MIMO: benefits and challenges IEEE J. Sel. Topics Signal Process. vol. 6 no.5 pp Oct [5] H. Yang and T. L. Marzetta Performance of conjgate and zeroforcing beamforming in large-scale antenna systems IEEE J. Sel. Areas Commn. vol. 31 no. pp Feb [6] X. Gao O. Edfors F. Rse and F. Tfvesson Linear Pre-Coding Performance in Measred Very-Large MIMO Channels in Proc. IEEE Vehi. Tech. Conf. (VTC) San Francisco CA S Sept. 011 pp [7] H. Q. Ngo E. G. Larsson and T. L. Marzetta Energy and spectral efficiency of very large mltiser MIMO systems IEEE Trans. Commn. vol. 61 no. 4 pp Apr