Research On The Performance Of Multi-cell Multi-user Uplink MIMO TDD System

Multiple-input multiple-output(MIMO)technology which provides multiplexing gain,diversity gain and array gain can greatly improve the spectral efficiency and link reliability of communication system.It is well known that the state of the channel and the acquisition of channel state information(CSI)at base station(BS)are of essential importance to optimize the celluar system performance,as well as the structures of transmitter and receiver.If the MIMO technology is directly applied to the traditional cellular system,there will be serious inter-cell interference.If the number of BS antennas goes to infinite(massive MIMO),the channels of different users become gradually orthogonal,and the effects of Gaussian noise and uncorrelated inter-cell interference can be ignored.In the multi-cell scenario,non-orthogonal training sequences must be used due to the limitation of orthogonal pilot resources which are limited by the coherence time of the channel.This non-orthogonal nature causes pilot contamination when the channel estimate at target cell becomes polluted by users from other cells.So far,pilot contamination becomes the biggest bottleneck of the massive MIMO system performances.In this dissertation,the performances of multi-cell multi-user Time Division Duplexing(TDD)MIMO system are mainly studied,and the main contents are as follows:Firstly,we derive the symbol error rate(SER)expressions for a system with minimum mean square error(MMSE)receiver under correlated(BS-side correlation)Rayleigh fading channel in a system model similar to Wyner.Employing an equivalent channel model with linear minimum mean square error(LMMSE)channel estimation,and taking interference from adjacent cells and channel estimation errors as uncorrelated additive noise,we get the approximated signal to interference and noise ratio(SINR).According to the approximated SINR and the equivalent channel model of LMMSE channel estimation,we derive closed-form expressions for SER of uncoded M-ary phase shift keying(M-PSK).The closed-form expressions directly show that the pilot contamination greatly reduces the system reliability,and the bigger the number of users and the strength of inter-cell interference are,the bigger SER is.When the eigenvalues of the matrix representing the correlation between BS antennas are identical or distinct,the complicated functions of SER can be simplified.We also prove that in the high signal to noise ratio(SNR)region,the SER performance is independent of the correlation between BS antennas.And due to the existence of pilot contamination,the SER goes to a constant which is determined by the number of users in each cell and the interference strength between the cells.For a general system model,when the channel is i.i.d.and the large-scale fading of the equivalent channel of other users in the target cell are distinct,we can also get the simplified expression for SER.Simulation results verify our analysis.Secondly,we study the performance of the diversity-rate tradeoff for a system with MMSE receiver under i.i.d.Rayleigh fading channel in a system model same to the one of chapter 2.The diversity-rate performance in high SNR and finite SNR are discussed respectively.In high SNR,due to the effect of pilot contamination and inter-cell interference,the users cannot get any diversity no matter how small the target rate is.However,in finite SNR,the users can get some diversity which depends on the target rate,the numbers of users and BS antennas,and the ratio of pilot sequence power to user data power.Simulation results show that the diversity first rises up and then moves down as the SNR increases,and finally tends to 0.And the SNR corresponding to the maximum diversity is lowered as the number of BS antennas increases.Besides,the increase of pilot sequence power causes the SNR corresponding to the maximum diversity decrease while the maximum value of the diversity almost remains unchanged.Thirdly,we study the performances of the sum-rate of the massive MIMO in correlated Rayleigh channel taking both pilot contamination and CSI delay into consideration.We first provide the closed-form expression for the achievable rate assuming perfect CSI and study its asymptotical performance when the number of BS antennas goes without bound.The results show that when the number of BS antennas goes without bound,the sum-rate equals the one of single-cell.Considering the correlation between the actual channel and the estimated one,we derive an equivalent channel model with LMMSE channel estimation and one-tap prediction.Employing this equivalent channel model,we then obtain the lower bound of the sum-rate,and study its asymptotical performance when the number of BS antennas goes without bound.Based on the expression,we find that if we schedule the k-th user of all cells who have the same prediction coefficient,the sum-rate is the same as the one with no CSI delay when the number of BS antennas goes without bound at a much greater rate than the number of users.Simulation results show that,the closed-form expressions are very accurate even for not very large number of antennas.And we also find that large antenna array can not only potentially reduce uplink transmit power,but also compensate for the decay due to user mobility.Finally,we study the performances of spectral efficiency in correlated Ricean fading channel.We de-duce the respective closed-form expressions for two methods.The first method is maximum ratio combining(MRC)based on pilot-assisted LMMSE estimation,the other one is MRC based on line-of-sight(LOS)part.Simulation results show the two expressions are precise even when the number of the antennas is not so large.Due to the existence of pilot contamination,the uplink achievable rate of pilot-assisted LMMSE estimation method approaches to a finite one when the BS antenna number goes without bound.We give the closed-form expression of the asymptotic rate which shows that the rate will increase with the increase of Ricean factor.However,the infinite uplink achievable rate of LOS method goes linearly with the number of BS antennas,which means that as the number of BS antennas increase,the gap between the two methods will become smaller and smaller,and finally the rate of LOS method will exceed the one of pilot-assisted LMMSE esti-mation method.Besides,the bigger the Ricean factor,the smaller the turning point of antenna number.The expression of the achievable rate of LOS method also show that for Ricean channel,the correlation between the BS antennas may not only decrease the rate,but also increase the rate,which depends on the locations of the users.So if the locations of the users make antenna correlation increase the rate,with the increase of Ricean factor the rate of pilot-assisted LMMSE estimation method will become larger due to antenna corre-lation since the effect of LOS part becomes more and more strong.We also discuss the power scaling law of the two methods.When the base station antenna number goes without bound,the asymptotical expressions of the two methods are the same and independent with the antenna correlation.In a word,for Ricean channel,the uplink achievable rate of LOS method will exceed the one of pilot-assisted LMMSE estimation method with the increase of antenna number,and the two methods have the same power scaling law.Based on these,we conclude that for massive MIMO it has little meaning for pilot-assisted LMMSE estimation.