Performance of massive MIMO uplink with zero-forcing receivers under delayed channels

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper, we analyze the performance of the uplink communication of massive multicell multiple-input multiple-output (MIMO) systems under the effects of pilot contamination and delayed channels because of terminal mobility. The base stations (BSS) estimate the channels through the uplink training and then use zero-forcing (ZF) processing to decode the transmit signals from the users. The probability density function (pdf) of the signal-to-interference-plus-noise ratio (SINR) is derived for any finite number of antennas. From this pdf, we derive an achievable ergodic rate with a finite number of BS antennas in closed form. Insights into the impact of the Doppler shift (due to terminal mobility) at the low signal-to-noise ratio (SNR) regimes are exposed. In addition, the effects on the outage probability are investigated. Furthermore, the power scaling law and the asymptotic performance result by infinitely increasing the numbers of antennas and terminals (while their ratio is fixed) are provided. The numerical results demonstrate the performance loss for various Doppler shifts. Among the interesting observations revealed is that massive MIMO is favorable even under channel aging conditions.Peer reviewe

Impact of User Mobility on Optimal Linear Receivers in Cellular Networks

We consider the uplink of non-cooperative multi-cellular systems deploying multiple antenna elements at the base stations (BS), covering both the cases of conventional and very large number of antennas. Given the inevitable pilot contamination and an arbitrary path-loss for each link, we address the impact of time variation of the channel due to the relative movement between users and BS antennas, which limits system's performance even if the number antennas is increased, as shown. In particular, we propose an optimal linear receiver (OLR) maximizing the received signal-to-interference-plus-noise (SINR). Closed-form lower and upper bounds are derived as well as the deterministic equivalent of the OLR is obtained. Numerical results reveal the outperformance of the proposed OLR against known linear receivers, mostly in environments with high interference and certain user mobility, as well as that massive MIMO is preferable even in time-varying channel conditions.Comment: 3 figures, 6 pages, accepted in ICC 201

Towards a Realistic Assessment of Multiple Antenna HCNs: Residual Additive Transceiver Hardware Impairments and Channel Aging

Given the critical dependence of broadcast channels by the accuracy of channel state information at the transmitter (CSIT), we develop a general downlink model with zero-forcing (ZF) precoding, applied in realistic heterogeneous cellular systems with multiple antenna base stations (BSs). Specifically, we take into consideration imperfect CSIT due to pilot contamination, channel aging due to users relative movement, and unavoidable residual additive transceiver hardware impairments (RATHIs). Assuming that the BSs are Poisson distributed, the main contributions focus on the derivations of the upper bound of the coverage probability and the achievable user rate for this general model. We show that both the coverage probability and the user rate are dependent on the imperfect CSIT and RATHIs. More concretely, we quantify the resultant performance loss of the network due to these effects. We depict that the uplink RATHIs have equal impact, but the downlink transmit BS distortion has a greater impact than the receive hardware impairment of the user. Thus, the transmit BS hardware should be of better quality than user's receive hardware. Furthermore, we characterise both the coverage probability and user rate in terms of the time variation of the channel. It is shown that both of them decrease with increasing user mobility, but after a specific value of the normalised Doppler shift, they increase again. Actually, the time variation, following the Jakes autocorrelation function, mirrors this effect on coverage probability and user rate. Finally, we consider space division multiple access (SDMA), single user beamforming (SU-BF), and baseline single-input single-output (SISO) transmission. A comparison among these schemes reveals that the coverage by means of SU-BF outperforms SDMA in terms of coverage.Comment: accepted in IEEE TV

Degrees of Freedom of Uplink-Downlink Multiantenna Cellular Networks

An uplink-downlink two-cell cellular network is studied in which the first base station (BS) with $M_1$ antennas receives independent messages from its $N_1$ serving users, while the second BS with $M_2$ antennas transmits independent messages to its $N_2$ serving users. That is, the first and second cells operate as uplink and downlink, respectively. Each user is assumed to have a single antenna. Under this uplink-downlink setting, the sum degrees of freedom (DoF) is completely characterized as the minimum of $(N_1N_2+\min(M_1,N_1)(N_1-N_2)^++\min(M_2,N_2)(N_2-N_1)^+)/\max(N_1,N_2)$, $M_1+N_2,M_2+N_1$, $\max(M_1,M_2)$, and $\max(N_1,N_2)$, where $a^+$ denotes $\max(0,a)$. The result demonstrates that, for a broad class of network configurations, operating one of the two cells as uplink and the other cell as downlink can strictly improve the sum DoF compared to the conventional uplink or downlink operation, in which both cells operate as either uplink or downlink. The DoF gain from such uplink-downlink operation is further shown to be achievable for heterogeneous cellular networks having hotspots and with delayed channel state information.Comment: 22 pages, 11 figures, in revision for IEEE Transactions on Information Theor

Deterministic equivalent performance analysis of time-varying massive MIMO systems

© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Delayed channel state information at the transmitter (CSIT) due to time variation of the channel, coming from the users' relative movement with regard to the BS antennas, is an inevitable degrading performance factor in practical systems. Despite its importance, little attention has been paid to the literature of multi-cellular multiple-input massive multiple-output (MIMO) system by investigating only the maximal ratio combining (MRC) receiver and the maximum ratio transmission (MRT) precoder. Hence, the contribution of this work is designated by the performance analysis/comparison of/with more sophisticated linear techniques, i.e., a minimum-mean-square-error (MMSE) detector for the uplink and a regularized zero-forcing (RZF) precoder for the downlink are assessed. In particular, we derive the deterministic equivalents of the signal-to-interference-plus-noise ratios (SINRs), which capture the effect of delayed CSIT, and make the use of lengthy Monte Carlo simulations unnecessary. Furthermore, prediction of the current CSIT after applying a Wiener filter allows to evaluate the mitigation capabilities of MMSE and RZF. Numerical results depict that the proposed achievable SINRs (MMSE/RZF) are more efficient than simpler solutions (MRC/MRT) in delayed CSIT conditions, and yield a higher prediction at no special computational cost due to their deterministic nature. Nevertheless, it is shown that massive MIMO are preferable even in time-varying channel conditions.Peer reviewe