Performance of downlink massive MIMO in Ricean fading channels with ZF precoder

We investigate the achievable sum rate and energy efficiency of zero-forcing precoded downlink massive multiple-input multiple-output systems in Ricean fading channels. A simple and accurate approximation of the average sum rate is presented, which is valid for a system with arbitrary rank channel means. Based on this expression, the optimal power allocation strategy maximizing the average sum rate is derived. Moreover, considering a general power consumption model, the energy efficiency of the system with rank-1 channel means is characterized. Specifically, the impact of key system parameters, such as the number of users N, the number of BS antennas M, Ricean factor K and the signal-to-noise ratio (SNR) ρ are studied, and closed-form expressions for the optimal ρ and M maximizing the energy efficiency are derived. Our findings show that the optimal power allocation scheme follows the water filling principle, and it can substantially enhance the average sum rate in the presence of strong line-of-sight effect in the low SNR regime. In addition, we demonstrate that the Ricean factor K has significant impact on the optimal values of M, N and ρ.

Achievable sum-rate of multiuser massive MIMO downlink in ricean fading channels

We investigate the achievable ergodic sum-rate of multi-user multiple-input multiple-output systems in Ricean fading channels. We first derive a lower bound on the average signal-to-leakage-and-noise ratio by utilizing the Mullen's inequality, which is then used to analyze the effect of channel mean information on the achievable sum-rate. With these results, a novel statistical-eigenmode space-division multipleaccess downlink transmission scheme is proposed. For this scheme, we derive an exact closed-form expression for the achievable ergodic sum-rate. Our results show that the achievable ergodic sum-rate converges to a saturation value in the high signal-to-noise ratio (SNR) region and reaches to a lower limit value in the lower Ricean K-factor range. In addition, we present tractable upper and lower bounds, which are shown to be tight for any SNR and Ricean K-factor value. Finally, the theoretical analysis is validated via numerical simulations.

Uplink Performance of Conventional and Massive MIMO Cellular Systems with Delayed CSIT

This work studies the uplink of a cellular network with zero-forcing (ZF) receivers under imperfect channel state information at the base station. More specifically, apart from the pilot contamination, we investigate the effect of time variation of the channel due to the relative users' movement with regard to the base station. Our contributions include analytical expressions for the sum-rate with finite number of BS antennas, and also the asymptotic limits with infinite power and number of BS antennas, respectively. The numerical results provide interesting insights on how the user mobility degrades the system performance which extends previous results in the literature.

Energy efficiency optimization in hardware-constrained large-scale MIMO systems

Large-scale multiple-input multiple-output (MIMO) communication systems can bring substantial improvement in spectral efficiency and/or energy efficiency, due to the excessive degrees-of-freedom and huge array gain. However, large-scale MIMO is expected to deploy lower-cost radio frequency (RF) components, which are particularly prone to hardware impairments. Unfortunately, compensation schemes are not able to remove the impact of hardware impairments completely, such that a certain amount of residual impairments always exists. In this paper, we investigate the impact of residual transmit RF impairments (RTRI) on the spectral and energy efficiency of training-based point-to-point large-scale MIMO systems, and seek to determine the optimal training length and number of antennas which maximize the energy efficiency. We derive deterministic equivalents of the signal-to-noise-and-interference ratio (SINR) with zero-forcing (ZF) receivers, as well as the corresponding spectral and energy efficiency, which are shown to be accurate even for small number of antennas. Through an iterative sequential optimization, we find that the optimal training length of systems with RTRI can be smaller compared to ideal hardware systems in the moderate SNR regime, while larger in the high SNR regime. Moreover, it is observed that RTRI can significantly decrease the optimal number of transmit and receive antennas.

Energy efficiency analysis of rank-1 Ricean fading MIMO channels

This paper studies the energy efficiency (EE) of a point-to-point rank-1 Ricean fading multiple-input-multiple-output (MIMO) channel. In particular, a tight lower bound and an asymptotic approximation for the EE of the considered MIMO system are presented, under the assumption that the channel is unknown at the transmitter and perfectly known at the receiver. Moreover, the effects of different system parameters, namely, transmit power, spectral efficiency (SE), and number of transmit and receive antennas, on the EE are analytically investigated. An important observation is that, in the high signal-to-noise ratio regime and with the other system parameters fixed, the optimal transmit power that maximizes the EE increases as the Ricean-K factor increases. On the contrary, the optimal SE and the optimal number of transmit antennas decrease as K increases.

Massive MIMO in sparse channels

Massive multi-user multiple-input multiple-output (MU-MIMO) systems are cellular networks where the base stations (BSs) are equipped with hundreds of antennas, N, and communicate with tens of mobile stations (MSs), K, such that, N ≫ K ≫ 1. Contrary to most prior works, in this paper, we consider the uplink of a single-cell massive MIMO system operating in sparse channels with limited scattering. This case is of particular importance in most propagation scenarios, where the prevalent Rayleigh fading assumption becomes idealistic. We derive analytical approximations for the achievable rates of maximum-ratio combining (MRC) and zero-forcing (ZF) receivers. Furthermore, we study the asymptotic behavior of the achievable rates for both MRC and ZF receivers, when N and K go to infinity under the condition that N/K → c ≥ 1. Our results indicate that the achievable rate of MRC receivers reaches an asymptotic saturation limit, whereas the achievable rate of ZF receivers grows logarithmically with the number of MSs.

Multipair massive MIMO full-duplex relaying with MRC/MRT processing

We consider a multipair relay channel, where multiple sources communicate with multiple destinations with the help of a full-duplex (FD) relay station (RS). All sources and destinations have a single antenna, while the RS is equipped with massive arrays. We assume that the RS estimates the channels by using training sequences transmitted from sources and destinations. Then, it uses maximum-ratio combining/maximum-ratio transmission (MRC/MRT) to process the signals. To significantly reduce the loop interference (LI) effect, we propose two massive MIMO processing techniques: i) using a massive receive antenna array; or ii) using a massive transmit antenna array together with very low transmit power at the RS. We derive an exact achievable rate in closed-form and evaluate the system spectral efficiency. We show that, by doubling the number of antennas at the RS, the transmit power of each source and of the RS can be reduced by 1.5 dB if the pilot power is equal to the signal power and by 3 dB if the pilot power is kept fixed, while maintaining a given quality-of-service. Furthermore, we compare FD and half-duplex (HD) modes and show that FD improves significantly the performance when the LI level is low.

Circuit-aware design of energy-efficient massive MIMO systems

Densification is a key to greater throughput in cellular networks. The full potential of coordinated multipoint (CoMP) can be realized by massive multiple-input multiple-output (MIMO) systems, where each base station (BS) has very many antennas. However, the improved throughput comes at the price of more infrastructure; hardware cost and circuit power consumption scale linearly/affinely with the number of antennas. In this paper, we show that one can make the circuit power increase with only the square root of the number of antennas by circuit-aware system design. To this end, we derive achievable user rates for a system model with hardware imperfections and show how the level of imperfections can be gradually increased while maintaining high throughput. The connection between this scaling law and the circuit power consumption is established for different circuits at the BS.

An Efficient Precoder Design for Multiuser MIMO Cognitive Radio Networks with Interference Constraints

We consider a linear precoder design for an underlay cognitive radio multiple-input multiple-output broadcast channel, where the secondary system consisting of a secondary base-station (BS) and a group of secondary users (SUs) is allowed to share the same spectrum with the primary system. All the transceivers are equipped with multiple antennas, each of which has its own maximum power constraint. Assuming zero-forcing method to eliminate the multiuser interference, we study the sum rate maximization problem for the secondary system subject to both per-antenna power constraints at the secondary BS and the interference power constraints at the primary users. The problem of interest differs from the ones studied previously that often assumed a sum power constraint and/or single antenna employed at either both the primary and secondary receivers or the primary receivers. To develop an efficient numerical algorithm, we first invoke the rank relaxation method to transform the considered problem into a convex-concave problem based on a downlink-uplink result. We then propose a barrier interior-point method to solve the resulting saddle point problem. In particular, in each iteration of the proposed method we find the Newton step by solving a system of discrete-time Sylvester equations, which help reduce the complexity significantly, compared to the conventional method. Simulation results are provided to demonstrate fast convergence and effectiveness of the proposed algorithm.