Secure Transmission in Cooperative Relaying Networks with Multiple Antennas

We investigate the secrecy performance of dualhop amplify-and-forward (AF) multi-antenna relaying systems over Rayleigh fading channels, by taking into account the direct link between the source and destination. In order to exploit the available direct link and the multiple antennas for secrecy improvement, different linear processing schemes at the relay and different diversity combining techniques at the destination are proposed, namely, 1) Zero-forcing/Maximal ratio combining (ZF/MRC), 2) ZF/Selection combining (ZF/SC), 3) Maximal ratio transmission/MRC (MRT/MRC) and 4) MRT/Selection combining (MRT/SC). For all these schemes, we present new closed-form approximations for the secrecy outage probability. Moreover, we investigate a benchmark scheme, i.e., cooperative jamming/ZF (CJ/ZF), where the secrecy outage probability is obtained in exact closed-form. In addition, we present asymptotic secrecy outage expressions for all the proposed schemes in the high signal-to-noise ratio (SNR) regime, in order to characterize key design parameters, such as secrecy diversity order and secrecy array gain. The outcomes of this paper can be summarized as follows: a) MRT/MRC and MRT/SC achieve a full diversity order of M + 1, ZF/MRC and ZF/SC achieve a diversity order of M, while CJ/ZF only achieves unit diversity order, where M is the number of antennas at the relay. b) ZF/MRC (ZF/SC) outperforms the corresponding MRT/MRC (MRT/SC) in the low SNR regime, while becomes inferior to the corresponding MRT/MRC (MRT/SC) in the high SNR. c) All of the proposed schemes tend to outperform the CJ/ZF with moderate number of antennas, and linear processing schemes with MRC attain better performance than those with SC.

Secure Transmission in Spectrum Sharing MIMO Networks with Generalized Antenna Selection over Nakagami-m Channels

In this paper, we investigate the secrecy outage performance of spectrum sharing multiple-input multiple-output networks using generalized transmit antenna selection with maximal ratio combining over Nakagami-m channels. In particular, the outdated channel state information is considered at the process of antenna selection due to feedback delay. Considering a practical passive eavesdropper scenario, we derive the exact and asymptotic closed-form expressions of secrecy outage probability, which enable us to evaluate the secrecy performance with high efficiency and present a new design insight into the impact of key parameters on the secrecy performance. In addition, the analytical results demonstrate that the achievable secrecy diversity order is only determined by the parameters of the secondary network, while other parameters related to primary or eavesdropper’s channels have a significantly impact on the secrecy coding gain. 

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.

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.