Exact ZF Analysis and Computer-Algebra-Aided Evaluation in Rank-1 LoS Rician Fading

We study zero-forcing detection (ZF) for multiple-input/multiple-output (MIMO) spatial multiplexing under transmit-correlated Rician fading for an N_R X N_T channel matrix with rank-1 line-of-sight (LoS) component. By using matrix transformations and multivariate statistics, our exact analysis yields the signal-to-noise ratio moment generating function (m.g.f.) as an infinite series of gamma distribution m.g.f.'s and analogous series for ZF performance measures, e.g., outage probability and ergodic capacity. However, their numerical convergence is inherently problematic with increasing Rician K-factor, N_R , and N_T. We circumvent this limitation as follows. First, we derive differential equations satisfied by the performance measures with a novel automated approach employing a computer-algebra tool which implements Groebner basis computation and creative telescoping. These differential equations are then solved with the holonomic gradient method (HGM) from initial conditions computed with the infinite series. We demonstrate that HGM yields more reliable performance evaluation than by infinite series alone and more expeditious than by simulation, for realistic values of K , and even for N_R and N_T relevant to large MIMO systems. We envision extending the proposed approaches for exact analysis and reliable evaluation to more general Rician fading and other transceiver methods.Comment: Accepted for publication by the IEEE Transactions on Wireless Communications, on April 7th, 2016; this is the final revision before publicatio

Location-Based Beamforming for Rician Wiretap Channels

We propose a location-based beamforming scheme for wiretap channels, where a source communicates with a legitimate receiver in the presence of an eavesdropper. We assume that the source and the eavesdropper are equipped with multiple antennas, while the legitimate receiver is equipped with a single antenna. We also assume that all channels are in a Rician fading environment, the channel state information from the legitimate receiver is perfectly known at the source, and that the only information on the eavesdropper available at the source is her location. We first describe how the beamforming vector that minimizes the secrecy outage probability of the system is obtained, illustrating its dependence on the eavesdropper's location. We then derive an easy-to-compute expression for the secrecy outage probability when our proposed location-based beamforming is adopted. Finally, we investigate the impact location uncertainty has on the secrecy outage probability, showing how our proposed solution can still allow for secrecy even when the source has limited information on the eavesdropper's location.Comment: 6 pages, 4 figure

On Outage Probability and Diversity-Multiplexing Tradeoff in MIMO Relay Channels

Fading MIMO relay channels are studied analytically, when the source and destination are equipped with multiple antennas and the relays have a single one. Compact closed-form expressions are obtained for the outage probability under i.i.d. and correlated Rayleigh-fading links. Low-outage approximations are derived, which reveal a number of insights, including the impact of correlation, of the number of antennas, of relay noise and of relaying protocol. The effect of correlation is shown to be negligible, unless the channel becomes almost fully correlated. The SNR loss of relay fading channels compared to the AWGN channel is quantified. The SNR-asymptotic diversity-multiplexing tradeoff (DMT) is obtained for a broad class of fading distributions, including, as special cases, Rayleigh, Rice, Nakagami, Weibull, which may be non-identical, spatially correlated and/or non-zero mean. The DMT is shown to depend not on a particular fading distribution, but rather on its polynomial behavior near zero, and is the same for the simple "amplify-and-forward" protocol and more complicated "decode-and-forward" one with capacity achieving codes, i.e. the full processing capability at the relay does not help to improve the DMT. There is however a significant difference between the SNR-asymptotic DMT and the finite-SNR outage performance: while the former is not improved by using an extra antenna on either side, the latter can be significantly improved and, in particular, an extra antenna can be traded-off for a full processing capability at the relay. The results are extended to the multi-relay channels with selection relaying and typical outage events are identified.Comment: accepted by IEEE Trans. on Comm., 201

Asymptotic SER and Outage Probability of MIMO MRC in Correlated Fading

This letter derives the asymptotic symbol error rate (SER) and outage probability of multiple-input multiple-output (MIMO) maximum ratio combining (MRC) systems. We consider Rayleigh fading channels with both transmit and receive spatial correlation. Our results are based on new asymptotic expressions which we derive for the p.d.f. and c.d.f. of the maximum eigenvalue of positive-definite quadratic forms in complex Gaussian matrices. We prove that spatial correlation does not affect the diversity order, but that it reduces the array gain and hence increases the SER in the high SNR regime.Comment: 10 pages, 2 figures, to appear in IEEE Signal Processing Letter

Fluid Antenna Systems

Over the past decades, multiple antenna technologies have appeared in many different forms, most notably as multiple-input multiple-output (MIMO), to transform wireless communications for extraordinary diversity and multiplexing gains. The variety of technologies has been based on placing a number of antennas at fixed locations which dictates the fundamental limit on the achievable performance. By contrast, this paper envisages the scenario where the physical position of an antenna can be switched freely to one of the N positions over a fixed-length line space to pick up the strongest signal in the manner of traditional selection combining. We refer to this system as a fluid antenna system (FAS) for tremendous flexibility in its possible shape and position. The aim of this paper is to study the achievable performance of a single-antenna FAS system with a fixed length and N in arbitrarily correlated Rayleigh fading channels. Our contributions include exact and approximate closed-form expressions for the outage probability of FAS. We also derive an upper bound for the outage probability, from which it is shown that a single-antenna FAS given any arbitrarily small space can outperform an L-antenna maximum ratio combining (MRC) system if N is large enough. Our analysis also reveals the minimum required size of the FAS, and how large N is considered enough for the FAS to surpass MRC.Comment: 26 pages, 5 figure