Generalized Spatial Modulation in Large-Scale Multiuser MIMO Systems

Generalized spatial modulation (GSM) uses $n_t$ transmit antenna elements but fewer transmit radio frequency (RF) chains, $n_{rf}$. Spatial modulation (SM) and spatial multiplexing are special cases of GSM with $n_{rf}=1$ and $n_{rf}=n_t$, respectively. In GSM, in addition to conveying information bits through $n_{rf}$ conventional modulation symbols (for example, QAM), the indices of the $n_{rf}$ active transmit antennas also convey information bits. In this paper, we investigate {\em GSM for large-scale multiuser MIMO communications on the uplink}. Our contributions in this paper include: ($i$) an average bit error probability (ABEP) analysis for maximum-likelihood detection in multiuser GSM-MIMO on the uplink, where we derive an upper bound on the ABEP, and ($ii$) low-complexity algorithms for GSM-MIMO signal detection and channel estimation at the base station receiver based on message passing. The analytical upper bounds on the ABEP are found to be tight at moderate to high signal-to-noise ratios (SNR). The proposed receiver algorithms are found to scale very well in complexity while achieving near-optimal performance in large dimensions. Simulation results show that, for the same spectral efficiency, multiuser GSM-MIMO can outperform multiuser SM-MIMO as well as conventional multiuser MIMO, by about 2 to 9 dB at a bit error rate of $10^{-3}$. Such SNR gains in GSM-MIMO compared to SM-MIMO and conventional MIMO can be attributed to the fact that, because of a larger number of spatial index bits, GSM-MIMO can use a lower-order QAM alphabet which is more power efficient.Comment: IEEE Trans. on Wireless Communications, accepte

On the Distribution of MIMO Mutual Information: An In-Depth Painlev\'{e} Based Characterization

This paper builds upon our recent work which computed the moment generating function of the MIMO mutual information exactly in terms of a Painlev\'{e} V differential equation. By exploiting this key analytical tool, we provide an in-depth characterization of the mutual information distribution for sufficiently large (but finite) antenna numbers. In particular, we derive systematic closed-form expansions for the high order cumulants. These results yield considerable new insight, such as providing a technical explanation as to why the well known Gaussian approximation is quite robust to large SNR for the case of unequal antenna arrays, whilst it deviates strongly for equal antenna arrays. In addition, by drawing upon our high order cumulant expansions, we employ the Edgeworth expansion technique to propose a refined Gaussian approximation which is shown to give a very accurate closed-form characterization of the mutual information distribution, both around the mean and for moderate deviations into the tails (where the Gaussian approximation fails remarkably). For stronger deviations where the Edgeworth expansion becomes unwieldy, we employ the saddle point method and asymptotic integration tools to establish new analytical characterizations which are shown to be very simple and accurate. Based on these results we also recover key well established properties of the tail distribution, including the diversity-multiplexing-tradeoff.Comment: Submitted to IEEE Transaction on Information Theory (under revision

Finite Random Matrix Theory Analysis of Multiple Antenna Communication Systems

Multiple-antenna systems are capable of providing substantial improvement to wireless communication networks, in terms of data rate and reliability. Without utilizing extra spectrum or power resources, multiple-antenna technology has already been supported in several wireless communication standards, such as LTE, WiFi and WiMax. The surging popularity and enormous prospect of multiple-antenna technology require a better understanding to its fundamental performance over practical environments. Motivated by this, this thesis provides analytical characterizations of several seminal performance measures in advanced multiple-antenna systems. The analytical derivations are mainly based on finite dimension random matrix theory and a collection of novel random matrix theory results are derived. The closed-form probability density function of the output of multiple-input multiple-output (MIMO) block-fading channels is studied. In contrast to the existing results, the proposed expressions are very general, applying for arbitrary number of antennas, arbitrary signal-to-noise ratio and multiple classical fading models. Results are presented assuming two input structures in the system: the independent identical distributed (i.i.d.) Gaussian input and a product form input. When the channel is fed by the i.i.d. Gaussian input, analysis is focused on the channel matrices whose Gramian is unitarily invariant. When the channel is fed by a product form input, analysis is conducted with respect to two capacity-achieving input structures that are dependent upon the relationship between the coherence length and the number of antennas. The mutual information of the systems can be computed numerically from the pdf expression of the output. The computation is relatively easy to handle, avoiding the need of the straight Monte-Carlo computation which is not feasible in large-dimensional networks. The analytical characterization of the output pdf of a single-user MIMO block-fading channels with imperfect channel state information at the receiver is provided. The analysis is carried out under the assumption of a product structure for the input. The model can be thought of as a perturbation of the case where the statistics of the channel are perfectly known. Specifically, the average singular values of the channel are given, while the channel singular vectors are assumed to be isotropically distributed on the unitary groups of dimensions given by the number of transmit and receive antennas. The channel estimate is affected by a Gaussian distributed error, which is modeled as a matrix with i.i.d. Gaussian entries of known covariance. The ergodic capacity of an amplify-and-forward (AF) MIMO relay network over asymmetric channels is investigated. In particular, the source-relay and relay-destination channels undergo Rayleigh and Rician fading, respectively. Considering arbitrary-rank means for the relay-destination channel, the marginal distribution of an unordered eigenvalue of the cascaded AF channel is presented, thus the analytical expression of the ergodic capacity of the system is obtained. The results indicate the impact of the signal-to-noise ratio and of the Line-of-Sight component on such asymmetric relay network

Asymptotic Performance of Linear Receivers in MIMO Fading Channels

Linear receivers are an attractive low-complexity alternative to optimal processing for multi-antenna MIMO communications. In this paper we characterize the information-theoretic performance of MIMO linear receivers in two different asymptotic regimes. For fixed number of antennas, we investigate the limit of error probability in the high-SNR regime in terms of the Diversity-Multiplexing Tradeoff (DMT). Following this, we characterize the error probability for fixed SNR in the regime of large (but finite) number of antennas. As far as the DMT is concerned, we report a negative result: we show that both linear Zero-Forcing (ZF) and linear Minimum Mean-Square Error (MMSE) receivers achieve the same DMT, which is largely suboptimal even in the case where outer coding and decoding is performed across the antennas. We also provide an approximate quantitative analysis of the markedly different behavior of the MMSE and ZF receivers at finite rate and non-asymptotic SNR, and show that while the ZF receiver achieves poor diversity at any finite rate, the MMSE receiver error curve slope flattens out progressively, as the coding rate increases. When SNR is fixed and the number of antennas becomes large, we show that the mutual information at the output of a MMSE or ZF linear receiver has fluctuations that converge in distribution to a Gaussian random variable, whose mean and variance can be characterized in closed form. This analysis extends to the linear receiver case a well-known result previously obtained for the optimal receiver. Simulations reveal that the asymptotic analysis captures accurately the outage behavior of systems even with a moderate number of antennas.Comment: 48 pages, Submitted to IEEE Transactions on Information Theor