Asymptotic Mutual Information Statistics of Separately-Correlated Rician Fading MIMO Channels

Precise characterization of the mutual information of MIMO systems is required to assess the throughput of wireless communication channels in the presence of Rician fading and spatial correlation. Here, we present an asymptotic approach allowing to approximate the distribution of the mutual information as a Gaussian distribution in order to provide both the average achievable rate and the outage probability. More precisely, the mean and variance of the mutual information of the separatelycorrelated Rician fading MIMO channel are derived when the number of transmit and receive antennas grows asymptotically large and their ratio approaches a finite constant. The derivation is based on the replica method, an asymptotic technique widely used in theoretical physics and, more recently, in the performance analysis of communication (CDMA and MIMO) systems. The replica method allows to analyze very difficult system cases in a comparatively simple way though some authors pointed out that its assumptions are not always rigorous. Being aware of this, we underline the key assumptions made in this setting, quite similar to the assumptions made in the technical literature using the replica method in their asymptotic analyses. As far as concerns the convergence of the mutual information to the Gaussian distribution, it is shown that it holds under some mild technical conditions, which are tantamount to assuming that the spatial correlation structure has no asymptotically dominant eigenmodes. The accuracy of the asymptotic approach is assessed by providing a sizeable number of numerical results. It is shown that the approximation is very accurate in a wide variety of system settings even when the number of transmit and receive antennas is as small as a few units.Comment: - submitted to the IEEE Transactions on Information Theory on Nov. 19, 2006 - revised and submitted to the IEEE Transactions on Information Theory on Dec. 19, 200

Spatial Coded Modulation

In this paper, we propose a spatial coded modulation (SCM) scheme, which improves the accuracy of the active antenna detection by coding over the transmit antennas. Specifically, the antenna activation pattern in the SCM corresponds to a codeword in a properly designed codebook with a larger minimum Hamming distance than its counterpart conventional spatial modulation. As the minimum Hamming distance increases, the reliability of the active antenna detection is directly enhanced, which in turn improves the demodulation of the modulated symbols and yields a better system reliability. In addition to the reliability, the proposed SCM scheme also achieves a higher capacity with the identical antenna configuration compared to the conventional spatial modulation technique. Moreover, the proposed SCM scheme strikes a balance between spectral efficiency and reliability by trading off the minimum Hamming distance with the number of available codewords. The optimal maximum likelihood detector is first formulated. Then, a low-complexity suboptimal detector is proposed to reduce the computational complexity, which has a two-step detection. Theoretical derivations of the channel capacity and the bit error rate are presented in various channel scenarios, i.e., Rayleigh, Rician, Nakagami-m, imperfect channel state information, and spatial correlation. Further derivation on performance bounding is also provided to reveal the insight of the benefit of increasing the minimum Hamming distance. Numerical results validate the analysis and demonstrate that the proposed SCM outperforms the conventional spatial modulation techniques in both channel capacity and system reliability.Comment: 30 pages, 17 figure

Two-Timescale Design for Reconfigurable Intelligent Surface-Aided Massive MIMO Systems with Imperfect CSI

This paper investigates the two-timescale transmission scheme for reconfigurable intelligent surface (RIS)-aided massive multiple-input multiple-output (MIMO) systems, where the beamforming at the base station (BS) is adapted to the rapidly-changing instantaneous channel state information (CSI), while the nearly-passive beamforming at the RIS is adapted to the slowly-changing statistical CSI. Specifically, we first consider a system model with spatially independent Rician fading channels, which leads to tractable expressions and offers analytical insights on the power scaling laws and on the impact of various system parameters. Then, we analyze a more general system model with spatially correlated Rician fading channels and consider the impact of electromagnetic interference (EMI) caused by any uncontrollable sources present in the considered environment. For both case studies, we apply the linear minimum mean square error (LMMSE) estimator to estimate the aggregated channel from the users to the BS, utilize the low-complexity maximal ratio combining (MRC) detector, and derive a closed-form expression for a lower bound of the achievable rate. Besides, an accelerated gradient ascent-based algorithm is proposed for solving the minimum user rate maximization problem. Numerical results show that, in the considered setup, the spatially independent model without EMI is sufficiently accurate when the inter-distance of the RIS elements is sufficiently large and the EMI is mild. In the presence of spatial correlation, we show that an RIS can better tailor the wireless environment. Furthermore, it is shown that deploying an RIS in a massive MIMO network brings significant gains when the RIS is deployed close to the cell-edge users. On the other hand, the gains obtained by the users distributed over a large area are shown to be modest

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