Abstract-Multiple-input multiple output (MIMO) communication architecture has recently emerged as a new paradigm for wireless communications in rich multipath environment, which has spectral efficiencies far beyond those offered by conventional techniques. Channel capacity of the MIMO architecture in independent Rayleigh channels scales linearly as the number of antennas. However, the correlation of a real-world wireless channel may result in a substantial degradation of the MIMO architecture performance. In this letter, we investigate the MIMO channel capacity in correlated channels using the exponential correlation matrix model. We prove that, for this model, increase in correlation is equivalent to decrease in signal-to-noise ratio (SNR). For example, = 0 7 is the same as 3-dB decrease in SNR.

Abstract-An analytical approach to the performance analysis of the V-BLAST algorithm is presented in this paper, which is based on the analytical model of the Gramm-Schmidt process. Closed-form analytical expressions of the vector signal at i-th processing step and its power are presented. A rigorous proof that the diversity order at i-th step (without optimal ordering) is (n-m+i) is given. It is shown that the optimal ordering is based on the least correlation criterion and that the afterprocessing signal power is determined by the channel correlation matrices in a fashion similar to the channel capacity.Index Terms-MIMO, V-BLAST, multi-antenna system, fading

Motivated by a recent surge of interest in convex optimization techniques, convexity/concavity properties of error rates of the maximum likelihood detector operating in the AWGN channel are studied and extended to frequency-flat slow-fading channels. Generic conditions are identified under which the symbol error rate (SER) is convex/concave for arbitrary multi-dimensional constellations. In particular, the SER is convex in SNR for any one-and two-dimensional constellation, and also in higher dimensions at high SNR. Pairwise error probability and bit error rate are shown to be convex at high SNR, for arbitrary constellations and bit mapping.Universal bounds for the SER 1 st and 2 nd derivatives are obtained, which hold for arbitrary constellations and are tight for some of them. Applications of the results are discussed, which include optimum power allocation in spatial multiplexing systems, optimum power/time sharing to decrease or increase (jamming problem) error rate, an implication for fading channels ("fading is never good in low dimensions") and optimization of a unitaryprecoded OFDM system. For example, the error rate bounds of a unitary-precoded OFDM system with QPSK modulation, which reveal the best and worst precoding, are extended to arbitrary constellations, which may also include coding. The reported results also apply to the interference channel under Gaussian approximation, to the bit error rate when it can be expressed or approximated as a non-negative linear combination of individual symbol error rates, and to coded systems.

Abstract-The Bell Labs layered space-time (BLAST) algorithm is simple, and hence, a popular choice for a multiple-input multiple-output (MIMO) receiver. Its bit-error rate (BER) performance has been studied mainly using numerical (Monte Carlo) techniques, since exact analytical evaluation presents serious difficulties. Close examination of the problem of BLAST BER performance analysis reveals that the major difficulty for analytical evaluation is due to the optimal ordering procedure. Hence, we analyze the algorithm performance without optimal ordering. While this is a disadvantage of the analysis, there are certain advantages as well. Exact closed-form analytical evaluation is possible for arbitrary number of transmit and receive antennas in an independent, identically distributed Rayleigh fading channel, which provides deep insight and understanding that cannot be gained using the Monte Carlo approach alone. A result on the maximum ratio combining weights, which is used at each detection step, is derived to obtain a number of results: independence of noise, distribution of signal-to-noise ratio (SNR), and block-or bit-error rates. We present a detailed analysis and expressions for uncoded error rates at each detection step, which hold true for any modulation format and take simple closed form in some cases. Asymptotic form of these expressions for large SNRs is particularly simple. Extensive Monte Carlo simulations validate the analytical results and conclusions.Index Terms-Bit-error rate (BER), Bell Labs layered space-time (BLAST), error propagation, multiantenna systems, multiple-input multiple-output (MIMO), performance analysis.

Optimal signaling for secrecy rate maximization in Gaussian MIMO wiretap channels is considered.While this channel has attracted a significant attention recently and a number of results have been obtained, including the proof of the optimality of Gaussian signalling, an optimal transmit covariance matrix is known for some special cases only and the general case remains an open problem. An iterative custom-made algorithm to find a globally-optimal transmit covariance matrix in the general case is developed in this paper, with guaranteed convergence to a global optimum. While the original optimization problem is not convex and hence difficult to solve, its minimax reformulation can be solved via the convex optimization tools, which is exploited here. The proposed algorithm is based on the barrier method extended to deal with a minimax problem at hand. Its convergence to a global optimum is proved for the general case (degraded or not) and a bound for the optimality gap is given for each step of the barrier method. The performance of the algorithm is demonstrated via numerical examples. In particular, 20 to 40 Newton steps are already sufficient to solve the sufficient optimality conditions with very high precision (up to the machine precision level), even for large systems. Even fewer steps are required if the secrecy capacity is the only quantity of interest. The algorithm can be significantly simplified for the degraded channel case and can also be adopted to include the per-antenna power constraints (instead or in addition to the total power constraint). It also solves the dual problem of minimizing the total power subject to the secrecy rate constraint.S. Loyka is with the