Abstract-It is well known that multiple input multiple output (MIMO) systems offer the promise of achieving very high spectrum efficiencies (many tens of bit/s/Hz) in a mobile environment. The gains in MIMO capacity are sensitive to the presence of spatial correlation introduced by the radio environment. In this letter we consider the capacity outage performance of MIMO systems in correlated environments. For systems with large numbers of antennas Gaussian approximations are very accurate. Hence, we concentrate on systems with small numbers of antennas and derive exact densities and distribution functions for the capacity, which are simple and rapid to compute.

Let A(t) be a complex Wishart process defined in terms of the M × N complex Gaussian matrix X(t) by A(t) = X(t)X(t) H . The covariance matrix of the columns of X(t) is . If X(t), the underlying Gaussian process, is a correlated process over time, then we have dependence between samples of the Wishart process. In this paper, we study the joint statistics of the Wishart process at two points in time, t 1 , t 2 , where t 1 < t 2 .In particular, we derive the following results: the joint density of the elements of A(t 1 ), A(t 2 ), the joint density of the eigenvalues of −1 A(t 1 ), −1 A(t 2 ), the characteristic function of the elements of A(t 1 ), A(t 2 ), the characteristic function of the eigenvalues of −1 A(t 1 ), −1 A(t 2 ). In addition, we give the characteristic functions of the eigenvalues of a central and non-central complex Wishart, and some applications of the results in statistics, engineering and information theory are outlined.

It is well known that multiple input multiple output (MIMO) systems offer the promise of achieving very high spectrum efficiencies (many tens of bit/s/Hz) in a mobile environment. The gains in MIMO capacity are sensitive to the type of channel encountered in the radio environment. To date most analytical work has concentrated on Rayleigh fading channels. Hence, in this letter we consider the capacity outage performance of MIMO systems in Ricean channels. Due to analytical complexity we concentrate on dual antenna systems (either two transmit or two receive antennas) and derive exact densities and distribution functions for the capacity.

Abstract-In this paper we consider transmit and receive selection methods designed to achieve high channel capacities in a single-user MIMO link. A variety of radio channels are considered, including i.i.d. Rayleigh, correlated Rayleigh and Ricean fading environments. Also considered is the presence of imperfect channel state information (CSI) and a simplified waterfilling scheme. In all cases, we evaluate the performance of optimal selection, simple norm-based selection and other benchmark selection techniques. The major contribution is a general approach to analyzing the capacity of the norm-based selection schemes via a simple power scaling factor. We are able to assess the impact of different channels, imperfect CSI and power allocation using this power scaling factor. Furthermore, the analysis is valid for all scenarios: transmit selection, receive selection and joint transmit-receive selection. Results are shown which compare the capacity performance over a wide range of cases. A notable conclusion is that optimal selection, which is computationally intensive, is outperformed at low signal-to-noiseratios by the simple norm-based approach with power allocation.

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Abstract-In this paper we derive a generalized method to compute the error probabilities of singular value decompositionbased receivers for a MIMO system with uncoded transmission. The method can be used for a wide class of flat fading environments, including i.i.d. and semi-correlated Rayleigh and i.i.d. Ricean channels. Although we apply the method to equalpower BPSK, it can easily be extended to higher order M-PSK and M-QAM signal constellations and adaptive "water-filling" schemes. The error probability curves derived from closed-form formulas and simulations demonstrate very close agreement. We also compare the error performances of CI, MMSE and ZF receivers with the SVD receiver.

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