Abstract—The analysis of the multiple-antenna capacity in the high- regime has hitherto focused on the high- slope (or maximum multiplexing gain), which quantifies the multiplicative increase as a function of the number of antennas. This traditional characterization is unable to assess the impact of prominent channel features since, for a majority of channels, the slope equals the minimum of the number of transmit and receive antennas. Furthermore, a characterization based solely on the slope captures only the scaling but it has no notion of the power required for a certain capacity. This paper advocates a more refined characterization whereby, as a function of �f, the high- capacity is expanded as an affine function where the impact of channel features such as antenna correlation, unfaded components, etc., resides in the zero-order term or power offset. The power offset, for which we find insightful closed-form expressions, is shown to play a chief role for levels of practical interest. Index Terms—Antenna correlation, channel capacity, coherent communication, fading channels, high- analysis, multiantenna arrays, Ricean channels.

The asymptotic --in the number of antennas-- theoretic capacity of a MIMO (Multiple Input Multiple Output) system is derived when considering Rice distribution entries. Assuming perfect knowledge of the channel at the receiver, analytical expressions of the capacity are derived in the case of perfect and partial (based on the mean and limiting eigenvalue distribution of the mean) knowledge at the transmitter. Remarkably, the capacity depends only on a few meaningful parameters, namely, the limiting eigenvalue distribution of the mean matrix, the signal to noise ratio (SNR), the Ricean factor, and the system load. These results show in particular that, for a given SNR and in contrast to the SISO (Single Input Single Output) case, the MIMO Rice channel does not always outperform the MIMO Rayleigh channel in terms of capacity. Moreover, the results are also useful to quantify the effect of feedback on general MIMO systems.

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We investigate the high-SNR probability density function of the mutual information of the Ricean MIMO channel for Gaussian code books and the case where the channel’s fixed component has rank 1. The purpose of this paper is three-fold: 1) We propose an illustrative geometrical technique characterizing the mutual information as the log of the random volume of a parallelotope spanned by the random MIMO channel matrix. 2) We then show that the density function of the rank-1 Ricean MIMO channel approaches a non-central Gaussian density in the large antenna limit. We provide expressions for the density function in the finite antenna case which shed light on the question why the mutual information has Gaussian behavior both in the Rayleigh and the Ricean case even for a small number of antennas. 3) Finally, we provide accurate approximations to the mean and the variance of the mutual information of the rank-1-Ricean MIMO channel which allows a thorough discussion of the impact of the K-factor on capacity. I.

This paper presents an explicit expression for the marginal probability density distribution of the unordered eigenvalues of a noncentral Wishart matrix HH † where H can represent a multiple-input multiple-output channel obeying the Ricean law. By integrating over this marginal density distribution, the corresponding ergodic mutual information is characterized also in explicit form. 1.

In this paper we consider the computation of channel capacity for ergodic multiple-input multiple-output channels with additive white Gaussian noise. Two scenarios are considered. Firstly, a time-varying channel is considered in which both the transmitter and the receiver have knowledge of the channel realization. The optimal transmission strategy is water-filling over space and time. It is shown that this may be achieved in a causal, indeed instantaneous fashion. In the second scenario, only the receiver has perfect knowledge of the channel realization, while the transmitter has knowledge of the channel gain probability law. In this case we determine an optimality condition on the input covariance for ergodic Gaussian vector channels with arbitrary channel distribution under the condition that the channel gains are independent of the transmit signal. Using this optimality condition, we find an iterative algorithm for numerical computation of optimal input covariance matrices. Applications to correlated Rayleigh and Ricean channels are given. I.