Capacity-Approaching Multiple Coding for MIMO Rayleigh Fading Systems With Transmit Channel State Information

We study transmit power adaptation and capacity-approaching coding/decoding in multiple-input-multiple-output (MIMO) Rayleigh fading channels under the assumption that perfect channel state information (CSI) is known at both the transmitter and the receiver. The capacity in MIMO systems with transmitter CSI can be achieved via two schemes: 1) a multiple-coding scheme with temporal and spatial water filling and 2) a single-coding scheme with temporal and spatial water filling. The former requires an infinite number of different codes, and the latter one requires interblock coding and, therefore, a very long code. We propose three simple but powerful methods for transforming the MIMO fading channel into a set of additive white Gaussian noise channels to which standard codes for the Gaussian channel can then be applied. We show through a number of examples that these methods can closely approach channel capacity. As a by-product, the closed-form expressions of the marginal probability density function of the ordered and unordered eigenvalues of Wishart matrices are derived.