An integral formula for large random rectangular matrices and its application to analysis of linear vector channels

A statistical mechanical framework for analyzing random linear vector channels is presented in a large system limit. The framework is based on the assumptions that the left and right singular value bases of the rectangular channel matrix H are generated independently from uniform distributions over Haar measures and the eigenvalues of H^TH asymptotically follow a certain specific distribution. These assumptions make it possible to characterize the communication performance of the channel utilizing an integral formula with respect to H, which is analogous to the one introduced by Marinari et. al. in J. Phys. A 27, 7647 (1994) for large random square (symmetric) matrices. A computationally feasible algorithm for approximately decoding received signals based on the integral formula is also provided.