A Deterministic Equivalent Approach to the Performance Analysis of Isometric Random Precoded Systems

In this work, a general wireless channel model for different types of code-division multiple access (CDMA) and space-division multiple-access (SDMA) systems with isometric random signature or precoding matrices over frequency-selective and flat fading channels is considered. For such models, deterministic approximations of the mutual information and the signal-to-interference-plus-noise ratio (SINR) at the output of the minimum-mean-square-error (MMSE) receiver are derived. Also, a simple fixed-point algorithm for their computation is provided, which is proved to converge. The deterministic approximations are asymptotically exact, almost surely, but shown by simulations to be very accurate even for small system dimensions. Our analysis is based on the Stieltjes transform method which enables the derivation of spectral limits of the large dimensional random matrices under study but requires neither arguments from free probability theory nor the asymptotic freeness or the convergence of the spectral distributions of the various matrices involved in the model. The results presented in this work are as such also a novel contribution to the field of random matrix theory and might be useful to further applications involving isometric random matrices.