Analysis of Multi-Stage Receivers Under Finite Sample-Support

We derive the output SINR of a multi-stage CDMA receiver based on the Krylov-subspace spanned by the covariance matrix of the received signal, under the practical assumption of a finite number of samples available at the receiver. The evaluation of the SINR is addressed as an approximation problem in the asymptotic regime defined when both the sample-size and the observation dimension grow together without bound at the same rate. Limiting SINR values in this double-limit context are then more representative of the reality because, as it happens in realistic scenarios, both quantities are considered to be of the same order of magnitude. Our results are based on the asymptotic spectrum of the powers of certain random matrix models, which can be conveniently studied using the combinatorial approach to the theory of free probability