Performance of reduced-rank linear interference suppression

The performance of reduced-rank linear filtering is studied for the suppression of multiple-access interference. A reduced-rank filter resides in a lower dimensional space, relative to the full-rank filter, which enables faster convergence and tracking. We evaluate the large system output signal-to-interference plus noise ratio (SINR) as a function of filter rank for the multistage Wiener filter (MSWF) presented by Goldstein and Reed. The large system limit is defined by letting the number of users and the number of dimensions tend to infinity with fixed. For the case where all users are received with the same power, the reduced-rank SINR converges to the full-rank SINR as a continued fraction. An important conclusion from this analysis is that the rank needed to achieve a desired output SINR does not scale with system size. Numerical results show that = 8 is sufficient to achieve near-full-rank performance even under heavy loads ( = 1). We also evaluate the large system output SINR for other reduced-rank methods, namely, Principal Components and Cross-Spectral, which are based on an eigendecomposition of the input covariance matrix, and Partial Despreading (PD). For those methods, the large system limit lets with fixed. Our results show that for large systems, the MSWF allows a dramatic reduction in rank relative to the other techniques considered.