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 D for the multistage Wiener filter (MSWF) presented by Goldstein and Reed. The large system limit is defined by letting the number of users K and the number of dimensions N tend to infinity with K/N 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 D needed to achieve a desired output SINR does not scale with system size. Numerical results show that D = 8 is sufficient to achieve near-full-rank performance even under heavy loads (K/N = 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 D → ∞ with D/N fixed. Our results show that for large systems, the MSWF allows a dramatic reduction in rank relative to the other techniques considered.