Multi-stage reduced-rank adaptive filter with flexible structure

An adaptive reduced-rank filter based on Conjugate-Gradient Algorithm is presented - Conjugate-Gradient Reduced-Rank Filter (CGRRF). The proposed method computes reduced-rank Wiener solutions iteratively starting from rank 1 (matched filter). It is shown that any of these filters is equivalent to the Multi-Stage Wiener Filter proposed by Goldstein and Reed of a particular rank. Contrary to other techniques of comparable performance, the rank of CGRRF (number of stages) can be easily adapted to achieve required performance/complexity trade-off. This property is illustrated numerically using adaptive rank selection technique along with other examples showing good transient and asymptotic performance of the method.