On the equivalence of RLS implementations of LCMV and GSC processors

This letter compares the transients of the constrained recursive least squares (CRLS) algorithm with the generalized sidelobe canceler (GSC) employing the recursive least squares (RLS) algorithm. We prove that the two adaptive implementations are equivalent everywhere regardless of the blocking matrix chosen. This guarantees that algorithm tuning is not affected by the blocking matrix. This result differs from the more restrictive case for transient equivalence of the constrained least mean-square (CLMS) algorithm and the GSC employing the least mean square (LMS) algorithm, for in this case the blocking matrix needs to be unitary.