  This paper presents novel adaptive space-time reduced-rank interference
suppression least squares algorithms based on joint iterative optimization of
parameter vectors. The proposed space-time reduced-rank scheme consists of a
joint iterative optimization of a projection matrix that performs
dimensionality reduction and an adaptive reduced-rank parameter vector that
yields the symbol estimates. The proposed techniques do not require singular
value decomposition (SVD) and automatically find the best set of basis for
reduced-rank processing. We present least squares (LS) expressions for the
design of the projection matrix and the reduced-rank parameter vector and we
conduct an analysis of the convergence properties of the LS algorithms. We then
develop recursive least squares (RLS) adaptive algorithms for their
computationally efficient estimation and an algorithm for automatically
adjusting the rank of the proposed scheme. A convexity analysis of the LS
algorithms is carried out along with the development of a proof of convergence
for the proposed algorithms. Simulations for a space-time interference
suppression application with a DS-CDMA system show that the proposed scheme
outperforms in convergence and tracking the state-of-the-art reduced-rank
schemes at a comparable complexity.
