Reduced-Rank Space–Time Adaptive Interference Suppression With Joint Iterative Least Squares Algorithms for Spread-Spectrum Systems

This paper presents novel adaptive space-time reduced-rank interference-suppression least squares (LS) algorithms based on a 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 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 LS (RLS) adaptive algorithms for their computationally efficient estimation and an algorithm that automatically adjusts 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 direct-sequence code-division multiple-access (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.