  This paper presents a novel adaptive reduced-rank {multi-input multi-output}
(MIMO) equalization scheme and algorithms based on alternating optimization
design techniques for MIMO spatial multiplexing systems. The proposed
reduced-rank equalization structure consists of a joint iterative optimization
of two equalization stages, namely, a transformation matrix that performs
dimensionality reduction and a reduced-rank estimator that retrieves the
desired transmitted symbol. The proposed reduced-rank architecture is
incorporated into an equalization structure that allows both decision feedback
and linear schemes for mitigating the inter-antenna and inter-symbol
interference. We develop alternating least squares (LS) expressions for the
design of the transformation matrix and the reduced-rank estimator along with
computationally efficient alternating recursive least squares (RLS) adaptive
estimation algorithms. We then present an algorithm for automatically adjusting
the model order of the proposed scheme. An analysis of the LS algorithms is
carried out along with sufficient conditions for convergence and a proof of
convergence of the proposed algorithms to the reduced-rank Wiener filter.
Simulations show that the proposed equalization algorithms outperform the
existing reduced-rank and full-rank algorithms, while requiring a comparable
computational cost.
