Differential MMSE: new adaptive algorithms for equalization, interference suppression, and beamforming

This paper provides a reformulation of the linear minimum mean squared error (MMSE) criterion so that it applies to systems in which the quantity to be tracked is the ratio of the data appearing in two successive observations. The resulting differential MMSE criterion leads to a number of novel algorithms for adaptive implementation of the MMSE receiver. Applications include the following: (a) equalization for single user systems in fast fading (b) adaptive multiuser detection, or interference suppression, for direct sequence CDMA systems employing short spreading sequences in fast fading; (c) blind beamforming using a receive antenna array for direct sequence CDMA systems with long spreading sequences. Note that standard MMSE adaptation either fails in fast fading environments such as (a) and (b), or incurs significant overhead in terms of pilot symbols for tracking the fades. Application (c) applies directly to third generation wideband CDMA proposals, and the algorithms we provide perform significantly better than the state of the art.