We consider the minimum-mean-square-error (MMSE) filter estimation in a multiuser communication environment with side user information (knowledge of the signature waveforms of a group of users). Unlike the approach adopted by the past research work known as "group-blind" linear multiuser detection, in this paper we attack directly the problem of estimating the input data covariance matrix with side user information under small sample support, and build an MMSE filter estimate using the improved covariance matrix estimate. For known Gaussian channel noise variance and signal waveforms of a group of users, we derive a closed form filter estimate, obtain its asymptotic covariance matrix, and demonstrate numerically that it coincides with the Cramer-Rao bound. When they are unknown, a recursive optimization procedure with guaranteed convergence is also developed. Simulation studies in the context of DS-CDMA communications demonstrate the state-of-the-an performance of the proposed filter estimates.
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