Robust least-squares estimators based on semidefinite programming

We apply recently developed semidefinite programming (SDP) techniques to robust estimation and equalization problems in communication systems with uncertain channels. We derive robust versions of three widely used estimators: the zero-forcing estimator (ZFE), the minimum-mean squared error estimator (MMSEE), and the minimum-mean squared error decision feedback estimator (MMSE-DFE). The formulation of the robust estimation problem takes into account structure in the uncertainty, modeled as an ellipsoidal family of possible FIR channels. The robust estimators are found as the global minimizers of the worst-case residual, and can be computed at a moderate computational cost via semidefinite programming.