Condition Number-Constrained Matrix Approximation With Applications to Signal Estimation in Communication Systems

This letter introduces condition number-constrained approximation to matrices used for signal estimation and detection. Under a Frobenius norm criterion, the closed-form solution to the optimal approximation is derived, which can be found efficiently for arbitrary condition number constraints. The resulting approximation techniques are applied to the imperfectly estimated covariance and channel matrices used for estimating transmit signals in communication systems. With an appropriately chosen value of condition number, the robustness of the linear and decision-feedback estimators (DFE) against model mismatch can be significantly improved.