An interior point method for a semidefinite relaxation based equalizer incorporating prior information

The problem of maximum likelihood estimation of digital data transmitted over an intersymbol interference channel may be cast as a quadratically constrained quadratic program (QCQP). This problem may be solved approximately but efficiently using a semidefinite relaxation (SDR) technique in which the quadratic objective and constraints are converted into linear functions of a matrix variable. Recently the authors extended the basic SDR technique using maximum a posteriori probability (MAP) estimation to incorporate prior probabilities on the bits. The resulting estimator is a soft-input soft-output equalizer that can be used in iterative (turbo) equalization in situations where true optimal MAP equalization (implemented via the BCJR algorithm) is impractical because of its exponential complexity. This paper develops a custom interior point algorithm using the barrier method to solve the extended SDR problem which is convex. This custom solver is more computationally efficient than a general purpose solver because it can exploit the structure inherent in the equalization problem. Simulation experiments are provided that compare the running times of the new algorithm and a general purpose code (CVX). The new algorithm is more computationally efficient than the more general purpose solver and delivers results with equal accuracy. Refinements in initialization strategies and stopping criteria can improve the computational efficiency of the new algorithm.