Incorporating prior information into semidefinite relaxation of quadratic optimization problems

This paper focuses on equalization as a representative of the large class of communications receiver problems that can all be cast as the optimization of a quadratic objective function subject to quadratic constraints (QCQP problems). It is well known that approximate solutions to QCQP problems can be obtained efficiently through a relaxation technique which results in a linear program subject to a semidefinite constraint. This paper extends the semidefinite relaxation (SDR) approach to incorporate prior probabilities on the bits. With this extension, the SDR approach may used in the setting of turbo equalization and in other forms of iterative receiver processing. In this paper, the soft-in soft-out SDR-based equalizer is compared to an optimal maximum a posteriori probability based equalizer implemented via the BCJR algorithm.