Linear Fractional Semidefinite Relaxation Approaches to Discrete Fractional Quadratic Optimization Problems

This report considers a discrete fractional quadratic optimization problem motivated by a recent application in blind maximum-likelihood (ML) detection of higher-order QAM orthogonal spacetime block codes (OSTBCs) in wireless multiple-input multiple-output (MIMO) communications. Since this discrete fractional quadratic optimization problem is NP-hard in general, we present a suboptimal approach, called linear fractional semidefinite relaxation (LFSDR), for obtaining an accurate approximate solution in polynomial complexity. Three possible relaxation possibilities are presented, namely the bounded-constrained LFSDR (BC-LFSDR), the virtually-antipodal LFSDR (VA-LFSDR), and the polynomial-inspired LFSDR (PI-LFSDR). We compare the three LFSDR methods in terms of their approximation performances and complexities. Simulation results under the scenario of blind ML higher-order QAM OSTBC detection are presented to show the performance of the three LFSDR methods as well as their computational complexities.