Abstract
The blind maximum-likelihood (ML) detection of orthogonal space-time block codes(OSTBCs) is a computationally challenging optimization problem. Fortunately, for BPSK and QPSK OSTBCs, it has been shown that the blind ML detection problem can be efficiently and accurately approximated by a semidefinite relaxation (SDR) approach and optimally solved by sphere decoding [1]. This thesis considers the situation where the 16-QAM signals are employed. Due to the nonconstant modulus nature of 16-QAM signals, the associated blind ML OSTBC detection problem has its objective function exhibiting a Rayleigh quotient structure, which makes the SDR approach and sphere decoding not directly applicable. In this thesis, a linear fractional SDR (LF-SDR) approach is proposed for efficient approximation of the optimum blind ML solution. In fact, LF-SDR is a quasi-convex relaxation problem owing to the associated objective function with a fractional quadratic form. Quasi-convex problems in general may be computationally more complex to handle than convex problems, but we show that the optimum solution of our quasi-convex problem can instead be efficiently obtained by solving a convex problem, namely a semidefinite program (SDP). This LF-SDR approach is developed based on the relaxation technique of bound-constrained SDR (BC-SDR), [13] previously proposed for dealing with the coherent MIMO ML detection problem with 16-QAM. We also apply some other existing 16-QAM SDR techniques, namely polynomial-inspired SDR (PI-SDR) [19], and virtually-antipodal SDR (VA-SDR) [20], to develop the LF-SDR. We prove that the three SDR techniques (BC-SDR, PI-SDR, VA-SDR) achieve the same approximation performance. Since the LF-SDR is an approximate ML detector which is suboptimal, we propose a modified sphere decoder to our fractional quadratic problem to obtain the optimal blind ML solution. Simulation results demonstrate that the proposed LF-SDR based blind ML detector outperforms the norm relaxed blind ML detector and the blind subspace channel estimator [5], especially in the one-receive-antenna scenario. It is also found that the proposed LF-SDR and modified sphere decoder exhibit very close symbol error performance; while the former is much more appropriate for large size problem due to its relatively low complexity.