On implementing the blind ML receiver for orthogonal space-time block codes

We consider the problem of blind maximum-likelihood (NIL) detection for the orthogonal space-time block code (OSTBC) scheme. Our previous work has shown that for OSTBCs the blind ML detection problem can be simplified to a Boolean quadratic program (BQP). This sequel focuses on effective optimization methods for that BQP, which, from an optimization viewpoint, is still a computationally hard problem. First, we consider semi-definite relaxation (SDR), a high-precision BQP approximation algorithm with a computational cost that is polynomial in the problem size. We also propose a simple method that can significantly reduce the average complexity of the SDR technique. Second, we consider sphere decoding, an exact BQP solver that can be computationally expensive in the worst case, but generally incurs a reasonable average complexity particularly at high SNRs. Simulation results indicate that these two blind ML algorithms provide very similar bit error rate performance. Moreover, numerical studies show that SDR provides better complexity performance than sphere decoding in the worst-case sense, while sphere decoding provides better complexity performance in the average sense.