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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 semideflnite relaxation (SDR) approach . This paper 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 not directly applicable. In the paper, a linear fractional SDR (LF-SDR) approach is proposed for efficient approximation of the optimum blind ML solution. In this approach, the blind ML 16-QAM OSTBC detection problem is first approximated by a quasi-convex relaxation problem. Generally quasi-convex problems may be computationally more complex to handle than convex problems, but we show that the optimum solution of our quasi-convex problem can be efficiently obtained by solving a convex problem, namely a semideflnite program. 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 , especially in the one- receive-antenna scenario.