Hybrid likelihood ratio bit-rate detectors for variable-gain multiple-access systems in unknown noise variance

We assume a linear equidistance antenna array as the receiver for a fixed frame-length multipleaccess system which employs variable-gain receiver power and repetition encoding. We propose a robust Maximum A posteriori Probability (MAP) Blind Bit-Rate Detector (BBRD). This detector considers the Rate Detection (RD) as a multi-hypothesis test and maximizes the Likelihood Functions (LF)s to find the true bit-rate, while the complex amplitude of the received signal, the noise variance and the direction of arrival are unknown parameters. First, assuming that the location parameter is known and the information sequence are independent and uniformly distributed random variables, we propose a Hybrid Likelihood Ratio Test (HLRT). The proposed HLRT requires to solve a set of nonlinear equations which have no closed form solution. Thus, we propose an iterative numerical algorithm. In addition, we propose a Quasi-HLR detector which has a significantly lower computational complexity. In the case of unknown location parameter, we develop two Quasi-HLR methods. We use fast Fourier transform and search in order to estimate the unknown location. In Q-HLRT-Method-I, the nonlinear equation similar to the one in known location parameter is iteratively solved. In Q-HLRT-Method-II, a low complexity solution is proposed. Simulation examples evaluate and compare the performances of the proposed BBRDs.