Maximum a posteriori bit-rate detectors for variable-gain multiple-access systems in unknown Gaussian channel

We propose a MAP blind bit-rate detector for a fixed frame-length multiple-access system which employs variable-gain transmitter power and repetition encoding. This detector considers the problem as a multi-hypothesis testing problem and maximizes the likelihood functions to find the true bit-rate. In contrast of the existing literature, the proposed bit-rate detector assumes no knowledge about the transmitter gain and the noise variance of the system and provides an efficient implementable closed form solution using the maximum likelihood (ML) estimates of the unknown parameters in the likelihood functions (LFs). Assuming the information sequence also as unknown deterministic values and substituting their ML estimates, a GLRT-based detector is obtained. However, this detector fails since a possible transmitted sequence of one hypothesis is also a possible transmitted sequence for all next hypotheses. To overcome this problem, we assume the information sequence as samples of an independent uniformly distributed random variable and average the likelihood functions (after substitution of the ML estimates of the transmitter gain and the noise variance) over the information sequence. The implementation of the resulting hybrid LRT (HLRT) is computationally complex. Therefore, we propose a suboptimal solution with substantially less complexity and compare its performance with the existing bit-rate detector obtained assuming known parameters