Data Detection in 1-bit Quantized MIMO Systems

We address the problem of data detection for the multiple-input multiple-output (MIMO) channel employing one-bit quantizers at the receiver, taking into account different settings of channel state information (CSI) at the receiver (CSIR). In the first part and under perfect CSI conditions, we propose a two-step low-complexity data detection algorithm that reduces the maximum likelihood (ML) search space. The key idea is based on constructing a list of constellation points exploiting the Hessian matrix of the log-likelihood function. We convert the original detection problem under binary observations into the classical integer least-squares optimization enabling direct use of efficient sphere-decoding algorithms. This method is then extended to the multi-bit case along with an assessment of the computational complexity. In the second part, we focus on a real channel model and assume only the availability of statistical CSIR. We formulate the optimal detection metric under a pilot training scheme and present the main challenges in its evaluation, then employ the Laplace method to retrieve an approximation in closed form. We demonstrate through numerical experiments near-optimality of our proposed solutions in terms of vector error rates with respect to oracle lower bounds on their corresponding ML metric. Finally, we also investigate the performance in practical spatially correlated massive MIMO channels.