Robust Online Multiuser Detection: A Hybrid Model-Data Driven Approach

We study the problem of robust online multiuser detection in the context of non-orthogonal multiple access. The optimal multiuser detector (in terms of the uncoded bit error rate) is the nonlinear maximum a posteriori (MAP) filter. Learning good nonlinear functions of this type (e.g., with deep neural networks) typically requires a large number of training samples and complicated signal processing, which poses a fundamental problem in dynamic wireless environments. Furthermore, compared with linear approaches, nonlinear filters are generally less robust against changes in the environment. To overcome these problems, we first show that the optimal MAP filter belongs to reproducing kernel Hilbert spaces (RKHSs) associated with Gaussian kernels whose widths satisfy a condition related to the standard deviation of the receiver noise. Second, we show how to approximate the optimal MAP filter with a computationally simple signal processing algorithm using a relatively small number of training samples. Third, to make the filter robust against changes in the wireless environment, we design a partially linear filter in the sum of an RKHS containing the MAP filter and an RKHS of a linear kernel. Finally, based on this partially linear design, we propose a multiuser detection framework that, in contrast to some state-of-the-art approaches, has the following desired features: (i) it has low complexity; (ii) it can work with small sample sets; (iii) it shows better robustness than a purely nonlinear receiver; and (iv) it does not require user parameter estimation (e.g., channels), which is prone to errors and may not be possible in certain scenarios.