Maximum Signal Minus Interference to Noise Ratio Multiuser Receive Beamforming

Motivated by massive deployment of low data rate Internet of things (IoT) and ehealth devices with requirement for highly reliable communications, this paper proposes receive beamforming techniques for the uplink of a single-input multiple-output (SIMO) multiple access channel (MAC), based on a per-user probability of error metric and one-dimensional signalling. Although beamforming by directly minimizing probability of error (MPE) has potential advantages over classical beamforming methods such as zero-forcing and minimum mean square error beamforming, MPE beamforming results in a non-convex and a highly nonlinear optimization problem. In this paper, by adding a set of modulationbased constraints, the MPE beamforming problem is transformed into a convex programming problem. Then, a simplified version of the MPE beamforming is proposed which reduces the exponential number of constraints in the MPE beamforming problem. The simplified problem is also shown to be a convex programming problem. The complexity of the simplified problem is further reduced by minimizing a convex function which serves as an upper bound on the error probability. Minimization of this upper bound results in the introduction of a new metric, which is termed signal minus interference to noise ratio (SMINR). It is shown that maximizing SMINR leads to a closed-form expression for beamforming vectors as well as improved performance over existing beamforming methods.