Stochastic resonance (SR) is a noise-enhancement phenomenon that enables the detection of sub-threshold signals by adding noise and using nonlinear systems. This paper explores the applicability of SR in a BPSK receiver with sub-threshold signals. Although received signals are amplified as a result of the nonlinear behavior of the receiver, they are somewhat distorted. This results in the lower performance of SR receivers in comparison with linear receivers. Employing a parallel network of SR systems is expected to solve this problem. The present theoretical analysis demonstrates that in a certain noise intensity range, the output of the network can fully describe an input sub-threshold signal, and hence, the performance close to that of the linear receivers can be obtained. The effectiveness of the SR receiver was also demonstrated through a numerical example of the bit error rate (BER). However, achieving good BER performance requires an infinite number of arrayed SR systems, which is not realistic in practical systems. A design framework for an SR network with a finite number of elements and an appropriate noise intensity that can realize BER performance close to that in linear systems is also provided.