Stochastic geometry analysis of error probability in interference limited wireless networks

In this paper, we present mathematical frameworks for error performance analysis in interference limited networks such as cellular networks. Due to the increasing irregularity in the spatial deployment of nodes in the emerging heterogeneous cellular networks (HCNs), we employ stochastic geometry approach by abstracting the node locations as a homogeneous Poisson point process (PPP). First, we characterize the average error probability of an intended communication link with a given transmitter-receiver separation, which is subject to interference from these Poisson distributed nodes. More specifically, we develop uniform approximation (UA), which is highly accurate over the whole range of signal-to-interference ratio (SIR) and hence, serve as an alternative to existing complex analytical results. Error probability UAs for both single-antenna and maximal ratio combining (MRC) receivers are derived in this paper. Next, we evaluate the average error probability of any typical user in the network, which is served by the node providing the maximum received power. Mellin-transform based method is proposed in this case, which often yield closed-form solution. An example of BPSK modulation is given in the paper.