On decoding the kth strongest user in poisson networks with arbitrary fading distribution

Consider a d-dimensional network whose transmitters form a non-uniform Poisson point process and whose links are subject to arbitrary fading. Assuming interference from the k - 1 strongest users is canceled, we derive the probability of decoding the k-th strongest user in closed-form. As a special case, when k = 1, this probability is the standard coverage probability. This analytical result has immediate applications in networks with successive interference cancellation (SIC) capability. We use it to find closed-form upper and lower bounds on the probability of decoding at least k users and the mean number of successively decodable users. These bounds show that transmitter clustering is beneficial in exploiting SIC.