Spatial Transmitter Density Allocation for Frequency-Selective Wireless Ad Hoc Networks

We consider a network of pairs of nodes that perform ad hoc simultaneous communications over frequency-selective channels. We assume that the whole frequency band is divided into a number of subbands, and each transmitter can only use one subband. Assuming that the network is geometrically infinite, we use the transmission capacity (TC) as a measure of the network throughput. We consider the problem of allocating nodes to the subbands so that the total TC is maximized, under the constraint of a fixed total spatial node density. The optimization problem turns out to be nonconvex. We investigate the detailed structure of the functions involved in the optimization and identify a set of properties of the optimal transmitter density over the subbands. An iterative resource allocation scheme with low complexity is derived to obtain the global optimal solution of the TC maximization problem. The solution can be loosely interpreted as a water-filling solution for a nonconvex optimization problem. Based on numerical simulations, it is shown that the optimal solution obtained through the theoretical analysis is consistent with the one obtained through an exhaustive search, which reveals that the outage probability and the total spatial transmitter density are the keys to determining the network TC.