Channel Diversity in Random Wireless Networks

The goal of this paper is to explore the benefits of channel diversity in wireless ad hoc networks. Our model is that of a Poisson point process of transmitters, each with a receiver at a given distance. A packet is divided in blocks which are transmitted over different subbands determined by random frequency hopping. At the receiver, a maximum-likelihood decoder is employed to estimate the transmitted packet/codeword. We show that, if L is the Hamming distance of the error correction code and ε is a constraint on the packet error probability, the transmission capacity of the network is proportional to ε^{1/L}, when ε → 0. The proportionality constant depends on the code selection, the packet length, the geometry of the symbol constellation and the number of receive antennas. This result implies that, at the cost of a moderate decoding complexity, large gains can be achieved by a simple interference randomization scheme during packet transmission. We also address practical issues such as channel estimation and power control. We find that reliable channel information can be obtained at the receiver without significant rate loss and demonstrate that channel-inversion power control can increase the transmission capacity.