A Lower Bound for the Achievable Throughput in Large Random Wireless Networks Under Fixed Multipath Fading

We consider the problem of achievable per-node throughput in an extended distributed wireless network where the node locations are random and the channel attenuation between pairs of nodes exhibits independent random multipath fading. In [1] a clever protocol construction based on percolation theory was used to show that a per-node throughput of a constant times 1/√n bits per second is achievable with probability approaching one as the expected number of nodes in the network, n, becomes large (i.e. w.h.p.), for networks with random node locations under a deterministic channel gain modeling path-loss and absorption. We use a similar approach to extend the result to a more realistic channel gain model where the channel gains are random due to multipath effects. In particular, we show that a constant times 1/√n bps/node is also achievable, w.h.p., when the channel gains are random. The result applies to independent, frequency flat fading channel models where the tail probability exhibits an exponential decay (e.g., any mixture of line of sight and Rayleigh, Rice and Nakagami distributions).