Determination of Optimum Transmission Ranges in a Multi-Hop Spread Spectrum Network

In this paper we obtain the optimum transmission ranges to maximize throughput for a multi-hop spread spectrum network. In the analysis we model the network self-interference as a random variable which is equal to the sum of the interference power of all other terminals. For a spread spectrum network with an effective capacity equal to K simultaneous transmissions and an inverse fourth power propagation law we found that a terminal should transmit with a range so that on the average there are approximately 1.3¿K terminals closer to the transmitter than the receiver. We found that for the inverse fourth power propagation law, the probability density of the interference power at a given terminal is the inverse Gaussian probability density. More generally, if the propagation law is an inverse ¿^th power (¿ ≫ 2), then the probability law of the interference power is the stable law of exponent 2/¿.