Optimum transmission ranges in multihop packet radio networks in the presence of fading

The evaluation of optimum transmission ranges in a packet radio network in a fading and shadowing environment is considered. It is shown that the optimal probability of transmission of each user is independent of the system model and is p_o≃0.271. The optimum range should be chosen so that on the average there are χ(G/b)²η/ terminals closer to the transmitter than the receiver, where G is the spread spectrum processing gain, b is the outage signal-to-noise ratio threshold, η is the power loss factor and χ depends on the system parameters and the propagation model. The performance index is given in terms of the optimal normalized expected progress per slot, given by ϑ(G/b)¹η/ where ϑ is proportional to the square root of χ. A comparison with the results obtained by using deterministic propagation models shows, for typical values of fading and shadowing parameters, a reduction up to 40% of the performance index