One-Hop vs. Two-Hop Routing in Simple Networks with Fading: An Outage Probability Analysis Addressing Spectral Efficiency

This paper compares one-hop and two-hop routing in a simple three node network consisting of two mobiles and a base station. The channel model assumes additive white Gaussian noise, attenuation due to path loss, and slow Rayleigh fading; the network is assumed to use time division multiple access to ameliorate interference for two-hop routing. The outage probabilities of the two schemes are compared to derive conclusions about the relative advantages of multi-hop (two-hop) routing as a function of required end-to-end spectral efficiency. This analysis is carried out under two different assumptions regarding the allocation of power between the mobiles - one scenario in which a total sum power is allocated optimally and another scenario in which each mobile is allocated the same fixed power. The analysis also includes two different assumptions about the receiver\´s operation in two-hop mode - one in which the receiver bases its estimate of the data solely on the signal transmitted by the relay, and another in which the receiver uses code combining to exploit both the relay-transmitted signal and the source-transmitted signal. For the case in which the receiver ignores the source-transmitted signal, it is shown that one-hop routing outperforms two-hop routing when the required end-to-end spectral efficiency is above R* = log₂(2^alpha-1 -1), where alpha is the path loss exponent. When code combining is employed at the receiver, this "critical rate" is substantially increased.