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 * = log 2 (2 α−1 − 1), where α is the path loss exponent. When code combining is employed at the receiver, this "critical rate" is substantially increased.
This paper compares routing strategies in a simple four node network consisting of a source, a destination, and two parallel relays. Relay-to-relay communication is not considered, so there are three possible routing strategies: (1.) direct (source-to-destination) transmission; (2.) two-hop transmission that makes use of exactly one relay (i.e., the better-placed relay); and (3.) two-hop transmission wherein both relays are used during the second hop. The channel model assumes additive white Gaussian noise and attenuation due to path loss; for two-hop routing, time division multiple access is assumed for interference mitigation. Using simple capacity arguments, the paper first compares two-hop routing through one relay and two-hop routing through two relays and characterizes the relay placements for which one mode is preferable to the other. Then, two-hop transmission exploiting both relays is compared with direct transmission. It is shown that if the desired end-to-end rate is above a critical spectral efficiency, it is always preferable to transmit the signal directly no matter where the two relays are located.
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