Models and Theory for Relay Channels with Receive Constraints
Gerhard G. Kramer · 2004
Relay channels where terminals cannot receive and transmit at the same time are modeled as being memoryless with cost constraints. Cost functions are considered that measure the power consumed in each of three sleep-listen-or-talk (SLoT) modes, as well as the fraction of time the modes are used. It is shown that strategies that have the SLoT modes known ahead of time by all terminals are generally suboptimal. It is further shown that Gaussian input distributions are generally suboptimal for Gaussian channels. For several types of models and SLoT constraints, it is shown that multi-hopping (or decode-andforward) achieves the information-theoretic capacity if the relay is geometrically near the source terminal, and if the fraction of time the relay listens to the source is lower bounded by a positive number. SLoT constraints for which the capacity claim might not be valid are discussed. Finally, it is pointed out that a lack of symbol synchronization between the relays has little or no effect on the capacity theorems if the signals are bandlimited and if independent input signals are optimal. 1