Best Relay Selection for DF Underlay Cognitive Networks with Different Modulation Levels

In an underlay setting, a secondary user shares the spectrum with a primary user under the condition that the interference at this primary user is lower than a certain threshold. The said condition limits the transmission power and therefore, limits the coverage area. Hence, to reach remote destinations, relaying the signal between the source and destination can be an adequate solution to enhance the secondary network’s performance. Selective relaying in underlay cognitive networks has been studied in many previous literatures. The source and relay nodes in most of this literature use the same modulation level. The use of multiple modulation levels by the transmitting terminals has not been explored comprehensively from the physical layer point of view. In this paper, the error performance of a secondary cognitive network with a source and multiple decode and forward (DF) relays using different modulation levels sharing the spectrum with a nearby primary user has been investigated. In particular, a closed form expression for the error probability for two scenarios have been obtained. In the first scenario, where the relays have fixed transmission power, we additionally present an approximate error probability expression that is exact at high signal-to-noise ratio. In the second scenario, where the relays adjust their transmission power such that the interference at the primary user is below a certain threshold with a defined tolerable error, it is referred to as the interference outage scenario.