Performance of Relay Selection for NOMA Based Cooperative Networks Over Shadowed Fading Channels

In this work, a non-orthogonal multiple access (NOMA) based transmission between a source and two end users is examined over slow Generalized-K distributed (GKD) fading channels, where a single relay using decode-and-forward (DF) protocol is selected out of a set of full-duplex/half-duplex (FD/HD) multiple relays with the quality of service requirements. Two stage relay selection (RS), selecting a relay out of a set of relays providing service quality for user 1 to maximize data rate of user 2, is analyzed. Additionally, not only perfect successive interference cancellation (pSIC) but also imperfect SIC (ipSIC) is considered. Self-interference (SI) and ipSIC are assumed to be Nakagami-m distributed, additionally, Gaussian and channel gain dependent modelling of ipSIC are also considered. A new expression for cumulative distribution function (CDF) of GKD is provided, thereafter, robust approximated probability density function (PDF) and CDF for GKD based on generalized Gauss-Laguerre quadrature are derived. Since outage probability (OP) analysis with exact CDF is found to be unstable, approximated and asymptotic OP expressions are derived and validated via Monte Carlo simulation technique. Approximated CDF, in turn OP, expression is almost excellent. Unlike existing works, our expressions are unique and valid for all cases such as FD and HD together with pSIC and ipSIC, i.e. expressions are not given separately but in a single compact form. Effects of SI, ipSIC, fading and shadowing parameters on OP are demonstrated and it is also shown that RS can significantly reduce OP. Finally, nonzero diversity order is asserted and details are provided.