Improper Signaling in Two-Path Relay Channels
  Inter-relay interference (IRI) challenges the operation of two-path relaying systems. Furthermore, the unavailability of the channel state information (CSI) at the source and the limited detection capabilities at the relays prevent neither eliminating the interference nor adopting joint detection at the relays nodes. Improper signaling is a powerful signaling scheme that has the capability to reduce the interference impact at the receiver side and improves the achievable rate performance. Therefore, improper signaling is adopted at both relays, which have access to the global CSI. Then, improper signal characteristics are designed to maximize the total end-to-end achievable rate at the relays. To this end, both the power and the circularity coefficient, a measure of the impropriety degree of the signal, are optimized at the relays. Although the optimization problem is not convex, optimal power allocation for both relays for a fixed circularity coefficient is obtained. Moreover, the circularity coefficient is tuned to maximize the rate for a given power allocation. Finally, a joint solution of the optimization problem is proposed using a coordinate descent method based on alternate optimization. The simulation results show that employing improper signaling improves the achievable rate at medium and high IRI. 
Mohamed Gaafar, Osama Amin, Rafael F. Schaefer, and Mohamed-Slim   Alouini
cs.IT math.IT