The Capacity Inner and Outer Bounds for the Wireless Interference Channel with a Cognitive Relay

Interference channel with a cognitive relay (IFC-CR), as one of the complex channels, consists of two transmitter-receiver pairs, where, one relay knowing some information of transmitted messages cooperates with transmitters to improve the achievable rate region and overall communication performance. The cognitive relays hold a pivotal role in the context of cognitive radio networks (CRN), where efficient spectrum utilization is a paramount concern. To study the impact of a cognitive relay in a wireless interference channel it is necessary to compute the rate region of wireless IFC-CR. In this paper, the capacity inner and outer bounds of IFC-CR known for discrete alphabet and memoryless channels are extended to the continuous alphabet wireless version. Due to High computational complexity, the gap between the outer and inner bounds is determined through Numerical Results. Various scenarios about transmitter power levels and noise variance are considered to encompass a diverse range of real-world conditions. The inner and outer bounds provided in this paper become valuable tools for various aspects of practical analysis, for example, the inner bound can be used to investigate the coverage region and the outer bound for the outage probability, thereby, facilitating practical decision-making in wireless communication system design and optimization.