Spectrum-Sharing Multi-Hop Cooperative Relaying: Performance Analysis Using Extreme Value Theory

In spectrum-sharing cognitive radio systems, the transmit power of secondary users has to be very low due to the restrictions on the tolerable interference power dictated by primary users. In order to extend the coverage area of secondary transmission and reduce the corresponding interference region, multi-hop amplify-and-forward (AF) relaying can be implemented for the communication between secondary transmitters and receivers. This paper addresses the fundamental limits of this promising technique. Specifically, the effect of major system parameters on the performance of spectrum-sharing multi-hop AF relaying is investigated. To this end, the optimal transmit power allocation at each node along the multi-hop link is firstly addressed. Then, the extreme value theory is exploited to study the limiting distribution functions of the lower and upper bounds on the end-to-end signal-to-noise ratio of the relaying path. Our results disclose that the diversity gain of the multi-hop link is always unity, regardless of the number of relaying hops. On the other hand, the coding gain is proportional to the water level of the optimal water-filling power allocation at secondary transmitter and to the large-scale path-loss ratio of the desired link to the interference link at each hop, yet is inversely proportional to the accumulated noise, i.e. the product of the number of relays and the noise variance, at the destination. These important findings do not only shed light on the performance of the secondary transmissions but also benefit system designers improving the efficiency of future spectrum-sharing cooperative systems.