Ergodic Secrecy Rate of Optimal Source-Destination Pair Selection in Frequency-Selective Fading

Node selection is a simple technique to achieve diversity and thereby enhance the physical layer security in future wireless communication systems which require low complexity. High-speed data transmission often encounters frequency selective fading. In this context, we evaluate the exact closed-form expression for the ergodic secrecy rate (ESR) of the optimal source-destination pair selection scheme with single-carrier cyclic-prefix modulation, where the destination and eavesdropper channels both exhibit independent frequency selective fading with an arbitrary number of multipath components. A simplified analysis in the high-SNR scenario along with an asymptotic analysis is also provided. We also derive and compare the corresponding results for the sub-optimal source-destination pair selection scheme. We show that our analysis produces the corresponding ESR results under narrowband independent Nakagami-$m$ fading channel with any arbitrary integer parameter $m$. The effect of transmitters, destination and eavesdropping paths correlation on the ESR is also demonstrated. Our solution approach is general and can be used to find the ESR of a wider variety of transmitter selection schemes.