Average Contiguous Duration – A Novel Metric for Characterizing Wireless Fading Channels

Abstract – We define the average contiguous duration (ACD) of the received fading signal as the average time duration during which the signal envelope contiguously remains within a bounded amplitude interval. Also, the multi-interval ACD or K-ACD function is defined as the set of ACD values for K non-overlapping amplitude-intervals whose union spans the received envelope's amplitude range. We derive closed-form expressions of the ACD for Rayleigh, Rice, and Nakagami-m fading signals, which are widely analyzed in the literature. The derived expressions hold practical significance for several signal processing applications such as non-uniform quantization of channel samples for secret key generation (SKG) in physical layer security (PLS) techniques. The well-known channel fading metric of average fade duration (AFD) is shown as a special case of the proposed ACD metric and the proposed theoretical analysis is validated by simulations.