Average contiguous duration: a novel metric for characterizing wireless fading channels

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 {L} -ACD function is defined as the set of ACD values for {L} 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.