Level-crossing rate and average duration of fades of the envelope of mobile-to-mobile fading channels in K-parallel dual-hop relay networks

This paper studies the fading behavior of narrowband mobile-to-mobile (M2M) fading channels in dual-hop distributed cooperative multi-relay systems under non-line-of-sight (NLOS) propagation conditions. M2M fading channels considered here are associated with amplify-and-forward relay networks, where K mobile relays are connected in parallel between the source mobile station and the destination mobile station. Such M2M fading channels are referred to as K-parallel dual-hop relay M2M fading channels. We study the fading behavior of these channels by analyzing the level-crossing rate (LCR) and the average duration of fades (ADF) of the received signal envelope. We derive analytical integral expressions of the aforementioned quantities along with the cumulative distribution function (CDF) of the envelope. These statistical quantities are derived assuming that the underlying stochastic processes are independent but not necessarily identically distributed. In addition, the statistical analysis pertaining to the special case of independent and identically distributed (i.i.d.) processes is also presented in this paper. The validity of the presented expressions is confirmed by simulations. Our results are very beneficial for future performance analysis of overall dual-hop distributed cooperative multi-relay systems.