Power allocation and effective capacity of AF successive relays

In the relay based telecommunications with K relays between the source and destination, K+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K+1$$\end{document} time or frequency slots are required for a single frame transmission. However, without the relays, only one time or frequency slot is used for a single frame transmission. Therefore, despite the benefits of relaying systems, this type of communications is not efficient from the spectral efficiency viewpoint. One solution to reduce this issue might be the full-duplex (FD) relays. An old technique which is reconsidered recently to improve the spectral efficiency of telecommunication systems. However, FD relays have a certain complexity, so, some similar techniques such as successive relays with nearly the same performance but less complexity is taken into account now. In successive relaying systems, two relays between the source and destination are employed which receive the transmitted frames from the source and relay it to the destination successively. This structure generally acts like an FD relays. In this paper, the effective capacity performance of an amplify and forward successive relaying systems with power allocation strategy at the relays are studied perfectly. However, while the inter-rely interference (IRI) between two successive relays has to be managed well, the power allocation and the effective capacity is derived under different assumptions about the IRI. In this way, we assume weak or strong, short or long-term constraints on the IRI. Then we extract the optimal transmitted power at the relay to maximize the effective capacity under these constraints.