Performance Analysis of Multi-User Multi-Round Linear Network Coded Cooperation

Abstract

This letter presents a novel linear network coded cooperation (LNCC) scheme, called multi-user multi-round LNCC (M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -LNCC), for many-to-one communications in wireless networks. The scheme involves multiple users, each of which has an independent message destined to a common base station (BS). The peculiarity of the M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -LNCC is that, not only the native messages, but also the codewords generated via linear network coding (LNC) in the previous time slots participate in the subsequent LNCC operations. Thus, the LNCC operation is performed for multiple rounds and the benefits of LNCC are further exploited. The closed-form expression for the tight approximation of the outage probability is derived in this letter, and the analyses on the asymptotic outage probability and diversity order are also presented. The analysis results show that the M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -LNCC scheme with M(M ≥ 2) users and N + 1(N ≥ 1) time slots is able to achieve the diversity order MN + 1. Monte Carlo simulations are conducted to verify the correctness of our theoretical analyses.