Optimization for filter-and-forward relaying systems

Abstract

Increasing demand to the higher throughput network requires the relays in the wireless communication systems. Among several relaying schemes, we look into the simple and practical amplify-and-forward (AF) scheme for implementation. We can generalize the AF scheme into arbitrary linear relaying scheme, but, with time-varying framework, it is difficult to determine the linear combination coefficients. However, by introducing the time-invariant requirement, we could further calculate the coefficients to optimize the achievable rate. In this thesis, we propose filter design algorithms for the linear relay systems. We formulated the achievable rate maximization problem of the linear time-invariant (LTI) relaying, also denoted as filter-and-forward (FF) relaying in this thesis, based on the Toeplitz distribution theorem. The optimization problem is evaluated numerically in the flat-fading channel, and we checked that the FF relaying performs similar to the AF relaying. To verify the validity of FF relaying, the two-hop linear relay system with no direct link is considered in the selective-fading channel. The optimization problem for FF relaying is the function of the filters` power spectrum, and we apply the infinite-dimensional vector space method. The problem is shown to be bi-convex, and the alternating projected gradient method (PGM) is applied to obtain the local optimum source and relay filters. The FF relay changes the frequency response of the overall channel to increase the achievable rate, and outperforms 4\% at SNR=20 dB to the simple AF scheme, shown by the numerical simulations. Additionally, we develop the filter design algorithms for the FF relay systems with the direct link between the source and the relay. In order to capture the time-varying scenario, we apply the joint source and relay filter design to maximize the transmission rate based on the adaptive projected subgradient method (APSM), instead of the PGM. We assume that filters at the source ...