Feedback-Aided Pilot Placement and Subcarrier Pairing for AF OFDM Relay Channels

Abstract—This paper examines the use of channel feedback to adaptively determine pilot placement among subcarri-ers in amplify-and-forward (AF) orthogonal frequency-division multiplexing (OFDM) relay systems. With feedback of the previ-ous channel estimate, pilot subcarriers at the source and relay can be reassigned to reduce channel estimation error and ensure that good subcarriers are made available for data transmission. The minimum effective signal-to-noise ratio (SNR) among data subcar-riers is utilized as the performance metric for the optimization of the pilot locations. The effective SNR is defined as the receive SNR at the destination, taking into consideration the source-to-relay (SR) and relay-to-destination (RD) channels, as well as their re-spective channel estimation errors. The feedback gain, which is defined as the ratio between the minimum effective SNR achieved with the optimal feedback-aided pilot placement and that achieved with the equal-spaced pilot placement, is used to measure the gains achieved through feedback. In this paper, we first derive an analytic lower bound on the optimal feedback gain and show its rate of increase with respect to the number of subcarriers. These studies are performed for systems both without and with sub-carrier pairing (SP) at the relay. Specifically, in systems without SP, the relay forwards each datum on the same subcarrier on which it is received. In systems with SP, the relay is allowed to re-assign the subcarriers used to forward the data received from the source. With the goal of maximizing the minimum effective SNR, the optimal SP scheme is shown to be an inverse mapping between the SR and RD subcarriers with respect to their channel gains. Due to the complexity of finding the optimal placement, a suboptimal but efficient algorithm called the iterative pilot relocation (IterPR) scheme is then proposed. The effectiveness of the proposed IterPR schemes is demonstrated through numerical simulations. Index Terms—Channel estimation, feedback, orthogonal frequency-division multiplexing (OFDM), pilot placement, relaying, subcarrier pairing (SP)