Optimization of Amplify-and-Forward Multicarrier Two-Hop Transmission

In this paper, frequency-domain relay processing in a two-hop transmission system is investigated. The relay is constrained to be "non-regenerative"; that is, the relay is only allowed to perform a symbol-by-symbol memoryless transformation of its received signals. Multicarrier modulation, e.g., orthogonal frequency division multiplexing (OFDM), is utilized to convert each hop into a collection of non-interfering parallel subcarriers. In contrast to conventional scalar amplify-and-forward (AF) relays that scale all the subcarriers uniformly, it is possible to suppress relay noise and to exploit frequency-domain diversity by optimizing the relay scaling coefficients of different subcarriers jointly with subcarrier power allocation at the source transmitter. This type of scheme is denoted by multicarrier amplify-and-forward (MCAF). Although the end-to-end achievable rate of MCAF is a non-concave function of the power allocation vectors, its optimization is accomplished with an algorithm (O-MCAF) whose computational complexity grows only quadratically with the number of subcarriers, by utilizing a structural property of the problem. Further motivated by the problem structure, a suboptimal algorithm (WF-MCAF) with a linear complexity is also proposed, in which each hop performs waterfilling separately over a selected subset of subcarriers. For hops with a frequency-flat channel response, the maximum achievable rate is explicitly derived from the associated optimization. For hops with Rayleigh fading frequency-domain channel responses, numerical results are presented and it is illustrated that the proposed low-complexity WF-MCAF algorithm usually achieves near-optimal performance.