Noncoherent Detection in Amplify-and-Forward Relay Systems

In amplify-and-forward single-relay systems that employ an average relay power constraint, one-shot detection at the destination terminal is not optimal when the channel between the source and relay terminals is unknown. In this work, we derive the maximum-likelihood (ML) block noncoherent detector and show that it can be expressed as a reduced-rank quadratic form maximization. We introduce an auxiliary real variable and prove that the maximization form can be closely approximated by a rank-2 positive semidefinite quadratic form through appropriate selection of the auxiliary variable. Motivated by recent developments on the polynomial-time maximization of reduced-rank quadratic forms over finite alphabets, we develop an efficient detector that has polynomial complexity in the block length and demonstrated near-ML performance.