Generalized maximum likelihood noncoherent block detection for decode-and-forward relay systems

This paper considers noncoherent cooperative decode-and-forward (DF) half-duplex multi-branch relay systems. Each relay branch is modeled as a probabilistic transition system at the last hop, and thus it can be considered as a relaying chain comprising multi-hop relays. An approximation to the generalized maximum likelihood (ML) noncoherent block detection is derived for uncoded M-ary modulation in a faded noisy environment. In particular, the derived noncoherent block detection in a noiseless case is equivalent to a multichannel reception with full diversity. Furthermore, the generalized detection is extended specifically to block coded M-ary phase shift keying (MPSK) modulation. For a DF three node relay system using block coded quadrature phase shift keying (QPSK), simulation results are provided to examine the end-to-end error performance of the noncoherent detection with considering the effects of network geometry and power allocation, respectively. It is shown that under a fixed power allocation, a proper relay placement can yield near full diversity for large signal-to-noise ratio.