Optimal memoryless relays with noncoherent modulation

We derive optimal memoryless relays using noncoherent modulation over additive white Gaussian noise (AWGN) channels with or without fading. The derivation is flexible, as it can be applied to any binary hypothesis test regarding the observations at the relay. We investigate several channels, including random phase and fading, and apply different modulation schemes, namely on-off-keying (OOK) and orthogonal frequency-shift-keying (FSK). We find that at low signal-to-noise ratio (SNR) the relay censors its observation, as it only transmits at non-zero energy if the observations seem reliable. Compared to the known results that optimal memoryless relays using coherent BPSK are combinations of soft-information and hard-limiter [1]-[3], the noncoherent relays have considerably less emphasis on soft-information and converge much faster to the hard-limiter.