  This paper investigates simultaneous wireless information and power transfer
(SWIPT) in energy harvesting (EH) relay systems. Unlike existing SWIPT schemes
requiring the channel state information (CSI) for coherent information
delivery, we propose a noncoherent SWIPT framework for decode-and-forward (DF)
relay systems bypassing the need for CSI and consequently saving energy in the
network. The proposed SWIPT framework embraces power-splitting noncoherent DF
(PS-NcDF) and time-switching noncoherent DF (TS-NcDF) in a unified form, and
supports arbitrary M-ary noncoherent frequency-shift keying (FSK) and
differential phase-shift keying (DPSK). Exact (noncoherent) maximum-likelihood
detectors (MLDs) for PS-NcDF and TS-NcDF are developed in a unified form, which
involves integral evaluations yet serves as the optimum performance benchmark
for noncoherent SWIPT. To reduce the computational cost of the exact MLDs, we
also propose closed-form approximate MLDs achieving near-optimum performance,
thus serving as a practical solution for noncoherent SWIPT. Numerical results
demonstrate a performance tradeoff between the first and second hops through
the adjustment of time switching or power splitting parameters, whose optimal
values minimizing the symbol-error rate (SER) are strictly between 0 and 1. We
demonstrate that M-FSK results in a significant energy saving over M-DPSK for M
>= 8; thus M-FSK may be more suitable for EH relay systems.
