Until recently, the theory of noncoherent communications was premised on the use of orthogonal multi-pulse modulation such as frequency shift keying. The main drawback of this modulation scheme has been its poor spectral efficiency (rate/bandwidth). This paper considers instead the more general non-orthogonal multi-pulse modulation (NMM) technique. Optimal and suboptimal noncoherent detection strategies for NMM are reviewed and their asymptotic (high SNR) performances are characterized for the additive Gaussian as well as the Rayleigh fading channels. The resulting non-Euclidean distance measures are then used to design NMM signal sets that yield significantly higher bandwidth efficiencies than their orthogonal counterparts. NMM in conjunction with convolutional coding is also studied as a way to improve energy efficiency. Several optimal convolutional codes
Michael L. McCloud, Mahesh K. Varanasi