Bandwidth efficient signal sets with partitioned equicorrelated properties for the AWGN channel

Signal sets are considered which give rise to multitone M-ary frequency shift keying (MT-MFSK) modulation, which represents a bandwidth efficient alternative to optimum performance modulation schemes for the AWGN channel (simplex signaling for coherent detection and orthogonal signaling for noncoherent detection). The channel is examined in the power-limited region, and it is shown that MT-MFSK modulation exhibits optimum asymptotic performance with bandwidth efficiency gains of an order of magnitude over the orthogonal MFSK modulation technique for sets of finite size. MT-MFSK is viewed as a class of signal sets derived from combinatorial designs. The main properties and structure of such sets are presented and exploited to derive tight upper bounds for the error probability