Bandwidth-power efficient four-dimensional modulation

A four-dimensional phase-shift keying (4D PSK) modulation technique is described and analyzed. The format for the transmitted signal consists of two orthogonal carriers each of which is phase-modulated through p discrete phase shifts. The combinatorial nature of the signal design problem for an arbitrary dimensionality N=2n (n is an integer) is presented, and a strategy for signal selection for the special case of four dimensions is discussed. The error rate performance is presented for the Gaiussian and Rayleigh fading channels and compared to that of well-known two-dimensional modulation techniques. It is shown that selected signal configurations yield both power- and bandwidth-efficient modulation schemes. When implementing this modulation technique, several practical issues are discussed, such as, constant vs. nonconstant envelope signal structures, coherent transmitter/receiver implementation, expurgation techniques to yield symmetric signal sets, and maximum likelihood detection in a fading environment