Generalized Chu polyphase sequences

The perfect sequences are so ideal that all out-of-phase autocorrelation coefficients are zero. A method to generate a prime number N of perfect sequences with length N is presented. Moreover, these new sets have one more perfect sequence than Chu polyphase sets with the same maximum absolute value of periodic cross-correlation, and are slightly better for asynchronous direct sequence code division multiple access (DS-CDMA). The new sequences are more robust than Chu sequences when used with M-ary quadrature amplitude modulation (QAM). The reason for this improvement is that the new sequences are designed to be orthogonal to the M-ary QAM carriers. Other sequence transformations are also suggested and may be used to obtain many other perfect sequences with the same correlation properties. For example, the new sequences can be transformed into quadriphase sequences, also with good correlation properties.