Polyphase related-prime sequences

The well known family of binary twin-prime sequences is generalised to the multiple-valued case by employing a polyphase representation of the sequenc e elements. These polyphase versions exhibit similar periodic and aperiodic auto-correlation properties to their binary counterparts, and are referred to as q-phase related-prime (RP) sequences. These sequences have length L = r.s, for r and s both prime, and with s = r + k. They are constructed by combining two polyphase Legendre sequences of lengths r and s, and modifyin g the resulting composite sequence at certain points. A two-dimensional arr ay structure is employed in the construction and analysis of these sequence s. The original q-phase Legendre sequences are derived by converting the in dex sequences of lengths r and s to modulo-q form. When q is even, two clas ses of RP sequence arise, depending on whether L = q + 1 mod 2q or L = 1 mo d 2q. For odd q, only a single class is available, and here L = 1 mod 2q. T he out-of-phase periodic correlation values of these RP sequences are indep endent of the sequence length, and depend only on the number of phases q an d the difference k between the two related primes. The maximum out-of-phase correlation values is given by 1 - k. Tables of available sequences are pr esented.