Autocorrelation functions and double difference sequences

The double difference sequences of the mod-H codeword sequences are introduced as convenient tools for analysis related to aperiodic autocorrelation functions (AACF) of H-PSK sequences. Each double difference sequence, together with its reverse and complement, are related to a collection of PSK sequences whose AACF's differ by linear phase or conjugate only. These sequences have the same merit factor, peak sidelobe level, complementary property, and peak-to-mean envelope power (PMEPR) when used in OFDM signaling. The enumeration of characteristic double difference sequences for various sequence lengths and PSK alphabet size is derived. The double difference sequences can be used to reduce the exhaustive computer search time for sequences with good AACF properties, and shorten the description of the search results.