New Optimal Low Correlation Sequences for Wireless Communications

This paper presents three new sets of frequency hopping sequences, which are converted into sequences for CDMA. One of the CDMA sequence families is optimal with respect to theWelch bound, and two are nearly optimal. Our sequences are available for more lengths, and have much higher linear complexity than other CDMA sequences. They have a similar structure to the small Kasami set, but are balanced. The CDMA sequences are constructed using a composition method, which combines new shift sequences with pseudonoise columns to form an array. The array dimensions are relatively prime, so it is unfolded using the Chinese Remainder Theorem. Each of our constructions gives rise to two additional families with larger family sizes but worse correlation as explained in Section 4.2.