Lower Bounds on the Maximum Periodic and Aperiodic Correlation of Signal Sets with Arbitrary Energy Distribution

Abstract

THIS IS AN UPDATED VERSION OF THE ORIGINAL PAPER Welch and Sidelnikov have obtained lower bounds on the maximum nontrivial correlations of complex signal sets constrained to have uniform signal energy. These results have long been used as a benchmark for testing the merit of signal sets, e.g., in the design of good CDMA sequence families. The Welch lower bound is generalized here to allow for arbitrary signal energy for each member of the signal set, with a view towards considering the application of CDMA to QAM signals. The generalized lower bound is compared to the original bound and a bound on their ratio is also derived. An example of a QAM-CDMA sequence family concludes the paper.