Improved Lower Bound on Peak Correlation for Phase Coded Waveform Set

The studies of the lower bound on peak value of aperiodic auto- and cross-correlation functions are of great significance for the multiple input multiple output (MIMO) radar phase coded waveform set design. The lower bound limits the performance of the phase coded waveform sets. However, existing lower bounds are not tight. In this paper, the mathematical relations among the 1) lower bound on peak of correlation functions of the complementary sequence set, 2) lower bound on peak of aperiodic correlation functions, 3) lower bound on peak of periodic correlation functions and 4) lower bound on peak of inner products are studied by analyzing the Welch lower bounds. Based on the mappings among these four kinds of lower bounds and a tighter lower bound on peak of correlation functions of the complementary sequence set obtained by using a frequency domain approach, a new improved lower bound on peak aperiodic correlation functions is proposed. The lower bound proposed in this paper is 18% higher than the Welch bound for some specific values of the set size M and sequence length N. When the sequence length N is sufficiently large, the proposed lower bound is tighter than the lower bound on peak of aperiodic correlation functions improved by the lower bound on peak of inner products.