Lower bound on the total squared correlation of the bandwidth constrained, time-limited signal sets

Welch´s (1974) bound for a set of K equal-energy sequences of length N (K>N) is defined as the lower bound on the sum of the squared correlations between all pairs of these sequences. The sets of sequences that achieve the Welch bound are desirable in many signal design problems for multiple access communications. Here a similar bound for the set of K equal-energy, time-limited signals is derived when no specific format of signal waveforms is assumed and when the bandwidth of the signal set is taken into account. Signal sets that achieve the lower bound are also obtained