Generalized Extended Welch Bound for Multi-Cell Non-Orthogonal Sequence Sets

Sequence sets with minimum total squared correlation (TSC) have important application in communications. In a multi-cell system, due to the difference in channel strength between the home cell and the neighboring cells, the TSC can be expressed as the sum of squares of weighted correlations among sequences. In this letter, we obtain a closed-form expression for the lower bound of weighted TSC under multi-cell systems which can be regarded as a generalization of the extended Welch bound, namely generalized extended welch bound (GEWB). Moreover, we find a class of sequence sets whose parameters can achieve the theoretical lower bound of the weighted TSC, indicating that the derived GEWB is tight.