A Fast Elementwise Update Algorithm for Mean-Square Aperiodic Correlation Metrics

We present a low-complexity algorithm for updating the mean-square aperiodic correlation metrics of a signature-sequence set containing arbitrary complex-valued elements. The algorithm is linear-time with respect to the common length of the sequences in the set. The approach reduces from known approaches both the computational complexity and the memory overhead by a factor related to the number of sequences in the set. A simplified algorithm is also given for the special case where each element in the sequence set has the same magnitude (assumed, for simplicity, to be unity). Several applications of the algorithm are also briefly reviewed.