Zadoff-Chu sequence design for random access initial uplink synchronization in LTE-like systems

A Zadoff-Chu (ZC) sequence is uncorrelated with a non-zero cyclically shifted version of itself. However, this alone is insufficient to mitigate inter-code interference in LTE initial uplink synchronization. The performance of the state-of-the-art algorithms vary widely depending on the specific ZC sequences employed. We develop a systematic procedure to choose the ZC sequences that yield the optimum performance. It turns out that the procedure for ZC code selection in LTE standard is suboptimal when the carrier frequency offset is not small.