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The autocorrelation of a Zadoff-Chu (ZC) sequence with a non-zero cyclicallyshifted version of itself is zero. Due to the interesting property, ZCsequences are widely used in the LTE air interface in the primarysynchronization signal (PSS), random access preamble (PRACH), uplink controlchannel (PUCCH) etc. However, this interesting property of ZC sequence is notuseful in the random access initial uplink synchronization problem due to somespecific structures of the underlying problem. In particular, the state of theart uplink synchronization algorithms do not perform equally for all ZCsequences. In this work, we show a systematic procedure to choose the ZCsequences that yield the optimum performance of the uplink synchronizationalgorithms. At first, we show that the uplink synchronization is a sparsesignal recovery problem on an overcomplete basis. Next, we use the theory ofsparse recovery algorithms and identify a factor that controls performance ofthe algorithms. We then suggest a ZC sequence design procedure to optimallychoose this factor. The simulation results show that the performance of most ofthe state of the art uplink synchronization algorithms improve significantlywhen the ZC sequences are chosen by using the proposed technique.

Zadoff-Chu sequence design for random access initial uplink synchronization