Random access sequence set design in wireless cellular communication networks

In modern wireless cellular communication systems, Zadoff–Chu (ZC) sequences have been chosen as random access sequences due to their perfect autocorrelation and cross-correlation properties. However, the orthogonality between these sequences is no longer true when there is a frequency offset between the access device and access point. Thereby, the overall performance of ZC sequence-based random access signals will be limited. In this paper, we give a comprehensive analysis on the effect of frequency offset. We show how frequency offset affects the orthogonal property between sequences, and hence incurs the “energy attenuation” and “energy leakage” problems. Consequently, the detection probabilities of the transmitted random access sequences and the false alarm probabilities of the unsent sequences are affected. A frequency offset resistant detection metric is proposed in this paper to improve the detection probability. In order to resist the frequency offset effect as well as apply to the proposed detection metric, mathematical properties of the optimized roots and cyclic shift set are exploited. Finally, we illustrate how to construct a practical random access signal set under the given timing and frequency offset uncertainties. This analytical framework provides a useful insight into ZC sequence-based random access signal design and performance analyses in wireless cellular communication systems.