A Construction of Long-Period Sequences Based on Lightweight Generation and High Probability

In practice, sequences with long period but lightweight generation are always welcome in the applications of communication systems; however, the generation is not easy. From a certain angle of very high probability, this paper presents a solution, which is performed using cyclic difference sequences. As an application, the generated sequences can be interleaved to obtain good correlation properties. Furthermore, synchronization with blind detection is often required but difficult to be achieved. Even harder, periodic sequences may be affected to be ultimately periodic sequences with overhead because of device switching or noise. The determinations of the ultimate periods of above sequences and corresponding distributions are also investigated in this paper.