Novel Zero Circular Convolution Sequences for Detection and Channel Estimations

Abstract

Multiuser communication systems or multiple access scheme systems favor sequences possessing the ideal periodic cross-correlation function (PCCF) property. In comparison, channel estimation, equalization, and synchronization applications favor sequences possessing the ideal periodic auto-correlation function (PACF) property. However, there is no set of sequences possessing both the ideal PCCF and PACF properties simultaneously, where auto-correlation and cross-correlation balance each other. In this work, sequences possessing the ideal PACF property are used as the base sequences. Then, a modulation technique is applied upon these base sequences to construct a set of zero circular convolution (ZCC) sequences within which an arbitrary pair of two sequences possesses the ideal PCCF property. Compared with least squares (LS) and minimum mean squared error (MMSE) algorithm, the simulation results show that the channel estimation performance of ZCC is better than MMSE and LS algorithms, and the computational complexity of the algorithm is the same as LS algorithm, but far lower than MMSE algorithm. This is the first study on ZCC sequences reported in the literature, in which their fundamental theorems, properties, construction, and applications are investigated. The advantage of possessing the desired PACF and the ideal PCCF properties allows the ZCC sequences to be used in a broader range of applications than other sets of sequences.