Low/Zero Correlation Zone Theory and Spread Spectrum Communication System Sequences Design: Top 100 Excellent Doctoral Dissertations in China

Author: Tang Xiaohu
Publisher:
Publish Date: 2006-05-01
Features: Ideally, the spread spectrum sequence set used in CDMA communication systems should have the following correlation characteristics: 1. The autocorrelation function of each spread spectrum sequence should be an impulse function, i.e., it should be zero everywhere except at zero delay; 2. The cross-correlation function value between any pair of spread spectrum sequences should be zero everywhere. Unfortunately, it has been proven that there is no sequence set with such ideal correlation characteristics. In recent years, research on low/zero correlation zone (LZCZ) spread spectrum sequences has attracted widespread attention. It targets the characteristics of quasi-synchronous CDMA systems, where the synchronization error is controlled within a certain range, such as one or a few chip cycles, requiring the spread spectrum sequences to exhibit (near) ideal correlation characteristics within the synchronization error range. This thesis focuses on the theory of LZCZ, conducting in-depth research on five aspects: the theoretical bounds of LZCZ sequences, the design of low correlation zone (LCZ) sequences, the design of two-dimensional signals with LZCZ, the design of orthogonal sequence sets on a circle, and the design of LA sequences. For sequences with LZCZ characteristics in certain correlation functions (including non-periodic, periodic, and periodic odd correlation functions), a unified theoretical bound is established based on the Welch inner product bound. The study shows that, with appropriate modifications, all known general sequence theoretical bounds can be applied to LZCZ sequences, as long as the correlation range is limited to the LZCZ. A method for generating multi-phase LCZ sequence sets by combining GMW sequences is proposed, where the side lobe value of the correlation function within the LCZ is -1; more precisely, the correlation function equals -1 everywhere except at isolated points within its domain. By selecting appropriate sampling relationships for pairs of m-sequences, a large class of asymptotically optimal multi-phase LCZ sequence sets is obtained. Using a different construction idea, this thesis also presents a class of asymptotically optimal binary LCZ sequence sets with simple implementation. The concept of LZCZ is extended from one dimension to two dimensions, and several methods for constructing two-dimensional signals with zero correlation zones using two-dimensional orthogonal non-periodic complementary sequence sets are proposed. Low correlation zone two-dimensional signals are successfully generated, where their correlation functions are very small or zero within a rectangular region around the origin. Similarly, the construction methods described in this thesis can also be extended to high-dimensional signal design. Based on the autocorrelation properties of m-sequences, this thesis generates orthogonal sequence sets on a Galois ring using the trace function of elements on the ring and implements the sequence set using two shift registers. A fast two-level despreading algorithm is proposed to perform fast generalized Hadamard transform on sampled signals, significantly reducing computational complexity. A mathematical model for LA sequences is established, and the theoretical lower bound for the length of LA sequences is derived. Several construction methods are proposed. The results show that the construction method based on evolutionary algorithms is the best, with the generated LA sequences far outperforming known results, and most new LA sequences achieving the theoretical lower bound for their lengths. The LZCZ sequences designed in this thesis can be used in quasi-synchronous CDMA spread spectrum communication systems to reduce or even eliminate co-channel interference and improve system capacity.