相控序列的快速生成算法与实现及Gold序列搜索

【作者】 严春林；

【导师】 周亮；

【作者基本信息】 电子科技大学 ， 通信与信息系统， 2001， 硕士

【摘要】 具有优良相关性，大线性复杂度，平衡性，长周期的伪随机序列广泛应用于CDMA系统，扩跳频通信系统。相控序列是一种新的性能优越的伪随机序列。长为（2ⁿ-1）²的相控序列线性复杂度不小于n（2ⁿ-1），互相关和异相自相关为五值｛1，1±2ⁿ，1±2ⁿ⁺¹｝，一族序列有（2ⁿ-1）个，且每个序列都是平衡的。 生成相控序列的关键是生成GMW序列。通过预置本原元向量表达的初始值，不断的进行向量循环移位来生成有限域中的元素。生成有限域中所有元素后，即可按迹函数计算出GMW序列。生成GMW序列后便可生成与相控序列相伴的交织序列。将长为（2ⁿ-1）²的与相控序列相伴的交织序列排成（2ⁿ-1）行（2ⁿ-1）列，用长为（2ⁿ-1）的GMW序列与相控序列相伴的交织序列每一行模2相加，即得一个相控序列。改变长为（2ⁿ-1）的GMW序列的初始相位即得不同的相控序列（这也是相控序列名称的由来），且彼此移位不等价。我们根据上述算法在赛扬400MHz的计算机上实现了12秒内生成66960个长为961相控序列。 本文还提出了对相控序列的改进。改进后的相控序列线性复杂度比改进前相控序列的线性复杂度大几倍，而平衡性，相关性，每一族的序列数与改进前相同。 我们用计算机搜索了生成长为31，63，127，511，1023，2047，8191的Gold序列所需的全部m序列优选对，计算所得数目比其它文献给出的数目多。更多还原

【Abstract】 Pseudo-random sequences with optimal properties such as correlation, high linear spans, balance and long period are widely used in CDMA system, spread spectrum and hopping communication systems. Phase-Controlled (PC) sequence is a new kind of sequence with perfect properties. The PC sequences with period of (2n~1)2 have linear spans no less than n(2~?), five cross-correlation and out-of phase auto-correlation values of { 1,1 ?~, 1 ?n+1 },number of (2敆l) sequences in one family and exact balance for each sequence.Generating GMW sequences is the key to generate PC sequences. By initiating the values of vector description for a primitive element, all finite field elements could be generated by continue cyclic shifting, GMW sequences then could be generated by trace function calculation. And interleaved sequences can be generated after the GMW sequences generated. By rearranging the interleaved sequence with length of (2n~l)2 as an array of (2~?) rows and (2~?) columns and adding GMW sequence with period of (2~?) to each row of the array, a PC sequence could be constructed. Other PC sequences could be constructed by changing the phase of the GMW sequence, this is the name of phase-controlled sequence comes from, and all these PC sequences are not shift equivalent. 66960 PC sequences have been generated by personal computer with CPU of Celeron 400 MHz in less than 12 seconds.The PC sequences are improved in this paper. The linear span of the improved PC sequences is a few times as large as the unimproved by computer simulation verifying and the other properties, such as the balance, the correlation and the number counts in one family, are as same as the unimproved.Also we have searched Gold sequences with different periods of 31,63,127,511,1023,2047,8191 .The number of Gold codes searched is more than that of some other references [12] [22] presented.更多还原