Welch’s Bound and Sequence Sets for Code-Division Multiple-Access Systems
Welch’s Bound and Sequence Sets for Code-Division Multiple-Access Systems
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DOI：
10.1007/978-1-4613-9323-8_7
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
J. Massey;T. Mittelholzer
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文献类型：
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作者：
J. Massey;T. Mittelholzer
一组M复等能量序列的Welch界被认为是所有这些序列对之间的内积的幅度的平方和的下界。本文指出，在同步码分多址（S-CDMA）系统中，当分配给M个用户的序列是二进制（±-1）序列时，这个和正好决定了各个用户所看到的用户间干扰的方差之和。它进一步表明，韦尔奇的界限，在一般情况下，保持相等的当且仅当阵列具有M个序列作为行具有正交和等能量的列。对于满足Welch界等式的二进制（±-1值）序列的情况，证明了在S-CDMA系统中使用时，所有用户的用户间干扰方差相同的意义下，该序列是一致好的。本文证明了二元线性码对应的序列集达到Welch界的等价性当且仅当二元线性码不含汉明重量为2的码字。给出了在Welch界中保持相等的序列集的变换和组合，并用于说明非同步CDMA系统序列集的设计和分析。
Welch’s bound for a set of M complex equi-energy sequences is considered as a lower bound on the sum of the squares of the magnitudes of the inner products between all pairs of these sequences. It is shown that, when the sequences are binary (±-1 valued) sequences assigned to the M users in a synchronous code-division multiple-access (S-CDMA) system, precisely such a sum determines the sum of the variances of the interuser interference seen by the individual users. It is further shown that Welch’s bound, in the general case, holds with equality if and only if the array having the M sequences as rows has orthogonal and equi-energy columns. For the case of binary (±-1 valued) sequences that meet Welch’s bound with equality, it is shown that the sequences are uniformly good in the sense that, when used in a S-CDMA system, the variance of the interuser interference is the same for all users. It is proved that a sequence set corresponding to a binary linear code achieves Welch’s bound with equality if and only if the dual code contains no codewords of Hamming weight two. Transformations and combination of sequences sets that preserve equality in Welch’s bound are given and used to illustrate the design and analysis of sequence sets for non-synchronous CDMA systems.