23 July 2003 Performance analysis of doubly optimal CDMA spreading codes with odd length
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Abstract
A doubly optimal binary signature set is a set of binary spreading sequences that can be used for code division multiplexing purposes and exhibits minimum total-squared-correlation (TSC)and minimum maximum-squared-correlation (MSC) at the same time. In this article, we focus on such sets with signatures of odd length and we derive closed-form expressions for the signature cross-correlation matrix, its eigenvalues, and its inverse. Then, we derive analytic expressions for (i) the bit-error-rate (BER) upon decorrelating processing,(ii) the maximum achievable signal-to-interference-plus-noise (SINR) ratio upon minimum-mean-square-error (MMSE) filtering, and (iii) the total asymptotic efficiency of the system. We find that doubly optimal sets with signature length of the form 4m+1, m=1, 2,..., are in all respects superior to doubly optimal sets with signature length of the form 4m-1 (the latter class includes the familiar Gold sets as a small proper subset). "4m+1" sets perform practically at the single-user-bound (SUB) after decorrelating or MMSE processing (not true for "4m-1" sets). The total asymptotic efficiency of "4m+1" sets is lower bounded by 2/e for any system user load. The corresponding lower bound for "4m-1" sets is zero.
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George N. Karystinos, George N. Karystinos, Dimitris A. Pados, Dimitris A. Pados, } "Performance analysis of doubly optimal CDMA spreading codes with odd length", Proc. SPIE 5100, Digital Wireless Communications V, (23 July 2003); doi: 10.1117/12.487748; https://doi.org/10.1117/12.487748
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