Minimum Total-squared-correlation Quaternary Sets: New Bounds and Optimal Designs
نویسندگان
چکیده
We derive new bounds on the total squared correlation (TSC) of quaternary (quadriphase) signature/sequence sets for all lengths L and set sizes K. Then, for all K,L, we design minimum-TSC optimal sets that meet the new bounds with equality. Direct numerical comparison with the TSC value of the recently obtained optimal binary sets shows under what K,L realizations gains are materialized by moving from the binary to the quaternary code-division multiplexing alphabet. On the other hand, comparison with the Welch TSC value for real/complex-field sets shows that, arguably, not much is to be gained by raising the alphabet size above four for any K,L. The sum-capacity (as well as the maximum squared correlation and total asymptotic efficiency) of minimum TSC quaternary sets is also evaluated in closed-form and contrasted against the sum capacity of minimum-TSC optimal binary and real/complex sets.
منابع مشابه
New Bounds and Optimal Binary Signature Sets–Part I: Periodic Total Squared Correlation
We derive new bounds on the periodic (cyclic) total squared correlation (PTSC) of binary antipodal signature sets for any number of signatures K and any signature length L. Optimal designs that achieve the new bounds are then developed for several (K,L) cases. As an example, it is seen that complete (K = L + 2) Gold sets are PTSC optimal, but not, necessarily, Gold subsets of K < L + 2 signatur...
متن کاملBinary CDMA signature sets with concurrently minimum total-squared-correlation and maximum-squared-correlation
We derive lower bounds on the maximum-squaredcorrelation (MSC) of binary antipodal signature sets for any number of signatures K and any signature length L with K ≤ L (underloaded systems). We establish the tightness of the bounds for all cases except K = L ≡ 1 (mod 4) and we prove that the minimum total-squared-correlation (TSC) binary antipodal signature sets that were recently designed are, ...
متن کاملNew bounds on the total squared correlation and optimum design of DS-CDMA binary signature sets
The Welch lower bound on the total-squaredcorrelation (TSC) of signature sets is known to be tight for real-valued signatures and loose for binary signatures whose number is not a multiple of 4. In this paper, we derive new bounds on the TSC of binary signature sets for any number of signatures K and any signature length L: For almost all K; L in f1; 2; : : : ; 200g, we develop simple algorithm...
متن کاملMinimum total-squared-correlation design of DS-CDMA binary signature sets
Abstract— The Welch lower bound on the total-squaredcorrelation (TSC) of signature sets is known to be tight for realvalued signatures and loose for binary signatures whose number is not a multiple of 4. In this paper, we derive new bounds on the TSC of binary signature sets for any number of signatures and any signature length For almost all in , we develop simple algorithms for the design of ...
متن کاملQuarter-fraction Factorial Designs Constructed via Quaternary Codes1 by Frederick
The research of developing a general methodology for the construction of good nonregular designs has been very active in the last decade. Recent research by Xu and Wong [Statist. Sinica 17 (2007) 1191–1213] suggested a new class of nonregular designs constructed from quaternary codes. This paper explores the properties and uses of quaternary codes toward the construction of quarter-fraction non...
متن کامل