Minimum Total-Squared-Correlation Quaternary Signature Sets: New Bounds and Optimal Designs

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 2009
Accession Number
ADA517403

Entities

People

  • Dimitris A. Pados
  • John D. Matyjas
  • Ming Li
  • Stella N. Batalama

Organizations

  • University at Buffalo

Tags

DTIC Thesaurus Topics

  • Air Force Research Laboratories
  • Alphabets
  • Code Division Multiplexing
  • Communication Channels
  • Communication Systems
  • Cross Correlation
  • Efficiency
  • Electrical Engineering
  • Finite Alphabet
  • Information Theory
  • Multiple Access
  • Multiplexing
  • Sequences
  • Signal Processing
  • Theorems

Readers

  • Aquatic Ecology
  • Radio communications and signal processing.
  • Regression Analysis.