Circuits, Systems, and Signal Processing

, Volume 32, Issue 1, pp 143-166

First online:

Paired Bernoulli Circular Spreading: Attaining the BER Lower Bound in a CSK Setting

  • T. PapamarkouAffiliated withDepartment of Statistics, University of Warwick
  • , A. J. LawranceAffiliated withDepartment of Statistics, University of Warwick Email author 

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This paper is concerned with the Paired Bernoulli Circular Spreading (PBCS), a way of generating optimal spreading for the single-user coherent chaos shift-keying (CSK) system. PBCS is optimal spreading in the sense that it attains the Bit Error Rate (BER) lower bound of the system, therefore it has a potential engineering impact on the choice of signal carrier in CSK communications. PBCS optimality is justified theoretically and is further demonstrated through BER simulations. The statistical properties of PBCS are of interest too, as it is an invariant stochastic process with a mixed joint density which allows to sample infinitely many points from a circle.


Optimal spreading Bit error rate (BER) CSK communications