Two Aspects of Optimum CSK Communication: Spreading and Decoding

Abstract

Abstract. This paper focuses on the optimization of performance of single-user chaos shift-keying (CSK). More efficient signal transmission is achieved in the coherent case by introducing the class of the so called deformed circular maps for the generation of spreading. Also, the paired Bernoulli circular spreading (PBCS) is introduced as an optimal choice, which attains the lower bound of bit error rate (BER). As interest shifts to the non-coherent version of the system, attention moves to the receiver end. Maximum likelihood (ML) decoding is utilized serving as an improvement over the correlation decoder. To make the methodology numerically realizable, a Monte Carlo likelihood approach is employed. Assume that the information source comprises of K binary bits, each of which is transmitted N times for reliability purposes. Let b = ±1 denote any single binary bit out of the K, which is replicated N times.A stationary process X := (X 0 , X 1 , . . . , X N−1 ) of mean µ X and variance σ 2 X is involved in the modulation process. X is called the spreading and N the spreading factor.The transmitter emits the scalar product T := b(X − µ X 1 ). The N -length transmitted signal T is degraded as it passes through the channel. Stochastic channel noise ǫ := (ǫ 0 , ǫ 1 , . . . , ǫ N −1 ) models the corruption of T . It is assumed that the system is affected by white channel noise, which means that ǫ ∼ N (0, σ 2 ǫ I), where 0 and I stand for the N -length null vector and the N × N identity matrix respectively.A first modelling approach would be to set the received signal R to be the transmitted signal T distorted by the additive channel noise ǫ, that is R := T + ǫ = b(X − µ X 1 ) + ǫ.(1)