Exact calculation of bit error rates in communication systems with chaotic modulation

Lawrance, A. J.; Ohama, G.

doi:10.1109/tcsi.2003.818612

Cited by 53 publications

(63 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Exact Gaussian Theory (EGT) for BER from correlation decoding in multi-user CSK is developed from the single-user case [17] and was initiated in [30]. First, by combining the covariance sum of the correlator (15) with its components (16) into a single expression, the BER probability in (17) becomes…”

Section: Exact Gaussian Theory (Egt) For Bermentioning

confidence: 99%

See 1 more Smart Citation

Chaos Communication Performance: Theory and Computation

Kaddoum

Lawrance

Chargé³

et al. 2010

Circuits Syst Signal Process

View full text Add to dashboard Cite

In this paper new and existing approaches are developed to compute the bit error rate for chaos-based communication systems. The multi-user coherent antipodal chaos shift keying system is studied and evaluated in its coherent form, in the sense of perfect synchronization between transmitted and received chaotic sequences. Transmission is through an additive white Gaussian noise channel. Four methods are interrelated in the paper, three approximate ones and an exact one. The least accurate but most well known is based on simple Gaussian approximation; this is generalized to better reveal its structure. Two accurate and computationally efficient approximate methods are based on conditional Gaussian approximation and the statistical distribution of the typically non-constant bit energy. The most insightful but computationally expensive one is based on exact theory and rests on explicit mathematical results for particular chaotic maps used to spread binary messages. Both upper and lower bounds to the bit error rate are suggested. The relative advantages of the different approaches are illustrated with plots of bit error rate against signal to noise ratio.

show abstract

Section: Exact Gaussian Theory (Egt) For Bermentioning

confidence: 99%

“…in terms of standardized bit energy, the result from [17]. For exact results, the expectation has to be evaluated numerically.…”

Section: Single-user Exact Gaussian Theorymentioning

confidence: 99%

Chaos Communication Performance: Theory and Computation

Kaddoum

Lawrance

Chargé³

et al. 2010

Circuits Syst Signal Process

View full text Add to dashboard Cite

show abstract

“…For brevity, we omit the subscript (which is 1 in this case) in the variables and . The decision parameter for the th user is given by (7) where the conditioning is only on and not the others. With a Gaussian distribution assumed for the conditional decision parameter, the BER for user can then be evaluated by (8) where the two conditional error probabilities are approximated by (9) (10) In (9) and (10), represents the variance operator and denotes the complementary error function defined as (11) Suppose the th user is sending a " ."…”

Section: A Derivation Of Bers Based On Gaussian Approximationmentioning

confidence: 99%

“…In this section, we apply the approach of Lawrance and Ohama [7], which gave exact BERs for single-user CSK systems to derive exact analytical results for BERs in multiple-access CSK systems. This approach enables full dynamics of the chaotic spreading to be utilized and not just low order moments of the spreading.…”

Section: B Derivation Of Exact Bersmentioning

confidence: 99%

Exact Analytical Bit Error Rates for Multiple Access Chaos-Based Communication Systems

Tam

Lau

Tse

et al. 2004

IEEE Trans. Circuits Syst. II

Self Cite

View full text Add to dashboard Cite

Abstract-In this paper, exact analytical expressions for the bit error rates (BERs) in a multiple-access chaos-based digital communication system are derived. Comparisons are made with those obtained using traditional approximation methods which assume a Gaussian distribution for the conditional decision parameter. The obtained results are compared to the results of brute-force (BF) numerical simulations. It is found that the exact analytical BERs are in perfect agreement with BF simulations and hence provide better prediction of the BER performance than those given by traditional Gaussian-approximation-based methods.Index Terms-Chaos-based communications, exact bit error rate (BER), multiple access.

show abstract

“…1 Single-user coherent CSK: the model A brief description of single-user coherent CSK, based on [4], is provided.…”

mentioning

confidence: 99%

Two Aspects of Optimum CSK Communication: Spreading and Decoding

Papamarkou

2010

Chaotic Systems

View full text Add to dashboard Cite

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)

show abstract

Exact calculation of bit error rates in communication systems with chaotic modulation

Cited by 53 publications

References 12 publications

Chaos Communication Performance: Theory and Computation

Chaos Communication Performance: Theory and Computation

Exact Analytical Bit Error Rates for Multiple Access Chaos-Based Communication Systems

Two Aspects of Optimum CSK Communication: Spreading and Decoding

Contact Info

Product

Resources

About