On the Dirac Delta Approximation and the MGF Method for ASER Analyses of Digital Communications over Fading Channels

A novel chaos-based modulation scheme: adaptive threshold level chaotic on–offkeying for increased BER performance

“…The information signal was simulated as a Dirac delta function in unit-impulse time. The purpose of simulating the information signal as a Dirac delta function is the use of this function's integral as the comparison curve for signal processing purposes [19]. In the novel proposed communication system, the signal that was squared at the input of the receiver circuit was used as the comparison signal at the decision block.…”

Further Results on the Dirac Delta Approximation and the Moment Generating Function Techniques for Error Probability Analysis in Fading Channels

“…Similar to [15] and [22], we consider a normalized probability density function (PDF) of the fading channel SNR in the form…”

Asymptotic analysis of digital modulations in κ–μ , η–μ and α–μ fading channels

“…Wireless systems performance measures such as the average bit, symbol, or block error probabilities and the ergodic channel capacities typically involve taking the statistical expectation of the CEP or a logarithmic function with respect to the random variables that characterise the multichannel/multipath fading [1][2][3][4][5][6][7][8][9][10][11][12][13]. For at least six decades, researchers have studied problems of these types (i.e.…”

“…For example, analytical difficulties associated with computing the statistical expectations of the Gaussian-Q function (especially for diversity systems) or its integer powers with respect to their arguments have led to development of various bounds and approximations (e.g. [1][2][3][4][5][6][7][8][9][10][11][12][13]). Among these various known solutions, the analytical methods based on either the high-SNR approximation of the probability density function (PDF) of γ in a variety of fading environments/diversity techniques [1][2][3][4][5] or tight exponential-type approximations [10,11] for the CEPs of different modulation schemes are of significant interest owing to their simplicity, generality and also because they offer insights into how channel and modulation related parameters determine the 'diversity gain' and the 'coding gain' for various diversity combining/ modulation techniques.…”

“…Among these various known solutions, the analytical methods based on either the high-SNR approximation of the probability density function (PDF) of γ in a variety of fading environments/diversity techniques [1][2][3][4][5] or tight exponential-type approximations [10,11] for the CEPs of different modulation schemes are of significant interest owing to their simplicity, generality and also because they offer insights into how channel and modulation related parameters determine the 'diversity gain' and the 'coding gain' for various diversity combining/ modulation techniques. However, the accuracy of the asymptotic analysis [2] approach degrades rapidly as the mean SNR decreases, while the gap between the exact and approximate curves for the single-term exponential-type CEP approximation [6][7][8][9][10][11] technique widens as the channel experience more severe fading and/or for higher-order modulations. Since current wireless systems operate at mean SNR of 0-15 dB with average error rates as high as 10 −2 , a more precise or better closed-form average symbol error rate (ASER) approximations than [1][2][3][4][5][6] are desirable.…”