Asymptotic analysis and design of restricted uniform polar quantizer for Gaussian sources

Jovanović, Aleksandra; Perić, Zoran; Nikolić, Jelena; Dincic, Milan R.

doi:10.1016/j.dsp.2015.10.016

Cited by 9 publications

(8 citation statements)

References 18 publications

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“…we tabulate values for the asymptotically optimal x max and the asymptotically optimal SQNR. In particular, we determine the asymptotically optimal SQNR by using the asymptotic formula we propose in Equation (20) and by using the exact formula in Equation (21). Since the normalised support limit η opt depends only on N (see Equation 12), the asymptotic formula for maximum SQNR in Equation (20) does not depend on the input signal parameter σ.…”

Section: Results Analysismentioning

confidence: 99%

“…In particular, we determine the asymptotically optimal SQNR by using the asymptotic formula we propose in Equation (20) and by using the exact formula in Equation (21). Since the normalised support limit η opt depends only on N (see Equation 12), the asymptotic formula for maximum SQNR in Equation (20) does not depend on the input signal parameter σ. In other words, it is not necessary to know the value of σ in order to calculate the asymptotic formula for SQNR.…”

Section: Results Analysismentioning

confidence: 99%

“…Equation (20) points that maximum SQNR does not depend on the Rayleigh density parameter σ. That is, for a given N and a different σ, the appropriate maximums of asymptotic SQNR have equal values.…”

Section: : Computed (I )mentioning

confidence: 99%

“…Although asymptotic analysis simplifies the expression for the MSE distortion, minimising the asymptotic distortion over x max still remains complex [2,3]. Therefore, the derivation of analytical expressions for the optimal and asymptotically optimal x max for various quantisation models is a significant issue considered in numerous studies [2,3,[17][18][19][20][21][22][23][24][25]. This issue has greater importance in uniform quantisation than in non-uniform quantisation [2,3].…”

Section: Introductionmentioning

confidence: 99%

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Iterative algorithm for designing asymptotically optimal uniform scalar quantisation of the one‐sided Rayleigh density

2021

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Design of optimal and asymptotically optimal quantisation subject to the mean squared error (MSE) criterion is a complex issue, even in the case of uniform scalar quantisation (USQ). The reason is that the MSE distortion dependence on the key designing parameter of USQ for source densities with infinite supports are complex and limit analytical optimisation of USQs. This issue of USQ design has been addressed for some source densities derived from the generalised gamma density. However, to the best of our knowledge, USQ for the one-sided Rayleigh density has not been studied in detail. This has prompted our research so that this study provides a detailed analysis of USQ for the one-sided Rayleigh density and proposes an iterative algorithm for its asymptotically optimal design. To estimate signal to quantisation noise ratio, we derive an asymptotic formula having reasonable accuracy for rates higher than 3 bits/sample. Our analysis can be useful in digitalto-analogue and analogue-to-digital conversion in diversity systems, orthogonal frequency division multiplexing systems and medical image processing. 1 INTRODUCTION Uniform scalar quantisation (USQ) is the earliest, the simplest and the most researched type of quantisation commonly studied for the source densities derived from the generalised gamma density (Gaussian, Laplacian, the two-sided Rayleigh density) [1-6]. Detailed analyses were conducted in the field of USQ for some of these densities. However, to the best of our knowledge, USQ for the one-sided Rayleigh density has not been thoroughly studied although this density is widely used to model: fading in diversity systems [7, 8], the amplitude of orthogonal frequency division multiplexing (OFDM) signals [9-13] and the noise variance in magnetic resonance imaging [14-16]. This implies that studying USQ for the one-sided Rayleigh density with the goal to maximise its performance would be important for digital-to-analogue and analogue-to-digital conversion (DAC/ADC) in diversity systems, OFDM systems and medical image processing. Also, as shown in [9-13], due to Rayleigh distribution of OFDM signals, the peak power can be much larger than the average power resulting in the high value of peak-to-average power ratio (PAPR) that can adversely affect the OFDM system. The value of PAPR can be reduced by using This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Results Analysismentioning

confidence: 99%

Section: Results Analysismentioning

confidence: 99%

Section: : Computed (I )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Iterative algorithm for designing asymptotically optimal uniform scalar quantisation of the one‐sided Rayleigh density

2021

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“…As shown in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] the approximations for the -function not only facilitate performance analyses of various communication systems, but also provide further mathematical analyses limited by the nonexistence of the closed-form formula for the -function. Recall here that a Gaussian probability density function (PDF) characterizes speech signals, signals in wireless receivers, and OFDM modulated signals [15,16,[21][22][23][24][25][26][27][28], so that the suitable solution to the problem of the -function approximation we observe in this paper is of significance in many application areas. For instance, as shown in [2,3,[10][11][12], the problem of thefunction approximation is of importance in the evaluation of the symbol error probability (SEP) of digital modulations in the presence of additive white Gaussian noise and the average SEP over fading channels.…”

Section: Introductionmentioning

confidence: 99%

Proposal of Simple and Accurate Two-Parametric Approximation for the Q-Function

Nikolić

Perić

Marković

2017

Mathematical Problems in Engineering

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The approximations for the -function reported in the literature so far have mainly been developed to overcome not only the difficulties, but also the limitations, caused in different research areas, by the nonexistence of the closed form expression for the -function. Unlike the previous papers, we propose the novel approximation for the -function not for solving some particular problem. Instead, we analyze this problem in one general manner and we provide one general solution, which has wide applicability. Specifically, in this paper, we set two goals, which are somewhat contrary to each other. The one is the simplicity of the analytical form of -function approximation and the other is the relatively high accuracy of the approximation for a wide range of arguments. Since we propose a two-parametric approximation for the -function, by examining the effect of the parameters choice on the accuracy of the approximation, we manage to determine the most suitable parameters of approximation and to achieve these goals simultaneously. The simplicity of the analytical form of our approximation along with its relatively high accuracy, which is comparable to or even better than that of the previously proposed approximations of similar analytical form complexity, indicates its wide applicability.

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Performance of 5G NR-polar QAM-OFDM in nonlinear distortion plus Non-Gaussian noise over Rayleigh fading channel

Al-Rubaye

2023

AEU - International Journal of Electronics and Communications

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Asymptotic analysis and design of restricted uniform polar quantizer for Gaussian sources

Cited by 9 publications

References 18 publications

Iterative algorithm for designing asymptotically optimal uniform scalar quantisation of the one‐sided Rayleigh density

Iterative algorithm for designing asymptotically optimal uniform scalar quantisation of the one‐sided Rayleigh density

Proposal of Simple and Accurate Two-Parametric Approximation for the Q-Function

Performance of 5G NR-polar QAM-OFDM in nonlinear distortion plus Non-Gaussian noise over Rayleigh fading channel

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