A Survey-cum-Tutorial on Approximations to Gaussian ${Q}$  Function for Symbol Error Probability Analysis Over Nakagami-${m}$  Fading Channels

Aggarwal, Supriya

doi:10.1109/comst.2019.2907065

Cited by 29 publications

(22 citation statements)

References 70 publications

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“…where p γ (γ) is the fading PDF. Observing the similarities in Equations (8) and 9, we conclude that…”

Section: Application To Performance Analysismentioning

confidence: 73%

“…Therefore, approximations to Gaussian Q-function are used to arrive at an approximate closed-form solution. [8][9][10][11] While a lot of effort to approximate Q a ffiffi ffi γ p À Á is found in literature 8 (references to various approximations can be found here, citation to individual approximations is not included to limit the number of references), the same is not true for the product of two Gaussian-Q functions in the form Q a ffiffi ffi…”

Section: Introductionmentioning

confidence: 99%

“…The exact solution to the SEP integral is available for basic fading distributions like Rayleigh, 5 Nakagami‐ m , 6,7 and Rician, 6 but none is available for complex fading distributions. Therefore, approximations to Gaussian Q ‐function are used to arrive at an approximate closed‐form solution 8‐11 . While a lot of effort to approximate

Q ((), a \sqrt{γ})

is found in literature 8 (references to various approximations can be found here, citation to individual approximations is not included to limit the number of references), the same is not true for the product of two Gaussian‐ Q functions in the form

Q ((), a \sqrt{γ}) Q ((), b \sqrt{γ})

.…”

Section: Introductionmentioning

confidence: 99%

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Generalized solution to symbol error probability integral containing over different fading models

Aggarwal

2020

Int J Communication

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SummaryThis paper presents a generalized solution to the symbol error probability (SEP) integral containing the product of two Gaussian Q‐functions . Numerical integration technique is first used to approximate the polar form of as a sum of exponentials. This approximation is then used to derive a closed‐form solution to the related SEP integral. Due to the exponential nature of the approximation, solution to the integral is expressed in terms of moment generating function (MGF) of a fading distribution. Therefore, the solution to integral exists for all fading distributions which have well‐defined MGF. The mathematical complexity of the proposed solution is directly proportional to the complexity of MGF expression. For most of the fading models, the corresponding MGF involves power or exponential functions, which guarantees algebraic simplicity of the proposed solution. Further, this generalized solution is used to evaluate the SEP of various modulation schemes over different fading channels. Various computer simulations run in MATLAB for wide range of scenarios confirm the accuracy of the proposed approximation and solution.

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“…where p γ (γ) is the fading PDF. Observing the similarities in Equations (8) and 9, we conclude that…”

Section: Application To Performance Analysismentioning

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Q ((), a \sqrt{γ})

Q ((), a \sqrt{γ}) Q ((), b \sqrt{γ})

.…”

Section: Introductionmentioning

confidence: 99%

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Generalized solution to symbol error probability integral containing over different fading models

Aggarwal

2020

Int J Communication

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“…In addition, the NB-LDPC codes, often with better error correction performance than binary LDPC codes [21], could be better adapted to high-order modulations without considering the inter-conversion between bit probability and symbol probability. These advantages of the 7-QAM constellation are verified through the calculating of PAPR, the derivation of an exact intuitive geometric infinite double series for its symbol error probability (SEP) over the Additive White Gaussian Noise (AWGN) channel using the similar derivation in [22][23][24][25][26][27][28][29][30] and the analysis of its sensitivity to the nonlinearity of HPAs. Finally, the demodulation threshold of 7-QAM and the symbol error rate (SER) performance of the proposed coded modulation scheme are simulated.…”

Section: Introductionmentioning

confidence: 96%

Combination of High-Order Modulation and Non-Binary LDPC Codes over GF(7) for Non-Linear Satellite Channels

et al. 2019

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High-order modulations are necessary to improve the bandwidth efficiency of the satellite communication system. However, the non-linear characteristic of satellite channels limits the application of high-order modulations. In this paper, we propose a new 7-point constellation which is expected to be effectively applied to the satellite communication system, and combine it with non-binary low-density parity-check (NB-LDPC) codes over Galois field GF(7) to guarantee the reliability of the data transmission. The exact expression for the average symbol error probability (SEP) of 7-order quadrature amplitude modulation (7-QAM) over the Additive White Gaussian Noise (AWGN) channel is derived, and the non-linear distortion over satellite channels is also analyzed. Simulation results reveal that, compared with the traditional 8-order phase-shift keying (8-PSK), the 7-QAM method can achieve about 3 dB gain over the AWGN channel without channel coding at symbol error rate (SER) of 10 - 6 . Moreover, the proposed combined coded modulation scheme also has better SER performance than the NB-LDPC coded 8-PSK modulation scheme over the non-linear satellite channel.

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“…The complementary error function and Q ‐function have vital applications in analysing the error rates of communication systems [2–6], where Gaussian distributions are widely employed to model noise. For example, the symbol error probability of digital modulations in additive white Gaussian noise channels can be expressed in terms of complementary error function [6–8], and error rates in fading channels are also related to the complementary error function [8–10].…”

Section: Introductionmentioning

confidence: 99%

Improved upper bound on the complementary error function

Zhang

Fang²,

Lin³

et al. 2020

Electron. lett.

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The complementary error function is a fundamental function in statistics and plays a central role in numerous applications. Its upper bound is essential for simplifying many performance analysis in communications. This Letter develops a new upper bound, which is sharper than existing upper bounds, on the complementary error function. Simulation tests are also performed to illustrate the sharpness of the new upper bound.

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A Survey-cum-Tutorial on Approximations to Gaussian ${Q}$ Function for Symbol Error Probability Analysis Over Nakagami-${m}$ Fading Channels

Cited by 29 publications

References 70 publications

Generalized solution to symbol error probability integral containing over different fading models

Generalized solution to symbol error probability integral containing over different fading models

Combination of High-Order Modulation and Non-Binary LDPC Codes over GF(7) for Non-Linear Satellite Channels

Improved upper bound on the complementary error function

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