Tighter Bounds on the Gaussian $Q$ Function and Its Application in Nakagami- ${m}$ Fading Channel

Sadhwani, Dharmendra; Yadav, Ram Narayan; Aggarwal, Supriya

doi:10.1109/lwc.2017.2717907

Cited by 64 publications

(52 citation statements)

References 15 publications

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“…The approximations use trapezoidal rule for numerical integration to approximate the polar form of Q (·) as sum of exponentials; while the former divides the area under integration [0, π /2] into two unequal subintervals [0, π /3] and [ π /3, π /2], the later divides into three/four equal subintervals with limit breakpoints at π /6 and π /3 for three subintervals and at π /8, π /4, and 3 π /8 for four subintervals. The expressions obtained are

\begin{matrix} right Q (x) & left \approx E_{Chiani} (x) & right = \frac{1}{12} e^{- x^{2} / 2} + \frac{1}{4} e^{- 2 x^{2} / 3} . \\ right Q (x) & left \approx E_{SYA}^{3} (x) & right = \frac{1}{12} e^{- x^{2} / 2} + \frac{1}{6} e^{- 2 x^{2}} + & left \frac{1}{6} e^{- 2 x^{2} / 3} . \\ right Q (x) & left \approx E_{SYA}^{4} (x) & right = \frac{1}{16} e^{- x^{2} / 2} + \frac{1}{8} e^{- x^{2}} + & left \frac{1}{8} e^{- 10 x^{2} / 3} + \frac{1}{8} e^{- 10 x^{2} / 17} . \end{matrix}

…”

Section: Exponential‐based Approximations To Gaussian Q Functionmentioning

confidence: 99%

“…Over the decades, many different kinds of approximations to Gaussian‐ Q function are proposed using various mathematical techniques . The lower and upper bounds derived in Borjesson and Sundberg are more suitable for calculators rather than communication systems as the expressions are complex and require both exponent and algebraic computations.…”

Section: Introductionmentioning

confidence: 99%

“…A class of approximations that represent Q (·) as sum of exponentials are especially useful when we need to derive the closed‐form solutions to SEP integrals over generalized fading distributions η − μ and κ − μ using approximate computing. In Sadhwani et al, a similar approach is used to derive certain expressions over these fading distributions but are specific to hexagonal quadrature amplitude modulation (HQAM) and therefore cannot be used for other modulation schemes.…”

Section: Introductionmentioning

confidence: 99%

“…Firstly, the solution to integral containing

Q^{k} false(a \sqrt{γ} false)

is valid only for k ≤ 2, since it considers the integrals containing

Q false(a \sqrt{γ} false)

and

Q^{2} false(a \sqrt{γ} false)

as special cases of

Q false(a \sqrt{γ} false) Q false(b \sqrt{γ} false)

integral; therefore, the SEP of neither DE‐QPSK nor TQAM (as derived in Qureshi et al) can be calculated, as it requires integral solutions upto k =4 and k =6, respectively. Secondly, the solution is specifically derived for the exponential‐based approximation to Gaussian Q function of Sadhwani et al…”

Section: Introductionmentioning

confidence: 99%

“…The expressions are generic in nature, which to best of the author's knowledge, are unique and new. These generic expressions can be specifically tailored to calculate the SEP of any digital modulation technique by selecting any exponential‐based approximation to Q (·) among the available ones in literature . Further, we compare the accuracy of the SEP expressions so derived over the range of SNR –10 to 60 dB along with wide variations in parameters.…”

Section: Introductionmentioning

confidence: 99%

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Closed‐form solutions to SEP integrals over generalized fading distributions η−μ and κ−μ using approximate computing

Aggarwal

2019

Int J Communication

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Summary The fading channels often involve complex expressions, when it comes to computing the integrals required for performance evaluation of various digital modulation schemes. In this paper, usefulness of exponential‐based approximations to the Gaussian‐Q function in computing these integrals is discussed. We present generic symbol error probability (SEP) expressions over η−μ and κ−μ fading distributions, which can be tailored for any digital modulation technique using different approximations. The resulting expressions thus obtained comprise only elementary mathematical functions thereby avoiding complex evaluations of hypergeometric functions. We explore all the exponential‐based approximations proposed till date and conclude that apart from being mathematically simple, they also lead to accurate expressions for performance analysis of various digital modulation schemes.

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