Saddle Point Approximation for Outage Probability Using Cumulant Generating Functions

Guruacharya, Sudarshan; Tabassum, Hina; Hossain, Ekram

doi:10.1109/lwc.2016.2516543

Cited by 4 publications

(5 citation statements)

References 15 publications

(20 reference statements)

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“…Despite considering different fading models, all the aforementioned works consider specific scenarios in order to make the derivations of the OP tractable. In order to handle more complex scenarios, other techniques based on approximation methods [13]- [15] and efficient simulation approaches [16] have been proposed. However, these works are still only applicable for a set of specific scenarios.…”

Section: Introductionmentioning

confidence: 99%

A Unified Moment-Based Approach for the Evaluation of the Outage Probability With Noise and Interference

Rached

Kammoun

Alouini

et al. 2017

IEEE Trans. Wireless Commun.

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Section: Introductionmentioning

confidence: 99%

A Unified Moment-Based Approach for the Evaluation of the Outage Probability With Noise and Interference

Rached

Kammoun

Alouini

et al. 2017

IEEE Trans. Wireless Commun.

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“…Due to the highly accurate approximation it achieves, the SAP method has been widely used with great success by many authors. In [24], the authors employ the SAP to evaluate the outage probability of generalized wireless channels provided their moment generating function (MGF) M X (t) = E(e tX ) exists. Also, using the SAP technique, [25] consider the outage probability performance of maximum ratio combining (MRC) receiver in a variety of fading scenarios.…”

Section: B Saddlepoint Approximation Representationmentioning

confidence: 99%

Parameter Estimation of the Lognormal-Rician Channel Model Using Saddlepoint Approximation

Miao

2020

IEEE Access

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In this paper, the challenges of effective channel estimation for the lognormal-Rician turbulence model are addressed. We present a novel maximum likelihood estimation algorithm involving a saddlepoint approximation (SAP) method to estimate the shaping parameters of the lognormal-Rician distribution. An additional parameter k needs to be estimated in addition to r and σ 2 z under the SAP representation. The accuracy of the proposed estimator is investigated by using the mean square error and normalized mean square error. The simulated results show that the proposed estimator exhibits satisfactory performance over a wide range of turbulence conditions, and it can be easily applied to both noiseless and noisy situations. The effect of the estimated shaping parameters errors on the bit error rate (BER) for the on-off key (OOK) modulation is also investigated; it is shown that the BER performance derived with the SAP estimator becomes closer to the system performance with perfect shaping parameters as r increases. In particular, we present a qualitative comparison between the proposed SAP estimator and other algorithms available in the literature. INDEX TERMS Maximum likelihood estimation (MLE), SAP method, lognormal-Rician turbulence model, OOK modulation, qualitative comparison. I. INTRODUCTION Free space optical (FSO) communication, also known as outdoor optical wireless communication, has recently experienced extraordinary advances. High-speed data transmission can be provided by FSO communication in terms of its large available bandwidth. In addition, there are additional advantages of FSO communication over radio frequency (RF) communication including easy deployment, greater security, and unregulated spectrum resources [1]. Moreover, FSO communication has been intensively considered as a complementary technology to the RF communication in many application scenarios, which is known as hybrid (RF-FSO) communication [2]-[5]. Nevertheless, the performance of FSO links can be severely degraded by environment effects such as aerosol scattering, building-sway, and turbulenceinduced scintillation. Hence, in order to improve the reliable operation of FSO systems under a wide range of weather conditions, various types of processing techniques have been proposed to mitigate the adverse effects of the atmosphere (e.g., [6]-[9]). Many statistical models have been proposed to character

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“…Saddle point method has previously been utilized to evaluate detection probability [10], [11], error probability [12], coding and quantization [13], [14], [15], and estimation [16]. Recently, in [17], we exploited the SPA based on Lugannani-Rice formula to compute the SINR outage probability in a scenario where both the desired channel and the interfering channels are modeled using multi-path fading distributions (e.g., Nakagami-m, Nakagami-q, and Rician). The number of interferers and the distance geometry between the receivers and the transmitters were deterministic.…”

Section: A Background Workmentioning

confidence: 99%

SINR Outage Evaluation: Saddle Point Approximation Using Normal Inverse Gaussian Distribution

Guruacharya

Tabassum

Hossain

2018

IEEE Trans. Wireless Commun.

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Signal-to-noise-plus-interference ratio (SINR) outage probability is among one of the key performance metrics of a wireless cellular network. In this paper, we propose a semi-analytical method based on saddle point approximation (SPA) technique to calculate the SINR outage of a wireless system whose SINR can be modeled in the formYi where X i denotes the useful signal power, Y i denotes the power of the interference signal. Both M and N can also be random variables. The proposed approach is based on the saddle point approximation to cumulative distribution function (CDF) as given by Wood-Booth-Butler formula. The approach is applicable whenever the cumulant generating function (CGF) of the received signal and interference exists, and it allows us to tackle distributions with large skewness and kurtosis with higher accuracy. In this regard, we exploit a four parameter normal-inverse Gaussian (NIG) distribution as a base distribution. Given that the skewness and kurtosis satisfy a specific condition, NIG-based SPA works reliably. When this condition is violated, we recommend SPA based on normal or symmetric NIG distribution, both special cases of NIG distribution, at the expense of reduced accuracy. For the purpose of demonstration, we apply SPA for the SINR outage evaluation of a typical user experiencing a downlink coordinated multi-point transmission (COMP) from the base stations (BSs) that are modeled by homogeneous Poisson point process. Numerical results are presented to illustrate the accuracy of the proposed set of approximations.

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Saddle Point Approximation for Outage Probability Using Cumulant Generating Functions

Cited by 4 publications

References 15 publications

A Unified Moment-Based Approach for the Evaluation of the Outage Probability With Noise and Interference

A Unified Moment-Based Approach for the Evaluation of the Outage Probability With Noise and Interference

Parameter Estimation of the Lognormal-Rician Channel Model Using Saddlepoint Approximation

SINR Outage Evaluation: Saddle Point Approximation Using Normal Inverse Gaussian Distribution

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