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

Abstract

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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“…Note that the beam wander and mechanical vibration result in the pointing errors, and they have the same mathematical model with only differing in physical meaning of parameters [5], [6]. The research on the irradiance scintillation models have been studied extensively, and plenty of precise or mathematically tractable models have been proposed so far, such as Gamma-Gamma distribution [7], Fischer-Snedecor F distribution [8], lognormal-Rician distribution [9], and Málaga distribution [10]. Unfortunately, the results for the pointing errors models are greatly limited.…”

Parameter Estimation of Gamma‐Gamma Fading with Generalized Pointing Errors in FSO Systems

“…The parameter estimation methods for the lognormal distribution and K distribution have been discussed in [13,14]. The maximum likelihood estimation (MLE) with expectation-maximization (EM) or the saddlepoint approximation algorithm is applied to characterize the lognormal-Rician turbulence model parameters [15,16]. The iterative EM algorithm based on the generalized Newton method using a nonquadratic approximation for the MLE of Gamma-Gamma parameters is investigated in [17].…”

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“…With respect to the lognormal-Rician model, the results available so far for single-input single-output (SISO) and MIMO FSO systems in the literature are greatly limited since it does not has the closed-form PDF expression compared to the Gamma-Gamma and Malaga distribution. In [20], the author introduced the saddlepoint approximation method to approximate the lognormal-Rician distribution. In [8], the authors investigated the BER performance of coherent FSO systems in lognormal-Rician turbulence employing the MRC and select combining (SC) via the Padé approximation method.…”