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

Abstract

In this article, 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> needs to be estimated in addition to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{z}^{2}$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula> increases. In particular, we present a qualitative comparison between the proposed SAP estimator and other algorithms available in the literature.