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Journals >Laser & Optoelectronics Progress >Volume 60 >Issue 7 >Page 0706004 > Article

Laser & Optoelectronics Progress
Vol. 60, Issue 7, 0706004 (2023)

Estimation of Ricean Factor Based on Fitting

Zhongqing Fan^*, Hong Jiang, and Zhining Wang

Author Affiliations

School of Information Engineering, Southwest University of Science and Technology, Mianyang 621010, Sichuan, China

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DOI: 10.3788/LOP220553 Cite this Article Set citation alerts

Zhongqing Fan, Hong Jiang, Zhining Wang. Estimation of Ricean Factor Based on Fitting[J]. Laser & Optoelectronics Progress, 2023, 60(7): 0706004 Copy Citation Text

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Abstract

To solve the problem of low applicability and high complexity of the estimators based on the moments, this paper proposes an improved moment estimation algorithm based on fitting to improve the efficiency of Ricean-factor estimation. First, this improved model approximates the original function with a rational function, then inverts the approximate formula, and finally obtains two closed formulas pertaining to the Ricean factor. Simulation results show that the estimated efficiency increases at least 2.5 times when samples are 50000 or 1000. Further, under the condition of ensuring the estimation accuracy, the improved algorithm has less time complexity, leading to advantages in wireless communication scenarios wherein terminal resources are limited.

Keywords

estimation of Ricean factor fiber optics and optical communication fitting Ricean channel Ricean factor

y (t) = x (t) \otimes h (t) + n (t)

，（1）

P (r) = \frac{r}{σ^{2}} e x p (- \frac{r^{2} + A^{2}}{2 σ^{2}}) I_{0} (\frac{A r}{σ^{2}}), r \geq 0

，（2）

h (t) = \sqrt[]{\frac{K}{1 + K}} h_{l o s} (t) + \sqrt[]{\frac{K}{1 + K}} h_{n l o s} (t)

，（3）

\begin{matrix} μ_{n} = E [r^{n}] = \\ (σ^{2})^{n / 2} Γ (n / 2 + 1) e x p {(- K)}_{1} F_{1} (n / 2 + 1; 1; K) \end{matrix}

，（4）

f_{n m} (K) = \frac{μ_{n}^{m}}{μ_{m}^{n}}

。（5）

\begin{matrix} f_{12} (K) = μ_{1}^{2} / μ_{2}^{1} = \\ \frac{π e^{- K}}{4 (K + 1)} {[(K + 1) I_{0} (\frac{K}{2}) + K I_{1} (\frac{K}{2})]}^{2} \end{matrix}

，（6）

\{\begin{array}{l} I_{0} = \sum_{n = 0}^{\infty} \frac{x^{2 n}}{2^{2 n} {(n!)}^{2}} = 1 + \frac{x^{2}}{4} + \frac{x^{4}}{64} + \dots \\ I_{1} = (\frac{x}{2}) \sum_{n = 0}^{\infty} \frac{x^{2 n}}{2^{2 n} n! Γ (n + 2)} = \frac{x}{2} + \frac{x^{3}}{16} + \frac{x^{5}}{384} + \dots \end{array}

。（7）

f_{24} (K) = μ_{2}^{4} / μ_{4}^{2} = {[\frac{{(K + 1)}^{2}}{K^{2} + 4 K + 2}]}^{2}

，（8）

{\hat{K}}_{24} = \frac{- 2 μ_{2}^{2} + μ_{4} - μ_{2} \sqrt[]{2 μ_{2}^{2} - μ_{4}}}{μ_{2}^{2} - μ_{4}}

。（9）

\{\begin{array}{l} I_{0} = 1 + \frac{x^{2}}{4} + \frac{x^{4}}{64} + \frac{x^{6}}{2304} \\ I_{1} = \frac{x}{2} + \frac{x^{3}}{16} + \frac{x^{5}}{384} \end{array}, 0 \leq x \leq 2.5

。（10）

{\hat{K}}_{n b} = \frac{\sqrt[]{G_{a_n b}^{2} - G_{v_n b}}}{G_{a_n b} - \sqrt[]{G_{a_n b}^{2} - G_{v_n b}}}

，（11）

(\frac{{\hat{K}}_{R F R}}{1 + {\hat{K}}_{R F R}}) = \sqrt[]{2 {\hat{R}}_{r r}^{2} - {\hat{R}}_{r r r r}}

，（12）

{\hat{K}}_{R F R} = \frac{\sqrt[]{2 {\hat{R}}_{r r}^{2} - {\hat{R}}_{r r r r}}}{1 - \sqrt[]{2 {\hat{R}}_{r r}^{2} - {\hat{R}}_{r r r r}}}

。（13）

\frac{μ_{1}^{2}}{μ_{2}} = p_{0} K^{4} + p_{1} K^{3} + p_{2} K^{2} + p_{3} K + p_{4}

，（14）

\frac{μ_{1}^{2}}{μ_{2}} = q_{0} K^{5} + q_{1} K^{4} + q_{2} K^{3} + q_{3} K^{2} + q_{4} K + q_{5}

，（15）

\frac{μ_{1}^{2}}{μ_{2}} = \frac{K + 2.37}{K + 3}

，（16）

\frac{μ_{1}^{2}}{μ_{2}} = \frac{0.9998 K^{2} + 1.967 K + 2.67}{K^{2} + 2.459 K + 3.403}

，（17）

{\hat{K}}_{f i t 1} = \frac{2.16 μ_{2} - 2.828 μ_{1}^{2}}{μ_{1}^{2} - 1.008 μ_{2}}

，（18）

{\hat{K}}_{f i t 2} = \frac{(1.967 μ_{2} - 2.459 μ_{1}^{2}) - \sqrt[]{- 7.5653 μ_{1}^{4} + 14.6156 μ_{1}^{2} μ_{2} - 6.8088 μ_{2}^{2}}}{2 (μ_{1}^{2} - 0.9998 μ_{2})}

。（19）

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Zhongqing Fan, Hong Jiang, Zhining Wang. Estimation of Ricean Factor Based on Fitting[J]. Laser & Optoelectronics Progress, 2023, 60(7): 0706004

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