Estimation of Ricean Factor Based on Fitting

Fig. 4. Relationship between sample size and estimation bias. (a) Algorithm ${\hat{K}}_{R F R}$ and algorithm ${\hat{K}}_{f i t 1}$ ; (b) algorithm ${\hat{K}}_{n b}$ and algorithm ${\hat{K}}_{f i t 2}$

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Fig. 5. Relationship between signal to noise ratio (SNR) and estimation bias. (a) SNR is greater than or equal to 20 dB; (b) SNR is 20 dB

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Table 1. Evaluation indicators of four fitting functions
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Table 1. Evaluation indicators of four fitting functions
Evaluation index Formula（14） Formula（15） Formula（16） Formula（17）
RMSE 2.3000 $\times$ 10^-3 9.3824 $\times$ 10^-4 2.4190 $\times$ 10^-3 5.7567 $\times$ 10^-5
R-square 0.9974 0.9996 0.9972 1.0000

Table 2. Algorithm complexity analysis

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Table 2. Algorithm complexity analysis

Name	Algorithm principal function	Time complexity $T (n)$	Spatial complexity $S (n)$
Algorithm ${\hat{K}}_{12}$	Formulas（6）and（7）^［12］	$O_{1} (n) + O_{2} (n^{2}) = O (n^{2})$	$O_{3} (n) + O_{4} (1) = O (n)$
Algorithm ${\hat{K}}_{24}$	Formula（8）^［12］	$O_{1} (n) + O_{2} (1) = O (n)$	$O_{3} (0) + O_{4} (1) = O (1)$
Algorithm ${\hat{K}}_{B e s s e l}$	Formulas（6）and（10）^［13］	$O_{1} (n) + O_{2} (n) = O (n)$	$O_{3} (n) + O_{4} (1) = O (n)$
Algorithm ${\hat{K}}_{n b}$	Formula（11）^［14］	$O_{1} (n) + O_{2} (1) = O (n)$	$O_{3} (0) + O_{4} (1) = O (1)$
Algorithm ${\hat{K}}_{R F R}$	Formula（13）^［15］	$O_{1} (n) + O_{2} (1) = O (n)$	$O_{3} (0) + O_{4} (1) = O (1)$
Algorithm ${\hat{K}}_{f i t 1}$	Formula（18）	$O_{1} (n) + O_{2} (1) = O (n)$	$O_{3} (0) + O_{4} (1) = O (1)$
Algorithm ${\hat{K}}_{f i t 2}$	Formula（19）	$O_{1} (n) + O_{2} (1) = O (n)$	$O_{3} (0) + O_{4} (1) = O (1)$

Table 3. Multiple estimated running time of algorithms

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Table 3. Multiple estimated running time of algorithms

Name	Algorithm principal function	Sample of 50000		Sample of 1000
Name	Algorithm principal function	Run 1 time	Run 50 times	Run 1 time	Run 50 times
Algorithm ${\hat{K}}_{12}$	Formulas（6）and（7）^［12］	0.076651	0.113190	0.076153	0.083043
Algorithm ${\hat{K}}_{24}$	Formula（8）^［12］	0.001564	0.091190	0.000167	0.004170
Algorithm ${\hat{K}}_{B e s s e l}$	Formulas（6）and（10）^［13］	0.004968	0.073789	0.004908	0.006543
Algorithm ${\hat{K}}_{n b}$	Formula（11）^［14］	0.002024	0.153798	0.000509	0.059606
Algorithm ${\hat{K}}_{R F R}$	Formula（13）^［15］	0.001836	0.098246	0.000187	0.003937
Algorithm ${\hat{K}}_{f i t 1}$	Formula（18）	0.000321	0.035244	0.000095	0.001094
Algorithm ${\hat{K}}_{f i t 2}$	Formula（19）	0.000419	0.036243	0.000107	0.001467