Separation of Radar Co-Frequency Signal Based on Improved Crow Search Algorithm

Fig. 4. Convergence curves of text function. (a) Convergence curve of $f_{1}$ ; (b) convergence curve of $f_{2}$ ; (c) convergence curve of $f_{3}$ ; (d) convergence curve of $f_{4}$ ; (e) convergence curve of $f_{5}$ ; (f) convergence curve of $f_{6}$

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Fig. 5. Radar signal waveforms. (a) Target echo signal; (b) co-frequency interference signal 1; (c) co-frequency interference signal 2

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Fig. 6. Radar signal frequency spectra. (a) Target echo signal; (b) co-frequency interference signal 1; (c) co-frequency interference signal 2

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Fig. 7. Waveform and frequency spectrum of observed signal

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Fig. 8. Function fitness value change curve

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Fig. 9. Signal output waveforms after separation. (a) Separate signal 1; (b separate signal 2; (c) separate signal 3

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Fig. 10. Signal output frequency spectra after separation. (a) Separate signal 1; (b) separate signal 2; (c) separate signal 3

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Fig. 11. Signal matching filtering effect

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Table 1. Benchmark test function

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Table 1. Benchmark test function

Function name	Function expression	Dimension	Search space
Sphere	$f_{1} (x) = \sum_{i = 1}^{n} {x_{i}}^{2}$	30	$[- 100,100]$
Schwefel 2.22	$f_{2} (x) = \sum_{i = 1}^{n} \|x_{i}\| + \overset{n}{\prod_{i = 1}} \|x_{i}\|$	30	$[- 10,10]$
Quartic	$f_{3} (x) = \sum_{i = 1}^{n} i x_{i}^{4} + r a n d o m [0,1]$	30	$[- 1.28,1.28]$
Ackley	$f_{4} (x) = - 20 e x p (- 0.2 \sqrt[]{\frac{1}{n} \sum_{i = 1}^{n} x_{i}^{2}}) - e x p [\frac{1}{n} \sum_{i = 1}^{n} c o s (2 π x_{i})] + 20 + e$	30	$[- 32,32]$
Rastrigin	$f_{5} (x) = \sum_{i = 1}^{n} [{x_{i}}^{2} - 10 c o s (2 π x_{i}) + 10]$	30	$[- 5.12,5.12]$
Griewank	$f_{6} (x) = \frac{1}{4000} \sum_{i = 1}^{n} x_{i} - \overset{n}{\prod_{i = 1}} c o s (\frac{x_{i}}{\sqrt[]{i}}) + 1$	30	$[- 600,600]$

Table 2. Simulation results of different algorithms for six functions

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Table 2. Simulation results of different algorithms for six functions

Function	Algorithm	Optimal value	Worst value	Average value	Standard deviation
$f_{1}$	PSO	$1.0252 \times 10^{3}$	$2.8385 \times 10^{3}$	$2.0986 \times 10^{3}$	735.8144
	Gold-SA	$9.2358 \times 10^{- 304}$	$3.1718 \times 10^{- 215}$	$3.1718 \times 10^{- 214}$	0
	CSA	$2.1247 \times 10^{- 7}$	0.0112	0.0023	0.0041
	ICSA	$5.4221 \times 10^{- 70}$	$2.9862 \times 10^{- 41}$	$2.9864 \times 10^{- 42}$	$9.4430 \times 10^{- 42}$
	GSACSA	0	0	0	0
$f_{2}$	PSO	18.0383	31.1995	24.6222	4.4906
	Gold-SA	$8.7327 \times 10^{- 150}$	$2.0531 \times 10^{- 114}$	$1.0522 \times 10^{- 113}$	$4.3283 \times 10^{- 114}$
	CSA	0.0014	0.0383	0.0170	0.0149
	ICSA	$7.0486 \times 10^{- 34}$	$2.2356 \times 10^{- 24}$	$2.5050 \times 10^{- 25}$	$6.9985 \times 10^{- 25}$
	GSACSA	$2.0984 \times 10^{- 280}$	$3.8382 \times 10^{- 211}$	$3.8382 \times 10^{- 212}$	0
$f_{3}$	PSO	0.3081	1.9605	0.7914	0.5318
	Gold-SA	$1.5730 \times 10^{- 4}$	0.0016	0.0048	0.0017
	CSA	$9.3007 \times 10^{- 5}$	0.0022	$9.4556 \times 10^{- 4}$	$6.5185 \times 10^{- 4}$
	ICSA	$6.5843 \times 10^{- 5}$	$7.4332 \times 10^{- 4}$	$3.0638 \times 10^{- 4}$	$2.3329 \times 10^{- 4}$
	GSACSA	$7.6225 \times 10^{- 6}$	$4.9216 \times 10^{- 4}$	$1.9099 \times 10^{- 4}$	$1.4093 \times 10^{- 4}$
$f_{4}$	PSO	10.2037	14.2087	12.1394	1.2326
	Gold-SA	$8.8818 \times 10^{- 16}$	$1.5987 \times 10^{- 15}$	$4.4409 \times 10^{- 15}$	$1.4980 \times 10^{- 15}$
	CSA	$1.8075 \times 10^{- 5}$	0.0239	0.0097	0.0087
	ICSA	$8.8818 \times 10^{- 16}$	$4.4409 \times 10^{- 15}$	$1.2434 \times 10^{- 15}$	$1.1235 \times 10^{- 15}$
	GSACSA	$8.8818 \times 10^{- 16}$	$8.8818 \times 10^{- 16}$	$8.8818 \times 10^{- 16}$	0
$f_{5}$	PSO	104.4275	164.2278	132.3667	19.0805
	Gold-SA	0	0	0	0
	CSA	$6.2361 \times 10^{- 7}$	0.0063	0.0017	0.0023
	ICSA	0	0	0	0
	GSACSA	0	0	0	0
$f_{6}$	PSO	18.6614	42.1057	28.4701	6.4986
	Gold-SA	0	0	0	0
	CSA	$8.6892 \times 10^{- 8}$	0.1290	0.0217	0.0405
	ICSA	0	0	0	0
	GSACSA	0	0	0	0

Table 3. Separation degree and performance index of signals separated by each method
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Table 3. Separation degree and performance index of signals separated by each method
Method Separation degree Performance index Number of iterations
FastICA 0.9327 0.1238 53
IPSO-ICA 0.9519 0.0875 34
IWOA-ICA 0.9556 0.0822 29
CSA-ICA 0.9482 0.0961 37
GSACSA-ICA 0.9628 0.0748 22

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Yihan Chen, Yian Liu, Hailing Song. Separation of Radar Co-Frequency Signal Based on Improved Crow Search Algorithm[J]. Laser & Optoelectronics Progress, 2023, 60(12): 1228006

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