基于PSO-CNN的LPI雷达波形识别算法

doi:10.12305/j.issn.1001-506X.2021.12.17

Abstract

Abstract:

Low probability of intercept (LPI) radar is a new type of radar with strong anti-jamming ability and low interception characteristics. Accurate and efficient recognition of it has become a difficult problem in waveform recognition of radar confrontation. Aiming at the structural intelligent optimization problem of the mainstream classifier convolution neural network (CNN) in this direction, a waveform recognition algorithm based on particle swarm optimization (PSO)-CNN is proposed. The algorithm uses the optimization characteristics of PSO to automatically build CNN structure with indefinite layers, layer types and layer parameters in a large range, evaluate and iteratively optimize it. The algorithm uses a combination of recognition accuracy and network complexity to measure indicators, the proportion of the two can be adjusted according to requirements to achieve the choice of accuracy and lightness. The CNN structure obtained by the algorithm achieves better LPI radar waveform recognition effect than nine classic CNN structures. And the algorithm avoids the lack of intelligence and objectivity of artificially selecting CNN hyper parameters during radar waveform recognition, and improves the adaptability and efficiency of the selecting CNN structure.

Key words: low probability of intercept (LPI) radar, waveform recognition, convolution neural network (CNN) optimization, particle swarm optimization (PSO) algorithm

CLC Number:

TN973

Shuai ZHAO, Songtao LIU, Huiyang WANG. LPI radar waveform recognition algorithm based on PSO-CNN[J]. Systems Engineering and Electronics, 2021, 43(12): 3552-3563.

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References 21

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雷达波形	参数	取值范围
	f_c	U(f_s/6, f_s/5)
LFM	B	U(f_s/20, f_s/16)
	N	U[500, 1 920]
	L_Bc	{7, 11, 13}
Barker	f_c	U(f_s/6, f_s/5)
	N_cc	U[11,14]
	f_c	U(f_s/6, f_s/5)
Frank & P1	N_cc	{4, 5, 6}
	M	{6, 7, 8}
	f_c	U(f_s/6, f_s/5)
P2	N_cc	{4, 5, 6}
	M	{6, 8}
	f_c	U(f_s/6, f_s/5)
P3 & P4	N_cc	{4, 5, 6}
	m	{36, 49, 64}

信道参数	取值
采样频率/MHz	F_s=100
多径衰减/s	{0, 1.8, 3.4}/F_s
平均路径增益/dB	{0, -2, -10}
K-factor	4
最大多普勒频移/Hz	4
AWGN/dB	SNR=[-6∶6∶30]

设置项	训练集	测试集
SNR范围/dB	[-6, 30]	[-10, 10]
SNR间隔/dB	6	2
单类每SNR下图片数量	1 000/7	200
图片尺寸	80×80	80×80
总量	7 000	15 400

类别	参数项	取值
粒子群相关参数	粒子群迭代次数	10
	粒子群大小	10
	C_tsh	0.5
CNN粒子初始化相关参数	卷积核尺寸范围	[1×1, 7×7]
	卷积层输出通道范围	[3,256]
	全连接层神经元个数范围	[1,300]
	网络层数范围	[3,15]
	卷积层生成概率	0.6
	池化层生成概率	0.3
	全连接层生成概率	0.1
CNN粒子训练相关参数	训练批量	32
	粒子评估前训练epoch	1
	最优粒子测试前训练epoch	10
	Dropout	0.5
	层间是否采用正则化	是

类别	1	2	3	4	5	平均
acc-10	0.978 9	0.968 5	0.990 1	0.983 5	0.989 2	0.982 0
参数数量	320 771	2 757 398	1 469 133	3 420 182	3 477 612	2 289 019
训练时间/s	39 244	98 634	42 687	81 278	67 783	65 925

LPI radar waveform recognition algorithm based on PSO-CNN

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类别	平均检测精度(SNR≥0)/%	参数数量	检测时间/s
PSO-CNN-3	94.8	1.469×10⁶	3
PSO-CNN-5	87.8	3.477×10⁶	3
LeNet	71.0	5.492×10⁶	3
AlexNet	91.1	2.566 1×10⁷	3
ZFNet	70.9	2.565 5×10⁷	4
VGG13	76.6	3.868 1×10⁷	22
VGG16	72.2	4.399 1×10⁷	29
VGG19	72.5	4.930 1×10⁷	40
GoogleNet	78.7	1.244 6×10⁷	53
ResNet-34	67.5	2.268 3×10⁷	35
ResNet-50	64.1	4.574 6×10⁷	65

类别	3.5×10⁵	3.5×10⁶	1.05×10⁶	3.5×10⁵-0.5C_f
参数数量	131 285	583 591	552 586	127 887
训练时间/s	45 789	54 300	124 574	31 792
平均检测精度(SNR≥0)/%	84.2	80.1	77.8	70.4

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算法1 PSO-CNN
输入运行次数(N_r), PSO群体粒子数(N), PSO最大迭代次数(it_max), 训练数据(X, Y), 个体极值与全局极值的选择阈值(C_tsh), 网络层数范围(l_min, l_max), 卷积层最大卷积核尺寸(k_max), 全连接层最大神经元数(n_max), 网络输出维度(d_out), 粒子评估前训练epoch数(e_train), 最优框架测试前训练epoch数(e_test)。
输出最优CNN架构及其参数数量, 测试准确率。
1 for j=1 to N_r do
2 S={P₁, P₂, …, P_N}←粒子群初始化(N_r, N, l_min, l_max, k_max, n_max, d_out)
3 P₁.pbest←P₁, P₁.grade, P₁.pbest.grade←CNN粒子分数评估(P₁, X, Y, e_train)
4 gbest←P₁, gbest.grade←P₁.grade
5 for i=2 to N do
6 P_i.pbest←P_i, P_i.grade, P_i.pbest.grade←CNN粒子分数评估(P_i, X, Y, e_train)
7 if P_i.grade≥gbest.grade then
8 gbest←P_i
9 end
10 end
11 for it=1 to it_max do
12 for i=1 to N do
13 P_i.velocity←CNN粒子速度计算(P_i, C_tsh)
14 P_i←粒子更新(P_i, P_i.velocity)
15 P_i.grade←CNN粒子分数评估(P_i, X, Y, e_train)
16 if P_i.grade≥P_i.pbest.grade then
17 P_i.pbest←P_i, P_i.pbest.grade←P_i.grade
18 if P_i.pbest.grade≥gbest.grade then
19 gbest←P_i, gbest.grade←P_i.grade
20 end
21 end
22 end
23 end
24 CNN粒子分数评估(gbest, X, Y, e_test)←gbest
25 return gbest, gbest.n_paramaters, gbest.grade
26 end
27 return gbest, average of gbest.n_parameters, average of gbest.grade

算法2 粒子群初始化
输入 PSO群体粒子数(N), 网络层数范围(l_min, l_max), 卷积层最大卷积核尺寸(k_max), 卷积层最大输出通道数(C_conv-max), 全连接层最大神经元数(n_max), 网络输出维度(d_out), 随机选取卷积层、池化层及全连接层的概率(P_conv, P_pool, P_FC), 三者和为1。
输出初始粒子群S={P₁, P₂, …, P_N}。
1 for i=1 to N do
2 P_i.depth=rand(l_min, l_max)
3 for j=1 to P_i.depth do
4 if j==1 then
5 list_layers[j]←addconv(C_conv－max, k_max)
6 elif j==P_i.depth then
7 list_layers[j]←addFC(d_out)
8 elif list_layers[j－1].type==FC then
9 list_layers[j]←addFC(n_max)
10 else
11 layer_type←rand(0, 1)
12 if layer_type≤P_convthen
13 list_layers[j]←addconv(C_conv－max, k_max)
14 elif P_conv≤layer_type≤P_conv+P_pool then
15 list_layers[j]←addpool()
16 else
17 list_layers[j]←addFC(n_max)
18 end
19 end
20 end
21 P_i←list_layers
22 end
23 return S={P₁, P₂, …, P_N}

算法3 粒子差异计算
输入粒子P₁、P₂
输出 diff=P₁－P₂
1 index_P₁←寻找起始FC层索引(P₁), index_P₂←寻找起始FC层索引(P₂)
2 P_1copo←P₁[0:index_P₁－1], P_2copo←P₂[0:index_P₂－1]
3 P_1FC←P₁[P₁.length: －1:index_P₁], P_2FC←P₂[P₂.length: －1:index₂: ]
4 L=length_diff←max(index_P₁, index_P₂)+max(P_1FC.length, P_2FC.length)
5 for i=0 to max (index_P₁, index_P₂)do
6 if P_1copo[i]≠None and P_2copo[i]≠None then
7 if P_1copo[i].type=P_2copo[i].type then
8 diff[i]←0
9 else diff[i]←P_1copo[i].type end
10 elif P_1copo[i]≠None and P_2copo[i]=None then
11 diff[i]←P_1copo[i].type
12 else P_1copo[i]=None and P_2copo[i]≠None then
13 diff[i]←None
14 end
15 end
16 for j=0 to max(P_1FC.length, P_2FC.length)do
17 if P_1FC[j]≠None and P_2FC[j]≠None then
18 diff[L－j]←0
19 elif P_1FC[j]≠None and P_2FC[j]=None then
20 diff[L－j]←P_1FC[j].type
21 else P_1FC[j]=None and P_2FC[j]≠None then
22 diff[L－j]←None
23 end
24 end
25 return diff