matlab_chirp信号模型应用于GPS捕获中的虚警概率

clc clear all; close all; %% 系统参数 B = 4e6; % 带宽 T = 256e-6; % 符号持续时间 miu = B/T; % 调频率 D = B*T; % 时宽带宽积 fs = 4e6; % 采样频率 over_fs = fs*2; % 过采样的采样频率 chirp_len = floor(T*fs); % 离散化信号长度（符号采样点数） over_len = floor(T*over_fs); % 过采样的符号采样点数 %% 基带信号产生 p = rand(1,chirp_len)*2*pi; % 均匀相位序列 k0 = 0; k1 = 1; a = raylrnd(1/sqrt(2),[1,chirp_len]); % 瑞利幅度序列 t = 0:1/fs:T-1/fs; % 时间轴 over_t=0:1/over_fs:T-1/over_fs; % 过采样的时间轴 chirp = exp(j*pi*miu*over_t.^2); % 正调频率chirp信号 %% 信息调制 bit = 4; % 每个符号携带的比特数 M = 2^bit; % CCSK调制阶数 Num_x = 20; % 总的信息比特数 delta_len = floor(over_len/M) % CCSK调制的分段长度 CN0db = 40:0.5:46; %EbN0db = 7; % Eb/N0 %SNR = EbN0db-10*log10(chirp_len)+10*log10(bit); SNR = CN0db-10*log10(over_fs); loop_times = 10000; fal_cnt = 0; CNW_refer = a.*exp(j*pi*miu*t.^2).*exp(j*k0*p); % 升类噪声chirp信号 over_refer = ifft([fft(CNW_refer),zeros(1,chirp_len)]); % 过采样的升类噪声chirp信号 for ii = 1:Num_x trans_carrier(:,ii) = imag(over_refer); % 参考信号 end trans = reshape(trans_carrier,1,[]); % 并串转换，生成发射信号 trans_I = [zeros(1,700),trans,zeros(1,400)]; %% 成型滤波 L = 8; % 内插倍数 tr_inter_I = reshape([trans_I;zeros(L-1,length(trans_I))],1,[]); % 内插0之后的信号 [yf,tf] = rcosine(1,L,'fir/sqrt'); % 成型滤波器系数 [tr_filter_I,to] = rcosflt(tr_inter_I,1,L,'filter/Fs',yf); % 成型滤波 tr_shape_I = tr_filter_I(L*3+1:length(tr_filter_I)-L*3)'; %% 加入频偏(上变频) fc = 20e6; fd = [0 100e3 400e3 800e3]; % 多普勒频偏值 tt = 0:1/(L*over_fs):(length(tr_shape_I)-1)/(L*over_fs); % 时间轴2 %% 加噪声 for ll = 1:length(SNR) for mm = 1:length(fd) doppler = exp(j*2*pi*(fd(mm)+fc)*tt); tr_doppler = tr_shape_I.*cos(2*pi*(fd(mm)+fc)*tt); dec_cnt = 0; for jj = 1:loop_times tr_noised = awgn(tr_doppler,SNR(ll),'measured'); %% 下变频 tr_I = tr_noised.*cos(2*pi*fc*tt); tr_Q = tr_noised.*sin(2*pi*fc*tt); %% 匹配滤波 [rx_match_I,to] = rcosflt(tr_I,1,L,'filter/Fs',yf); % 匹配滤波 rx_cept_I = rx_match_I(L*3+1:length(rx_match_I)-L*3)'; rx_comp_I = rx_cept_I(1:L:length(rx_cept_I)); [rx_match_Q,to] = rcosflt(tr_Q,1,L,'filter/Fs',yf); % 匹配滤波 rx_cept_Q = rx_match_Q(L*3+1:length(rx_match_Q)-L*3)'; rx_comp_Q = rx_cept_Q(1:L:length(rx_cept_Q)); %% 信号检测 peak_find0_I = xcorr(rx_comp_I,real(chirp)); % 捕获匹配滤波输出 peak_find1_I = xcorr(rx_comp_I,imag(chirp)); % 捕获匹配滤波输出 peak_find0_Q = xcorr(rx_comp_Q,imag(chirp)); % 捕获匹配滤波输出 peak_find1_Q = xcorr(rx_comp_Q,real(chirp)); % 捕获匹配滤波输出 peak_find0_full = (peak_find0_I-peak_find0_Q).^2+(peak_find1_I+peak_find1_Q).^2; peak_find0 = peak_find0_full(length(rx_comp_I)-over_len+1:end); Pfa = 1e-4; N0 = sum(peak_find0(over_len+1:2*over_len))/over_len/2; %thre = erfcinv(2*Pfa)*N0+N0; % 检测门限 thre = N0*(-2*log(Pfa)); syn_sequ0 = find(peak_find0>thre); % 搜索高于门限的峰 delta_len1 = 700-round(fd(mm)/B*over_len); sum_initial = 1; sum_thre = 1; sum1 = sum_initial; for kk = 1:Num_x if peak_find0(kk*over_len+delta_len1)>thre sum1 = sum1+1; else sum1 = sum1-1; end if sum1>sum_thre dec_cnt = dec_cnt+1; break else if sum1<1 dec_cnt = dec_cnt; %sum1 = sum_initial; break end end end end d_num(mm,ll) = dec_cnt end end pd = d_num/loop_times plot(CN0db,pd(1,:),'-o');hold on plot(CN0db,pd(2,:),'->'); plot(CN0db,pd(3,:),'-s'); plot(CN0db,pd(4,:),'-p'); grid on xlabel('C/N0(db)'); ylabel('Pd'); legend('fd=0','fd=100kHz','fd=400kHz','fd=800kHz');