bpsk_spectral.rar_BPSK循环谱_bpsk信号循环谱_cyclic spectrum_三维循环谱_循环谱

%%%% 本程序思想： %2015.7.6 BPSK循环平稳 % 初步认定为频域加窗的SSCA算法，运用信号与其复共扼频谱相乘的方式来表达循环谱。被处理信号为运用BPSK调制产生的码源序 %%%% 列。关于频率f和循环频率alfa的表达式计算值得关注（只与采样频率有关）。 %数据设置部分 clc,clear all; Rb = 2; %码元速率 Ts = 1/Rb; %码元间隔 L = 2^7; %单位时间内信号抽样点数 num = 16; %一个段落中码元个数 N = num*L; %一个段落内总的抽样点数 (4096) fc = 12; %载波频率 dt = Ts/L; %抽样时间间隔 df = 1/(dt*N); %频率间隔 Bs = df*N/2; %带宽 BPSK的带宽是基带符号速率的2倍,如果知道基带符号速率,BPSK带宽就确定了 fs = Bs*2; f = df/2-Bs:df:Bs; %抽样频率 t = dt/2:dt:num*Ts; %抽样时间 t= 1/(4*64) : 1/(2*64) : 8; a=sign(randn(1,num)); %码源序列 generate the initial signal (length is 16) %%%%%%%%%%%% BPSK调制信号产生 %通过基带成型滤波器后的信号 function for rr=1:num I((rr-1)*L+1:rr*L)=a(rr); % number of I is 1024 .extend the length of signal 'a' to 64 times length. end %最终调制信号 the signal modulated by BPSK carrier s0 = I.*cos(2*pi*fc*t); % the number of 't'and 's' are the same.(1024) figure(1) plot(t,s0,'r-'); axis([0 0.5 -1 1]); %look 35/1024 percent of the plot. %%%%%%%%%%%%加性高斯白噪声信道%%%%%%%%%%%%%%%% snrdb = 8; Ec = sum(abs(s0).^2)./length(s0); snr_ratio = 10.^(snrdb/10); noise_var = sqrt(Ec/(2*snr_ratio)); [s] = add_whitenoise2(s0,noise_var); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% M = 2; % ?????????????????????????? Fs=fs; N = (M*Fs)/df; % the new value of 'N'is 2 times the value of old 'N'. (2048) %%%%N = pow2 (nextpow2(N)); % windowing record for FFT (2048) % NEXTPOW2(N) returns the first P such that 2^P >= abs(N) % X = POW2(Y) for each element of Y is 2 raised to the power Y %设置FFT点数为1024 X = fft(s0,N); % fft of the truncated(被删节的) (or zero padded) time series (2048 columns) X = fftshift(X);% shift components of fft (2048 columns) Xc = conj(X); % precompute the complex conjugate(复共轭) vector (2048 columns) S = zeros (N,N); % size of the Spectral Correlation Density matrix f = zeros (N,N); % size of the frequency matrix; alfa = zeros (N,N); % size of the cycle frequency matrix F = Fs/(2*N); % precompute(预先计算的) constants - F = Fs/(2*N); G = Fs/N; % precompute constants - G = Fs/N; m = -M/2+1:M/2; % set frequency smoothing window index % m(0)=0,m(1)=1. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Algorithm: for k = 1:N % fix k (2048 columns) % the function of fix is choose the integral value towards '0'. % computes vectors of f and alfa, % store frequency and cycle frequency data for given k. k1 = 1:N; f(k,k1) = F*(k+k1-1) - Fs/2; % Computes f values and shift them to center in zero (f = (K+L)/2N) [1] alfa(k,k1) = G*(k-k1 + N-1) - Fs; % Computes alfa values and shift them to center in zero (alfa = (K-L)/N) [1] for k1 = 1:N %fix k1 = J %calculate X(K+m) & conj (X(J+m)) for arguments of X(1:N) only B = max(1-k, 1-k1); % Largest min of 1 <= (K+m)| (J+m) <= N A = min (N-k, N-k1); % Smallest max of 1 <= (K+m)| (J+m) <= N n = m((m<=A) & (m>=B)); % fix the index out of range problem by truncating the window. % m(0)=0,m(1)=1. if isempty(n) S(k,k1) = 0; else p = k+n; q = k1+n; Y = X(p).*Xc(q); S(k,k1) = sum(Y); % the power spetral Correlation destiny function end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % haha=length(sign([real(Y)])) S = abs(S./max(max(S)));% normalize output matrix alfa f figure(2); mesh(alfa, f, S); grid; ylabel('Frequency (Hz)');xlabel('Cycle frequency (Hz)'); title('BPSK循环谱三维图'); figure(3); plot(alfa,S,'r'); % 'alfa'is cycle frequency.'f'is frequency.'S'is Spetral Correlation Density Function. axis([-100 100 0 1]); ylabel('S');xlabel('Cycle frequency (Hz)'); figure(4); plot(f,S,'r'); axis([-100 100 0 1]); ylabel('S');xlabel('Frequency (Hz)');