def sampling_phase(sampling_period, sampling_time, corr_ab=0.9, corr_ae=0.4):
'''
sampling_period: 采样周期/采样间隔。单位ms。每隔一个采样周期，可采集到一个样本
sampling_time: 采样时间。单位s。一共采样了这么长的时间，也即每隔一个采样时间，更新一次密钥/导频位置
corr_ab: Alice和Bob的信道测量值的相关系数
corr_ae: Alice和Eve的信道测量值的相关系数
注：在给定相关系数corr时，得到与samples_A满足corr的samples_B(或samples_E)
返回值: 采样序列。一共有time/period个采样点。如period=1，time=25，共采样25*1000/1=25000个
'''
sampling_num = sampling_time * 1000 / sampling_period
corr_SNR_dict = {
0.1: 6,
0.2: 8,
0.3: 10,
0.4: 12,
0.5: 14,
0.6: 17,
0.7: 20,
0.8: 23,
0.9: 29,
1.0: 1000
}
samples_A = 2 * pi * random(sampling_num) # [0,2pi)之间均匀分布
samples_B = mod(awgn(samples_A, corr_SNR_dict[corr_ab]), 2 * pi)
samples_E = mod(awgn(samples_A, corr_SNR_dict[corr_ae]), 2 * pi)
return samples_A, samples_B, samples_E
def transmission(x, SNR=dSNR, L=dL, K=dK, N=dN, Ncp=dNcp):
'''
x: 发送端的发送信号
SNR: 信噪比
L: 信道长度
K: 稀疏度
N: 子载波数
Ncp: 循环前缀长度
'''
''' 时域的信道脉冲响应'''
h = channel(L, K)
''' 信道频率响应H '''
W = fftMatrix(N, L) # 傅里叶正变换矩阵，即：使稀疏的h变为不稀疏的H的基
H = dot(W, h) # 频率的冲激响应
H.shape = (N, 1)
''' 不考虑循环前缀在信道中的传输 '''
x = x[:, Ncp:]
x = x.reshape(N)
# 将发送信号作为观测矩阵的对角元素,X=diag(X(0),X(1),...,X(N-1))是N*N的子载波矩阵
X = fft(x)
''' 测量矩阵 '''
X = diag(X)
''' 理想信道传输 '''
X_H = dot(X, H)
''' 添加高斯白噪声，得接收信号向量Y '''
Y = awgn(X_H, SNR) # 加入复高斯白噪声,得到接收到的信号（频域表示）
#No = Y-X_H # Y = X*H + No
y = ifft(Y, axis=0)
y = y.reshape(1, N)
y = np.c_[y[:, -Ncp:], y]
return h, H, y
def draw_SNR_corr(stype, sampling_period, sampling_time):
SNR = range(0, 51, 1)
group = 100
SNR_num = len(SNR)
corr = zeros((group, SNR_num))
if stype == 'RSSI':
samples_A, temp, temp = sampling_RSSI(sampling_period, sampling_time)
elif stype == 'Phase':
samples_A, temp, temp = sampling_phase(sampling_period, sampling_time)
for i in range(group):
print 'running...', i
for j in range(SNR_num):
samples_B = awgn(samples_A, SNR[j])
if stype == 'Phase':
samples_B = mod(samples_B, 2 * pi)
corr[i, j] = corrcoef(samples_A, samples_B, rowvar=0)[0, 1]
corr = mean(corr, 0)
plt.figure(figsize=(8, 5))
plt.plot(SNR, corr, 'bo-')
plt.xlabel('SNR(dB)')
plt.ylabel('Corrcoef')
plt.title('Corrcoef in different SNR for ' + stype)
def transmission(x, L, K, N, M, Ncp, Nt, Nr, SNR):
'''
x: 发送端的发送信号
L: 信道长度
K: 稀疏度
N: 子载波数
M: 每帧的OFDM符号数
Ncp: 循环前缀长度
Nt: 发送天线数
Nr: 接收天线数
SNR: 信噪比
'''
''' 时域/频域的信道响应'''
h = zeros((Nr, Nt, L), dtype=np.complex)
H = zeros((Nr, Nt, N), dtype=np.complex)
for r in range(Nr):
for t in range(Nt):
h[r, t, :] = channel(L, K) # 第r个接收天线，与第t个发送天线的1个符号周期内的信道脉冲响应
H[r, t, :] = dot(fftMatrix(N, L), h[r, t, :]) # 信道频率响应
''' 傅里叶正变换矩阵 '''
W = fftMatrix((N + Ncp), L) # 傅里叶正变换矩阵，即：使稀疏的h变为不稀疏的H的基
W_M = W # 对于慢时变信道，在M个符号周期内，H保持不变。相当于对W做M次重复
for i in range(M - 1):
W_M = np.r_[W_M, W]
for t in range(Nt):
''' 第t个天线的发送数据 '''
x_t = x[:, t]
''' 将时域的发送信号，变换到频域 '''
X_t = fft(x_t)
''' 测量矩阵 '''
X_t = diag(
X_t) # 将发送信号作为观测矩阵的对角元素,X=diag(X(0),X(1),...,X(N-1))是N*N的子载波矩阵
if t == 0:
X_wave = dot(X_t, W_M)
else:
X_wave = np.c_[X_wave, dot(X_t, W_M)]
''' X_wave与Nr*Nr单位矩阵的克罗内克积 '''
Kronecker = kron(eye(Nr, Nr), X_wave)
''' Nt*Nr*L的信道脉冲响应向量 '''
for r in range(Nr):
for t in range(Nt):
h_rt = h[r, t, :].reshape(-1, 1) # 第r个接收天线，与第t个发送天线的1个符号周期内的信道脉冲响应
if r == 0 and t == 0:
h_vector = h_rt
else:
h_vector = np.r_[h_vector, h_rt]
''' 理想信道传输 '''
Y = dot(Kronecker, h_vector)
''' AWGN '''
Y = awgn(Y, SNR)
y = Y.reshape(-1, Nr)
y = ifft(y, axis=0)
return h, H, y
corr_SNR_dict = {
0.1: 6,
0.2: 8,
0.3: 10,
0.4: 12,
0.5: 14,
0.6: 17,
0.7: 20,
0.8: 23,
0.9: 29,
1.0: 1000
}
samples_A = 2 * pi * random(sampling_num) # [0,2pi)之间均匀分布
samples_B = awgn(samples_A, corr_SNR_dict[corr_ab])
samples_E = awgn(samples_A, corr_SNR_dict[corr_ae])
return samples_A, samples_B, samples_E
def draw_SNR_corr(stype, sampling_period, sampling_time):
SNR = range(0, 51, 1)
group = 100
SNR_num = len(SNR)
corr = zeros((group, SNR_num))
samples_A, temp, temp = sampling(stype, sampling_period, sampling_time)
for i in range(group):
print 'running...', i
for j in range(SNR_num):
