如何生成具有指定信噪比的复杂白噪声？

Question

我正在使用以下代码生成具有指定 SNR（信噪比）和零均值的复杂白噪声：

import numpy as np

def GenerateNoise(signal, SNR_dB): # desiredSNR [dB]; signal is an array with complex values
   n = np.zeros((len(signal),1), dtype=complex)
   # SNR = var_signal^2 / var_n^2
   snr = 10.0**(SNR_dB/10.0) # Desired linear SNR
   var_signal = signal.var() # Measure power of signal
   var_n = var_signal / snr # Calculate required noise power for desired SNR
   if (var_n == 0): # In case of a null signal
       var_n = snr
   e = np.random.normal(0, np.sqrt(var_n/2), size=(len(signal), 2)).view(np.complex) # Generate noise with calculated power
   for i in range(0, len(signal)):
        n[i,0] = n[i,0] + e[i][0]
   print(10.0*np.log10((np.var(signal)**2)/(np.var(n)**2)))
   return n

代码灵感来源于此。问题是显示的 SNR 是指定 SNR 的两倍（例如，SNR_dB = -10 [dB]，打印值是 ~ -20 [dB]）。

有人知道错在哪里吗？

Answer 1

我已经弄明白了。我没有计算，也没有正确显示噪音。这是修改后的代码，如果对大家有用的话：

import numpy as np
def GenerateNoise(signal, SNR_dB): # desiredSNR [dB]; signal is an array with complex values
   n = np.zeros((len(signal),1), dtype=complex)
   # SNR = var_signal / var_n
   snr = 10.0**(SNR_dB/10.0) # Desired linear SNR
   var_signal = signal.var() # Measure power of signal
   var_n = var_signal / snr # Calculate required noise power for desired SNR
   if (var_n == 0): # In case of a null signal
       var_n = snr
   e = np.random.normal(0, np.sqrt(var_n*2.0)/2.0, size=(len(signal), 2)).view(np.complex) # Generate noise with calculated power
   for i in range(0, len(signal)):
       n[i,0] = n[i,0] + e[i][0]
   print(10.0*np.log10((np.var(signal))/(np.var(n))))
   return n

如何生成具有指定信噪比的复杂白噪声？

How to generate complex white noise with specified SNR?

python

random

noise

complex-numbers