Es/N0、EbN0与SNR区别

对复输入信号而言，Es/No (dB) = 10*log10(Tsymbol / Tsampling) + SNR(dB)   （1）
对实输入信号而言，Es/No (dB) = 10*log10(2 * Tsymbol / Tsampling) + SNR(dB)  （2）
其中Tsymbol为信号的符号周期，Tsampling为信号的采样周期。


对于复输入信号而言，matlab的help是这样推导（1）的：
Es/No(dB) = 10*log10((S*Tsymbol)/(N/Bn)) 
           = 10*log10((Tsymbol*Fs)*(S/N))
           = 10*log10((Tsymbol/Tsampling)+SNR(dB)
其中，
S = Input signal power, in watts
N = Noise power, in watts
Bn = Noise bandwidth, in Hz
Fs = Sampling frequency, in Hz.

Note that Bn= Fs = 1/Tsampling

For complex input signals, the AWGN Channel block relates Eb/N0, Es/N0, and SNR according to the following equations:
Es/N0 = (Tsym/Tsamp)·SNR
Es/N0 = Eb/N0 + 10log10(k)  in dB


where
      Es = Signal energy (Joules)
      Eb = Bit energy (Joules)
      N0 = Noise power spectral density (Watts/Hz)
      Tsym is the Symbol period parameter of the block in Es/No mode
      k is the number of information bits per input symbol
      Tsamp is the inherited sample time of the block, in seconds


For real signal inputs, the AWGN Channel block relates Es/N0 and SNR according to the following equation:
Es/N0 = 0.5 (Tsym/Tsamp)·SNR


Note that the equation for the real case differs from the corresponding equation for the complex case by a factor of 2. This is so because the block uses a noise power spectral density of N0/2 Watts/Hz for real input signals, versus N0 Watts/Hz for complex signals.