An AWGN channel adds white Gaussian noise to the signal that passes through it. You can
create an AWGN channel in a model using the
object™, the AWGN Channel block, or the
The relative power of noise in an AWGN channel is typically described by quantities such as
Signal-to-noise ratio (SNR) per sample. This is the actual input parameter to the
Ratio of bit energy to noise power spectral density (EbN0). This quantity is used by
BER Analyzer Tool and performance evaluation
functions in this toolbox.
Ratio of symbol energy to noise power spectral density (EsN0)
The relationship between EsN0 and EbN0, both expressed in dB, is as follows:
where k is the number of information bits per symbol.
In a communication system, k might be influenced by the size of the modulation alphabet or the code rate of an error-control code. For example, if a system uses a rate-1/2 code and 8-PSK modulation, then the number of information bits per symbol (k) is the product of the code rate and the number of coded bits per modulated symbol: (1/2) log2(8) = 3/2. In such a system, three information bits correspond to six coded bits, which in turn correspond to two 8-PSK symbols.
The relationship between EsN0 and SNR, both expressed in dB, is as follows:
where Tsym is the symbol period of the signal and Tsamp is the sampling period of the signal.
For example, if a complex baseband signal is oversampled by a factor of 4, then EsN0 exceeds the corresponding SNR by 10 log10(4).
Derivation for Complex Input Signals. You can derive the relationship between EsN0 and SNR for complex input signals as follows:
S = Input signal power, in watts
N = Noise power, in watts
Bn = Noise bandwidth, in Hertz
Fs = Sampling frequency, in Hertz
Note that Bn= Fs = 1/Tsamp.
Behavior for Real and Complex Input Signals. The following figures illustrate the difference between the real and complex cases by showing the noise power spectral densities Sn(f) of a real bandpass white noise process and its complex lowpass equivalent.