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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 comm.AWGNChannel System object™, the AWGN Channel block, or the awgn function.
The following examples use an AWGN Channel: QPSK Transmitter and ReceiverQPSK Transmitter and Receiver and scattereyedemoscattereyedemo.
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 awgn function.
Ratio of bit energy to noise power spectral density (EbNo). This quantity is used by BERTool and performance evaluation functions in this toolbox.
Ratio of symbol energy to noise power spectral density (EsNo)
The relationship between EsNo and EbNo, both expressed in dB, is as follows:
$${E}_{s}/{N}_{0}\text{(dB)}={E}_{b}/{N}_{0}\text{(dB)}+10{\mathrm{log}}_{10}(k)$$
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) log_{2}(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 EsNo and SNR, both expressed in dB, is as follows:
$$\begin{array}{l}{E}_{s}/{N}_{0}\text{(dB)}=10{\mathrm{log}}_{10}\left({T}_{sym}/{T}_{samp}\right)+SNR\text{}\text{(dB)forcomplexinputsignals}\\ {E}_{s}/{N}_{0}\text{(dB)}=10{\mathrm{log}}_{10}\left(0.5{T}_{sym}/{T}_{samp}\right)+SNR\text{}\text{(dB)forrealinputsignals}\end{array}$$
where T_{sym} is the signal's symbol period and T_{samp} is the signal's sampling period.
For example, if a complex baseband signal is oversampled by a factor of 4, then EsNo exceeds the corresponding SNR by 10 log_{10}(4).
Derivation for Complex Input Signals. You can derive the relationship between EsNo and SNR for complex input signals as follows:
$$\begin{array}{c}{E}_{s}/{N}_{0}\text{(dB)}=10{\mathrm{log}}_{10}\left((S\cdot {T}_{sym})/(N/{B}_{n})\right)\\ =10{\mathrm{log}}_{10}\left(({T}_{sym}{F}_{s})\cdot (S/N)\right)\\ =10{\mathrm{log}}_{10}\left({T}_{sym}/{T}_{samp}\right)+SNR\text{}\text{(dB)}\end{array}$$
where
S = Input signal power, in watts
N = Noise power, in watts
B_{n} = Noise bandwidth, in Hertz
F_{s} = Sampling frequency, in Hertz
Note that B_{n}= F_{s} = 1/T_{samp}.
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 S_{n}(f) of a real bandpass white noise process and its complex lowpass equivalent.