| Communications Toolbox | |
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 (Eb/N0). This quantity is used by BERTool and performance evaluation functions in this toolbox.
Ratio of symbol energy to noise power spectral density (Es/N0)
The relationship between Es/N0 and Eb/N0, 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 Es/N0 and SNR, both expressed in dB, is as follows:
where Tsym is the signal's symbol period and Tsamp is the signal's sampling period.
For example, if a complex baseband signal is oversampled by a factor of 4, then Es/N0 exceeds the corresponding SNR by 10 log10(4).
Derivation for Complex Input Signals. You can derive the relationship between Es/N0 and SNR for complex input signals as follows:
where
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/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.
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