matlab awgn channel,AWGN Channel

Relationship Between EsN0 and SNR

The relationship between EsN0 and SNR, both expressed in dB, is as follows:

Es/N0(dB)=10log10(Tsym/Tsamp)+SNR(dB) for complex input signalsEs/N0(dB)=10log10(0.5Tsym/Tsamp)+SNR(dB) for real input signals

where Tsym is the symbol period of the

signal and Tsamp is the sampling period of the

signal.

For a complex baseband signal oversampled by a factor of 4, the 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:

Es/N0(dB)=10log10((S⋅Tsym)/(N/Bn))=10log10((TsymFs)⋅(S/N))=10log10(Tsym/Tsamp)+SNR(dB)

where

S = Input signal power, in watts

N = Noise power, in watts

Bn = Noise bandwidth, in Hertz =

Fs =

1/Tsamp.

Fs = Sampling frequency, in

Hertz

Behavior for Real and Complex Input Signals.These figures illustrate the difference between the real and complex cases by

showing the noise power spectral densities of a real bandpass white noise process and

its complex lowpass equivalent.

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