awgn

Add white Gaussian noise to signal

Syntax

y = awgn(x,snr)

y = awgn(x,snr,signalpower)

y = awgn(x,snr,signalpower,randobject)

y = awgn(x,snr,signalpower,seed)

y = awgn(___,powertype)

[y,var] = awgn(___)

Description

y = awgn(x,snr) adds white Gaussian noise to the vector signal x. This syntax assumes that the power of x is 0 dBW. For more information about additive white Gaussian noise, see What is AWGN?

y = awgn(x,snr,signalpower) accepts an input signal power value in dBW. To measure the power of x before adding noise, specify signalpower as 'measured'. The 'measured' option does not generate the requested average SNR for repeated awgn function calls in a loop if the input signal power varies over time due to fading and the coherence time of the channel is larger than the input duration.

y = awgn(x,snr,signalpower,randobject) additionally accepts a random number stream object to generate normal random noise samples. For information about producing repeatable noise samples, see Tips.

y = awgn(x,snr,signalpower,seed) specifies a seed value for initializing the normal random number generator that is used to add white Gaussian noise to the input signal.

y = awgn(___,powertype) specifies the signal and noise power type as 'dB' or 'linear' in addition to the input arguments in any of the previous syntaxes. For information on the relationships between SNR and other measures of the relative power of the noise, such as E_s/N₀, and E_b/N₀, see AWGN Channel Noise Level.

[y,var] = awgn(___) also returns the total noise variance used to produce random noise samples.

Examples

Add AWGN to Sawtooth Signal

Create a sawtooth wave.

t = (0:0.1:60)';
x = sawtooth(t);

Add white Gaussian noise and plot the results.

y = awgn(x,10,'measured');
plot(t,[x y])
legend('Original Signal','Signal with AWGN')

General QAM Modulation over AWGN Channel

Transmit and receive data using a nonrectangular 16-ary constellation in the presence of Gaussian noise. Show the scatter plot of the noisy constellation and estimate the symbol error rate (SER) for two different SNRs.

Create a 16-QAM constellation based on the V.29 standard for telephone-line modems.

c = [-5 -5i 5 5i -3 -3-3i -3i 3-3i 3 3+3i 3i -3+3i -1 -1i 1 1i];
sigpower = pow2db(mean(abs(c).^2));
M = length(c);

Generate random symbols.

data = randi([0 M-1],2000,1);

Modulate the data by using the genqammod function. General QAM modulation is necessary because the custom constellation is not rectangular.

modData = genqammod(data,c);

Pass the signal through an AWGN channel with a 20 dB SNR.

rxSig = awgn(modData,20,sigpower);

Display a scatter plot of the received signal and the reference constellation c.

h = scatterplot(rxSig);
hold on
scatterplot(c,[],[],'r*',h)
grid
hold off

Demodulate the received signal by using the genqamdemod function. Determine the number of symbol errors and the SER.

demodData = genqamdemod(rxSig,c);
[numErrors,ser] = symerr(data,demodData)

numErrors = 1

ser = 5.0000e-04

Repeat the transmission and demodulation process with an AWGN channel with a 10 dB SNR. Determine the SER for the reduced SNR. As expected, the performance degrades when the SNR is decreased.

rxSig = awgn(modData,10,sigpower);
demodData = genqamdemod(rxSig,c);
[numErrors,ser] = symerr(data,demodData)

numErrors = 461

ser = 0.2305

Repeatable AWGN Simulation

Generate random data symbols and the 4-PSK modulated signal.

M = 4;
k = log2(M);
snr = 3;
data = randi([0 M-1],2000,1);
x = pskmod(data,M);

Set the random number generator seed.

seed = 12345;

Generate repeatable random noise using the rng function before calling the awgn function.

rng(seed);
y = awgn(x,snr);

Compute the bit errors.

dataHat = pskdemod(y,M);
numErr1 = biterr(data,dataHat,k)

numErr1 = 321

Reset the random number generator seed.

rng(seed);

Demodulate the PSK signal and compute the bit errors.

y = awgn(x,snr);
dataHat = pskdemod(y,M);
numErr2 = biterr(data,dataHat,k)

numErr2 = 321

Compare numErr1 to numErr2. The errors are equal even after you reset the random number generator seed.

isequal(numErr1, numErr2)

ans = logical
   1

Repeatable AWGN with RandStream

Generate white Gaussian noise addition results using a RandStream object and the reset object function.

Specify the power of X as 0 dBW, add noise to produce an SNR of 10 dB, and use a local random stream.

S = RandStream('mt19937ar','Seed',5489);
sigin = sqrt(2)*sin(0:pi/8:6*pi);
sigout1 = awgn(sigin,10,0,S);

Add white Gaussian noise to sigin. Use isequal to compare sigout1 to sigout2. The outputs are not equal when you do not reset the random stream.

sigout2 = awgn(sigin,10,0,S);
isequal(sigout1,sigout2)

ans = logical
   0

Reset the random stream object, returning the object to its state prior to adding AWGN to sigout1. Add AWGN to sigin and compare sigout1 to sigout3. The outputs are equal when you reset the random stream.

reset(S);
sigout3 = awgn(sigin,10,0,S);
isequal(sigout1,sigout3)

ans = logical
   1

Input Arguments

x — Input signal

scalar | vector | array

Input signal, specified as a scalar, vector, or array. The power of the input signal is assumed to be 0 dBW.

Data Types: double
Complex Number Support: Yes

snr — Signal-to-noise ratio

scalar

Signal-to-noise ratio in dB, specified as a scalar. The function applies the same snr value to each channel. The columns of the input signal represent the different channels of a multichannel signal.

Data Types: double

signalpower — Signal power

scalar | 'measured'

Signal power, specified as a scalar or 'measured'.

• Scalar — The value is used as the signal level of in to determine the appropriate noise level based on the value of snr.

• 'measured' — The signal level of in is computed to determine the appropriate noise level based on the value of snr.

If the input signal is a multichannel signal, the function calculates the signalpower value across all channels as a single value. It then uses the value to calculate the noise level for all the channels.

Data Types: double

randobject — Random number stream object

RandStream object

Random number stream object, specified as a RandStream object. The state of the random stream object determines the sequence of numbers produced by the randn function. Configure the random stream object using the reset (RandStream) function and its properties.

For information about producing repeatable noise samples, see Tips.

seed — Random number generator seed

scalar

Random number generator seed value, specified as a scalar.

Data Types: double

powertype — Signal power unit

'dB' (default) | 'linear'

Signal power unit, specified as 'dB' or 'linear'.

• When powertype is 'dB', snr is measured in dB and signalpower is measured in dBW.

• When powertype is 'linear', the snr is measured as a ratio and signalpower is measured in watts assuming a reference load of 1 ohms.

To set the powertype argument, you must also set snr and signalpower.

Output Arguments

y — Output signal

scalar | vector | array

Output signal, returned as a scalar, vector, or array. The returned output signal is the input signal with added white Gaussian noise.

var — Noise variance

scalar

Total noise variance, returned as a positive scalar. The function uses the noise variance to generate random noise samples.

More About

What is AWGN?

Additive white Gaussian noise (AWGN) is a simple noise model that represents electron motion in the RF front end of a receiver. As the name implies, the noise gets added to the signal. The noise is called “white” because it is spectrally flat across the entire sampling bandwidth. Analogously, the color white contains equal spectral power levels at all frequencies of the visible light spectrum. The noise is Gaussian because its amplitude can be modeled with a normal probability distribution.

The AWGN channel is often used to model a satellite communications channel, since that channel typically does not suffer from common terrestrial impairments like fading, multipath, and interference. An AGWN channel serves as a good starting point for the analysis of terrestrial wireless links because it establishes a best-case bound on the bit error rate performance of a terrestrial link.

Tips

• For information on the relationships between SNR and other measures of the relative power of the noise, such as E_s/N₀, and E_b/N₀, see AWGN Channel Noise Level.

• To generate repeatable white Gaussian noise samples, do one of the following:

  • Use rng(seed) before calling the awgn function to generate repeatable random noise.

  • Provide a static seed value as an input to awgn.

  • Use the reset (RandStream) function on the randobject before passing it as an input to awgn.

  • Provide randobject in a known state as an input to awgn. For more information, see RandStream.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Code generation supported, except for syntaxes that include a RandStream object.

Version History

Introduced before R2006a