AWGN Channel

Add white Gaussian noise to input signal

• Library:

• Communications Toolbox / Channels

• 

Description

The AWGN Channel block adds white Gaussian noise to the input signal. It inherits the sample time from the input signal.

Ports

Input

In — Input data signal

vector | matrix

Input data signal, specified as an N_S-by-1 vector or an N_S-by-N_C matrix.

N_S represents the number of samples in the input signal. N_C represents the number of channels, as determined by the number of columns in the input signal matrix. Both N_S and N_C can be equal to 1.

The block adds frames of length-N_S Gaussian noise to each of the N_C channels, using a distinct random distribution per channel.

Data Types: double | single
Complex Number Support: Yes

Var — Variance of additive white Gaussian noise

positive scalar | vector

Variance of additive white Gaussian noise, specified as a positive scalar or a 1-by-N_C vector. N_C represents the number of channels, as determined by the number of columns in the input signal matrix. For more information, see Specifying the Variance Directly or Indirectly.

Dependencies

To enable this port, set Mode to Variance from port.

Data Types: double

Output

Out — Output data signal

vector | matrix

Output data signal for the AWGN channel, returned as a vector or matrix. The datatype and dimensions of Out match those of the input signal, In.

Parameters

Initial seed — Noise generator initial seed

67 (default) | positive scalar | vector

Noise generator initial seed, specified as a positive scalar or a 1-by-N_C vector.

This block uses the Random Source block to generate noise. Random numbers are generated using the Ziggurat method (V5 RANDN algorithm). The block reuses the same initial seeds every time you rerun the simulation, so that this block outputs the same signal each time you run a simulation.

When the input signal is complex, the block creates random data as:

randData = randn(2*NS,NC) 
noise = randData(1:2:end) + 1i(randData(2:2:end))

N_S is the number of samples and N_C is the number of channels.

You can specify different seed values for each DLL build.

Tunable: Yes

Mode — Variance mode

Signal to noise ratio (Eb/No) (default) | Signal to noise ratio (Es/No) | Signal to noise ratio (SNR) | Variance from mask | Variance from port

Variance mode, specified as Signal to noise ratio (Eb/No), Signal to noise ratio (Es/No), Signal to noise ratio (SNR), Variance from mask, or Variance from port. For more information, see Relationship Among Eb/No, Es/No, and SNR Modes and Specifying the Variance Directly or Indirectly.

Eb/No (dB) — Ratio of information bit energy per symbol to noise power spectral density

10 (default) | scalar | vector

Ratio of information bit energy per symbol to noise power spectral density in decibels, specified as a scalar or vector. The information bit energy is the magnitude without channel coding.

Tunable: Yes

Dependencies

To enable this parameter, set Mode to Eb/No.

Es/No (dB) — Ratio of information symbol energy per symbol to noise power spectral density

10 (default) | scalar | vector

Ratio of information symbol energy per symbol to noise power spectral density in decibels, specified as a scalar or vector. The information bit energy is the magnitude without channel coding.

Tunable: Yes

Dependencies

To enable this parameter, set Mode to Es/No.

SNR (dB) — Ratio of signal power to noise power

10 (default) | scalar | vector

Ratio of signal power to noise power in decibels, specified as a scalar or vector.

Tunable: Yes

Dependencies

To enable this parameter, set Mode to SNR.

Number of bits per symbol — Number of bits in each input symbol

1 (default) | scalar | vector

Number of bits in each input symbol, specified as a scalar or vector.

Dependencies

To enable this parameter, set Mode to Eb/No.

Input signal power, referenced to 1 ohm (watts) — Mean square power of input

1 (default) | scalar | vector

Mean square power of the input in watts, specified as a scalar or vector.

• When Mode is Eb/No or Es/No, the parameter is the mean square power of the input symbols.

• When Mode is SNR, this parameter is the mean square power of the input samples.

Tunable: Yes

Dependencies

To enable this parameter, set Mode to Eb/No, Es/No, or SNR.

Symbol period (s) — Duration of an information channel

1 (default) | positive scalar | vector

Duration of an information channel symbol in seconds, specified as a positive scalar or vector. The duration of the information channel is measured without channel coding.

Dependencies

To enable this parameter, set Mode to Eb/No or Es/No.

Variance — Variance of white Gaussian noise

1 (default) | scalar | vector

Variance of the white Gaussian noise, specified as a scalar or vector. For more information, see Specifying the Variance Directly or Indirectly.

Tunable: Yes

Dependencies

To enable this parameter, set Mode to Variance from mask.

Model Examples

LLR vs. Hard Decision Demodulation in Simulink

The improvement in BER performance when using log-likelihood ratio (LLR) instead of hard decision demodulation in a convolutionally coded communication link.

Block Characteristics

Data Types	double | single
Multidimensional Signals	no
Variable-Size Signals	no

Tips

• You can tune parameters in normal mode, accelerator mode, or rapid accelerator mode.

• Unless otherwise indicated, parameters are nontunable.

  • For nontunable parameters, when you use the Simulink^® Coder™ rapid simulation (RSIM) target to build an RSIM executable, you cannot change their values without recompiling the model.

  • If a parameter is tunable, you can change its value at any time. This is useful for Monte Carlo simulations in which you run the simulation multiple times (such as on multiple computers) with different amounts of noise.

Algorithms

Relationship Among Eb/No, Es/No, and SNR Modes

For uncoded complex input signals, the AWGN Channel block relates E_b/N_0, E_s/N₀, and SNR according to these equations:

E_s/N₀ = (T_sym/T_samp) · SNR

E_s/N₀ = E_b/N₀ + 10log₁₀(k)  in dB

• E_s represents the signal energy in joules.

• E_b represents the bit energy in joules.

• N₀ represents the noise power spectral density in watts/Hz.

• T_sym represents the Symbol period (s) parameter of the block in Es/No mode.

• k represents the number of information bits per input symbol, Number of bits per symbol.

• T_samp represents the inherited sample time of the block, in seconds.

For real signal inputs, the AWGN Channel block relates E_s/N₀ and SNR according to this equation:

E_s/N₀ = 0.5 (T_sym/T_samp) · SNR

Note

• All values of power assume a nominal impedance of 1 ohm.

• The equation for the real case differs from the corresponding equation for the complex case by a factor of 2. Specifically, the object uses a noise power spectral density of N₀/2 watts/Hz for real input signals, versus N₀ watts/Hz for complex signals.

For more information, see AWGN Channel Noise Level.

Specifying the Variance Directly or Indirectly

To directly specify the variance of the noise generated by AWGN Channel, specify the Mode as:

• Variance from mask, where you specify the variance in the dialog box. The value must be positive.

• Variance from port, where you provide the variance as an input to the block. The variance input must be positive, and its sampling rate must equal that of the input signal.

For Variance from mask and Variance from port mode:

• If the variance is a scalar, then all signal channels are uncorrelated but share the same variance.

• If the variance is a vector whose length is the number of channels in the input signal, then each element represents the variance of the corresponding signal channel.

  Note

  If you apply complex input signals to the AWGN Channel block, then it adds complex zero-mean Gaussian noise with the calculated or specified variance. The variance for each quadrature component of the complex noise is half of the calculated or specified value.

To specify the variance indirectly, that is, to have the block calculate the variance, specify the Mode as:

• Signal to noise ratio (Eb/No), where the block calculates the variance from these quantities that you specify in the dialog box:

  • Eb/No (dB), the ratio of bit energy to noise power spectral density

  • Number of bits per symbol

  • Input signal power, referenced to 1 ohm (watts), the actual power of the symbols at the input of the block

  • Symbol period (s)

• Signal to noise ratio (Es/No), where the block calculates the variance from these quantities that you specify in the dialog box:

  • Es/No (dB), the ratio of signal energy to noise power spectral density

  • Input signal power, referenced to 1 ohm (watts), the actual power of the symbols at the input of the block

  • Symbol period (s)

• Signal to noise ratio (SNR), where the block calculates the variance from these quantities that you specify in the dialog box:

  • SNR (dB), the ratio of signal power to noise power

  • Input signal power, referenced to 1 ohm (watts), the actual power of the samples at the input of the block

Changing the symbol period in the AWGN Channel block affects the variance of the noise added per sample, which also causes a change in the final error rate.

$$NoiseVariance=\frac{SignalPower\times SymbolPeriod}{SampleTime\times {10}^{\frac{Es/No}{10}}}$$

Tip

Select the symbol period equal to the symbol period of the model. The value depends on what constitutes a symbol and what the oversampling applied to it is. For example, a symbol could have 3 bits and be oversampled by 4. For more information, see AWGN Channel Noise Level.

References

[1] Proakis, John G. Digital Communications. 4th Ed. McGraw-Hill, 2001.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.