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AWGN Channel - Add white Gaussian noise to input signal

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Channels

Description

The AWGN Channel block adds white Gaussian noise to a real or complex input signal. When the input signal is real, this block adds real Gaussian noise and produces a real output signal. When the input signal is complex, this block adds complex Gaussian noise and produces a complex output signal. This block inherits its sample time from the input signal.

This block uses the Signal Processing Blockset™ Random Source block to generate the noise. Random numbers are generated using the Ziggurat method, which is the same method used by the MATLAB randn function. The Initial seed parameter in this block initializes the noise generator. Initial seed can be either a scalar or a vector whose length matches the number of channels in the input signal. For details on Initial seed, see the Random Source block reference page in the Signal Processing Blockset documentation set.

The signal inputs can only be of type single or double. The port data types are inherited from the signals that drive the block.

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

Frame-Based Processing and Input Dimensions

This block can process multichannel signals that are frame-based or sample-based. The guidelines below indicate how the block interprets your data, depending on the data's shape and frame status:

If your input is a sample-based scalar, then the block adds scalar Gaussian noise to your signal.
If your input is a sample-based vector or a frame-based row vector, then the block adds independent Gaussian noise to each channel.
If your input is a frame-based column vector, then the block adds a frame of Gaussian noise to your single-channel signal.
If your input is a frame-based m-by-n matrix, then the block adds a length-m frame of Gaussian noise independently to each of the n channels.

The input cannot be a sample-based m-by-n matrix if both m and n are greater than 1.

Specifying the Variance Directly or Indirectly

You can specify the variance of the noise generated by the AWGN Channel block using one of these modes:

Signal to noise ratio (Eb/No), where the block calculates the variance from these quantities that you specify in the dialog box:
- Eb/No, the ratio of bit energy to noise power spectral density
- Number of bits per symbol
- Input signal power, the actual power of the symbols at the input of the block
- Symbol period
Signal to noise ratio (Es/No), where the block calculates the variance from these quantities that you specify in the dialog box:
- Es/No, the ratio of signal energy to noise power spectral density
- Input signal power, the actual power of the symbols at the input of the block
- Symbol period
Signal to noise ratio (SNR), where the block calculates the variance from these quantities that you specify in the dialog box:
- SNR, the ratio of signal power to noise power
- Input signal power, the actual power of the samples at the input of the block
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. If the first input signal is sample-based, then the variance input must be sample-based. If the first input signal is frame-based, then the variance input can be either frame-based with exactly one row, or sample-based.

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.

A good rule of thumb for selecting the Symbol period value is to set it to be what you model as the symbol period in the model. The value would depend upon what constitutes a symbol and what the oversampling applied to it is (e.g., a symbol could have 3 bits and be oversampled by 4).

In both Variance from mask mode and Variance from port mode, these rules describe how the block interprets the variance:

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 of each of the quadrature components of the complex noise is half of the calculated or specified value.

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

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

E_s/N₀ = (T_sym/T_samp) · SNR

E_s/N₀ = E_b/N₀ + 10log₁₀(k) in dB

where

E_s = Signal energy (Joules)
E_b = Bit energy (Joules)
N₀ = Noise power spectral density (Watts/Hz)
T_sym is the Symbol period parameter of the block in Es/No mode
k is the number of information bits per input symbol
T_samp is the inherited sample time of the block, in seconds

For real signal inputs, the AWGN Channel block relates E_s/N₀and SNR according to the following equation:

E_s/N₀ = 0.5 (T_sym/T_samp) · SNR

Note that the equation for the real case differs from the corresponding equation for the complex case by a factor of 2. This is so because the block 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 about these quantities, see Describing the Noise Level of an AWGN Channel in the Communications Toolbox documentation.

Tunable Block Parameters

The following table indicates which parameters are tunable, for different block modes.

Mode	Tunable Parameters
`Eb/No`	Eb/No, Input signal power
`Es/No`	Es/No, Input signal power
`SNR`	SNR, Input signal power
`Variance from mask`	Variance

You can tune parameters in normal mode, Accelerator mode and the Rapid Accelerator mode.

If you use the Real-Time Workshop® rapid simulation (RSIM) target to build an RSIM executable, then you can tune the parameters listed in the previous table without recompiling the model. This is useful for Monte Carlo simulations in which you run the simulation multiple times (perhaps on multiple computers) with different amounts of noise.

Dialog Box

Initial seed: The seed for the Gaussian noise generator.
Mode: The mode by which you specify the noise variance: Signal to noise ratio (Eb/No), Signal to noise ratio (Es/No), Signal to noise ratio (SNR), Variance from mask, or Variance from port.
Eb/No (dB): The ratio of bit energy per symbol to noise power spectral density, in decibels. This field appears only if Mode is set to Eb/No.
Es/No (dB): The ratio of signal energy per symbol to noise power spectral density, in decibels. This field appears only if Mode is set to Es/No.
SNR (dB): The ratio of signal power to noise power, in decibels. This field appears only if Mode is set to SNR.
Number of bits per symbol: The number of bits in each input symbol. This field appears only if Mode is set to Eb/No.
Input signal power, referenced to 1 ohm (watts): The mean square power of the input symbols (if Mode is Eb/No or Es/No) or input samples (if Mode is SNR), in watts. This field appears only if Mode is set to Eb/No, Es/No, or SNR.
Symbol period (s): The duration of a channel symbol, in seconds. This field appears only if Mode is set to Eb/No or Es/No.
Variance: The variance of the white Gaussian noise. This field appears only if Mode is set to Variance from mask.