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AWR Proprietary

Additive White Gaussian Noise Channel: AWGN

Symbol

Summary

AWGN implements an Additive White Gaussian Noise (AWGN) channel. This model adds independent Gaussian noise samples to its input signal.

Topology

This model is similar to the following subcircuit, with additional options for specifying the power level:

Parameters

Name Data Type Description Unit Type Default
ID N Element ID Text A1
PWR R Power level Varies 0
PWRTYP E Power level type   Avg. Power, Symbol
LOSS R Transmission loss dB 0
*NORMF R Normalization factor Scalar  
*RSEED I Random number generator seeds Scalar  
*RNG E Random number generator algorithm   Auto

* indicates a secondary parameter

Parameter Details

PWR. The output level of the added noise. Its interpretation depends on the PWRTYP setting. See "Recommended Usage and Warnings" for a thorough explanation of how the different settings in AWGN relate to corresponding settings in transmitter blocks, if such blocks precede the AWGN.

PWRTYP. Determines how PWR is interpreted. In the following N0 is the single-sided noise power spectral density, fs is the sampling frequency of the input signal, and SMPSYM is the number of samples per symbol from the input signal (data rate = fs / SMPSYM).

  • Auto: The interpretation of PWR will be determined from the transmitter preceding the AWGN block in the simulation chain, if such a transmitter (e.g., a QAM source) exists. If no transmitter is found, PWRTYP will be treated as "Avg. Power over fs (dBW)". If a transmitter is found and the OLVLTYP parameter of that transmitter is set to either normalized symbol energy or normalized bit energy, PWRTYP will be treated as "Normalized N0/2 (dBW/Hz)". If a transmitter is found and the OLVLTYP parameter is set to "Avg. Power (dBW)" PWRTYP will be treated as "Avg. Power, Symbol (dBW)". If a transmitter is found and the OLVLTYP parameter is set to "Avg. Power (dBm)" PWRTYP will be treated as "Avg. Power, Symbol (dBm)".

  • Avg. Power, Symbol (dBW), Avg. Power, Symbol (dBm): PWR is the average noise power in the symbol rate bandwidth. The units are either dBW or dBm.

    If NORMF is specified, SMPSYM is replaced by NORMF. Use this setting to measure Es/N0 when the transmitter power is specified as average power.

  • Avg. Power, Bit (dBW), Avg. Power, Bit (dBm): PWR is the average noise power in the bit rate bandwidth. The units are either dBW or dBm.

    where k is the number of bits per symbol. If NORMF is specified, SMPSYM/k is replaced by NORMF.

    Use this setting to measure Eb/N0 when the transmitter power is specified as average power.

  • Avg. Power over fs (dBW), Avg. Power over fs (dBm): PWR is the average noise power in the sampling frequency bandwidth. The units are either dBW or dBm.

    If NORMF is specified, fs is replaced by NORMF.

  • Double-sided PSD(dBW/Hz), Double-sided PSD (dBm/Hz): PWR is the double-sided power spectral density N0/2. The units are either dBW/Hz or dBm/Hz.

    If NORMF is specified, fs is replaced by NORMF when computing the average power.

  • Single-sided PSD(dBW/Hz), Single-sided PSD(dBm/Hz): PWR is the single-sided power spectral density N0. The units are either dBW/Hz or dBm/Hz.

    If NORMF is specified, fs is replaced by NORMF when computing the average power.

  • Normalized N0/2 (dBW/Hz), Normalized N0/2 (dBm/Hz): PWR is the double-sided PSD multiplied by the sampling frequency. The units are either dBW/Hz or dBm/Hz.

    If NORMF is specified, fs is replaced by NORMF. Use this setting to either measure Eb/N0 when the transmitter power is specified as normalized bit energy, or measure Es/N0 when the transmitter power is specified as normalized symbol energy.

  • SNR (dB): PWR is the signal to noise ratio in dB. The input signal must be generated by a block that specifies the signal power level, such as a transmitter or a TONE source. The single sided noise PSD generated by the AWGN block is then computed to be:

    where SNR = 10PWR/10.The signal to noise ratio of the output signal is then PWR, in dB, within the signal bandwidth DRATE = fs/SMPSYM .

  • Eb/N0 (dB): PWR is the bit energy to noise PSD ratio in dB. The input signal must be generated by a block that specifies the signal power level and bits per symbol, such as a transmitter. The single sided noise PSD generated by the AWGN block is then computed to be:

    where Eb/N0=10PWR/10 and M is the number of bits per symbol. The bit energy to noise PSD ratio of the output signal is then PWR, in dB.

  • Es/N0 (dB): PWR is the symbol energy to noise PSD ratio in dB. The input signal must be generated by a block that specifies the signal power level, such as a transmitter. The single sided noise PSD generated by the AWGN block is then computed to be:

    where Es/N0=10PWR/10. The symbol energy to noise PSD ratio of the output signal is then PWR, in dB.

Note that when using the PSD option of the power spectrum measurement, the results for complex signals are always single-sided PSD. For real signals the results are double-sided PSD if negative frequencies are displayed and are single-sided PSD if they are not displayed.

LOSS. Optional transmission loss through the channel.

NORMF. If specified, this is the normalization scaling used to convert between the PWR parameter and N0. See the PWRTYP parameter description for more details.

RSEED. The seeds for the random number generator. See the RND_D model for details about the random number generators.

If this is left empty, a seed will be generated based on a hash of the block name and the ID parameter (if the block is within a subcircuit, the ID parameters of the parents are also used). This will in general result in different instances of the block generating different sequences, though it is not guaranteed.

If this is set to -1, the seed will vary from sweep to sweep in a single simulation run. An initial seed value similar to that generated from the block name and ID parameter is used, with a different offset added to it each new sweep. The seed sequence is deterministic between simulation runs.

RNG. Determines the generator algorithm to use.

Data Input

Node No. Type Purpose
1 Real, Complex Input Signal

Data Output

Node No. Type Purpose
2 Real, Complex Modified Signal

Implementation Details

This model adds real or complex noise to the input signal. The noise has a probability density function of:

For real signals the average total power is N0/2·fs. For complex signals the average total power is N0·fs due to the separate real and imaginary components.

For details on the generation of the Gaussian noise, see the WHITENS model.

Recommended Usage and Warnings

Performing BER/SER Measurements

When performing BER or SER measurements, the AWGN block should be placed such that its output signal represents the signal to noise ratio to be measured. For example, if measuring the signal to noise ratio at the input of a receiver, the AWGN block should be placed just prior to the input of the receiver.

The swept signal to noise ratio, in either SNR, Eb/N0 or Es/N0 can then be directly specified at the AWGN block. To do this, set the PWR parameter to the swept signal to noise ratio and set the PWRTYP parameter to either "SNR (dB)", "Eb/N0 (dB)" or "Es/N0 (dB)". The SWPVAR parameter of the BER or SER meter should then be set to the same value as the PWR parameter. The x-axis of the BER/SER graph will then correspond to the desired signal to noise ratio at the output of the AWGN block.

In the Absence of a Transmitter Block

In the absence of a transmitter block (e.g., a QAM source) preceding the AWGN block in the simulation, an explicit setting of the PWRTYP parameter of the AWGN is needed. Setting to "Auto" will result in the warning: "Could not determine PWRTYP from input, will use Normalized N0/2 (dBW/Hz)'." since there is no preceding transmitter to help the AWGN block automatically configure its PWRTYP. A similar warning reading "Could not determine bits per symbol on input signal, PWRTYP will be treated as Avg. Power, Symbols (dBW)'." is issued when the PWRTYP setting is "Avg. Power, Bit (dBW)" in the absence of a transmitter, since there is nothing prior to the AWGN block to set the number of bits per symbol. Similar behavior occurs for "Avg. Power, Bit (dBm)". All the other settings result in no warnings. For example, to set the total noise power inside the sampling bandwidth, one would set PWRTYP to "Avg. Power over fs (dBW)" or "Avg. Power over fs (dBm)", as explained in the section above.

In the Presence of a Transmitter Set to "AVG. Power (DBm)"

It is expected that most of the time, when a transmitter block (a QAM source) precedes the AWGN block in a simulated chain, the OLVLTYP of that transmitter will be set to "Avg. Power (dBm)". In such a case, no warnings are ever issued and the settings of the PWRTYP parameter of the AWGN block work as follows:

i) "Auto" or "Avg. Power, Symbol (dBm)": the BER reference curve is followed for a Es/N0 sweep.

ii) "Avg. Power, Bit (dBm)": the BER reference curve is followed for a Eb/N0 sweep.

iii) "Avg. Power over fs (dBm)": the user specifies the total noise power in the entire sampling bandwidth, hence the SNR in the entire sampling bandwidth can be defined as:

which makes the SNR defined above be equal to (Es/N0)dB-10·log(SMPSYM). In this case (i.e., Transmitter set to "Avg. Power (dBm)" and AWGN set to "Avg. Power over fs (dBm)") the SNR above represents the signal-to-noise power ratio in the full bandwidth of the sampling, and it would be seen at a receiver prior to any filtering for noise rejection. After such filtering, the noise bandwidth (and hence also the noise power) would clearly be reduced.

iv) "Double-sided PSD" or "Single-sided PSD": the user is directly setting the PSD (note: in dBW/Hz) so no BER reference curve will be followed.

v) "Normalized N0/2": again, no BER reference curves are expected to be followed in this case; this option is mainly intended to be used when the OLVLTYP of the preceding transmitter block is set to "Symbol Energy (dB)" or "Bit Energy (dB)" to follow BER reference curves in those cases, as explained in the paragraphs below.

vi) "SNR (dB)": the BER reference curve is followed for an SNR sweep.

vii) "Eb/N0 (dB)": the BER reference curve is followed for an Eb/N0 sweep.

viii) "Es/N0 (dB)": the BER reference curve is followed for an Es/N0 sweep.

In The Presence Of A Transmitter Set To "Symbol Energy (Db)"

In this case, with a transmitter block present and its OLVLTYP set to "Symbol Energy (dB)", it appears that the user is trying to set up a Es/N0 sweep. For that, the PWRTYP setting of the AWGN block should be "Auto" or "Normalized N0/2 (dBW/Hz)". Other settings will result in warnings. Specifically:

i) if the PWRTYP of AWGN is set to either "Auto" or "Normalized N0/2 (dBW/Hz)", no warning appears, and the BER curve corresponds to that of a Es/N0 sweep.

ii) if the PWRTYP is set to "Avg. Power, Bit", "Avg. Power over fs", "Double-sided PSD", "Single-sided PSD", "SNR (dB)" or "Eb/N0 (dB)", for either the dBW or dBm units, the following warning is issued (although the simulation continues to run): "Transmitter appears to be configured for Es/N0. PWRTYP should be set to Auto' or Normalized N0/2' for Es/N0."

iii) if the PWRTYP of AWGN is set to "Es/N0 (dB)", no warning appears, and the BER curve corresponds to that of a Es/N0 sweep.

In the Presence of a Transmitter Set to "BIT ENERGY (db)"

Similarly in this case, with a transmitter block present and its OLVLTYP set to "Bit Energy (dB)", it appears that the user is trying to set up a Eb/N0 sweep. For that, the PWRTYP setting of the AWGN block should be "Auto" or "Normalized N0/2 (dBW/Hz)". Other settings will result in warnings. Specifically:

i) if the PWRTYP of AWGN is set to either "Auto" or "Normalized N0/2 (dBW/Hz)", no warning appears, and the BER curve corresponds to that of a Eb/N0 sweep.

ii) if the PWRTYP is set to "Avg. Power, Symbol", "Avg. Power over fs", "Double-sided PSD", "Single-sided PSD", "SNR (dB)" or "Es/N0 (dB)", for either the dBW or dBm units, the following warning is issued (although the simulation continues to run): "Transmitter appears to be configured for Eb/N0. PWRTYP should be set to Auto' or Normalized N0/2' for Eb/N0."

iii) if the PWRTYP of AWGN is set to "Eb/N0 (dB)", no warning appears, and the BER curve corresponds to that of a Eb/N0 sweep.

AWR Proprietary

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