convertSNR

Convert SNR values

Since R2022a

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Syntax

y = convertSNR(x,inputmode)

y = convertSNR(x,inputmode,outputmode)

y = convertSNR(x,inputmode,Name=Value)

Description

y = convertSNR(x,inputmode) converts the input signal-to-noise ratio value x to an SNR.

example

y = convertSNR(x,inputmode,outputmode) converts the input signal-to-noise ratio value x to the ratio specified by outputmode. For more information, see Algorithms.

y = convertSNR(x,inputmode,Name=Value) specifies additional name-value arguments.

example

Examples

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Add Noise to 8-PSK Modulated Signal for Eb/No Value

Open Live Script

Generate random data symbols and the 8-PSK modulated signal.

d = randi([0 7],100,1);
M = 8;                  % 8-PSK
k = log2(M);            % bits per symbol
psk = pskmod(d,M);

Add the noise equivalent of a 6 dB Eb/No value to the modulated signal. To do so, first convert the Eb/No value to an SNR.

EbNo = 6;
SNR = convertSNR(EbNo,'ebno',BitsPerSymbol=k)

SNR = 
10.7712

y = awgn(psk,SNR);

Plot the signal with and without the noise component.

figure
plot(real(psk));
hold on
plot(real(y))
legend("Perfect Signal","Noisy Signal")

Figure contains an axes object. The axes object contains 2 objects of type line. These objects represent Perfect Signal, Noisy Signal.

Convert Eb/N0 Value to SNR Value

Open Live Script

Set the simulation parameters

M = 16;        % Modulation order
k = log2(M);   % bits per symbol
nSamp = 4;     % Number of samples

Create the raised cosine transmit and receive filters

txfilter = comm.RaisedCosineTransmitFilter( ...
    OutputSamplesPerSymbol=nSamp);
rxfilter = comm.RaisedCosineReceiveFilter( ...
    InputSamplesPerSymbol=nSamp, ...
    DecimationFactor=nSamp);

Generate random data symbols and the filtered 16-QAM modulated signal.

d = randi([0 1],1000,1);
modsig = qammod(d,M,InputType="bit");
txsig = txfilter(modsig);

Add the noise equivalent of 10 dB $E_{b} / N_{0}$ to the modulated signal. To do so, first convert the $E_{b} / N_{0}$ value to SNR.

EbN0 = 10;
snr = convertSNR(EbN0,"ebno", ...
    BitsPerSymbol=k, ...
    SamplesPerSymbol=nSamp, ...
    CodingRate=1/3)

snr = 
5.2288

[sig2,var] = awgn(txsig,snr);
rxsig = rxfilter(sig2);
demodsig = qamdemod(rxsig,M, ...
    OutputType="llr", ...
    NoiseVariance=var);

Plot the demodulated QAM signal.

plot(demodsig,'.')
xlabel('Bit Number')
ylabel('LLR')

Figure contains an axes object. The axes object with xlabel Bit Number, ylabel LLR contains a line object which displays its values using only markers.

Convert SNR Per Subcarrier to SNR

Open Live Script

Convert the SNR per subcarrier to an SNR value for an OFDM symbol with unused subcarriers.

Define QPSK and OFDM modulation related variables.

M = 4;                  % Modulation order for QPSK
SNRsc = 15;             % SNR per subcarrier
nfft = 128;             % Total number of subcarriers
cplen = 16;             % Cyclic prefix length
nnull = 30;             % Number of null subcarriers
nullidx = ...           % Null indices
    [1:nnull nfft/2+1 nfft-nnull+1:nfft]'; 
nsc = nfft-(2*nnull)-1; % Number of active subcarriers

QPSK-modulate random data.

data = randi([0 3],nsc,100);
x = qammod(data,M,UnitAveragePower=true);

OFDM-modulate and normalize the signal to unity power.

txscale = nfft/sqrt(nsc);
y = txscale * ofdmmod(x,nfft,cplen,nullidx);

Compute the SNR equivalent value of the SNR per subcarrier and filter the OFDM-modulated signal through an AWGN channel.

SNR = convertSNR(SNRsc,'snrsc',...
    FFTLength=nfft,NumActiveSubcarriers=nsc);
r = awgn(y,SNR);

Compute and display SNR values.

n = r - y;
fprintf('SNR of OFDM symbols = %1.1f dB\n', 10*log10(var(y)/var(n)));

SNR of OFDM symbols = 12.3 dB

Ssc = var(y) / nsc;
Nsc = var(n) / nfft;
fprintf('SNR per subcarrier = %1.1f dB\n', 10*log10(Ssc/Nsc));

SNR per subcarrier = 15.1 dB

Input Arguments

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`x` — Input value
numeric row vector

Input value in dB, specified as a numeric row vector.

Data Types: double

`inputmode` — Input mode
`"ebno"` | `"esno"` | `"snr"` | `"snrsc"`

Input mode for x, specified as "ebno", "esno", "snr", or "snrsc".

"ebno" — x is the energy per bit to noise power spectral density ratio (Eb/N0).
"esno" — x is the energy per symbol to noise power spectral density ratio (Es/N0).
"snr" — x is the SNR.
"snrsc" — x is the SNR per subcarrier in a multicarrier modulation scheme.

For more information, see Algorithms.

`outputmode` — Output mode
`"ebno"` | `"esno"` | `"snr"` | `"snrsc"`

Output mode for y, specified as "ebno", "esno", "snr", or "snrsc".

"ebno" — y is the energy per bit to noise power spectral density ratio (Eb/N0).
"esno" — y is the energy per symbol to noise power spectral density ratio (Es/N0).
"snr" — y is the SNR.
"snrsc" — y is the SNR per subcarrier in a multicarrier modulation scheme.

For more information, see Algorithms.

Name-Value Arguments

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Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: y = convertSNR(x,inputmode,outputmode,SamplesPerSymbol=2)

`SamplesPerSymbol` — Samples per symbol
`1` (default) | positive integer

Samples per symbol, specified as a positive integer. The function ignores SamplesPerSymbol value if you set:

inputmode to "ebno" and outputmode to "esno".
inputmode to "esno" and outputmode to "ebno".

Data Types: double

`BitsPerSymbol` — Bits per symbol
`1` (default) | positive integer

Bits per symbol, specified as a positive integer. The function ignores BitsPerSymbol value if you set:

inputmode to "esno" and outputmode to "snr".
inputmode to "snr" and outputmode to "esno".

Data Types: double

`CodingRate` — Coding rate
`1` (default) | scalar in the range (0, 1]

Coding rate, specified as a scalar in the range (0, 1]. The function ignores CodingRate value if you set:

inputmode to "esno" and outputmode to "snr".
inputmode to "snr" and outputmode to "esno".

Data Types: double

`FFTLength` — Total number of subcarriers
`64` (default) | positive integer

Total number of subcarriers in a multicarrier modulated signal, specified as a positive integer. The function ignores FFTLength value if "snrsc" is not the inputmode or outputmode setting.

Data Types: double

`NumActiveSubcarriers` — Number of active subcarriers
`64` (default) | positive integer

Number of active subcarriers, specified as a positive integer. The number of active subcarriers must be equal to or less than FFTLength. The function ignores NumActiveSubcarriers if "snrsc" is not the inputmode or outputmode setting.

Data Types: double

Output Arguments

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`y` — Output value
row vector of numeric values

Output value in dB, returned as a row vector of numeric values. For more information, see Algorithms.

Algorithms

This table shows the valid input to output mode conversions.

`inputmode` to `outputmode`	Conversion
`"ebno"` to `"snr"`	SNR = E_b / N₀ + 10log10((N_bps×R) / N_sps)
`"snr"` to `"ebno"`	E_b / N₀ = SNR – 10log10((N_bps×R) / N_sps)
`"ebno"` to `"esno"`	E_s / N₀ = E_b / N₀ + 10log10(N_bps×R)
`"esno"` to `"ebno"`	E_b / N₀ = E_s / N₀ – 10log10(N_bps×R)
`"esno"` to `"snr"`	SNR = E_s / N₀ – 10log10(N_sps)
`"snr"` to `"esno"`	E_s / N₀ = SNR + 10log10(N_sps)
`"snrsc"` to `"snr"`	SNR = SNR_SC + 10log10(N_SC / FFTLen)
`"snr"` to `"snrsc"`	SNR_SC = SNR – 10log10(N_SC / FFTLen)

Where

N_bps is the BitsPerSymbol value.
N_sps is the SamplesPerSymbol value.
R is the CodingRate value.
FFTLen is the FFTLength value.
N_SC is the NumActiveSubcarriers value.
E_b / N₀ is the x value input or y value output when you set inputmode or outputmode, respectively, to "ebno".
E_s / N₀ is the x value input or y value output when you set inputmode or outputmode, respectively, to "esno".
SNR is the x value input or y value output when you set inputmode or outputmode, respectively, to "snr".
SNR_SC is the x value input or y value output when you set inputmode or outputmode, respectively, to "snrsc".

Version History

Introduced in R2022a

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R2023b: Convert SNR per subcarrier

You can now use the convertSNR function to convert between SNR per subcarrier in a multicarrier modulation scheme and SNR.

convertSNR

Syntax

Description

Examples

Add Noise to 8-PSK Modulated Signal for Eb/No Value

Convert Eb/N0 Value to SNR Value

Convert SNR Per Subcarrier to SNR

Input Arguments

x — Input value numeric row vector

inputmode — Input mode "ebno" | "esno" | "snr" | "snrsc"

outputmode — Output mode "ebno" | "esno" | "snr" | "snrsc"

Name-Value Arguments

SamplesPerSymbol — Samples per symbol 1 (default) | positive integer

BitsPerSymbol — Bits per symbol 1 (default) | positive integer

CodingRate — Coding rate 1 (default) | scalar in the range (0, 1]

FFTLength — Total number of subcarriers 64 (default) | positive integer

NumActiveSubcarriers — Number of active subcarriers 64 (default) | positive integer

Output Arguments

y — Output value row vector of numeric values

Algorithms

Version History

R2023b: Convert SNR per subcarrier

See Also

`x` — Input value
numeric row vector

`inputmode` — Input mode
`"ebno"` | `"esno"` | `"snr"` | `"snrsc"`

`outputmode` — Output mode
`"ebno"` | `"esno"` | `"snr"` | `"snrsc"`

`SamplesPerSymbol` — Samples per symbol
`1` (default) | positive integer

`BitsPerSymbol` — Bits per symbol
`1` (default) | positive integer

`CodingRate` — Coding rate
`1` (default) | scalar in the range (0, 1]

`FFTLength` — Total number of subcarriers
`64` (default) | positive integer

`NumActiveSubcarriers` — Number of active subcarriers
`64` (default) | positive integer

`y` — Output value
row vector of numeric values