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genqammod

General quadrature amplitude modulation (QAM)

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Syntax

Y = genqammod(X,const)

Description

Y = genqammod(X,const) returns the complex envelop of the QAM for message signal X. Input const specifies the signal mapping for the modulation.

example

Examples

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Open Live Script

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

Figure Scatter Plot contains an axes object. The axes object with title Scatter plot, xlabel In-Phase, ylabel Quadrature contains 2 objects of type line. One or more of the lines displays its values using only markers This object represents Channel 1.

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 = 
4

ser = 
0.0020

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 = 
457

ser = 
0.2285
Open Live Script

Create the points that describe a hexagonal constellation.

inphase = [1/2 1 1 1/2 1/2 2 2 5/2];
quadr = [0 1 -1 2 -2 1 -1 0];
inphase = [inphase;-inphase]; inphase = inphase(:);
quadr = [quadr;quadr]; quadr = quadr(:);
const = inphase + 1i*quadr;

Plot the constellation.

h = scatterplot(const);

Figure Scatter Plot contains an axes object. The axes object with title Scatter plot, xlabel In-Phase, ylabel Quadrature contains a line object which displays its values using only markers. This object represents Channel 1.

Generate input data symbols. Modulate the symbols using this constellation.

x = [3 8 5 10 7];
y = genqammod(x,const);

Demodulate the modulated signal, y.

z = genqamdemod(y,const);

Plot the modulated signal in same figure.

hold on;
scatterplot(y,1,0,'ro',h);
legend('Constellation','Modulated signal');
hold off;

Figure Scatter Plot contains an axes object. The axes object with title Scatter plot, xlabel In-Phase, ylabel Quadrature contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Constellation, Modulated signal.

Determine the number of symbol errors between the demodulated data to the original sequence.

numErrs = symerr(x,z)
numErrs = 
0

Input Arguments

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Message signal, specified as a scalar, vector, matrix, numeric array, or a dlarray (Deep Learning Toolbox) object. For more information, see Array Support. The message signal must consist of integers in the range [0,length(const) – 1]. If X is a matrix with multiple rows, the function processes the columns independently.

Data Types: double | single | fi | int8 | int16 | uint8 | uint16

Signal mapping, specified as a complex vector.

Data Types: double | single | fi | int8 | int16 | uint8 | uint16
Complex Number Support: Yes

Output Arguments

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Complex envelope, returned as a scalar, vector, matrix, or 3-D array of numeric values. The length of Y is the same as the length of input X.

Data Types: double | single | fi | int8 | int16 | uint8 | uint16

More About

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Array Support

The genqammod function supports input signals represented in a numeric array, dlarray (Deep Learning Toolbox), or gpuArray (Parallel Computing Toolbox). If inputs are specified as a combination of dlarray and gpuArray, the returned matrix is a dlarray object on the GPU.

The number of batch observations (NB) is an optional dimension that can be added to the input for all supported data types.

  • X — The input data can be a 3-D array, specified as NSym-by-NChan-by-NB array.

NSym is the number of symbols. NChan is the number of channels.

For a list of Communications Toolbox™ features that support dlarray objects, see AI for Wireless.

Extended Capabilities

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

Version History

Introduced before R2006a

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See Also

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