genqammod

General quadrature amplitude modulation (QAM)

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.

Examples

Estimate Symbol Rate for General QAM Modulation in AWGN Channel

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

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 = 1

ser = 5.0000e-04

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 = 461

ser = 0.2305

General QAM Modulation and Demodulation

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);

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;

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

numErrs = symerr(x,z)

numErrs = 0

Input Arguments

x — Message signal

scalar | vector | matrix | 3-D array

Message signal, specified as a scalar, vector, matrix, or 3-D array of numeric values. The message signal must consist of integers from 0 and 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

const — Signal mapping

complex vector

Signal mapping, specified as a complex vector.

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

Output Arguments

y — Complex envelope

scalar | vector | matrix | 3-D array

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

Extended Capabilities

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

Version History

Introduced before R2006a