qammod

Quadrature amplitude modulation

Syntax

y = qammod(x,M)

y = qammod(x,M,symOrder)

y = qammod(___,Name,Value)

Description

y = qammod(x,M) returns a baseband quadrature amplitude modulated (QAM) signal given input signal x and modulation order M.

y = qammod(x,M,symOrder) returns a modulated signal and specifies the symbol order.

y = qammod(___,Name,Value) specifies modulation behavior using Name,Value pairs and any of the previous syntaxes.

Input Arguments

x — Input signal

scalar | vector | matrix | 3-D array

Input signal, specified as a scalar, vector, matrix, or 3-D array. The elements of x must be binary values or integers that range from 0 to (M – 1), where M is the modulation order.

Note

To process input signal as binary elements, set the 'InputType' name-value pair to 'bit'. For binary inputs, the number of rows must be an integer multiple of log₂(M). Groups of log₂(M) bits are mapped onto a symbol, with the first bit representing the MSB and the last bit representing the LSB.

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

M — Modulation order

scalar integer

Modulation order, specified as a power-of-two scalar integer. The modulation order specifies the number of points in the signal constellation.

Example: 16

Data Types: double

symOrder — Symbol order

'gray' (default) | 'bin' | vector

Symbol order, specified as 'gray', 'bin', or a vector.

• 'gray' — Use Gray Code ordering

• 'bin' — Use natural binary-coded ordering

• Vector — Use custom symbol ordering

Vectors must use unique elements whose values range from 0 to M – 1. The first element corresponds to the upper-left point of the constellation, with subsequent elements running down column-wise from left to right.

Example: [0 3 1 2]

Data Types: char | double

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

'InputType' — Input type

'integer' (default) | 'bit'

Input type, specified as the comma-separated pair consisting of 'InputType' and either 'integer' or 'bit'. If you specify 'integer', the input signal must consist of integers from 0 to M – 1. If you specify 'bit', the input signal must contain binary values, and the number of rows must be an integer multiple of log₂(M).

Data Types: char

'UnitAveragePower' — Unit average power flag

false (default) | true

Unit average power flag, specified as the comma-separated pair consisting of UnitAveragePower and a logical scalar. When this flag is true, the function scales the constellation to an average power of 1 watt referenced to 1 ohm. When this flag is false, the function scales the constellation so that the QAM constellation points are separated by a minimum distance of 2.

Data Types: logical

'OutputDataType' — Output data type

numerictype object

Output data type, specified as the comma-separated pair consisting of 'OutputDataType' and a numeric type object. See numerictype for more information on constructing these objects. If OutputDataType is omitted, the output data type is double for double or built-in integer inputs, and single for single inputs.

'PlotConstellation' — Option to plot constellation

false (default) | true

Option to plot constellation, specified as the comma-separated pair consisting of 'PlotConstellation' and a logical scalar. To plot the QAM constellation, set PlotConstellation to true.

Data Types: logical

Output Arguments

y — Modulated signal

scalar | vector | matrix | 3-D array

Modulated signal, returned as a complex scalar, vector, matrix, or 3-D array. For integer inputs, output y has the same dimensions as input signal x. For bit inputs, the number of rows in y is the number of rows in x divided by log₂(M).

Data Types: double | single

Examples

Modulate Data Using QAM

Modulate data using QAM and display the result in a scatter plot.

Set the modulation order to 16 and create a data vector containing each of the possible symbols.

M = 16;
x = (0:M-1)';

Modulate the data using the qammod function.

y = qammod(x,M);

Display the modulated signal constellation using the scatterplot function.

scatterplot(y)

Set the modulation order to 256, and display the scatter plot of the modulated signal.

M = 256;
x = (0:M-1)';
y = qammod(x,M);
scatterplot(y)

Normalize QAM Signal by Average Power

Modulate random data symbols using QAM. Normalize the modulator output so that it has an average signal power of 1 W.

Set the modulation order and generate random data.

M = 64;
x = randi([0 M-1],1000,1);

Modulate the data. Use the 'UnitAveragePower' name-value pair to set the output signal to have an average power of 1 W.

y = qammod(x,M,'UnitAveragePower',true);

Confirm that the signal has unit average power.

avgPower = mean(abs(y).^2)

avgPower = 1.0070

Plot the resulting constellation.

scatterplot(y)
title('64-QAM, Average Power = 1 W')

QAM Symbol Ordering

Plot QAM constellations for Gray, binary, and custom symbol mappings.

Set the modulation order, and create a random data sequence.

M = 16;
d = randi([0 M-1],1000,1);

Modulate the data, and plot its constellation.

y = qammod(d,M,'PlotConstellation',true);

The default symbol mapping uses Gray ordering. The ordering of the points is not sequential.

Repeat the modulation process with binary symbol mapping.

z = qammod(d,M,'bin','PlotConstellation',true);

The symbol mapping follows a natural binary order and is sequential.

Create a custom symbol mapping.

smap = randperm(16)-1;

Modulate and plot the constellation.

w = qammod(d,M,smap,'PlotConstellation',true);

Quadrature Amplitude Modulation with Bit Inputs

Modulate a sequence of bits using 64-QAM. Pass the signal through a noisy channel. Display the resultant constellation diagram.

Set the modulation order, and determine the number of bits per symbol.

M = 64;
k = log2(M);

Create a binary data sequence. When using binary inputs, the number of rows in the input must be an integer multiple of the number of bits per symbol.

data = randi([0 1],1000*k,1);

Modulate the signal using bit inputs, and set it to have unit average power.

txSig = qammod(data,M,'InputType','bit','UnitAveragePower',true);

Pass the signal through a noisy channel.

rxSig = awgn(txSig,25);

Plot the constellation diagram.

cd = comm.ConstellationDiagram('ShowReferenceConstellation',false);
step(cd,rxSig)

Demodulate QAM Fixed-Point Signal

Demodulate a fixed-point QAM signal and verify that the data is recovered correctly.

Set the modulation order, and determine the number of bits per symbol.

M = 64;
bitsPerSym = log2(M);

Generate random bits. When operating in bit mode, the length of the input data must be an integer multiple of the number of bits per symbol.

x = randi([0 1],10*bitsPerSym,1);

Modulate the input data using a binary symbol mapping. Set the modulator to output fixed-point data. The numeric data type is signed with a 16-bit word length and a 10-bit fraction length.

y = qammod(x,M,'bin','InputType','bit','OutputDataType', ...
    numerictype(1,16,10));

Demodulate the 64-QAM signal. Verify that the demodulated data matches the input data.

z = qamdemod(y,M,'bin','OutputType','bit');
s = isequal(x,double(z))

s = logical
   1

More About

Gray Code

A Gray code, also known as a reflected binary code, is a system where the bit patterns in adjacent constellation points differ by only one bit.

Compatibility Considerations

Initial Phase Input Removed

Errors starting in R2018b

Starting in R2018b, you can no longer offset the initial phase for the QAM constellation using the qammod function.

Instead use genqammod to offset the initial phase of the data being modulated, or you can multiply the qammod output by the desired initial phase:

y = qammod(x,M) .* exp(1i*initPhase)

to adjust the initial phase of the QAM data.

Extended Capabilities

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