comm.GMSKModulator

Modulate using GMSK method

Description

The comm.GMSKModulator System object™ modulates using the Gaussian minimum shift keying (GMSK) method. The output is a baseband representation of the modulated signal. For more detail, see Algorithms.

To modulate a signal by using the GMSK method:

1. Create the comm.GMSKModulator object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

gmskmodulator = comm.GMSKModulator

gmskmodulator = comm.GMSKModulator(Name,Value)

Description

gmskmodulator = comm.GMSKModulator creates a modulator System object that modulates the input signal using the GMSK modulation method.

gmskmodulator = comm.GMSKModulator(Name,Value) sets properties using one or more name-value arguments. For example, comm.GMSKModulator(PulseLength=6) specifies the length of the Gaussian pulse shape as 6 symbol intervals.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

BitInput — Option to provide input as bits

false or 0 (default) | true or 1

Option to provide input as bits, specified as a numeric or logical 0 (false) or 1 (true).

• When you set this property to false, input X must be a column vector with values of -1 or 1.

• When you set this property to true, input X must be a column vector of 0s and 1s.

Data Types: logical

BandwidthTimeProduct — Product of bandwidth and symbol time

0.3 (default) | positive scalar

Product of the bandwidth and symbol time for the Gaussian pulse shape, specified as a positive scalar value. For more detail, see Algorithms.

To observe the effect of this property on the modulated signal, see the Effect of Bandwidth Time Product on GMSK Modulated Signal example.

Data Types: double

PulseLength — Length of frequency pulse shape

4 (default) | positive integer

Length of frequency pulse shape, specified as a positive integer. This parameter represents the truncated frequency pulse length of the Gaussian pulse shape in symbol intervals.

Data Types: double

SymbolPrehistory — Symbol prehistory

1 (default) | -1 | vector

Symbol prehistory, specified as -1, 1, or a vector with elements equal those values. The symbol prehistory indicates the data symbols that the modulator uses before the object processes symbols, in reverse chronological order.

• A scalar value expands to a vector of length PulseLength – 1.

• For a vector, the length must be PulseLength – 1.

Data Types: double

InitialPhaseOffset — Initial phase offset

0 (default) | numeric scalar

Initial phase offset of the modulated waveform in radians, specified as a numeric scalar.

Data Types: double

SamplesPerSymbol — Number of samples per output symbol

8 (default) | positive integer

Number of samples per output symbol, specified as a positive integer. The number of samples per symbol represents the upsampling factor from input samples to output samples.

Data Types: double

OutputDataType — Data type of output

'double' (default) | 'single'

Data type of output, specified as 'double' or 'single'.

Usage

Syntax

Y = gmskmodulator(X)

Description

Y = gmskmodulator(X) applies GMSK modulation to the input data and returns the modulated GMSK baseband signal.

Input Arguments

X — Input data

integer | column vector

Input data, specified as an integer or column vector of integers or bits.

• When you set BitInput to false, the input data must be double-precision or signed integer.

• When you set BitInput to true, the input data must be double-precision or logical.

This object accepts variable-size inputs. After the object is locked, you can change the frame size (number of rows) of the signal during simulation. For more information, see Variable-Size Signals in Code.

Data Types: double | int8 | int16 | int32 | logical

Output Arguments

Y — GMSK-modulated baseband signal

vector

GMSK-modulated baseband signal, returned as a column vector.

The length of output vector Y is equal to the number of input samples times the number of samples per symbol that you specify in the SamplesPerSymbol property value. The OutputDataType property specifies the data type of the output.

Data Types: double | single

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Map Binary Data to GMSK Signal

Map binary sequences of zeros and ones to the output of a GMSK modulator. This mapping also applies for MSK modulation.

Create a GMSK modulator that accepts binary inputs and has pulse length and samples per symbol values of 1.

gmskmodulator = comm.GMSKModulator( ...
    BitInput=true, ...
    PulseLength=1, ...
    SamplesPerSymbol=1);

Create an input sequence of all zeros. Modulate the sequence.

x = zeros(5,1);
y = gmskmodulator(x)

y = 5×1 complex

   1.0000 + 0.0000i
   0.0000 - 1.0000i
  -1.0000 - 0.0000i
  -0.0000 + 1.0000i
   1.0000 + 0.0000i

Determine the phase angle for each point. Use the unwrap function to show the trend.

theta = unwrap(angle(y))

theta = 5×1

         0
   -1.5708
   -3.1416
   -4.7124
   -6.2832

A sequence of zeros causes the phase to shift by -π/2 between samples.

Reset the modulator. Modulate an input sequence of all ones.

reset(gmskmodulator)
x = ones(5,1);
y = gmskmodulator(x)

y = 5×1 complex

   1.0000 + 0.0000i
   0.0000 + 1.0000i
  -1.0000 + 0.0000i
  -0.0000 - 1.0000i
   1.0000 - 0.0000i

Determine the phase angle for each point. Use the unwrap function to show the trend.

theta = unwrap(angle(y))

theta = 5×1

         0
    1.5708
    3.1416
    4.7124
    6.2832

A sequence of ones causes the phase to shift by +π/2 between samples.

GMSK Signal in AWGN

Create a GMSK modulator and demodulator pair. Create an AWGN channel object.

gmskmodulator = comm.GMSKModulator( ...
    BitInput=true, ...
    InitialPhaseOffset=pi/4);
gmskdemodulator = comm.GMSKDemodulator( ...
    BitOutput=true, ...
    InitialPhaseOffset=pi/4);
channel = comm.AWGNChannel( ...
    NoiseMethod='Signal to noise ratio (SNR)', ...
    SNR=0);

Create an error rate calculator and account for the delay between the modulator and demodulator, caused by the Viterbi algorithm.

errorRate = comm.ErrorRate( ...
    ReceiveDelay=gmskdemodulator.TracebackDepth);

Process 100 frames of data looping through these steps.

1. Generate vectors with 300 elements of random binary data.

2. GMSK-modulate the data.

3. Pass the modulated data through the AWGN channel.

4. GMSK-demodulate the data.

5. Collect error statistics on the frames of data.

for counter = 1:100
   % Transmit 100 3-bit words
   data = randi([0 1],300,1);
   modSignal = gmskmodulator(data);
   noisySignal = channel(modSignal);
   receivedData = gmskdemodulator(noisySignal);
   errorStats = errorRate(data, receivedData);
end

Display the error statistics.

fprintf('Error rate = %f\nNumber of errors = %d\n', ...
         errorStats(1), errorStats(2))

Error rate = 0.000133
Number of errors = 4

Effect of Bandwidth Time Product on GMSK Modulated Signal

This example demonstrates the effect of bandwidth time (BT) product on a GMSK modulated signal.

Create a binary data vector and apply GMSK modulation to the data.

d = [0 1 1 0 1 0 0 1 1 1]';
a = comm.GMSKModulator(BitInput=true,SamplesPerSymbol=10)

a = 
  comm.GMSKModulator with properties:

                BitInput: true
    BandwidthTimeProduct: 0.3000
             PulseLength: 4
        SymbolPrehistory: 1
      InitialPhaseOffset: 0
        SamplesPerSymbol: 10
          OutputDataType: 'double'

x = a(d);
BTa = sprintf('BT=%2.1f',a.BandwidthTimeProduct);

Plot the phase angles and use the unwrap function to show the trend better.

plot(unwrap(angle(x)),'red-');
title('Bandwidth Time Product Effect')
hold on; 
plot(1:10:length(x),unwrap(angle(x(1:10:end))),'*');
grid on

Set the BT product to 1 and plot the phase angles in the same plot.

a = comm.GMSKModulator(BitInput=true, ...
    SamplesPerSymbol=10,BandwidthTimeProduct=1)

a = 
  comm.GMSKModulator with properties:

                BitInput: true
    BandwidthTimeProduct: 1
             PulseLength: 4
        SymbolPrehistory: 1
      InitialPhaseOffset: 0
        SamplesPerSymbol: 10
          OutputDataType: 'double'

x = a(d);
BTb = sprintf('BT=%2.1f',a.BandwidthTimeProduct);
plot(unwrap(angle(x)),'blue-.');
plot(1:10:length(x),unwrap(angle(x(1:10:end))),'o');

Set the BT product to 0.1 and plot the phase angles in the same plot.

a = comm.GMSKModulator(BitInput=true, ...
    SamplesPerSymbol=10,BandwidthTimeProduct=0.1)

a = 
  comm.GMSKModulator with properties:

                BitInput: true
    BandwidthTimeProduct: 0.1000
             PulseLength: 4
        SymbolPrehistory: 1
      InitialPhaseOffset: 0
        SamplesPerSymbol: 10
          OutputDataType: 'double'

BTc = sprintf('BT=%2.1f',a.BandwidthTimeProduct);

The spread of this pulse is inversely proportional to the BT product and a lower BT causes a wider spread over the bit symbol period. The peak amplitude of the pulse is directly proportional to the BT product and a lower peak amplitude causes narrower spread over the bit symbol period. As the bandwidth of the pulse decreases, the pulse duration increases.

x = a(d);
plot(unwrap(angle(x)),'green--');
plot(1:10:length(x),unwrap(angle(x(1:10:end))),'x');
legend(BTa,'',BTb,'',BTc,'')
hold off;

Compare GMSK and MSK Modulation

Compare Gaussian minimum shift keying (GMSK) and minimum shift keying (MSK) modulation schemes by plotting the eye diagram for GMSK with different pulse lengths and for MSK.

Set the samples per symbol variable.

sps = 8;

Generate random binary data.

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

Create GMSK and MSK modulators that accept binary inputs. Set the PulseLength property of the GMSK modulator to 1.

gmskMod = comm.GMSKModulator( ...
    BitInput=true, ...
    PulseLength=1, ...
    SamplesPerSymbol=sps);
mskMod = comm.MSKModulator( ...
    BitInput=true, ...
    SamplesPerSymbol=sps);

Modulate the data using the GMSK and MSK modulators.

modSigGMSK = gmskMod(data);
modSigMSK = mskMod(data);

Pass the modulated signals through an AWGN channel having an SNR of 30 dB.

rxSigGMSK = awgn(modSigGMSK,30);
rxSigMSK = awgn(modSigMSK,30);

Use the eyediagram function to plot the eye diagrams of the noisy signals. With the GMSK pulse length set to 1, the eye diagrams are nearly identical.

eyediagram(rxSigGMSK,sps,1,sps/2)

eyediagram(rxSigMSK,sps,1,sps/2)

Set the PulseLength property for the GMSK modulator object to 3. Because the property is nontunable, the object must be released first.

release(gmskMod)
gmskMod.PulseLength = 3;

Generate a modulated signal using the updated GMSK modulator object and pass it through the AWGN channel.

modSigGMSK = gmskMod(data);
rxSigGMSK = awgn(modSigGMSK,30);

With continuous phase modulation (CPM) waveforms, such as GMSK, the waveform depends on values of the previous symbols as well as the present symbol. Plot the eye diagram of the GMSK signal to see that the increased pulse length results in an increase in the number of paths in the eye diagram.

eyediagram(rxSigGMSK,sps,1,sps/2)

Experiment by changing the PulseLength property of the GMSK modulator object to other values. If you set the property to an even number, you should set gmskMod.InitialPhaseOffset to pi/4 and update the offset argument of the eyediagram function from sps/2 to 0 for a better view of the modulated signal. In order to more clearly view the Gaussian pulse shape, you must use scopes that display the phase of the signal, as described in the View CPM Phase Tree Using Simulink example.

Algorithms

GMSK Modulation

GMSK is a Continuous-Phase Modulation scheme with no phase discontinuities because the frequency changes occur at the carrier zero-crossing points. For GMSK (and MSK), the frequency difference between the logical one and logical zero states is always equal to half the data rate. This difference can be expressed in terms of the modulation index. Specifically, an input symbol of 1 causes a phase shift of π/2 radians, which corresponds to a modulation index of 0.5. GMSK applies a Gaussian Pulse Shaping Filter.

Gaussian Pulse Shaping Filter

These equations define the frequency pulse shape of the Gaussian pulse shaping filter:

$$\begin{array}{c}g(t)=\frac{1}{2T}\left\{Q\left[2\pi B_b\frac{t-\frac{T}{2}}{\sqrt{\ln 2}}\right]-Q\left[2\pi B_b\frac{t+\frac{T}{2}}{\sqrt{\ln 2}}\right]\right\},\text{where}\\ Q(t)={\displaystyle {\int }_t^{\infty }\frac{1}{\sqrt{2\pi }}{e}^{-{\tau }^2/2}d\tau }\end{array}$$

B_b represents the bandwidth of the pulse and T is the symbol durations. Q(t) is the complementary cumulative distribution function.

The BandwidthTimeProduct property represents the bandwidth multiplied by time. Use this property to reduce the bandwidth at the expense of increased intersymbol interference. The PulseLength property measures the length of the Gaussian pulse shape in symbol intervals.

References

[1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase Modulation. New York: Plenum Press, 1986.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

Version History

Introduced in R2012a

R2024a: Variable-size support

This support enables you to vary the length of input signal each time you call the object. For more information, see input signal X.