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Modulate using GMSK method


The GMSKModulator object modulates using the Gaussian minimum shift keying method. The output is a baseband representation of the modulated signal.

To modulate a signal using Gaussian minimum shift keying:

  1. Define and set up your GMSK modulator object. See Construction.

  2. Call step to modulate a signal according to the properties of comm.GMSKModulator. The behavior of step is specific to each object in the toolbox.


Starting in R2016b, instead of using the step method to perform the operation defined by the System object™, you can call the object with arguments, as if it were a function. For example, y = step(obj,x) and y = obj(x) perform equivalent operations.


H = comm.GMSKModulator creates a modulator System object, H. This object modulates the input signal using the Gaussian minimum shift keying (GMSK) modulation method.

H = comm.GMSKModulator(Name,Value) creates a GMSK modulator object, H. This object has each specified property set to the specified value. You can specify additional name-value pair arguments in any order as (Name1,Value1,...,NameN,ValueN).



Assume input is bits

Specify whether the input is bits or integers. The default is false.

When you set the BitInput property to false, the step method input requires a double-precision or signed integer data type column vector with values of -1 or 1.

When you set the BitInput property to true, step method input requires a double-precision or logical data type column vector of 0s and 1s.


Product of bandwidth and symbol time of Gaussian pulse

Specify the product of the bandwidth and symbol time for the Gaussian pulse shape as a real, positive scalar value. The default is 0.3.


Pulse length

Specify the length of the Gaussian pulse shape in symbol intervals as a real, positive integer. The default is 4.


Symbol prehistory

Specify the data symbols the modulator uses prior to the first call to the step method in reverse chronological order. The default is 1. This property requires a scalar or vector with elements equal to -1 or 1. If the value is a vector, then its length must be one less than the value in the PulseLength property.


Initial phase offset

Specify the initial phase of the modulated waveform in radians as a real, numeric scalar value. The default is 0.


Number of samples per output symbol

Specify the upsampling factor at the output as a real, positive, integer scalar value. The default is 8. The upsampling factor is the number of output samples that the step method produces for each input sample.


Data type of output

Specify output data type as one of double | single. The default is double.


resetReset states of the GMSK modulator object
stepModulate using GMSK method
Common to All System Objects

Allow System object property value changes


collapse all

% Create a GMSK modulator, an AWGN channel, and a GMSK demodulator. Use a phase offset of pi/4.
    hMod = comm.GMSKModulator('BitInput', true, 'InitialPhaseOffset', pi/4);
    hAWGN = comm.AWGNChannel('NoiseMethod', ...
                    'Signal to noise ratio (SNR)','SNR',0);
    hDemod = comm.GMSKDemodulator('BitOutput', true, ...
                    'InitialPhaseOffset', pi/4);
% Create an error rate calculator, account for the delay caused by the Viterbi algorithm
    hError = comm.ErrorRate('ReceiveDelay', hDemod.TracebackDepth);
    for counter = 1:100
      % Transmit 100 3-bit words
      data = randi([0 1],300,1);
      modSignal = step(hMod, data);
      noisySignal = step(hAWGN, modSignal);
      receivedData = step(hDemod, noisySignal);
      errorStats = step(hError, data, receivedData);
    fprintf('Error rate = %f\nNumber of errors = %d\n', ...
      errorStats(1), errorStats(2))
Error rate = 0.000133
Number of errors = 4

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

Create a GMSK modulator that accepts binary inputs. Specify the pulse length and samples per symbol to be 1.

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

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

x = zeros(5,1);
y = gmsk(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 better show the trend.

theta = unwrap(angle(y))
theta = 5×1


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

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

x = ones(5,1);
y = gmsk(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 better show the trend.

theta = unwrap(angle(y))
theta = 5×1


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

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, ...
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.



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

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 GSMK, 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.


Experiment by changing the PulseLength parameter 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 CPM Phase Tree example.


This object implements the algorithm, inputs, and outputs described on the GMSK Modulator Baseband block reference page. The object properties correspond to the block parameters. For GMSK the phase shift per symbol is π/2, which is a modulation index of 0.5.

Extended Capabilities

Introduced in R2012a