comm.GMSKTimingSynchronizer

Recover symbol timing phase using fourth-order nonlinearity method

Description

The comm.GMSKTimingSynchronizer System object™ uses a fourth-order nonlinearity method to recover the symbol timing phase of a Gaussian minimum shift keying (GMSK) modulated signal. This object implements a general non-data-aided feedback method that is independent of carrier phase recovery but requires precompensation for the carrier frequency offset.

To recover the symbol timing phase of a GMSK modulated signal:

1. Create the comm.GMSKTimingSynchronizer 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

gmskTimingSync = comm.GMSKTimingSynchronizer

gmskTimingSync = comm.GMSKTimingSynchronizer(Name=Value)

Description

gmskTimingSync = comm.GMSKTimingSynchronizer creates a timing phase synchronizer System object, gmskTimingSync. This object recovers the symbol timing phase of a GMSK modulated signal using a fourth-order nonlinearity method.

gmskTimingSync = comm.GMSKTimingSynchronizer(Name=Value) sets properties using one or more optional name-value arguments. For example, comm.GMSKTimingSynchronizer(ErrorUpdateGain=0.045) sets the error update step size to 0.045.

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.

SamplesPerSymbol — Number of samples per symbol

4 (default) | integer in the range [2, ∞)

Number of samples per symbol, specified as an integer in the range [2, ∞).

Data Types: double

ErrorUpdateGain — Error update step size

0.05 (default) | positive scalar

Error update step size, specified as a positive scalar. Typically, this number is less than 1/SamplesPerSymbol, which corresponds to a slowly varying timing phase.

Tunable: Yes

Data Types: double

ResetInputPort — Synchronization reset input

false or 0 (default) | true or 1

Synchronization reset input, specified as a logical 0 (false) or 1 (true).

• When you set the ResetInputPort property to true or 1, the timing phase synchronizer enables the resetting of the timing phase recovery process based on an input argument value.

• When you set the ResetInputPort property to falseor 0, the timing phase synchronizer disables the restarting of the timing phase recovery process.

Data Types: logical

ResetCondition — Condition for resetting timing phase recovery

"Never" (default) | "Every frame"

Condition for resetting the timing phase recovery, specified as one of these options.

• "Never" — Never restart the phase recovery process. The object operates continuously, retaining information from one symbol to the next.

• "Every frame" — Restart the timing phase recovery at the start of each frame of data.

Dependencies

To enable this property, set the ResetInputPort property to false.

Usage

Syntax

[Y,phase] = gmskTimingSync(X)

[Y,phase] = gmskTimingSync(X,R)

Description

[Y,phase] = gmskTimingSync(X) recovers the timing phase and returns the time-synchronized signal, Y, and the estimated timing phase, phase, for the input signal, X.

[Y,phase] = gmskTimingSync(X,R) restarts the timing phase recovery process when you input a nonzero reset signal, R. To enable this syntax, set the ResetInputPort property to true.

Input Arguments

X — Input signal

complex column vector

Input signal, specified as a complex column vector.

Data Types: single | double
Complex Number Support: Yes

R — Reset signal

nonzero number

Reset signal, specified as a nonzero number.

Data Types: logical | double

Output Arguments

Y — Time-synchronized signal

column vector

Time-synchronized signal, returned as a complex column vector. Y has the same data type as the input argument X.

Complex Number Support: Yes

phase — Estimated timing phase

vector of nonnegative numbers

Estimated timing phase, returned as a vector of nonnegative numbers.

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

Recover Timing Phase of GMSK Signal

Create a GMSK modulator with the bit input set to true and the number of samples per symbol set to 14.

gmskMod = comm.GMSKModulator(BitInput=true, ...
    SamplesPerSymbol=14);

Define the timing offset value.

timingOffset = 0.2;

Create a variable fractional delay System object.

varDelay = dsp.VariableFractionalDelay;

Create an GMSK timing synchronizer System object with the number of samples per symbol set to 14 and the error update gain set to 0.045.

gmskTimingSync = comm.GMSKTimingSynchronizer(SamplesPerSymbol=14, ...
    ErrorUpdateGain=0.045);

Run a loop to process frames of data by following these steps.

1. Generate a random binary data vector.

2. Modulate the binary data using GMSK modulation.

3. Apply a timing offset error to the modulated data.

4. Perform timing phase recovery on the impaired signal.

5. Store the first phase estimate normalized by the number of samples per symbol.

phEst = zeros(50,1);
for i = 1:50
    data = randi([0 1],100,1);
    modData = gmskMod(data);
    impairedData = varDelay(modData,timingOffset*14);
    [~,phase] = gmskTimingSync(impairedData);
    phEst(i) = phase(1)/14;
end

Plot the original and estimated timing phase results.

plot(1:50,[0.2*ones(50,1) phEst])
legend( "Original","Estimated")
title("Original and Estimated Timing Phases")

Algorithms

The timing extraction algorithm consists of these steps:

1. Pass the sampled baseband signal through a fourth-order nonlinearity to extract timing information.

2. Differentiate the signal digitally following the nonlinearity.

3. Smooth the output of the digital differentiator to yield an error signal.

4. Use the error signal to adjust the sampling of the baseband signal.

More specifically, the algorithm employs a timing error detector that outputs a timing error value, e(k), for the kth symbol, as defined in as defined in Synchronization Techniques for Digital Receivers by Mengali, Umberto and Aldo N. D’Andrea (New York: Plenum Press, 1997) by this expression.

$$\begin{array}{c}e(k)={(}^{-}\mathrm{Re}\{r^2(kT-T_s+d_{k-1})r^{*2}((k-1)T-T_s+d_{k-2})\}\\ -{(}^{-}\mathrm{Re}\{r^2(kT+T_s+d_{k-1})r^{*2}((k-1)T+T_s+d_{k-1})\}\end{array}$$

where

• r is the input signal

• T is the symbol period

• T_s is the sampling period

• * means complex conjugate

• d_k is the phase estimate for the kth symbol

• D is 1 for MSK and 2 for Gaussian MSK modulation

References

[1] Mengali, Umberto and Aldo N. D’Andrea. Synchronization Techniques for Digital Receivers. New York: Plenum Press, 1997.

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