comm.CPFSKModulator

Modulate using CPFSK method

Description

The comm.CPFSKModulator System object™ modulates a signal using the continuous phase frequency shift keying (CPFSK) method. The output is a baseband representation of the modulated signal. For more information about the demodulation and filtering applied, see Algorithms.

To modulate using the CPFSK method:

1. Create the comm.CPFSKModulator 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

cpfskMod = comm.CPFSKModulator

cpfskMod = comm.CPFSKModulator(Name=Value)

cpfskMod = comm.CPFSKModulator(M,Name=Value)

Description

cpfskMod = comm.CPFSKModulator creates a modulator System object that modulates the input signal using the CPFSK modulation method.

cpfskMod = comm.CPFSKModulator(Name=Value) creates a CPFSK modulator object and sets properties using one or more name-value arguments. For example, comm.CPFSKModulator(InitialPhaseOffset=pi/4), configures the object with an initial phase offset of pi/4 radians.

cpfskMod = comm.CPFSKModulator(M,Name=Value) sets the ModulationOrder property to M, and optional name-value arguments.

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.

ModulationOrder — Modulation order

4 (default) | power-of-two scalar

Modulation order, specified as a power-of-two scalar. The modulation order M = 2^k specifies the number of points in the symbol alphabet. k is a positive integer indicating the number of bits per symbol.

BitInput — Option to provide input as bits

0 or false (default) | 1 or true

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

• Set this property to false to input data as integers.

• Set this property to true to input data as bits.

For more information, see Integer-Valued and Binary-Valued Input Signals.

SymbolMapping — Symbol mapping

Binary (default) | Gray

Symbol mapping, specified as 'Binary' or 'Gray'. This property determines how each integer maps to a group of output bits.

• Set this property to 'Binary' to map symbols using binary-coded ordering.

• Set this property to 'Gray' to map symbols using Gray-coded ordering.

For more information, see Integer-Valued and Binary-Valued Input Signals.

Dependencies

This property applies when you set the BitInput property to true.

ModulationIndex — Modulation index {h_i}

0.5 (default) | nonnegative scalar | column vector

Modulation index {h_i}, specified as a nonnegative scalar or column vector. The modulator operates in multi-h. For more information, see CPFSK Method.

InitialPhaseOffset — Initial phase offset

0 (default) | numeric scalar

Initial phase offset in radians, specified as a numeric scalar. This parameter value is initial phase offset of the modulated waveform.

SamplesPerSymbol — Symbol sampling rate

8 (default) | positive integer

Symbol sampling rate, specified as a positive integer. This property specifies the output symbol upsampling factor for each input sample.

OutputDataType — Data type of output

'double' (default) | 'single'

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

Usage

Syntax

Y = cpfskMod(X)

Description

Y = cpfskMod(X) applies CPFSK method to the input signal and returns the modulated CPFSK baseband signal.

Input Arguments

X — Input data

scalar | column vector

Input data, specified as an integer scalar or column vector.

• When you set BitInput to false, the object accepts odd integers in the range [ –(M–1), (M–1)]. M is the modulation order specified by the ModulationOrder property.

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

For more information, see Integer-Valued and Binary-Valued Input Signals.

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 — CPFSK-modulated baseband output

column vector

CPFSK-modulated baseband output, returned as a column vector. The modulated output symbols are oversampled by the SamplesPerSymbol property value. Use the OutputDataType property to specify the output data type.

Data Types: double | single
Complex Number Support: Yes

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

Demodulate CPFSK-Modulated Signal Encoded with Gray Symbol Mapping

Create a CPFSK modulator, an AWGN channel, and a CPFSK demodulator. Configure the modulator and demodulator with modulation order set to 8, bit input, and Gray-encoded symbol mapping.

M = 8; % Modulation order
cpfskMod = comm.CPFSKModulator(M, ...
    BitInput=true, ...
    SymbolMapping='Gray');
awgnChan = comm.AWGNChannel( ...
    NoiseMethod='Signal to noise ratio (SNR)', ...
    SNR=0);
cpfskDemod = comm.CPFSKDemodulator(M, ...
    BitOutput=true, ...
    SymbolMapping='Gray');

Define the simulation parameters. Create an error rate calculator, accounting for the delay caused by the Viterbi algorithm that the CPFSK demodulator uses.

numFrames = 1000; % Number of frames transmitted
k = log2(M);      % Bits per symbol 
spf = 100;        % Symobls per frame

delay = log2(M)*cpfskDemod.TracebackDepth;
errorRate = comm.ErrorRate( ...
    ReceiveDelay=delay);
for counter = 1:numFrames
    data = randi([0 1],k*spf,1);
    modSignal = cpfskMod(data);
    noisySignal = awgnChan(modSignal);
    receivedData = cpfskDemod(noisySignal);
    errorStats = errorRate(data,receivedData);
end

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

Error rate = 0.004247
Number of errors = 1274

More About

Integer-Valued and Binary-Valued Input Signals

When you set BitInput to false:

• The input signal must be a column vector of odd integer values in the range [–(M – 1), (M – 1)].

• The input signal must have a double-precision, single-precision, or signed-integer data type.

When you set BitInput to true:

• The input signal must be a column vector of k-length bit words.

• In binary input mode, the object follows this process:

  1. Divide the input bits into k-length bit words and map each bit-group to an integer L in the range [0, M – 1].

  2. Map each nonnegative integer to a k-length binary word using binary-coded ordering or Gray-coded ordering, as specified by the SymbolMapping property.

  3. Map each integer L to signed integers as 2L–(M–1).

  4. Proceed with modulation processing as in the integer input mode.

• The input signal must have a double-precision, single-precision, integer, or logical data type.

M is the modulation order, as specified by the ModulationOrder property. The modulation order, M = 2^k specifies the number of points in the symbol alphabet, where k is a positive integer indicating the number of bits per symbol.

Algorithms

CPFSK Method

The CPFSK method is a specific form of continuous phase modulation in which the pulse shaping filter g(t) is a rectangular pulse of duration LT=1.

Continuous phase modulation includes a convolutional encoder, a symbol mapper, and a modulator.

The output of the modulator is a baseband representation of the modulated signal:

$$\begin{array}{l}s(t)=\exp \left[j2\pi {\displaystyle \sum _{i=0}^n{\alpha }_i{h}_{i}q(t-iT)}\right]\text{ and}\\ nT<t<(n+1)T,\end{array}$$

where:

• {α_i} is a sequence of M-ary data symbols selected from the alphabet ±1, ±3, ±(M–1).

• M must have the form 2^k for some positive integer k, where M is the modulation order and specifies the size of the symbol alphabet.

• {h_i} is a sequence of modulation indices. h_i moves cyclically through a set of indices {h₀, h₁, h₂, ..., h_H-1}.

  • When H=1, only one modulation index exists, h₀, which is denoted as h. The phase shift over a symbol is π × h.

  • When h_i varies from interval to interval, the modulator operates in multi-h. To ensure a finite number of phase states, h_i must be a rational number.

Pulse Shape Filtering

The CPFSK modulation method uses pulse shaping to smooth the phase transitions of the modulated signal. The function q(t) is the phase response obtained from the frequency pulse g(t) through this relation:

$$q(t)={\displaystyle {\int }_{-\infty }^{t}g(t)dt}$$

.

The specified frequency pulse shape corresponds to this rectangular pulse shape expression for g(t).

$$g(t)=\{\begin{array}{cc}\frac{1}{2LT},& 0\le t\le LT\\ 0& \text{otherwise}\end{array}$$

• L is the main lobe pulse duration in symbol intervals.

• The duration of the pulse LT is the pulse length in symbol intervals. For CPFSK modulation, LT=1.

For more information on CPFSK modulation and pulse shape filtering, see [1].

References

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

[2] Proakis, John G. Digital Communications. 5th ed. New York: McGraw Hill, 2007.

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