comm.CPFSKDemodulator

Demodulate using CPFSK method and Viterbi algorithm

Description

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

To demodulate a signal that was modulated using the CPFSK method:

1. Create the comm.CPFSKDemodulator 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

cpfskDemod=comm.CPFSKDemodulator

cpfskDemod=comm.CPFSKDemodulator(Name=Value)

cpfskDemodcomm.CPFSKDemodulator(M,Name=Value)

Description

cpfskDemod=comm.CPFSKDemodulator creates a demodulator System object to demodulate input CPFSK-modulated signals using the Viterbi algorithm.

cpfskDemod=comm.CPFSKDemodulator(Name=Value) sets properties using one or more name-value arguments. For example, comm.CPFSKDemodulator(InitialPhaseOffset=pi/4,TracebackDepth=25), configures the object with an initial phase offset of pi/4 radians and a Viterbi algorithm traceback depth of 25.

cpfskDemodcomm.CPFSKDemodulator(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 number of points in the symbol alphabet. k is a positive integer indicating the number of bits per symbol.

BitOutput — Option to output data as bits

0 or false (default) | 1 or true

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

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

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

For more information, see Integer-Valued and Binary-Valued Output 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.

Dependencies

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

ModulationIndex — Modulation index {h_i}

0.5 (default) | 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 Demodulation.

InitialPhaseOffset — Initial phase offset

0 (default) | numeric scalar

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

SamplesPerSymbol — Symbol sampling rate

8 (default) | positive, integer scalar

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

TracebackDepth — Traceback depth for Viterbi algorithm

16 (default) | positive, integer scalar

Traceback depth for the Viterbi algorithm, specified as a positive integer. The traceback depth specifies the number of trellis branches that the Viterbi algorithm uses to construct each traceback path. The value of this parameter is also the output delay and the number of zero symbols that precede the first meaningful demodulated symbol in the output. For more information, see Traceback Depth and Output Delays.

OutputDataType — Data type of output

'double' (default) | 'logical' | 'int8' | 'int16' | 'int32'

Data type of the output, specified as 'double', 'int8', 'int16', 'int32', or 'logical'.

• When you set the BitOutput property to false, you can set the output to double-precision, or signed-integer data types.

• When you set the BitOutput property to true, you can set the output to double-precision or logical data types.

Usage

Syntax

Y = cpfskDemod(X)

Description

Y = cpfskDemod(X) demodulates the input signal by using the CPFSK method.

Input Arguments

X — CPFSK-modulated baseband signal

column vector

CPFSK-modulated baseband signal, specified as a column vector with a length equal to an integer multiple of the number of SamplesPerSymbol.

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 | single
Complex Number Support: Yes

Output Arguments

Y — Demodulated output signal

column vector | matrix

Demodulated output signal, returned as a column vector or a matrix. For more information, see Integer-Valued and Binary-Valued Output Signals and Traceback Depth and Output Delays.

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

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 Output Signals

When you set BitOutput to false:

• The object outputs an integer column vector of length equal to N/N_SPS. The output values are odd integers in the range [–(M–1), (M–1)].

• You can set the OutputDataType property to 'double', 'int8', 'int16', or 'int32'.

When you set BitOutput to true:

• The object outputs a binary column vector of length equal to k×(N/N_SPS).

• In bit output mode, the object follows this process:

  1. Map each demodulated symbol to an odd integer L in the range [–(M–1), (M–1)].

  2. Map L to the nonnegative integer (L + M–1)/2.

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

• You can set the OutputDataType property to 'double', 'single', 'logical', 'int8', 'int16', 'int32', 'uint8', 'uint16', or 'uint32'.

N is the number of input baseband modulated symbols in the input signal (specifically, the length of the input signal).

N_SPS represents the value of the SamplesPerSymbol property.

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.

Traceback Depth and Output Delays

The traceback depth, D, is the number of trellis branches used to construct each traceback path in the trellis description of the modulation scheme for demodulation using the Viterbi algorithm.

Determine the optimal setting for traceback depth by calculating the minimum squared Euclidean distance. Alternatively, you can use a common heuristic based on the number of states. Specifically, the five-times-the-constraint-length rule, which approximates the traceback depth as D=5log₂(numStates).

For a binary raised cosine pulse shape with a pulse length of 3 and h=2/3, applying this rule D=5log₂(3×2²) ~ 18 gives a result that is close to the optimum value of 20.

The Viterbi algorithm processing results in a delay preceding the first meaningful demodulated value in the output.

The length of the delay vector, which consists of zero-valued symbols prepended to the output signal, equals the value of the TracebackDepth property.

Algorithms

CPFSK Demodulation

CPFSK demodulation processing consists of a correlator followed by a maximum-likelihood sequence estimation (MLSE) detector that searches the paths through the state trellis for the minimum Euclidean distance path. When the modulation index is rational (h = m / p), a finite number of phase states exist in the symbol. The implementation uses the Viterbi algorithm to perform MLSE detection. The input to the demodulator is a baseband representation of the modulated signal.

The CPFSK demodulation implementation follows these steps to recover the original digital data from the modulated signal:

1. Apply a rectangular pulse-shaping filter to the input baseband signal to remove out-of-band noise and interference.

2. Use a quadrature demodulator to extract the in-phase (I) and quadrature (Q) components of the signal.

3. To improve tracking accuracy as the phase of the input signal changes over time, unwrap the phase to ensure continuity. For CPFSK, the phase shift per symbol is π × h, where h is the modulation index.

   Compute the instantaneous phase of the signal using the arctangent function:

   $$\theta (t)={\tan }^{-1}\left(\frac{Q(t)}{I(t)}\right)$$

   .

4. Differentiate the unwrapped phase to obtain the instantaneous frequency of the signal and extract the frequency deviation from the carrier frequency:

   $$f(t)=\frac{1}{2\pi }\frac{d\theta (t)}{dt}$$

   .

5. Symbol detection compares the instantaneous frequency to predefined frequency thresholds corresponding to different symbols in the M-ary symbol alphabet. Use a decision rule (e.g., maximum likelihood) to map the frequency deviations to the nearest symbol. When the modulation index is rational (h = m / p), a finite number of phase states exist in the symbol. The implementation uses the Viterbi algorithm to perform MLSE detection.

6. Bit recovery decodes the detected symbols into data symbols based on the modulation scheme and symbol mapping used.

7. Output the recovered data stream as bits or integers as specified by the configuration.

In your CPFSK modulated communications link, apply symbol synchronization to ensure that the sampling of the signal is synchronized with the symbol rate to prevent inter-symbol interference.

CPFSK Modulation Method

CPFSK modulation 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.

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.