comm.CPMModulator

Modulate signal using CPM method

Description

The comm.CPMModulator System object™ modulates an input signal using the continuous phase modulation (CPM) method. The output is a baseband representation of the modulated signal. For more information about the modulation and filtering applied, see CPM Method and Pulse Shape Filtering.

To modulate a signal using the CPM method:

Create the comm.CPMModulator object and set its properties.
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

cpmmod = comm.CPMModulator

cpmmod = comm.CPMModulator(Name=Value)

cpmmod = comm.CPMModulator(M,Name=Value)

Description

cpmmod = comm.CPMModulator creates a modulator System object to modulate input signals using the CPM method.

cpmmod = comm.CPMModulator(Name=Value) sets properties using one or more name-value arguments. For example, comm.CPMModulator(SymbolMapping='Gray') specifies gray-ordered symbol mapping for the modulated symbols.

example

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

example

Properties

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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 signal constellation, where k is a positive integer indicating the number of bits per symbol.

Data Types: double

`BitInput` — Option to provide input data as bits
`0` or `false` (default) | `1` or `true`

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

When you set this property to false, the input must be a column vector of odd integer values in the range [–(ModulationOrder – 1), (ModulationOrder – 1)].
When you set this property to true, the input must be a column vector of k-length bit words, where k = log2(ModulationOrder). For more information, see Symbol Sets.

Data Types: logical

`SymbolMapping` — Symbol mapping
`'Binary'` (default) | `'Gray'`

Symbol mapping of constellation bits, specified as 'Binary' or 'Gray'. For more information, see Symbol Sets.

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

To enable this property, set the BitInput property to true.

`ModulationIndex` — Modulation index
`0.5` (default) | nonnegative scalar | column vector

Modulation index, specified as a nonnegative scalar or column vector. For more information, see CPM Method.

Data Types: double

`FrequencyPulse` — Type of frequency pulse shaping
`'Rectangular'` (default) | `'Raised Cosine'` | `'Spectral Raised Cosine'` | `'Gaussian'` | `'Tamed FM'`

Type of frequency pulse shaping used by the modulator to smooth the phase transitions of the modulated signal, specified as 'Rectangular', 'Raised Cosine', 'Spectral Raised Cosine', 'Gaussian', or 'Tamed FM'. For more information, see Pulse Shape Filtering.

`MainLobeDuration` — Main lobe duration
`1` (default) | positive integer

Main lobe duration of the largest lobe in the spectral raised cosine pulse, specified as a positive integer representing the number of symbol intervals used by the modulator to pulse-shape the modulated signal.

Dependencies

To enable this property, set the FrequencyPulse property to 'Spectral Raised Cosine'.

Data Types: double

`RolloffFactor` — Roll-off factor
`0.2` (default) | scalar in the range [0, 1]

Roll-off factor of the spectral raised cosine pulse, specified as a scalar in the range [0, 1].

Dependencies

To enable this property, set the FrequencyPulse property to 'Spectral Raised Cosine'.

Data Types: double

`BandwidthTimeProduct` — Product of bandwidth and symbol time of Gaussian pulse shape
`0.3` (default) | positive scalar

Product of the bandwidth and symbol time of the Gaussian pulse shape, specified as a positive scalar. Use BandwidthTimeProduct to reduce the bandwidth, at the expense of increased intersymbol interference.

Dependencies

To enable this property, set the FrequencyPulse property to 'Gaussian'.

Data Types: double

`PulseLength` — Length of frequency pulse shape
`1` (default) | positive integer

Length of the frequency pulse shape in symbol intervals, specified as a positive integer. For more information on the frequency pulse length, refer to LT in Pulse Shape Filtering.

Data Types: double

`SymbolPrehistory` — Symbol prehistory
`1` (default) | scalar | vector

Symbol prehistory, specified as scalar or vector with odd integer elements in the range [– (ModulationOrder – 1), (ModulationOrder – 1)]. This property defines the data symbols used by the modulator prior to the first call of the object, 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) | scalar

Initial phase offset in radians of the modulated waveform, specified as a 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. This property represents the number of samples output for each integer or binary word input. For all nonbinary schemes, as defined by the pulse shapes, this value must be greater than 1.

Data Types: double

`OutputDataType` — Data type of output
`'double'` (default) | `'single'`

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

Usage

Syntax

Y = cpmmod(X)

Description

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

example

Input Arguments

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`X` — Input signal
column vector | matrix

Input signal data, specified as a column vector or matrix of integers or bits.

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

This object accepts variable-size inputs. After the object is locked, you can change the size of each input channel, but you cannot change the number of channels. For more information, see Variable-Size Signal Support with System Objects.

Output Arguments

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`Y` — CPM-modulated baseband signal
column vector

CPM-modulated baseband signal, returned as a column vector. The length of this output vector is equal to the number of input samples times the number of samples per symbol specified in the SamplesPerSymbol property. To specify the output data type use the OutputDataType property.

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)

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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

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CPM Modulate and Demodulate Signal with Gray Mapping and Bit Inputs

Open Live Script

Create CPM modulator, and CPM demodulator System objects.

    cpmmodulator = comm.CPMModulator(8, ...
        'BitInput',true, ...
        'SymbolMapping','Gray');
    cpmdemodulator = comm.CPMDemodulator(8, ...
        'BitOutput',true, ...
        'SymbolMapping','Gray');

Create an error rate calculator System object™, that accounts for the delay caused by the Viterbi algorithm.

    delay = log2(cpmdemodulator.ModulationOrder) ...
        * cpmdemodulator.TracebackDepth;
    errorRate = comm.ErrorRate('ReceiveDelay',delay);

Transmit 100 3-bit words and print the error rate results.

    for counter = 1:100
        data = randi([0 1],300,1);
        modSignal = cpmmodulator(data);
        noisySignal = awgn(modSignal,0);
        receivedData = cpmdemodulator(noisySignal);
        errorStats = errorRate(data,receivedData);
    end
    fprintf('Error rate = %f\nNumber of errors = %d\n', ...
      errorStats(1),errorStats(2))

Error rate = 0.004474
Number of errors = 134

Apply GFSK Modulation and Demodulation

Open Live Script

Using the comm.CPMModulator and comm.CPMDemodulator System objects, apply Gaussian frequency-shift keying (GFSK) modulation and demodulation to random bit data.

Create a GFSK modulator and demodulator pair.

gfskMod = comm.CPMModulator( ...
    'ModulationOrder',2, ...
    'FrequencyPulse','Gaussian', ...
    'BandwidthTimeProduct',0.5, ...
    'ModulationIndex',1, ...
    'BitInput',true);
gfskDemod = comm.CPMDemodulator( ...
    'ModulationOrder',2, ...
    'FrequencyPulse','Gaussian', ...
    'BandwidthTimeProduct',0.5, ...
    'ModulationIndex',1, ...
    'BitOutput',true);

Generate random bit data and apply GFSK modulation. Use a scatter plot to view the constellation.

numSym = 100;
x = randi([0 1],numSym*gfskMod.SamplesPerSymbol,1);
y = gfskMod(x);
eyediagram(y,16)

Figure Eye Diagram contains 2 axes objects. Axes object 1 with title Eye Diagram for In-Phase Signal, xlabel Time, ylabel Amplitude contains an object of type line. This object represents In-phase. Axes object 2 with title Eye Diagram for Quadrature Signal, xlabel Time, ylabel Amplitude contains an object of type line. This object represents Quadrature.

Demodulate the GFSK-modulated data. To verify that the demodulated signal data is equal to the original data, account for the delay introduced by the Gaussian filtering in the GFSK modulation and demodulation processes.

z = gfskDemod(y);
delay = finddelay(x,z);
isequal(x(1:end-delay),z(delay+1:end))

ans = logical
   1

Plot Phase Tree for Continuous Phase Modulation

Open Live Script

Plot the phase tree diagram for signals that have applied continuous phase modulation (CPM). A phase tree diagram superimposes many curves, each of which plots the phase of a modulated signal over time. The distinct curves result from different inputs to the modulator. This example defines settings for the CPM modulator, applies symbol mapping, and plots the results. Each curve represents a different instance of simulating the CPM modulator with a distinct (constant) input signal.

Define parameters for the example and create a CPM modulator System object™.

M = 2;                   % Modulation order
modindex = 2/3;          % Modulation index
sps = 8;                 % Samples per symbol
L = 5;                   % Symbols to display
pmat = zeros(L*sps,M^L); % Empty phase matrix 

cpm = comm.CPMModulator(M, ...
    ModulationIndex=modindex, ...
    FrequencyPulse="Raised Cosine", ...
    PulseLength=2, ...
    SamplesPerSymbol=sps);

Use a for-loop to apply the mapping of the input symbol to the CPM symbols, mapping 0 to -(M-1), 1 to -(M-2), and so on. Populate the columns of the phase matrix with the unwrapped phase angle of the modulated symbols.

for ip_sig = 0:(M^L)-1
    s = int2bit(ip_sig,L,1);
    s = 2*s + 1 - M;
    x = cpm(s);
    pmat(:,ip_sig+1) = unwrap(angle(x(:)));
end
pmat = pmat/(pi*modindex);
t = (0:L*sps-1)'/sps;

Plot the CPM phase tree.

plot(t,pmat);
title('CPM Phase Tree')
xlabel('Samples')
ylabel('Phase (radians)')

Figure contains an axes object. The axes object with title CPM Phase Tree, xlabel Samples, ylabel Phase (radians) contains 32 objects of type line.

More About

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CPM Method

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

$\begin{array}{l} s (t) = \exp [j 2 π \sum_{i = 0}^{n} α_{i} h_{i} q (t - i T)], and \\ n T < t < (n + 1) T . \end{array}$

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 object operates in multi-h. To ensure a finite number of phase states, h_i must be a rational number.

Pulse Shape Filtering

The CPM 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: $q (t) = \int_{- \infty}^{t} g (t) d t$ .

The specified frequency pulse shape corresponds to these pulse shape expressions for g(t).

Pulse Shape	Expression
Rectangular	$g (t) = {\begin{matrix} \frac{1}{2 L T}, & 0 \leq t \leq L T \\ 0 & otherwise \end{matrix}$
Raised cosine	$g (t) = {\begin{matrix} \frac{1}{2 L T} [1 - \cos (\frac{2 π t}{L T})], & 0 \leq t \leq L T \\ 0 & otherwise \end{matrix}$
Spectral raised cosine	$g (t) = \frac{1}{L_{main} T} \frac{\sin (\frac{2 π t}{L_{main} T})}{\frac{2 π t}{L_{main} T}} \frac{\cos (β \frac{2 π t}{L_{main} T})}{1 - {(\frac{4 β}{L_{main} T} t)}^{2}}, 0 \leq β \leq 1$
Gaussian	$\begin{matrix} g (t) = \frac{1}{2 T} {Q [2 π B_{b} \frac{t - \frac{T}{2}}{\sqrt{\ln 2}}] - Q [2 π B_{b} \frac{t + \frac{T}{2}}{\sqrt{\ln 2}}]}, where \\ Q (t) = \int_{t}^{\infty} \frac{1}{\sqrt{2 π}} e^{- τ^{2} / 2} d τ \end{matrix}$
Tamed FM (tamed frequency modulation)	$\begin{array}{l} g (t) = \frac{1}{8} [g_{0} (t - T) + 2 g_{0} (t) + g_{0} (t + T)], where \\ g_{0} (t) \approx \frac{1}{T} [\frac{\sin (\frac{π t}{T})}{\frac{π t}{T}} - \frac{π^{2}}{24} \frac{2 \sin (\frac{π t}{T}) - \frac{2 π t}{T} \cos (\frac{π t}{T}) - {(\frac{π t}{T})}^{2} \sin (\frac{π t}{T})}{{(\frac{π t}{T})}^{3}}] \end{array}$

L_main is the main lobe pulse duration in symbol intervals.
β is the roll-off factor of the spectral raised cosine.
B_b is the product of the bandwidth and the Gaussian pulse.
The duration of the pulse, LT, is the pulse length in symbol intervals. As defined by the expressions, the spectral raised cosine, Gaussian, and tamed FM pulse shapes have infinite length. For all practical purposes, LT specifies the truncated finite length.
T is the symbol durations.
Q(t) is the complementary cumulative distribution function.

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

Symbol Sets

In binary input mode, the object processing follows this procedure.

Divide the input bits into k-length bit words and map each bit-group to an integer, L, in the range [0, M – 1]. k = log2(M) and M is the modulation order specified by the ModulationOrder property. The binary word mapping options are binary-coded ordering or Gray-coded ordering, as specified by the SymbolMapping property.
Map each integer L to signed integers as 2L–(M–1).
Proceed with modulation processing as in the integer input mode.

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

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R2023b: Variable-size support

This support enables you to vary the length of input signal each time you call the object.

comm.CPMModulator

Description

Creation

Syntax

Description

Properties

ModulationOrder — Modulation order 4 (default) | power of two scalar

BitInput — Option to provide input data as bits 0 or false (default) | 1 or true

SymbolMapping — Symbol mapping 'Binary' (default) | 'Gray'

Dependencies

ModulationIndex — Modulation index 0.5 (default) | nonnegative scalar | column vector

FrequencyPulse — Type of frequency pulse shaping 'Rectangular' (default) | 'Raised Cosine' | 'Spectral Raised Cosine' | 'Gaussian' | 'Tamed FM'

MainLobeDuration — Main lobe duration 1 (default) | positive integer

Dependencies

RolloffFactor — Roll-off factor 0.2 (default) | scalar in the range [0, 1]

Dependencies

BandwidthTimeProduct — Product of bandwidth and symbol time of Gaussian pulse shape 0.3 (default) | positive scalar

Dependencies

PulseLength — Length of frequency pulse shape 1 (default) | positive integer

SymbolPrehistory — Symbol prehistory 1 (default) | scalar | vector

InitialPhaseOffset — Initial phase offset 0 (default) | scalar

SamplesPerSymbol — Number of samples per output symbol 8 (default) | positive integer

OutputDataType — Data type of output 'double' (default) | 'single'

Usage

Syntax

Description

Input Arguments

X — Input signal column vector | matrix

Output Arguments

Y — CPM-modulated baseband signal column vector

Object Functions

Common to All System Objects

Examples

CPM Modulate and Demodulate Signal with Gray Mapping and Bit Inputs

Apply GFSK Modulation and Demodulation

Plot Phase Tree for Continuous Phase Modulation

More About

CPM Method

Pulse Shape Filtering

Symbol Sets

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

Version History

R2023b: Variable-size support

See Also

Objects

Blocks

Topics

`ModulationOrder` — Modulation order
`4` (default) | power of two scalar

`BitInput` — Option to provide input data as bits
`0` or `false` (default) | `1` or `true`

`SymbolMapping` — Symbol mapping
`'Binary'` (default) | `'Gray'`

`ModulationIndex` — Modulation index
`0.5` (default) | nonnegative scalar | column vector

`FrequencyPulse` — Type of frequency pulse shaping
`'Rectangular'` (default) | `'Raised Cosine'` | `'Spectral Raised Cosine'` | `'Gaussian'` | `'Tamed FM'`

`MainLobeDuration` — Main lobe duration
`1` (default) | positive integer

`RolloffFactor` — Roll-off factor
`0.2` (default) | scalar in the range [0, 1]

`BandwidthTimeProduct` — Product of bandwidth and symbol time of Gaussian pulse shape
`0.3` (default) | positive scalar

`PulseLength` — Length of frequency pulse shape
`1` (default) | positive integer

`SymbolPrehistory` — Symbol prehistory
`1` (default) | scalar | vector

`InitialPhaseOffset` — Initial phase offset
`0` (default) | scalar

`SamplesPerSymbol` — Number of samples per output symbol
`8` (default) | positive integer

`OutputDataType` — Data type of output
`'double'` (default) | `'single'`

`X` — Input signal
column vector | matrix

`Y` — CPM-modulated baseband signal
column vector

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.