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 Algorithms.

To modulate a signal using the CPM method:

1. Create the comm.CPMModulator 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

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') configures the object with gray-coded symbol ordering for the modulated symbols.

cpmmod = comm.CPMModulator(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.

BitInput — Option to provide input data 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 output data as integers.

• Set this property to true to output 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.

Dependencies

To enable this property, 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 CPM Method.

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'.

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'.

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'.

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.

SymbolPrehistory — Symbol prehistory

1 (default) | scalar | vector

Symbol prehistory, specified as a scalar or vector with odd integer elements. Values must be in the range [–(M – 1), (M – 1)]. M is the modulation order specified by ModulationOrder. The SymbolPrehistory property defines the data symbols used by the modulator before 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.

InitialPhaseOffset — Initial phase offset

0 (default) | 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

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

Tip

To accurately model nonbinary pulse shapes, specifically pulse shapes other than rectangular, you should set the symbol sampling rate to values greater than 4.

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.

Input Arguments

X — Input signal

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 object accepts binary-valued inputs that represent integers.

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: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | logical

Output Arguments

Y — CPM-modulated baseband signal

column vector

CPM-modulated baseband signal, 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

CPM Modulate and Demodulate Signal with Gray Mapping and Bit Inputs

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

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. Plot the eye diagram of the modulated signal traces.

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

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

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)')

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

CPM Method

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

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

Pulse Shape	Expression
Rectangular	$$g(t)=\{\begin{array}{cc}\frac{1}{2LT},& 0\le t\le LT\\ 0& \text{otherwise}\end{array}$$
Raised cosine	$$g(t)=\{\begin{array}{cc}\frac{1}{2LT}\left[1-\cos \left(\frac{2\pi t}{LT}\right)\right],& 0\le t\le LT\\ 0& \text{otherwise}\end{array}$$
Spectral raised cosine	$$g(t)=\frac{1}{L_{\text{main}}T}\frac{\sin \left(\frac{2\pi t}{L_{\text{main}}T}\right)}{\frac{2\pi t}{L_{\text{main}}T}}\frac{\cos \left(\beta \frac{2\pi t}{L_{\text{main}}T}\right)}{1-{\left(\frac{4\beta }{L_{\text{main}}T}t\right)}^2},0\le \beta \le 1$$
Gaussian	$$\begin{array}{c}g(t)=\frac{1}{2T}\left\{Q\left[2\pi B_b\frac{t-\frac{T}{2}}{\sqrt{\ln 2}}\right]-Q\left[2\pi B_b\frac{t+\frac{T}{2}}{\sqrt{\ln 2}}\right]\right\},\text{where}\\ Q(t)={\displaystyle {\int }_t^{\infty }\frac{1}{\sqrt{2\pi }}{e}^{-{\tau }^2/2}d\tau }\end{array}$$
Tamed FM (tamed frequency modulation)	$$\begin{array}{l}g(t)=\frac{1}{8}\left[g_0(t-T)+2g_0(t)+g_0(t+T)\right],\text{where}\\ {\text{g}}_0(t)\approx \frac{1}{T}\left[\frac{\sin (\frac{\pi t}{T})}{\frac{\pi t}{T}}-\frac{{\pi }^2}{24}\frac{2\sin \left(\frac{\pi t}{T}\right)-\frac{2\pi t}{T}\cos \left(\frac{\pi t}{T}\right)-{\left(\frac{\pi t}{T}\right)}^2\sin \left(\frac{\pi t}{T}\right)}{{\left(\frac{\pi t}{T}\right)}^3}\right]\end{array}$$

• 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].

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

R2023b: 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.