Digital Modulation

In most media for communication, only a fixed range of frequencies is available for transmission. One way to communicate a message signal whose frequency spectrum does not fall within that fixed frequency range, or one that is otherwise unsuitable for the channel, is to alter a transmittable signal according to the information in your message signal. This alteration is called modulation, and it is the modulated signal that you transmit. The receiver then recovers the original signal through a process called demodulation.

The sections of this chapter are as follows.

Digital Modulation Features

Modulation Techniques

The figure below shows the modulation techniques that Communications System Toolbox™ supports for digital data. All the methods at the far right are implemented in library blocks.

Like analog modulation, digital modulation alters a transmittable signal according to the information in a message signal. However, in this case, the message signal is restricted to a finite set. Using this product, you can modulate or demodulate signals using various digital modulation techniques. You can also plot signal constellations. Modulation functions output the complex envelope of the modulated signal.

The available methods of modulation depend on whether the input signal is analog or digital. The tables below show the modulation techniques that Communications System Toolbox software supports for analog and digital signals, respectively.

Analog Modulation MethodAcronymFunction or Method
Amplitude modulation (suppressed or transmitted carrier)AMammod, amdemod
Frequency modulationFMfmmod, fmdemod
Phase modulationPMpmmod, pmdemod
Single sideband amplitude modulationSSBssbmod, ssbdemod


Digital Modulation MethodAcronymSystem object™
Differential phase shift keying modulationDPSK

comm.DPSKDemodulatorSystem object, comm.DPSKModulator System object

Frequency shift keying modulationFSKcomm.FSKDemodulator System object, comm.FSKModulator System object,
General Quadrature amplitude modulationGeneral QAM

comm.GeneralQAMDemodulator System object, comm.GeneralQAMModulator System object

Minimum shift keying modulationMSK

comm.MSKDemodulator System object, comm.MSKModulator System object

Offset quadrature phase shift keying modulationOQPSK

comm.OQPSKDemodulator System object, comm.OQPSKModulator System object

Phase shift keying modulationPSK

comm.PSKDemodulator System object, comm.PSKModulator System object

Pulse amplitude modulationPAM

comm.PAMDemodulator System object, comm.PAMModulator System object

Accessing Digital Modulation Blocks.  Open the Modulation library by double-clicking the icon in the main block library. Then open the Digital Baseband sublibrary by double-clicking its icon in the Modulation library.

The Digital Baseband library has sublibraries of its own. Open each of these sublibraries by double-clicking the icon listed in the table below.

Kind of ModulationIcon in Digital Baseband Library
Amplitude modulation AM
Phase modulation PM
Frequency modulation FM
Continuous phase modulation CPM
Trellis-coded modulation TCM

Some digital modulation sublibraries contain blocks that implement special cases of a more general technique and are, in fact, special cases of a more general block. These special-case blocks use the same computational code that their general counterparts use, but provide an interface that is either simpler or more suitable for the special case. The following table lists special-case modulators, their general counterparts, and the conditions under which the two are equivalent. The situation is analogous for demodulators.

General and Specific Blocks

General ModulatorSpecific ModulatorSpecific Conditions
General QAM Modulator BasebandRectangular QAM Modulator BasebandPredefined constellation containing 2K points on a rectangular lattice
M-PSK Modulator BasebandBPSK Modulator BasebandM-ary number parameter is 2.
QPSK Modulator BasebandM-ary number parameter is 4.
M-DPSK Modulator BasebandDBPSK Modulator BasebandM-ary number parameter is 2.
DQPSK Modulator BasebandM-ary number parameter is 4.
CPM Modulator BasebandGMSK Modulator BasebandM-ary number parameter is 2, Frequency pulse shape parameter is Gaussian.
MSK Modulator BasebandM-ary number parameter is 2, Frequency pulse shape parameter is Rectangular, Pulse length parameter is 1.
CPFSK Modulator BasebandFrequency pulse shape parameter is Rectangular, Pulse length parameter is 1.
General TCM EncoderRectangular QAM TCM EncoderPredefined signal constellation containing 2K points on a rectangular lattice
M-PSK TCM EncoderPredefined signal constellation containing 2K points on a circle

Furthermore, the CPFSK Modulator Baseband block is similar to the M-FSK Modulator Baseband block, when the M-FSK block uses continuous phase transitions. However, the M-FSK features of this product differ from the CPFSK features in their mask interfaces and in the demodulator implementations.

Baseband and Passband Simulation

For a given modulation technique, two ways to simulate modulation techniques are called baseband and passband. Baseband simulation, also known as the lowpass equivalent method, requires less computation. This product supports baseband simulation for digital modulation and passband simulation for analog modulation.

Baseband Modulated Signals Defined.  If you use baseband modulation to produce the complex envelope y of the modulation of a message signal x, then y is a complex-valued signal that is related to the output of a passband modulator. If the modulated signal has the waveform

Y1(t)cos(2πfct+θ)Y2(t)sin(2πfct+θ)

where fc is the carrier frequency and θ is the carrier signal's initial phase, then a baseband simulation recognizes that this equals the real part of

[(Y1(t)+jY2(t))ejθ]exp(j2πfct)

and models only the part inside the square brackets. Here j is the square root of -1. The complex vector y is a sampling of the complex signal

(Y1(t)+jY2(t))ejθ

If you prefer to work with passband signals instead of baseband signals, then you can build functions that convert between the two. Be aware that passband modulation tends to be more computationally intensive than baseband modulation because the carrier signal typically needs to be sampled at a high rate.

Modulation Terminology

Modulation is a process by which a carrier signal is altered according to information in a message signal. The carrier frequency, denoted Fc, is the frequency of the carrier signal. The sampling rate is the rate at which the message signal is sampled during the simulation.

The frequency of the carrier signal is usually much greater than the highest frequency of the input message signal. The Nyquist sampling theorem requires that the simulation sampling rate Fs be greater than two times the sum of the carrier frequency and the highest frequency of the modulated signal in order for the demodulator to recover the message correctly.

Representing Digital Signals

To modulate a signal using digital modulation with an alphabet having M symbols, start with a real message signal whose values are integers from 0 to M-1. Represent the signal by listing its values in a vector, x. Alternatively, you can use a matrix to represent a multichannel signal, where each column of the matrix represents one channel.

For example, if the modulation uses an alphabet with eight symbols, then the vector [2 3 7 1 0 5 5 2 6]' is a valid single-channel input to the modulator. As a multichannel example, the two-column matrix

[2 3;
 3 3;
 7 3;
 0 3;]

defines a two-channel signal in which the second channel has a constant value of 3.

Signals and Delays

All digital modulation blocks process only discrete-time signals and use the baseband representation. The data types of inputs and outputs are depicted in the following figure.

    Note   If you want to separate the in-phase and quadrature components of the complex modulated signal, use the Complex to Real-Imag block in the Simulink Math Operations library.

Integer-Valued Signals and Binary-Valued Signals

Some digital modulation blocks can accept either integer-valued or binary–valued signals. The corresponding demodulation blocks can output either integers or groups of individual bits that represent integers. This section describes how modulation blocks process integer or binary inputs; the case for demodulation blocks is the reverse. You should note that modulation blocks have an Input type parameter and that demodulation blocks have an Output type parameter.

When you set the Input type parameter to Integer, the block accepts integer values between 0 and M-1. M represents the M-ary number block parameter.

When you set the Input type parameter to Bit, the block accepts binary-valued inputs that represent integers. The block collects binary-valued signals into groups of K = log2(M) bits

where

K represents the number of bits per symbol.

The input vector length must be an integer multiple of K. In this configuration, the block accepts a group of K bits and maps that group onto a symbol at the block output. The block outputs one modulated symbol for each group of K bits.

Constellation Ordering (or Symbol Set Ordering)

Depending on the modulation scheme, the Constellation ordering or Symbol set ordering parameter indicates how the block maps a group of K input bits to a corresponding symbol. When you set the parameter to Binary, the block maps [u(1) u(2) ... u(K)] to the integer

i=1Ku(i)2Ki

and assumes that this integer is the input value. u(1) is the most significant bit.

If you set M = 8, Constellation ordering (or Symbol set ordering) to Binary, and the binary input word is [1 1 0], the block converts [1 1 0] to the integer 6. The block produces the same output when the input is 6 and the Input type parameter is Integer.

When you set Constellation ordering (or Symbol set ordering) to Gray, the block uses a Gray-coded arrangement and assigns binary inputs to points of a predefined Gray-coded signal constellation. The predefined M-ary Gray-coded signal constellation assigns the binary representation

M = 8; P = [0:M-1]';
de2bi(bitxor(P,floor(P/2)), log2(M),'left-msb')

to the Pth integer.

The following tables show the typical Binary to Gray mapping for M = 8.

Binary to Gray Mapping for Bits

Binary CodeGray Code
000000
001001
010011
011010
100110
101111
110101
111100

Gray to Binary Mapping for Integers

Binary CodeGray Code
00
11
23
32
46
57
65
74

Gray Encoding a Modulated Signal.  For the PSK, DPSK, FSK, QAM, and PAM modulation types, Gray constellations are obtained by selecting the Gray parameter in the corresponding modulation function or method.

For modulation objects, you can set the symbol order property to Gray to obtain Gray-encoded modulation.

The following example demonstrates use of the symbol order property. The Scatter plot shows the modulated symbols are Gray-encoded.

% Create 8-PSK Gray encoded modulator
hMod = comm.PSKModulator('ModulationOrder',8, ...
    'SymbolMapping','Gray','PhaseOffset',0);
% Create a scatter plot
constellation(hMod)

For modulation functions, set the symbol order argument to Gray.

Looking at the map above, notice that this is indeed a Gray-encoded map; all adjacent elements differ by only one bit.

Delays From Digital Modulation

Digital modulation and demodulation blocks sometimes incur delays between their inputs and outputs, depending on their configuration and on properties of their signals. The following table lists sources of delay and the situations in which they occur.

Delays Resulting from Digital Modulation or Demodulation

Modulation or Demodulation TypeSituation in Which Delay OccursAmount of Delay
FM demodulatorSample-based processingOne output period
All demodulators in CPM sublibrary Multirate processing, and the model uses a variable-step solver or a fixed-step solver with the Tasking Mode parameter set to SingleTasking
D = Traceback length parameter
D+1 output periods
Single-rate processing, D = Traceback depth parameterD output periods
OQPSK demodulatorSingle-rate processingOne output period
Multirate processing, and the model uses a fixed-step solver with Tasking Mode parameter set to Auto or MultiTasking.Two output periods
Multirate processing processing, and the model uses a variable-step solver or the Tasking Mode parameter is set to SingleTasking.One output period
All decoders in TCM sublibrary Operation mode set to Continuous, Tr = Traceback depth parameter, and code rate k/n Tr*k output bits

As a result of delays, data that enters a modulation or demodulation block at time T appears in the output at time T+delay. In particular, if your simulation computes error statistics or compares transmitted with received data, it must take the delay into account when performing such computations or comparisons.

First Output Sample in DPSK Demodulation.  In addition to the delays mentioned above, the M-DPSK, DQPSK, and DBPSK demodulators produce output whose first sample is unrelated to the input. This is related to the differential modulation technique, not the particular implementation of it.

Delays from Demodulation.  For an example that illustrates delays from demodulation, see the Delays from Demodulation example.

Upsample Signals and Rate Changes

Some digital modulation blocks can output an upsampled version of the modulated signal, while their corresponding digital demodulation blocks can accept an upsampled version of the modulated signal as input. In both cases, the Rate options parameter represents the upsampling factor, which must be a positive integer. Depending on whether the input signal is single-rate mode or multirate mode, the block either changes the signal's vector size or its sample time, as the following table indicates. Only the OQPSK blocks deviate from the information in the table, in that S is replaced by 2S in the scaling factors.

Process Upsampled Modulated Data (Except OQPSK Method)

Computation TypeInput StatusResult
Modulation Single-rate processingOutput vector length is S times the number of integers or binary words in the input vector. Output sample time equals the input sample time.
Modulation Multirate processingOutput vector is a scalar. Output sample time is 1/S times the input sample time.
Demodulation Single-rate processingNumber of integers or binary words in the output vector is 1/S times the number of samples in the input vector. Output sample time equals the input sample time.
Demodulation Multirate processingOutput signal contains one integer or one binary word. Output sample time is S times the input sample time.

Furthermore, if S > 1 and the demodulator is from the AM, PM, or FM sublibrary, the demodulated signal is delayed by one output sample period. There is no delay if S = 1 or if the demodulator is from the CPM sublibrary.

Illustrations of Size or Rate Changes.  The following schematics illustrate how a modulator (other than OQPSK) upsamples a triplet of frame-based and sample-based integers. In both cases, the Samples per symbol parameter is 2.

The following schematics illustrate how a demodulator (other than OQPSK or one from the CPM sublibrary) processes three doubly sampled symbols using both frame-based and sample-based inputs. In both cases, the Samples per symbol parameter is 2. The sample-based schematic includes an output delay of one sample period.

PM Modulation

DQPSK Signal Constellation Points and Transitions

The model below plots the output of the DQPSK Modulator Baseband block. The image shows the possible transitions from each symbol in the DQPSK signal constellation to the next symbol.

To open this model open this model enter doc_dqpsk_plot at the MATLAB command line. To build the model, gather and configure these blocks:

  • Random Integer Generator, in the Random Data Sources sublibrary of the Comm Sources library

    • Set M-ary number to 4.

    • Set Initial seed to any positive integer scalar, preferably the output of the randseed function.

    • Set Sample time to .01.

  • DQPSK Modulator Baseband, in the PM sublibrary of the Digital Baseband sublibrary of Modulation

  • Complex to Real-Imag, in the Simulink Math Operations library

  • XY Graph, in the Simulink Sinks library

Use the blocks' default parameters unless otherwise instructed. Connect the blocks as in the figure above. Running the model produces the following plot. The plot reflects the transitions among the eight DQPSK constellation points.

This plot illustrates π/4-DQPSK modulation, because the default Phase offset parameter in the DQPSK Modulator Baseband block is pi/4. To see how the phase offset influences the signal constellation, change the Phase offset parameter in the DQPSK Modulator Baseband block to pi/8 or another value. Run the model again and observe how the plot changes.

AM Modulation

Rectangular QAM Modulation and Scatter Diagram

The model below uses the M-QAM Modulator Baseband block to modulate random data. After passing the symbols through a noisy channel, the model produces a scatter diagram of the noisy data. The diagram suggests what the underlying signal constellation looks like and shows that the noise distorts the modulated signal from the constellation.

To open this modelopen this model, enter doc_qam_scatter at the MATLAB command line. To build the model, gather and configure these blocks:

  • Random Integer Generator, in the Random Data Sources sublibrary of the Comm Sources library

    • Set M-ary number to 16.

    • Set Initial seed to any positive integer scalar, preferably the output of the randseed function.

    • Set Sample time to .1.

  • Rectangular QAM Modulator Baseband, in the AM sublibrary of the Digital Baseband sublibrary of Modulation

    • Set Normalization method to Peak Power.

  • AWGN Channel, in the Channels library

    • Set Es/No to 20.

    • Set Symbol period to .1.

  • Constellation Diagram, in the Comm Sinks library

    • Set Symbols to display to 160.

Connect the blocks as in the figure. From the model window's Simulation menu, select Model Configuration parameters. In the Configuration Parameters dialog box, set Stop time to 250. Running the model produces a scatter diagram like the following one. Your plot might look somewhat different, depending on your Initial seed value in the Random Integer Generator block. Because the modulation technique is 16-QAM, the plot shows 16 clusters of points. If there were no noise, the plot would show the 16 exact constellation points instead of clusters around the constellation points.

Compute the Symbol Error Rate

The example generates a random digital signal, modulates it, and adds noise. Then it creates a scatter plot, demodulates the noisy signal, and computes the symbol error rate.

% Create a random digital message
M = 16;                     % Alphabet size
x = randi([0 M-1],5000,1);  % Random symbols

% Use 16-QAM modulation.
hMod = comm.RectangularQAMModulator('ModulationOrder',M);
hDemod = comm.RectangularQAMDemodulator('ModulationOrder',M);

% Create a constellation diagram object.
cpts = constellation(hMod);
hConst = comm.ConstellationDiagram('ReferenceConstellation',cpts, ...
    'XLimits',[-4 4],'YLimits',[-4 4]);

% Apply 16-QAM modulation.
y = step(hMod,x);

% Transmit signal through an AWGN channel.
ynoisy = awgn(y,15,'measured');

% Create constellation diagram from noisy data.
step(hConst,ynoisy)

% Demodulate ynoisy to recover the message.
z = step(hDemod,ynoisy);

% Check symbol error rate.
[num,rt] = symerr(x,z)

%%
% ==============================================
% Documentation example from
% "Constellation for 16-PSK"
% in modulation.xml

% begindocexample 16psk_const
% Use 16-PSK modulation with no phase offset and binary symbol mapping.
hMod = comm.PSKModulator(16,0,'SymbolMapping','binary');

% Create a scatter plot
constellation(hMod)
% enddocexample 16psk_const

%%
% ==============================================
% Documentation example from
% "Constellation for 32-QAM"
% in modulation.xml

% Example: Plotting Signal Constellations
% Constellation for 32-QAM

% Copyright 2003 The MathWorks, Inc.

close all;

% begindocexample 32qam_const
% Create 32-QAM modulator with binary symbol mapping
hMod = comm.RectangularQAMModulator(32,'SymbolMapping','binary');
% Create a scatter plot
constellation(hMod)
% enddocexample 32qam_const

doctouchupfigure(gcf,1);

%%
% ==============================================
% Documentation example from
% "Gray-Coded Signal Constellation"
% in modulation.xml

% begindocexample graycoded_const
% Create 8-QAM Gray encoded modulator
hMod = comm.RectangularQAMModulator(8);
% Create a scatter plot
constellation(hMod)
% enddocexample graycoded_const



The output and scatter plot follow. Your numerical results and plot might vary, because the example uses random numbers.

num =

    83


rt =

    0.0166

The scatter plot does not look exactly like a signal constellation. Where the signal constellation has 16 precisely located points, the noise causes the scatter plot to have a small cluster of points approximately where each constellation point would be.

Combine Pulse Shaping and Filtering with Modulation

Modulation is often followed by pulse shaping, and demodulation is often preceded by a filtering or an integrate-and-dump operation. This section presents an example involving rectangular pulse shaping. For an example that uses raised cosine pulse shaping, see Pulse Shaping Using a Raised Cosine Filter.

Rectangular Pulse Shaping.  Rectangular pulse shaping repeats each output from the modulator a fixed number of times to create an upsampled signal. Rectangular pulse shaping can be a first step or an exploratory step in algorithm development, though it is less realistic than other kinds of pulse shaping. If the transmitter upsamples the modulated signal, then the receiver should downsample the received signal before demodulating. The "integrate and dump" operation is one way to downsample the received signal.

The code below uses the rectpulse function for rectangular pulse shaping at the transmitter and the intdump function for downsampling at the receiver.

M = 16;                     % Alphabet size
x = randi([0 M-1],5000,1);  % Message signal
Nsamp = 4;                  % Oversampling rate

% Use 16-QAM modulation.
hMod = comm.RectangularQAMModulator;
hDemod = comm.RectangularQAMDemodulator;

% Modulate
y = step(hMod,x);

% Follow with rectangular pulse shaping.
ypulse = rectpulse(y,Nsamp);

% Transmit signal through an AWGN channel.
ynoisy = awgn(ypulse,15,'measured');

% Downsample at the receiver.
ydownsamp = intdump(ynoisy,Nsamp);

% Demodulate to recover the message.
z = step(hDemod,ydownsamp);

CPM Modulation

Phase Tree for Continuous Phase Modulation

This example plots a phase tree associated with a continuous phase modulation scheme. A phase tree is a diagram that 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 uses the CPM Modulator Baseband block for its numerical computations. The block is configured so that it uses a raised cosine filter pulse shape. The example also illustrates how you can use Simulink and MATLAB together. The example uses MATLAB commands to run a series of simulations with different input signals, to collect the simulation results, and to plot the full data set.

    Note   In contrast to this example's approach using both MATLAB and Simulink, the commcpmphasetree example produces a phase tree using a Simulink model without additional lines of MATLAB code.

The first step of this example is to build the model. To open the completed model, click herehere in the MATLAB Help browser. To build the model, gather and configure these blocks:

  • Constant, in the Simulink Commonly Used Blocks library

    • Set Constant value to s (which will appear in the MATLAB workspace).

    • Set Sampling mode to Frame-based.

    • Set Frame period to 1.

  • CPM Modulator Baseband

    • Set M-ary number to 2.

    • Set Modulation index to 2/3.

    • Set Frequency pulse shape to Raised Cosine.

    • Set Pulse length to 2.

  • To Workspace, in the Simulink Sinks library

    • Set Variable name to x.

    • Set Save format to Array.

Do not run the model, because the variable s is not yet defined in the MATLAB workspace. Instead, save the model to a folder on your MATLAB path, using the filename doc_phasetree.

The second step of this example is to execute the following MATLAB code:

% Parameters from the CPM Modulator Baseband block
M_ary_number = 2;
modulation_index = 2/3;
pulse_length = 2;
samples_per_symbol = 8;

L = 5;  % Symbols to display
pmat = [];
for ip_sig = 0:(M_ary_number^L)-1
    s = de2bi(ip_sig,L,M_ary_number,'left-msb');
    % Apply the mapping of the input symbol to the CPM
    % symbol 0 -> -(M-1), 1 -> -(M-2), etc.
    s = 2*s'+1-M_ary_number;
    sim('doc_phasetree', .9); % Run model to generate x.
    % Next column of pmat
    pmat(:,ip_sig+1) = unwrap(angle(x(:)));
end;
pmat = pmat/(pi*modulation_index);
t = (0:L*samples_per_symbol-1)'/samples_per_symbol;
plot(t,pmat); figure(gcf); % Plot phase tree.

This code defines the parameters for the CPM Modulator, applies symbol mapping, and plots the results. Each curve represents a different instance of simulating the CPM Modulator Baseband block with a distinct (constant) input signal.

Exact LLR Algorithm

The log-likelihood ratio (LLR) is the logarithm of the ratio of probabilities of a 0 bit being transmitted versus a 1 bit being transmitted for a received signal. The LLR for a bit b is defined as:

L(b)=log(Pr(b=0|r=(x,y))Pr(b=1|r=(x,y)))

Assuming equal probability for all symbols, the LLR for an AWGN channel can be expressed as:

L(b)=log(sS0e1σ2((xsx)2+(ysy)2)sS1e1σ2((xsx)2+(ysy)2))

where the variables represent the values shown in the following table.

VariableWhat the Variable Represents

r

Received signal with coordinates (x, y).

b

Transmitted bit (one of the K bits in an M-ary symbol, assuming all M symbols are equally probable.

S0

Ideal symbols or constellation points with bit 0, at the given bit position.

S1

Ideal symbols or constellation points with bit 1, at the given bit position.

sx

In-phase coordinate of ideal symbol or constellation point.

sy

Quadrature coordinate of ideal symbol or constellation point.

σ2

Noise variance of baseband signal.

σx2

Noise variance along in-phase axis.

σy2

Noise variance along quadrature axis.

    Note:   Noise components along the in-phase and quadrature axes are assumed to be independent and of equal power (i.e., σx2=σy2=σ2/2).

Approximate LLR Algorithm

Approximate LLR is computed by taking into consideration only the nearest constellation point to the received signal with a 0 (or 1) at that bit position, rather than all the constellation points as done in exact LLR. It is defined as [8]:

L(b)=1σ2(minsS0((xsx)2+ (ysy)2)minsS1((xsx)2+ (ysy)2))

Delays in Digital Modulation

Digital modulation and demodulation blocks sometimes incur delays between their inputs and outputs, depending on their configuration and on properties of their signals. The following table lists sources of delay and the situations in which they occur.

Delays Resulting from Digital Modulation or Demodulation

Modulation or Demodulation TypeSituation in Which Delay OccursAmount of Delay
FM demodulatorSample-based processingOne output period
All demodulators in CPM sublibrary Multirate processing, and the model uses a variable-step solver or a fixed-step solver with the Tasking Mode parameter set to SingleTasking
D = Traceback length parameter
D+1 output periods
Single-rate processing, D = Traceback depth parameterD output periods
OQPSK demodulatorSingle-rate processingOne output period
Multirate processing, and the model uses a fixed-step solver with Tasking Mode parameter set to Auto or MultiTasking.Two output periods
Multirate processing processing, and the model uses a variable-step solver or the Tasking Mode parameter is set to SingleTasking.One output period
All decoders in TCM sublibrary Operation mode set to Continuous, Tr = Traceback depth parameter, and code rate k/n Tr*k output bits

As a result of delays, data that enters a modulation or demodulation block at time T appears in the output at time T+delay. In particular, if your simulation computes error statistics or compares transmitted with received data, it must take the delay into account when performing such computations or comparisons.

First Output Sample in DPSK Demodulation

In addition to the delays mentioned above, the M-DPSK, DQPSK, and DBPSK demodulators produce output whose first sample is unrelated to the input. This is related to the differential modulation technique, not the particular implementation of it.

Example: Delays from Demodulation

Demodulation in the model below causes the demodulated signal to lag, compared to the unmodulated signal. When computing error statistics, the model accounts for the delay by setting the Error Rate Calculation block's Receive delay parameter to 0. If the Receive delay parameter had a different value, then the error rate showing at the top of the Display block would be close to 1/2.

To open this model open this model , enter doc_oqpsk_modulation_delay at the MATLAB command line. To build the model, gather and configure these blocks:

  • Random Integer Generator, in the Random Data Sources sublibrary of the Comm Sources library

    • Set M-ary number to 4.

    • Set Initial seed to any positive integer scalar.

  • OQPSK Modulator Baseband, in the PM sublibrary of the Digital Baseband sublibrary of Modulation

  • AWGN Channel, in the Channels library

    • Set Es/No to 6.

  • OQPSK Demodulator Baseband, in the PM sublibrary of the Digital Baseband sublibrary of Modulation

  • Error Rate Calculation, in the Comm Sinks library

    • Set Receive delay to 1.

    • Set Computation delay to 0.

    • Set Output data to Port.

  • Display, in the Simulink Sinks library

    • Drag the bottom edge of the icon to make the display big enough for three entries.

Connect the blocks as shown above. From the model window's Simulation, select Model Configuration parameters. In the Configuration Parameters dialog box, set Stop time to 1000. Then run the model and observe the error rate at the top of the Display block's icon. Your error rate will vary depending on your Initial seed value in the Random Integer Generator block.

Selected Bibliography for Digital Modulation

[1] Jeruchim, M. C., P. Balaban, and K. S. Shanmugan, Simulation of Communication Systems, New York, Plenum Press, 1992.

[2] Proakis, J. G., Digital Communications, 3rd ed., New York, McGraw-Hill, 1995.

[3] Sklar, B., Digital Communications: Fundamentals and Applications, Englewood Cliffs, NJ, Prentice-Hall, 1988.

[4] Anderson, J. B., T. Aulin, and C.-E. Sundberg, Digital Phase Modulation, New York, Plenum Press, 1986.

[5] Biglieri, E., D. Divsalar, P.J. McLane, and M.K. Simon, Introduction to Trellis-Coded Modulation with Applications, New York, Macmillan, 1991.

[6] Pawula, R.F., "On M-ary DPSK Transmission Over Terrestrial and Satellite Channels," IEEE Transactions on Communications, Vol. COM-32, July 1984, pp. 752–761.

[7] Smith, J. G., "Odd-Bit Quadrature Amplitude-Shift Keying," IEEE Transactions on Communications, Vol. COM-23, March 1975, pp. 385–389.

[8] Viterbi, A. J., "An Intuitive Justification and a Simplified Implementation of the MAP Decoder for Convolutional Codes," IEEE Journal on Selected Areas in Communications, vol. 16, No. 2, pp 260–264, Feb. 1998

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