comm.SOQPSKDemodulator

Demodulate signal using SOQPSK method and Viterbi algorithm

Since R2026a

Description

The comm.SOQPSKDemodulator System object™ demodulates an input signal that was modulated by using the shaped-offset quadrature phase shift keying (SOQPSK) 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 SOQPSK method:

Create the comm.SOQPSKDemodulator 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

soqpskdemod = comm.SOQPSKDemodulator

soqpskdemod = comm.SOQPSKDemodulator(Name=Value)

Description

soqpskdemod = comm.SOQPSKDemodulator creates a demodulator System object to demodulate input SOQPSK signals using the Viterbi algorithm.

soqpskdemod = comm.SOQPSKDemodulator(Name=Value) sets properties using one or more name-value arguments. For example, comm.SOQPSKDemodulator(FrequencyPulse='A') specifies type 'A' frequency pulse shaping.

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.

`FrequencyPulse` — Type of frequency pulse shaping
`'TG'` (default) | `'A'` | `'B'`

Type of frequency pulse shaping used by the modulator to smooth the phase transitions of the modulated signal, specified as 'TG', 'A', or 'B'. For more information, see Pulse Shape Filtering.

`InitialConditions` — Precoder initial input
[0 0] (default) | scalar | row vector

Precoder initial input, specified as a binary-valued scalar or a two-element row vector. When provided as a scalar, the same value applies to both elements.

This property defines the first data symbol used by the modulator before the first call of the object, in reverse chronological order.

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

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

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

Samples per symbol, specified as a positive even integer. This property specifies the output symbol upsampling factor for each input sample.

`TracebackDepth` — Traceback depth for Viterbi algorithm
`8` (default) | positive integer

Traceback depth for the Viterbi algorithm, specified as a positive integer representing the number of trellis branches that the Viterbi algorithm uses to construct each traceback path. For more information, see Traceback Depth and Output Delays.

`OutputDataType` — Data type of output
`'double'` (default) | `'single'` | `'int8'`

Data type of the output, specified as 'double', 'single', or 'int8'.

Usage

Syntax

Y = soqpskdemod(X)

Description

Y = soqpskdemod(X) demodulates the input signal by using the SOQPSK method.

example

Input Arguments

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`X` — SOQPSK-modulated signal
column vector

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

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

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`Y` — Demodulated output signal
column vector

Demodulated output signal, returned as a column vector with 2×N_Samp/(N_SPS) elements. N_Samp is the length of input Y and N_SPS is the value of SamplesPerSymbol.

To specify the output data type, use the OutputDataType property.

The output has a processing delay. For more information, see Traceback Depth and Output Delays.

Data Types: single | double | int8

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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Demodulate Noisy SOQPSK-B Waveform

Open Live Script

Demodulate a noisy SOQPSK-B-modulated waveform by using hard-decision processing.

Create SOQPSK modulator and demodulator objects, and a frame of random binary data. Set an $\frac{E_{b}}{N_{0}}$ level for the AWGN channel and convert the value to SNR.

soqpskMod = comm.SOQPSKModulator(FrequencyPulse="B")

soqpskMod = 
  comm.SOQPSKModulator with properties:

        FrequencyPulse: "B"
     InitialConditions: [0 0]
    InitialPhaseOffset: 0
      SamplesPerSymbol: 8
        OutputDataType: "double"

soqpskDemod = comm.SOQPSKDemodulator(FrequencyPulse="B")

soqpskDemod = 
  comm.SOQPSKDemodulator with properties:

        FrequencyPulse: "B"
     InitialConditions: [0 0]
    InitialPhaseOffset: 0
      SamplesPerSymbol: 8
        TracebackDepth: 8
        OutputDataType: "double"

data = randi([0 1],1e3,1);
EbNodB = 11;
snrdB = convertSNR(EbNodB,'ebno', ...
    BitsPerSymbol=2,SamplesPerSymbol=soqpskMod.SamplesPerSymbol);

Apply SOQPSK modulation, add AWGN to the modulated signal, and then demodulate the received symbols.

txOut = soqpskMod(data);
rxIn = awgn(txOut,snrdB,'measured');
rxOut = soqpskDemod(rxIn);

Account for the delay, which equals the sum of the traceback depth and the filter delay, and then calculate the number of errors. The delay equals TracebackDepth + PulseLength/2. Set the delay based on the traceback depth length and the frequency pulse type used for demodulation.

if soqpskMod.FrequencyPulse=="B"
    delay = soqpskDemod.TracebackDepth+8;
else
    delay = soqpskDemod.TracebackDepth+4;
end

Confirm the expected delay by using the finddelay function.

delaycheck = finddelay(data,rxOut)

delaycheck = 
16

isequal(delay,delaycheck)

ans = logical
   1

numErr = sum(data(1:end-delay)~=rxOut(delay+1:end))

numErr = 
0

More About

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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. The Viterbi algorithm processing and the frequency pulse length add to determine the delay preceding the first meaningful demodulated value in the output. The combined delay is (D + L/2) symbols. This table lists the pulse length L in bit duration for each frequency pulse type.

`FrequencyPulse` Value	Pulse Length, L (Bit Duration)
`'TG'`	8
`'A'`	8
`'B'`	16

Algorithms

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This implementation of the SOQPSK method conforms to the specification in IRIG Standard 106-17, Chapter 2 [1], and includes support for SOQPSK-TG, SOQPSK-A, and SOQPSK-B frequency pulse-shapes.

SOQPSK Demodulation

SOQPSK demodulation is a hybrid mixture of CPM and OQPSK. The phase output of partial response SOQPSK-TG can approximate the phase output of full response rectangular SOQPSK by using a pulse truncation method that reduces the frequency pulse shaping filter to T_bduration. This pulse truncation effectively makes the partial response SOQPSK-TG behave as a full response CPM and reduces the trellis state to four phase states. This equation represents a pulse shaping filter q, where duration T equals T_b and L is the pulse length in bit duration.

$q_{P T} (t) = {\begin{matrix} 0, \\ q (t + (L - 1) T / 2), \\ 1 / 2, \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} t < 0 \\ 0 \leq t \leq T \\ t > T \end{matrix}$

For both odd and even current symbol values, the precoder equation has a dependency on two previous symbols. The precoder implementation uses a four-state trellis with different sections for n-even and n-odd case to demodulate SOQPSK signals.

This constellation diagram shows the one-to-one mapping between precoder state variables and phase state variables.

SOQPSK Method

The SOQPSK method is a family of constant-envelope CPM waveforms. This block diagram from Section 2.3.3.2 of IRIG Standard 106-17 shows the input signal flow through a precoder, a pulse shaping filter, and a modulator:

Precoding performed on binary input data generates ternary symbols {–1,0,1}. The Q branch is offset from the I branch by T_b, where T_b is the bit duration in seconds. For each new bit the precoder processes, the modulator outputs a new ternary symbol.

The ternary symbol mapping follows these rules:

$\begin{array}{l} a_{k} = {\begin{matrix} - 1, k^{t h} b i t = 0 \\ + 1, k^{t h} b i t = 1 \end{matrix} \\ α_{k} = (^{- 1) k + 1} \frac{a_{k - 1} (a_{k} - a_{k - 2})}{2} \end{array}$

The SOQPSK precoder uses this mapping for input data:

SOQPSK Precoding Table for IRIG-106 Compatibility
Map α_K from I_K					Map α_K+1 from Q_K+1
I_k	Q_k–1	I_k–2	ΔΦ	α_k	Q_k+1	I_k	Q_k–1	ΔΦ	α_k+1
–1	+1 or –1	–1	0	0	–1	+1 or –1	–1	0	0
+1	+1 or –1	+1	0	0	+1	+1 or –1	+1	0	0
–1	–1	+1	–π/2	–1	–1	–1	+1	+π/2	+1
–1	+1	+1	+π/2	+1	–1	+1	+1	–π/2	–1
+1	–1	–1	+π/2	+1	+1	–1	–1	–π/2	–1
+1	+1	–1	–π/2	–1	+1	+1	–1	+π/2	+1
Included from Table 2-5 in IRIG Standard 106-17

Since I and Q do not vary at the same instant, the ternary symbols generated are constrained so that in a given bit interval, a precoded symbol can be mapped from the set {0,–1} or {0,+1}. Specifically, +1 cannot be followed by –1 and vice versa.

For SOQPSK, the modulation index is ½. The output of the modulator is a baseband representation of the modulated signal:

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

Pulse Shape Filtering

The SOQPSK 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 a spectrally raised cosine windowed by a modified temporal raised-cosine function expression for g(t).

$\begin{array}{l} g (t) = n (t) w (t) \\ w h e r e \\ n (t) = [\frac{A \cos π θ_{1} (t)}{1 - 4 θ_{_{1}}^{2} (t)}] [\frac{\sin θ_{2} (t)}{θ_{2} (t)}] \\ θ_{1} (t) = \frac{ρ B t}{T_{S}} \\ θ_{2} (t) = \frac{π B t}{T_{S}} \\ w (t) = \frac{1}{2} [1 + \cos (\frac{π (| \frac{t}{T_{S}} | - T_{1})}{T_{2}})], \begin{matrix} 1, | \frac{t}{T_{S}} | \\ T_{1} < | \frac{t}{T_{S}} | \leq T_{1} + T_{2} \\ 0, | \frac{t}{T_{S}} | > T_{1} + T_{2} \end{matrix} \end{array}$

The function n(t) is a modified spectral raised cosine filter of amplitude A, rolloff factor ρ, and an additional time scaling factor B.

The function w(t) is a time domain windowing function that limits the duration of g(t).

The SOQPSK-TG, -A, and -B frequency pulse-shapes use these parameters to realize the spectral raised cosine pulse shape filtering variants.

SOQPSK Type	ρ	B	T1	T2	Resulting Pulse Length (Bit Duration)
SOQPSK-TG (IG 106-04)	0.7	1.25	1.5	0.5	8
SOQPSK-A	1	1.35	1.4	0.6	8
SOQPSK-B	0.5	1.45	2.8	1.2	16

For more information on pulse shape filtering, see Section 2.3.3.2 of IRIG Standard 106-17.

References

[1] Inter-Range Instrumentation Group (IRIG) Telemetry Standards, IRIG Standard 106-17, Chapter 2, July 2017.

[2] E. Perrins and M. Rice, "Reduced-Complexity Approach to Iterative Detection of Coded SOQPSK," in IEEE^® Transactions on Communications, vol. 55, no. 7, pp. 1354-1362, July 2007, doi: 10.1109/TCOMM.2007.900614.

[3] E. Perrins, "FEC Systems for Aeronautical Telemetry," in IEEE Transactions on Aerospace and Electronic Systems, vol. 49, no. 4, pp. 2340-2352, OCTOBER 2013, doi: 10.1109/TAES.2013.6621820.

Extended Capabilities

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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 R2026a

comm.SOQPSKDemodulator

Description

Creation

Syntax

Description

Properties

`FrequencyPulse` — Type of frequency pulse shaping
`'TG'` (default) | `'A'` | `'B'`

`InitialConditions` — Precoder initial input
[0 0] (default) | scalar | row vector

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

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

`TracebackDepth` — Traceback depth for Viterbi algorithm
`8` (default) | positive integer

`OutputDataType` — Data type of output
`'double'` (default) | `'single'` | `'int8'`

Usage

Syntax

Description

Input Arguments

`X` — SOQPSK-modulated signal
column vector

Output Arguments

`Y` — Demodulated output signal
column vector

Object Functions

Common to All System Objects

Examples

Demodulate Noisy SOQPSK-B Waveform

More About

Traceback Depth and Output Delays

Algorithms

SOQPSK Demodulation

SOQPSK Method

Pulse Shape Filtering

References

Extended Capabilities

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

Version History

See Also

Functions

Objects

Topics

comm.SOQPSKDemodulator

Description

Creation

Syntax

Description

Properties

FrequencyPulse — Type of frequency pulse shaping 'TG' (default) | 'A' | 'B'

InitialConditions — Precoder initial input [0 0] (default) | scalar | row vector

InitialPhaseOffset — Initial phase offset 0 (default) | scalar

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

TracebackDepth — Traceback depth for Viterbi algorithm 8 (default) | positive integer

OutputDataType — Data type of output 'double' (default) | 'single' | 'int8'

Usage

Syntax

Description

Input Arguments

X — SOQPSK-modulated signal column vector

Output Arguments

Y — Demodulated output signal column vector

Object Functions

Common to All System Objects

Examples

Demodulate Noisy SOQPSK-B Waveform

More About

Traceback Depth and Output Delays

Algorithms

SOQPSK Demodulation

SOQPSK Method

Pulse Shape Filtering

References

Extended Capabilities

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

Version History

See Also

Functions

Objects

Topics

`FrequencyPulse` — Type of frequency pulse shaping
`'TG'` (default) | `'A'` | `'B'`

`InitialConditions` — Precoder initial input
[0 0] (default) | scalar | row vector

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

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

`TracebackDepth` — Traceback depth for Viterbi algorithm
`8` (default) | positive integer

`OutputDataType` — Data type of output
`'double'` (default) | `'single'` | `'int8'`

`X` — SOQPSK-modulated signal
column vector

`Y` — Demodulated output signal
column vector

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