MAPSK Demodulator Baseband
Mary amplitude phase shift keying (APSK) demodulation
Libraries:
Communications Toolbox /
Modulation /
Digital Baseband Modulation /
APM
Description
The MAPSK Demodulator Baseband block demodulates a baseband representation of an Mary amplitude phase shift keying (APSK) modulated signal. M is the Modulation Order for MAPSK. For a description of MAPSK demodulation, see APSK Hard Demodulation and APSK Soft Demodulation.
Note
MAPSK Demodulator Baseband specifically applies to multiple ring PSK constellations. For a single ring PSK constellation, use MPSK Demodulator Baseband.
This icon shows the block with all ports enabled:
Examples
Demodulate Noisy 16APSK Signal Using Simulink
Apply 16APSK modulation to a signal of random data. Pass the modulated signal through an AWGN channel. Demodulate the noisy 16APSK signal. The example reports bit error rate (BER) and symbol error rate (SER) at two SNR settings.
The slex_16apsk_mod
model passes a 16APSK modulated signal through an AWGN channel, demodulates the signal and then computes the error rate statistics. The upper workflow computes the BER and the lower workflow computes the SER. Some block parameters get set by using workspace variables initialized in the PreLoadFcn
callback function loads simulation variables into the workspace. For more information, see Model Callbacks (Simulink).
Run the model with the AWGN channel blocks set to EbN0 = 6 dB and display the computed BER and SER. The AWGN Channel block in the lower workflow converts the EbN0 setting to an EsN0 setting. The results are saved to the workspace variables BERVec
and SERVec
in 1by3 row vectors. The first element contains the error rate.
With EbN0 set to 6.00 dB, BER: 0.070 With EsN0 set to 12.02 dB, SER: 0.160
Change the EbN0 of the AWGN channel block to 10 dB. Run the model, display the computed BER and SER, and observe the decrease in error rate.
With EbN0 set to 10.00 dB, BER: 0.016 With EsN0 set to 16.02 dB, SER: 0.051
Ports
Input
In — APSK modulated signal
scalar  vector  matrix
APSK modulated signal, specified as a scalar, vector, or matrix. When
this input is a matrix, each column is treated as an independent
channel. This port is unnamed until the Var
port is
enabled.
Data Types: double
 single
Complex Number Support: Yes
Var — Noise variance
positive scalar  vector of positive values
Noise variance, specified as a positive scalar or vector of positive values. When the noise variance or signal power result in computations involving extreme positive or negative magnitudes, see APSK Soft Demodulation for demodulation decision type considerations.
Dependencies
To enable this port, set Noise variance source to Input
port
.
Data Types: double
 single
Output
Out — Demodulated signal
scalar  vector  matrix
Demodulated signal, returned as a scalar, vector, or matrix. The data type and dimensions of the demodulated signal depend on the values specified by the Output type and Decision type parameters. This port is unnamed on the block.
Output type  Decision type  Demodulated Signal Description  Dimensions of Demodulated Signal 

Integer  —  Demodulated integer values in the range [0, (M – 1)]  The output signal has the same dimensions as the input signal. 
Bit  Hard decision  Demodulated bits  The number of rows in the output signal is log_{2}(M) times the number of rows in the input signal. Each demodulated symbol is mapped to a group of log_{2}(M) elements in a column, where the first element represents the MSB and the last element represents the LSB. 
Loglikelihood
ratio  Loglikelihood ratio value for each bit  
Approximate loglikelihood
ratio  Approximate loglikelihood ratio value for each bit  
M is the Modulation Order for MAPSK. 
Use Output data type to specify the output data type.
Data Types: single
 double
Parameters
To edit block parameters interactively, use the Property Inspector. From the Simulink^{®} Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.
Constellation points per circle — Constellation points per PSK ring
[4,12]
(default)  vector
Constellation points per PSK ring, specified as a vector with more than one element. Each vector element indicates the number of constellation points in its corresponding PSK ring. The first element corresponds to the innermost circle, and so on until the last element, which corresponds to the outermost circle. The sum of the elements in Constellation points per circle determines the modulation order. Element values must be multiples of four, and the modulation order must be a power of two.
Example: [4,12,16]
specifies a three PSK ring
constellation with a modulation order of 32.
Radius of each circle — Radius per PSK ring
[0.5,1]
(default)  vector
Radius per PSK ring, specified as a vector with the same length as Constellation points per circle. Each vector element indicates the radius of its corresponding PSK ring. The first element corresponds to the innermost circle, and so on until the last element, which corresponds to the outermost circle. These element values must be positive values arranged in increasing order.
Example: [0.5,1,2]
defines radii for three constellation
PSK rings. The inner ring has a radius of 0.5, the second ring has a radius
of 1.0, and the outer ring has a radius of 2.0.
Phase offset of each circle (rad) — Phase offset per PSK ring
[pi/4,pi/12]
(default)  scalar  vector
Phase offset per PSK ring in radians, specified as a scalar or vector with the same length as Constellation points per circle. Each vector element indicates the phase offset of its corresponding PSK ring. The first element corresponds to the innermost circle, and so on until the last element, which corresponds to the outermost circle. The Phase offset of each circle (rad) can be a scalar only if all the elements of Constellation points per circle are the same value.
Example: [pi/4,pi/12,pi/16]
defines phase offsets for
three constellation PSK rings. The inner ring has a phase offset of π/4, the
second ring has a phase offset of π/12, and the outer ring has a phase
offset of π/16.
Symbol mapping — Symbol mapping
Auto
(default)  Contourwisegray
 Gray
 Userdefined
Symbol mapping, specified as one of the following:
Contourwisegray
— Uses Gray mapping along the contour in the phase dimension for each PSK ring.Gray
— Uses Gray mapping along the contour in both the amplitude and phase dimensions. For Gray symbol mapping, all elements in Constellation points per circle must be equal, and all elements in Phase offset of each circle (rad) must be equal. For a description of the Gray mapping used, see [2].Userdefined
— See Custom symbol mapping.
The default symbol mapping depends on the
Constellation points per circle and Phase
offset of each circle (rad) parameters. When all elements in
Constellation points per circle are equal, and all
elements in Phase offset of each circle (rad) are
equal, the default is Gray
. For all other cases,
the default is Contourwisegray
.
Custom symbol mapping — Custom symbol mapping
[0,4,12,8,1,3,2,6,7,5,13,15,14,10,11,9]
(default)  integer vector
Custom symbol mapping, specified as an integer vector. This vector must consist of M unique elements with values in the range [0, (M – 1)], where M is the Modulation Order for MAPSK. The first element in Custom symbol mapping corresponds to the constellation point in the first quadrant of the innermost circle, with subsequent elements positioned counterclockwise around the PSK rings.
Example: The default value,
[0,4,12,8,1,3,2,6,7,5,13,15,14,10,11,9]
, specifies
contourwisegray symbol mapping. The distribution of constellation points is
nonuniform on all contours.
Dependencies
To enable this parameter, set Symbol
mapping to
Userdefined
.
Output type — Output type
Integer
(default)  Bit
Output type, specified as Integer
or
Bit
.
Decision type — Demodulation decision type
Hard decision
(default)  Loglikelihood ratio
 Approximate loglikelihood ratio
Demodulation decision type, specified as Hard
decision
, Loglikelihood ratio
,
or Approximate loglikelihood ratio
. See APSK Soft Demodulation for
algorithm selection considerations.
Dependencies
This parameter applies only when Output
type is set to Bit
.
Noise variance source — Noise variance source
Property
(default)  Input port
Noise variance source, specified as:
Property
— The noise variance is set using the Noise variance parameter.Input port
— The noise variance is set using the Var input port.
Dependencies
This parameter applies only when Decision type is set to either
Loglikelihood ratio
or
Approximate loglikelihood ratio
.
Noise variance — Noise variance
1
(default)  positive scalar  vector of positive values
Noise variance, specified as a positive scalar or vector of positive values.
When specified as a scalar, that value is used on all elements in the input signal.
When specified as a vector, the vector length must be equal to the number of columns in the input signal. Each noise variance vector element is applied to its corresponding column in the input signal.
When the noise variance or signal power result in computations involving extreme positive or negative magnitudes, see APSK Soft Demodulation for Decision type specification considerations.
Dependencies
This parameter applies only when Noise
variance source is set to
Property
and Decision type is set to either
Loglikelihood ratio
or
Approximate loglikelihood ratio
.
Output data type — Output data type
double
(default)  ...
Output data type, specified as one of the acceptable values from this table. Acceptable Output data type values depend on the Output type and Decision type parameter values.
Output type  Decision type  Output data type Options 

Integer  Not applicable  double ,
single ,
int8 ,
uint8 ,
int16 ,
uint16 ,
int32 , or
uint32 
Bit  Hard decision  double ,
single ,
int8 ,
uint8 ,
int16 ,
uint16 ,
int32 ,
uint32 , or
logical 
Loglikelihood ratio or
Approximate loglikelihood
ratio  The output signal is the same data type as the input signal. 
Dependencies
This parameter applies only when Output
type is set to Integer
or
when Output
type is set to Bit
and
Decision type is set to Hard
decision
.
Simulate using — Type of simulation to run
Interpreted execution
(default)  Code generation
Type of simulation to run, specified as Interpreted
execution
or Code generation
.
Interpreted execution
— Simulate the model by using the MATLAB^{®} interpreter. This option requires less startup time, but the speed of subsequent simulations is slower than with theCode generation
option. In this mode, you can debug the source code of the block.Code generation
— Simulate the model by using generated C code. The first time you run a simulation, Simulink generates C code for the block. The model reuses the C code for subsequent simulations unless the model changes. This option requires additional startup time, but the speed of the subsequent simulations is faster than with theInterpreted execution
option.
For more information, see Simulation Modes (Simulink).
Block Characteristics
Data Types 

Multidimensional Signals 

VariableSize Signals 

More About
Modulation Order for MAPSK
The modulation order, M, for MAPSK equals the sum of the vector elements in the Constellation points per circle parameter and is the total number of points in the signal constellation. Element values in Constellation points per circle must be multiples of four, and M must be a power of two.
APSK Hard Demodulation
The hard demodulation algorithm applies amplitude phase decoding, as described in [1].
APSK Soft Demodulation
For soft demodulation, two softdecision loglikelihood ratio (LLR) algorithms are available: exact LLR and approximate LLR. The exact LLR algorithm is more accurate but has slower execution speed than the approximate LLR algorithm. For further description of these algorithms, see the Hard vs. SoftDecision Demodulation topic.
Note
The exact LLR algorithm computes exponentials using finite precision arithmetic. For computations involving very large positive or negative magnitudes, the exact LLR algorithm yields:
Inf
orInf
if the noise variance is a very large valueNaN
if the noise variance and signal power are both very small values
The approximate LLR algorithm does not compute exponentials. You can avoid
Inf
, Inf
, and NaN
results by using
the approximate LLR algorithm.
Tips
For faster execution of the MAPSK Demodulator Baseband block, set the Simulate using parameter to:
Code generation
when using hard decision demodulation.Interpreted execution
when using soft decision demodulation.
References
[1] Sebesta, J. “Efficient Method for APSK Demodulation.” Selected Topics on Applied Mathematics, Circuits, Systems, and Signals (P. Pardalos, N. Mastorakis, V. Mladenov, and Z. Bojkovic, eds.). Vouliagmeni, Athens, Greece: WSEAS Press, 2009.
[2] Liu, Z., Q. Xie, K. Peng, and Z. Yang. "APSK Constellation with Gray Mapping." IEEE Communications Letters. Vol. 15, Number 12, December 2011, pp. 1271–1273.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced in R2018b
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