M-APSK Demodulator Baseband

M-ary amplitude phase shift keying (APSK) demodulation

• Library:

• Communications Toolbox / Modulation / Digital Baseband Modulation / APM

Description

The M-APSK Demodulator Baseband block demodulates a baseband representation of an M-ary amplitude phase shift keying (APSK) modulated signal. M is the Modulation Order for M-APSK. For a description of M-APSK demodulation, see APSK Hard Demodulation and APSK Soft Demodulation.

Note

M-APSK Demodulator Baseband specifically applies to multiple ring PSK constellations. For a single ring PSK constellation, use M-PSK Demodulator Baseband.

This icon shows the block with all ports enabled:

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 log2(M) times the number of rows in the input signal. Each demodulated symbol is mapped to a group of log2(M) elements in a column, where the first element represents the MSB and the last element represents the LSB.
	Log-likelihood ratio	Log-likelihood ratio value for each bit
	Approximate log-likelihood ratio	Approximate log-likelihood ratio value for each bit
M is the Modulation Order for M-APSK.

Use Output data type to specify the output data type.

Data Types: single | double

Parameters

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) | Contourwise-gray | Gray | User-defined

Symbol mapping, specified as one of the following:

• Contourwise-gray — 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].

• User-defined — 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 Contourwise-gray.

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 M-APSK. 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 contourwise-gray symbol mapping. The distribution of constellation points is nonuniform on all contours.

Dependencies

To enable this parameter, set Symbol mapping to User-defined.

Output type — Output type

Integer (default) | Bit

Output type, specified as Integer or Bit.

Data Types: char | string

Decision type — Demodulation decision type

Hard decision (default) | Log-likelihood ratio | Approximate log-likelihood ratio

Demodulation decision type, specified as Hard decision, Log-likelihood ratio, or Approximate log-likelihood 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 Log-likelihood ratio or Approximate log-likelihood 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 Log-likelihood ratio or Approximate log-likelihood ratio.

Data Types: double

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
	Log-likelihood ratio or Approximate log-likelihood 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:

• Code generation –– Simulate the model using generated C code. The first time you run a simulation, Simulink^® generates C code for the block. The C code is reused for subsequent simulations as long as the model does not change. This option requires additional startup time.

• Interpreted execution –– Simulate the model using the MATLAB^® interpreter. This option shortens startup time. In Interpreted execution mode, you can debug the source code of the block.

For information on execution speed, see Tips.

Model Examples

Demodulate Noisy 16-APSK Signal

Apply 16-APSK modulation to a signal of random data. Pass the modulated signal through an AWGN channel. Demodulate the noisy 16-APSK signal. Check the bit error rate (BER).

Open Model

Block Characteristics

Data Types	Boolean | double | integer | single
Multidimensional Signals	yes
Variable-Size Signals	no

More About

Modulation Order for M-APSK

The modulation order, M, for M-APSK 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 soft-decision log-likelihood ratio (LLR) algorithms are available: exact LLR and approximate LLR. This table compares these algorithms.

Algorithm	Accuracy	Execution Speed
Exact LLR	more accurate	slower execution
Approximate LLR	less accurate	faster execution

For further description of these algorithms, see Exact LLR Algorithm and Approximate LLR Algorithm.

Note

The exact LLR algorithm computes exponentials using finite precision arithmetic. Computation of exponentials with very large positive or negative magnitudes might yield:

• Inf or -Inf if the noise variance is a very large value

• NaN if both the noise variance and signal power are very small values

When the output returns any of these values, try using the approximate LLR algorithm because it does not compute exponentials.

Tips

• For faster execution of the M-APSK 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™.