apskmod

Amplitude phase shift keying (APSK) modulation

Syntax

Y = apskmod(X,M,radii)

Y = apskmod(X,M,radii,phaseoffset)

Y = apskmod(___,Name=Value)

Description

Y = apskmod(X,M,radii) performs APSK modulation on the input data, X, based on the specified number of constellation points per PSK ring, M, and the radius of each PSK ring, radii. For a description of APSK modulation, see Algorithms.

Note

apskmod specifically applies to multiple ring PSK constellations. For a single ring PSK constellation, use pskmod.

example

Y = apskmod(X,M,radii,phaseoffset) specifies an initial phase offset for each PSK ring of the APSK modulated signal.

example

Y = apskmod(___,Name=Value) specifies optional name-value arguments using any of the previous syntaxes. For example, apskmod(Y,M,PlotConstellation=true) modulates using modulation order M and plots the constellation. Specify name-value arguments after all other input arguments.

example

Examples

collapse all

Apply APSK Modulation

Open Live Script

Modulate data using APSK with an unequal number of constellation points on each circle.

Define vectors for modulation order and PSK ring radii. Generate data for constellation points.

M = [4 8 20];
radii = [0.3 0.7 1.2];
modOrder = sum(M);
x = 0:modOrder-1;

Apply APSK modulation to the data.

y = apskmod(x,M,radii);

Plot the resulting constellation using a scatter plot.

scatterplot(y)

Figure Scatter Plot contains an axes object. The axes object with title Scatter plot, xlabel In-Phase, ylabel Quadrature contains a line object which displays its values using only markers. This object represents Channel 1.

Apply APSK Modulation with Phase Offset

Open Live Script

Modulate a random data sequence using APSK with zero phase offset for the inner circle and pi/6 phase offset for the outer circle.

Define vectors for modulation order, PSK ring radii, and PSK ring phase offset. Generate random data.

M = [8 8];
modOrder = sum(M);
radii = [0.5 1];
phOff = [0 pi/6];

x = randi([0 modOrder-1],100,1);

Apply APSK modulation to the data.

y = apskmod(x,M,radii,phOff);

Plot the resulting constellation using a scatter plot and observe the phase offset between the constellation circles.

scatterplot(y)

Apply APSK Modulation Modifying Symbol Ordering

Open Live Script

Plot APSK constellations for Gray-coded and custom-coded symbol mappings.

Define vectors for modulation order and PSK ring radii. Generate bit data for constellation points.

M = [8 8];
modOrder = sum(M);
radii = [0.5 1.5];
x = 0:modOrder-1;

The apskmod function assumes the single channel binary input is left-MSB aligned and specified column-wise. Use the int2bit function to express the integer input symbols as a single column binary vector.

xBit = int2bit(x,log2(modOrder));

Apply APSK modulation to the data using the default phase offset. Since element values for M are equal and element values for phase offset are equal, the symbol mapping defaults to 'gray'. Plot the constellation using binary input to highlight the Gray-coded nature of the constellation mapping.

y = apskmod(xBit,M,radii,PlotConstellation=true,InputType='bit');

Figure contains an axes object. The axes object with title 16-APSK with Gray Mapping, xlabel In-phase Amplitude, ylabel Quadrature Amplitude contains 19 objects of type line, text. One or more of the lines displays its values using only markers

Create a custom-coded symbol mapping vector. This custom mapping happens to be another Gray-coded mapping.

cmap = [0;1;9;8;12;13;5;4;2;3;11;10;14;15;7;6];

Apply APSK modulation with a custom-coded symbol mapping. Plot the constellation using binary input to highlight that the custom mapping defines different Gray-coded symbol mapping.

z = apskmod(xBit,M,radii, ...
    SymbolMapping=cmap, ...
    PlotConstellation=true, ...
    InputType='bit');

Figure contains an axes object. The axes object with title 16-APSK with Custom Mapping, xlabel In-phase Amplitude, ylabel Quadrature Amplitude contains 19 objects of type line, text. One or more of the lines displays its values using only markers

Apply APSK Modulation to Input Bits

Open Live Script

Modulate a random bit sequence using APSK and output data type single. Pass the signal through a noisy channel and display the constellation diagram.

Define vectors for modulation order and PSK ring radii. Generate random binary data.

M = [8 12 20 24];
radii = [0.8 1.2 2 2.5];
bitsPerSym = log2(sum(M));

x = randi([0 1],2000*bitsPerSym,1);

Apply APSK modulation to the data and use a name-value pair to output as data type single.

y = apskmod(x,M,radii, ...
    InputType='bit', ...
    OutputDataType='single');

Pass through an AWGN channel with a 25 dB SNR.

yrec = awgn(y,25,'measured');

Plot the received constellation as a scatter plot.

scatterplot(yrec)

Input Arguments

collapse all

`X` — Input signal
scalar | vector | matrix

Input signal, specified as a scalar, vector, or matrix. The elements of X must be binary values or integers in the range [0, (sum(M)-1)].

Note

To process the input signal as binary elements, set the InputType argument to 'bit'. For binary inputs, the number of rows must be an integer multiple of log₂(sum(M)). Groups of log₂(sum(M)) bits in a column are mapped onto a symbol, with the first bit representing the MSB and the last bit representing the LSB.

`M` — Constellation points per PSK ring
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. Element values must be multiples of four and sum(M) must be a power of two. The modulation order is the total number of points in the signal constellation and equals the sum of the vector elements, sum(M).

Example: [4 12 16] specifies a three PSK ring constellation with a modulation order of sum(M) = 32.

Data Types: double

`radii` — Radius per PSK ring
vector

Radius per PSK ring, specified as a vector with the same length as M. The first element corresponds to the innermost circle, and so on, until the last element, which corresponds to the outermost circle. The elements must be positive and 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.

Data Types: double

`phaseoffset` — Phase offset per PSK ring
`[pi/M(1) pi/M(2) … pi/M(end)]` (default) | scalar | vector

Phase offset per PSK ring in radians, specified as a scalar or vector with the same length as M. The first element corresponds to the innermost circle, and so on, until the last element, which corresponds to the outermost circle. The phaseoffset can be a scalar only if all the elements of M are the same value.

Example: [pi/4 pi/12 pi/16] defines three constellation PSK ring phase offsets. The inner ring has a phase offset of pi/4, the second ring has a phase offset of pi/12, and the outer ring has a phase offset of pi/16.

Data Types: double

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: Y = apskmod(X,M,radii,InputType='bit',OutputDataType='single');

`SymbolMapping` — Symbol mapping
`'gray'` | `'contourwise-gray'` | integer vector

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 the values for M must be equal and all the values for phaseoffset must be equal. For a description of the Gray mapping used, see [2].
integer vector — Use custom symbol mapping. Vector must consist of sum(M) unique elements with values in the range [0, (sum(M)-1]. The first element corresponds to the constellation point in the first quadrant of the innermost circle, with subsequent elements positioned counterclockwise around the PSK rings.

The default symbol mapping depends on M and phaseOffset. When all the elements of M are equal and all the elements of phaseOffset are equal, the default is 'gray'. For all other cases, the default is 'contourwise-gray'.

Data Types: double | char | string

`InputType` — Input type
`'integer'` (default) | `'bit'`

Input type, specified as one of these options:

'integer' –– The input signal must consist of integers in the range [0, (sum(M) – 1)].
'bit' –– The input signal must contain binary values, and the number of rows must be an integer multiple of log₂(sum(M)). Binary input signals are assumed to be left-MSB aligned and specified column-wise. Groups of log₂(sum(M)) bits in a column are mapped onto a symbol, with the first bit representing the MSB and the last bit representing the LSB.

`OutputDataType` — Output data type
`'double'` (default) | `'single'`

Output data type, specified as 'double' or 'single'.

`PlotConstellation` — Plot reference constellation
`false` or `0` (default) | `true` or `1`

Option to plot constellation, specified as logical 0 (false) or 1 (true). To plot the constellation, set PlotConstellation to true.

Data Types: logical

Output Arguments

collapse all

`Y` — APSK modulated signal
scalar | vector | matrix

APSK modulated signal, returned as a complex scalar, vector, or matrix. The dimensions of Y depend on the specified 'InputType' value. Specify the data type of the output with OutputDataType

`InputType`	Dimensions of Output
`'integer'`	`Y` has the same dimensions as input `X`.
`'bit'`	The number of rows in `Y` equals the number of rows in `Y` divided by log₂(sum(`M`)).

Algorithms

The function implements a pure APSK constellation.

A pure M-APSK constellation is composed of N_C concentric rings or contours, each with uniformly spaced PSK points. The M-APSK constellation set is

$χ = {\begin{matrix} R_{1} \exp (j (\frac{2 π}{M_{1}} i + ϕ_{1})), & i = 0, \dots, M_{1} - 1, \\ R_{2} \exp (j (\frac{2 π}{M_{2}} i + ϕ_{2})), & i = 0, \dots, M_{2} - 1, \\ ⋮ & ⋮ \\ R_{N_{C}} \exp (j (\frac{2 π}{M_{N_{C}}} i + ϕ_{Nc})), & i = 0, \dots, M_{N_{C}} - 1, \end{matrix}$

where:

The modulation order is equal to the sum of all M_l for l = 1, 2, ... , N_C.
N_C is the number of concentric rings. N_C ≥ 2.
M_l is the number of constellation points in the lth ring.
R_l is the radius of the lth ring.
ϕ_l is the phase offset of the lth ring.
$j = \sqrt{- 1}$

References

[1] Corazza, Giovanni E. Digital Satellite Communications. New York: Springer Science Business Media, LLC, 2007.

[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 MATLAB® Coder™.

Version History

Introduced in R2018a

apskmod

Syntax

Description

Examples

Apply APSK Modulation

Apply APSK Modulation with Phase Offset

Apply APSK Modulation Modifying Symbol Ordering

Apply APSK Modulation to Input Bits

Input Arguments

`X` — Input signal
scalar | vector | matrix

`M` — Constellation points per PSK ring
vector

`radii` — Radius per PSK ring
vector

`phaseoffset` — Phase offset per PSK ring
`[pi/M(1) pi/M(2) … pi/M(end)]` (default) | scalar | vector

Name-Value Arguments

`SymbolMapping` — Symbol mapping
`'gray'` | `'contourwise-gray'` | integer vector

`InputType` — Input type
`'integer'` (default) | `'bit'`

`OutputDataType` — Output data type
`'double'` (default) | `'single'`

`PlotConstellation` — Plot reference constellation
`false` or `0` (default) | `true` or `1`

Output Arguments

`Y` — APSK modulated signal
scalar | vector | matrix

Algorithms

References

Extended Capabilities

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

Version History

See Also

Functions

Objects

apskmod

Syntax

Description

Examples

Apply APSK Modulation

Apply APSK Modulation with Phase Offset

Apply APSK Modulation Modifying Symbol Ordering

Apply APSK Modulation to Input Bits

Input Arguments

X — Input signal scalar | vector | matrix

M — Constellation points per PSK ring vector

radii — Radius per PSK ring vector

phaseoffset — Phase offset per PSK ring [pi/M(1) pi/M(2) … pi/M(end)] (default) | scalar | vector

Name-Value Arguments

SymbolMapping — Symbol mapping 'gray' | 'contourwise-gray' | integer vector

InputType — Input type 'integer' (default) | 'bit'

OutputDataType — Output data type 'double' (default) | 'single'

PlotConstellation — Plot reference constellation false or 0 (default) | true or 1

Output Arguments

Y — APSK modulated signal scalar | vector | matrix

Algorithms

References

Extended Capabilities

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

Version History

See Also

Functions

Objects

`X` — Input signal
scalar | vector | matrix

`M` — Constellation points per PSK ring
vector

`radii` — Radius per PSK ring
vector

`phaseoffset` — Phase offset per PSK ring
`[pi/M(1) pi/M(2) … pi/M(end)]` (default) | scalar | vector

`SymbolMapping` — Symbol mapping
`'gray'` | `'contourwise-gray'` | integer vector

`InputType` — Input type
`'integer'` (default) | `'bit'`

`OutputDataType` — Output data type
`'double'` (default) | `'single'`

`PlotConstellation` — Plot reference constellation
`false` or `0` (default) | `true` or `1`

`Y` — APSK modulated signal
scalar | vector | matrix

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