M-APSK Modulator Baseband
Modulates data using the M-APSK method.
Description
Unit M-APSK Modulator Baseband modulates the input signal using M-point amplitude phase shift keying (M-APSK) and returns a bandwidth representation of the modulated signal. Modulation order for M-APSK, defined by the parameters Constellation points per circle. For a description of M-APSK modulation, see . *Algorithms.
| Block M-APSK Modulator Baseband applies in particular to multi-ring PSK signalling constellations. For a signalling constellation with one PSK ring, use M-PSK Modulator Baseband. |
Ports
Input
#
In
—
input signal
scalar | vector | matrix
Details
Input signal specified as an integer scalar, integer vector, binary vector or matrix in the range ], where are the values of the parameters Constellation points per circle.
To treat the input signal as binary elements, set the Input type parameters to Bit. For binary inputs, the number of lines must be an integer multiple of . The bit groups in a column are mapped to a character, with the first bit representing the MSB and the last bit representing the LSB.
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| Data types |
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| Complex numbers support |
No |
Output
#
Out
—
M-APSK modulated output signal
Scalar | Vector | Matrix
Details
Output signal returned as a complex scalar, vector or matrix. The dimensionality of the output signal is determined by the value of the Input type parameters.
| Value of parameter Input type | Dimensions of the output signal |
|---|---|
|
The output signal has the same dimensions as the input signal. |
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The number of lines in the output signal is equal to the number of lines in the input signal divided by , where is the modulation order for M-APSK. |
| Data types |
|
| Complex numbers support |
Yes |
Parameters
Main
# Constellation points per circle — points of the signalling constellation to the PSK ring
Details
Signal constellation points per PSK ring, specified as a vector with more than one element. Each element of the vector indicates the number of signal constellation points in the 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. The element values must be multiples of four, and the modulation order must be equal to a power of two.
Example: [4,12,16] defines a ring signalling constellation of three PSKs with modulation order 32.
| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
# Radius of each circle — radius for PSK ring
Details
The radius of one PSK ring, is specified as a vector of the same length as the vector of the Constellation points per circle parameter. Each element of the vector indicates the radius of the 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 values of these elements must be positive and in ascending order.
Example: [0.5,1,2] defines the radii for the three rings of the PSK signalling constellation. 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.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# sPhase offset of each circle (rad) — phase offset per PSK ring
Details
The phase offset per PSK ring, is specified as a scalar or vector of the same length as the vector of the Constellation points per circle parameters. Each element of the vector indicates the phase offset of the 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 only be a scalar if all elements of Constellation points per circle have the same value.
Example: [pi/4,pi/12,pi/16] defines the phase offsets for the three rings of a PSK signalling constellation. 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.
| Default value |
|
| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
#
Symbol mapping —
character mapping
Auto | Contourwise-gray | Gray | User-defined
Details
Character Matching. Defined as:
-
Contourwise-gray- uses Gray’s contourwise-gray mapping in the phase dimension for each PSK ring. -
Gray- uses Gray’s contourwise-gray mapping in both the amplitude and phase dimensions. For Gray mapping of symbols, all values for Constellation points per circle must be equal, just as all values for Phase offset of each circle (rad) must be equal. See [2] for a description of the Gray mapping used. -
`User-defined' - see the Custom symbol mapping parameters.
By default, symbol mapping depends on Constellation points per circle and Phase offset of each circle (rad). When all elements of Constellation points per circle are equal and all elements of Phase offset of each circle (rad) are equal, Gray is used by default. In all other cases, Contourwise-gray is used by default.
| Values |
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| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
# Custom symbol mapping — custom character display
Details
A custom character mapping specified as an integer vector. This vector shall consist of unique elements with values in the range ], where is Modulation Order for M-APSK. The first element in the Custom symbol mapping corresponds to the signal constellation point in the first quadrant of the inner circle, and subsequent elements are arranged counterclockwise around the PSK rings.
| Example |
the by default value, |
Dependencies
To use this parameter, set the Symbol mapping parameter to User-defined.
| Default value |
|
| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
#
Input type —
input data type
Integer | Bit
Details
The type of input signal. Defined as:
-
Integer- the input signal must consist of integers in the range ]. -
Bit- the input signal shall contain binary values and the number of lines shall be an integer multiple of , where is Modulation order for M-APSK. It is assumed that the binary input signals are aligned to the left MSB and are specified column-wise. The bit groups of in a column are mapped to a symbol, with the first bit representing the MSB and the last bit representing the LSB.
| Values |
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| Default value |
|
| Program usage name |
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| Tunable |
No |
| Evaluatable |
No |
#
Output data type —
output data type
Float64 | Float32
Details
The data type of the modulated output signal type. Defined as:
-
Float64. -
Float32
| Values |
|
| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
No |
Additional Info
Modulation order for M-APSK
The modulation order, , for is the total number of points in the signal constellation. is equal to the sum of the elements in the vector of the Constellation points per circle parameters. The values of the elements in Constellation points per circle must be multiples of four. must be equal to a power of two.
*Algorithms
This block implements a simple APSK signalling constellation.
A simple M-APSK signalling constellation consists of concentric rings or contours, each containing uniformly distributed PSK points. The set of M-APSK signalling constellations is specified as:
where
-
The modulation order is equal to the sum of all for = 1, 2, … , .
-
- is the number of concentric rings. .
-
- is the number of signal constellation points in -th ring.
-
- is the radius of -th ring.
-
- phase shift of -th ring.
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Literature
-
Corazza, Giovanni E. "Digital Satellite Communications." New York: Springer Science Business Media, LLC, 2007.
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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.