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Amplitude phase shift keying (APSK) modulation

performs APSK modulation on the input data, `y`

= apskmod(`x`

,`M`

,`radii`

)`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`

.

specifies an initial phase offset for each PSK ring of the APSK modulated
signal.`y`

= apskmod(`x`

,`M`

,`radii`

,`phaseoffset`

)

specifies options using one or more name-value pair arguments using any of the
previous syntaxes. For example, `y`

= apskmod(___,`Name,Value`

)`'OutputDataType','double'`

specifies the desired output data type as double. Specify name-value pair arguments
after all other input arguments.

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

$$\chi =\{\begin{array}{cc}{R}_{1}\mathrm{exp}\left(j\left(\frac{2\pi}{{M}_{1}}i+{\theta}_{1}\right)\right),& i=0,\dots ,{M}_{1}-1,\\ {R}_{2}\mathrm{exp}\left(j\left(\frac{2\pi}{{M}_{2}}i+{\theta}_{2}\right)\right),& i=0,\dots ,{M}_{2}-1,\\ \vdots & \vdots \\ {R}_{{N}_{\text{C}}}\mathrm{exp}\left(j\left(\frac{2\pi}{{M}_{{N}_{\text{C}}}}i+{\theta}_{\text{Nc}}\right)\right),& i=0,\dots ,{M}_{{N}_{\text{C}}}-1,\end{array}$$

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*l*th ring.*R*_{l}is the radius of the*l*th ring.*θ*_{l}is the phase offset of the*l*th ring.$$j=\sqrt{-1}$$

[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.