Communications Toolbox

apkconst

Plot a combined circular ASK-PSK signal constellation

Syntax

• apkconst(numsig);
  apkconst(numsig,amp);
  apkconst(numsig,amp,phs);
  apkconst(numsig,amp,'n');
  apkconst(numsig,amp,phs,plotspec);
  y = apkconst(...);
  

Description

APK refers to a hybrid of amplitude- and phase-keying modulation. See the reference listed below for more details.

apkconst(numsig) plots a circular signal constellation. numsig is a vector of positive integers. The plot contains length(numsig) circles. The kth circle has radius k and contains numsig(k) evenly spaced constellation points. One point on each circle has zero phase.

apkconst(numsig,amp) is the same as the previous syntax, except that amp(k) is the radius of the kth circle. amp is a vector of positive real numbers. The lengths of amp and numsig must be the same.

apkconst(numsig,amp,phs) is the same as the previous syntax, except that it is not necessarily true that one point on each circle has zero phase. However, one point on the kth circle has phase phs(k). The lengths of phs, amp, and numsig must all be the same.

apkconst(numsig,amp,phs,'n') is the same as the previous syntax, except that the plot includes a number next to each constellation point. The number indicates how symbols would be mapped to constellation points if you were using numsig, amp, and phs in modulation and demodulation functions such as dmodce/ddemodce or modmap/demodmap.

apkconst(numsig,amp,phs,plotspec) is the same as apkconst(numsig,amp,phs), except that plotspec influences the appearance of the constellation points via the plot function. plotspec is a two-character string made up of one character from each odd-numbered column in the table below.

Color Character	Meaning	Marker-Type Character	Meaning
y	Yellow	.	Point
m	Magenta	o	Circle
c	Cyan	x	Cross
r	Red	+	Plus sign
g	Green	*	Asterisk
b	Blue	s	Square
w	White	d	Diamond
k	Black	v	Triangle (down)
		^	Triangle (up)
		<	Triangle (left)
		>	Triangle (right)
		p	Five-pointed star
		h	Six-pointed star

y = apkconst(...) does not produce a plot, but instead returns a complex vector y that represents the coordinates of the points in the constellation. The real part of y gives the in-phase component of each point and the imaginary part of y gives the quadrature component of each point.

Examples

The command below produces a plot having three circles. One circle has radius 1 and four points, one of which has zero phase. Another circle has radius 4 and five points, one of which has phase . The outermost circle has radius 5 and two points, one of which has phase /4. The plot follows.

• apkconst([4 5 2],[1 4 5],[0 pi pi/4])
  
  
  

The command below produces a vector containing the coordinates in the complex plane of the points in the figure above.

• y = apkconst([4 5 2],[1 4 5],[0 pi pi/4])
  
  y =
  
    Columns 1 through 4 
  
     1.0000             0.0000 + 1.0000i  -1.0000 + 0.0000i  -0.0000 - 1.0000i
  
    Columns 5 through 8 
  
    -4.0000 + 0.0000i  -1.2361 - 3.8042i   3.2361 - 2.3511i   3.2361 + 2.3511i
  
    Columns 9 through 11 
  
    -1.2361 + 3.8042i   3.5355 + 3.5355i  -3.5355 - 3.5355i
  

See Also
dmod, modmap, ddemod, demodmap

References

Thomas, C. Melvil, Michaeil Y. Weidner, and S. H. Durrani, "Digital Amplitude-Phase Keying with M-ary Alphabets," IEEE Transactions on Communications, Vol. Com-22, No. 2, Feb., 1974, pp. 168-180.

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