Pulse amplitude modulation


y = pammod(x,M)
y = pammod(x,M,ini_phase)
y = pammod(x,M,ini_phase,symbol_order)


y = pammod(x,M) outputs the complex envelope y of the modulation of the message signal x using pulse amplitude modulation. M is the alphabet size. The message signal must consist of integers between 0 and M-1. The modulated signal has a minimum Euclidean distance of 2. If x is a matrix with multiple rows, the function processes the columns independently.

y = pammod(x,M,ini_phase) specifies the initial phase of the modulated signal in radians.

y = pammod(x,M,ini_phase,symbol_order) specifies how the function assigns binary words to corresponding integers. If symbol_order is set to 'bin' (default), the function uses a natural binary-coded ordering. If symbol_order is set to 'gray', it uses a Gray constellation ordering.


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Generate random data symbols and apply pulse amplitude modulation.

Set the modulation order.

M = 8;

Generate random integers and apply PAM modulation having an initial phase of π/4.

data = randi([0 M-1],100,1);
modData = pammod(data,M,pi/4);

Display the PAM constellation diagram.


Plot PAM symbol mapping for Gray and natural binary encoded data.

Set the modulation order, and then create a data sequence containing a complete set of constellation points.

M = 8;
data = [0:M-1];

Modulate and demodulate Gray and natural binary encoded data.

symgray = pammod(data,M,0,'gray');
mapgray = pamdemod(symgray,M,0,'gray');

symbin = pammod(data,M,0,'bin');
mapbin = pamdemod(symbin,M,0,'bin');

Plot the constellation points using one of the symbol sets. For each constellation point, assign a label indicating the Gray and natural binary values for each symbol.

  • For Gray binary symbol mapping, adjacent constellation points differ by a single binary bit and are not numerically sequential.

  • For natural binary symbol mapping, adjacent constellation points follow the natural binary encoding and are sequential.

for k = 1:M
        dec2base(mapbin(k),2,4),'Color',[1 0 0]);
        num2str(mapbin(k)),'Color',[1 0 0]);
axis([-M M -2 2])

Extended Capabilities

Introduced before R2006a