Memory polynomial for a power amplifier

How to implement the momory polynomial (MP) for a power amlifier (PA) complex data? The MP equation is:

Where:

• y[n] => Instantaneous complex output signal

• x[n-j] => Instantaneous complex input signal

• M => Model memory depth

• N => Model nonlinear order

• a_ji => Model complex coefficients

The problem is that I'm not sure how to go back to the old input "x[n-j]".

Below is a simple example. The expected x_new is a 9x3 matrix. Could someone help me, please?

%% Clean up
% Clear all variables
clear;
% Close all figures
close all;
% Clear command window
clc;

%% Test
x = [20; 40; 60; 80; 100];
y = x.^2;

M = 5;
N = 3;

for j = 3:M
    for i = 1:N
        x_new(:,i) = x(j:-1:end) .* (abs(x(j:-1:end)).^(i-1));
    end
end

a_ji = x_new\y;           % Solve systems for linear equation Ax = B (mldivide, \)
y_new = x_new * a_ji;     % Memory polynomial output matrix y[n]

Answer 1

[Rajanya]

Hi @Ali,

The code provided will always throw an error while calculating “a_ji” because the equation in the loops will end up producing a 0x3 vector and hence the ‘\‘ operator would not work. Assuming you will be having ‘a_ji’ coefficient matrix as input, you can calculate the given equation in the following way:

y = zeros(size(x));
%Run n from 1 to length of input signal maybe,    
for j = 1:M+1
    if (n-j) > 0
        for i = 2:N+1
            y(n) = y(n) + a(j, i)*x(n-j)*abs(x(n-j))^(i-2);
        end
    end
end
%End the outermost loop to get y values for all n.

To avoid any out of bound array accesses, the condition and the indexing have been put accordingly.

Please note that if you don’t have “a_ji” as input and you need to get it using “mldivide” operator (as you have intended to do in the example code), make sure you are producing the correct dimensions of the matrices before performing the operation.

Thanks.

[Ali]

Thanks a lot for your answer and your time! I solved long ago, my answer is quiet similar. I computed the memory polynomial this way:

%% Test
x = [20; 40; 60; 80; 100];
y = x.^2;

M = 5;
N = 3;

% Initilize empty matrices
x_MP1 = [];
x_MP2 = [];     

% Compute x[n-j].|x[n-j]|^(i-1)
for n = M+1:numel(x)
    for i = 1:N
        for j = 0:M
            x_MP = x(n-j) .* abs(x(n-j)).^(i-1);
            x_MP1 = [x_MP1 x_MP];
        end
    end
    x_MP2 = [x_MP2; x_MP1];
    x_MP1 = [];
    x_MP = [];
end

% Solve for "a" coefficients, Xa = Y (Least square using backslash "\")
a_ij = x_MP2\y(M+1:1:end);        % Forward model extraction

% Evaluation of the forward model
y_new = x_MP2 * a_ij;