What is the Expectation Value of (X'*X)^-1 in MATLAB for Signal Constellations?

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SUMMARY

The expectation value of the inverse matrix (X'*X)^-1 in MATLAB for signal constellations such as QPSK can be expressed as E{(X'*X)^-1} = E{|1/Xk|^2}I, where I is the identity matrix. The matrix X is composed of QPSK symbols, and the discussion emphasizes that X'*X and its inverse are diagonal matrices. The user seeks guidance on implementing this expectation value calculation in MATLAB, specifically for QPSK signal constellations.

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  • Understanding of MATLAB programming
  • Familiarity with matrix operations in MATLAB
  • Knowledge of QPSK signal constellation
  • Basic concepts of expectation values in statistics
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  • Learn about calculating expectation values in MATLAB
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  • Investigate the statistical properties of signal constellations
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Signal processing engineers, MATLAB programmers, and researchers working with digital communication systems, particularly those focused on QPSK modulation and matrix operations.

florenti
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Hi,

as I am new in Matlab, so I need your help.

I want to replace the following inverse matrix (X'*X)^-1 with its expectation value:

E{(X'*X)^-1} = E{|1/Xk|^2}I

X'*X and (X'*X)^-1 is a diagonal matrix. Could anyone give me an Idea how to write it in MATLAB this expectation value. The elements of a matrix X are composed by QPSK symbols, or 16-QAM, or 64-QAM. Assume for now QPSK.

Assuming the same
signal constellation on all tones and equal probability on all constellation points.

Thanks in advande.
 
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