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Considering the Complex Least Squares Problem, one can write the cost function for estimating H (where Y = XH + Z) as:

Reference: Mimo-OFDM Wireless Communications with MATLAB book (page 190)

$J(\boldsymbol H) = ||\boldsymbol Y - \boldsymbol X \boldsymbol H ||^2 = (\boldsymbol Y - \boldsymbol X \boldsymbol H)^H(\boldsymbol Y - \boldsymbol X \boldsymbol H) = \boldsymbol Y^H \boldsymbol Y - \boldsymbol Y^H \boldsymbol X \boldsymbol H - \boldsymbol H^H \boldsymbol X^H \boldsymbol Y + \boldsymbol H^H \boldsymbol X^H \boldsymbol X \boldsymbol H$

Calculating the derivative of the above function with respect to H gives:

$\frac{\partial J( \boldsymbol H)}{\partial \boldsymbol H} = -2(\boldsymbol X^H \boldsymbol Y)^* + 2(\boldsymbol X^H \boldsymbol X \boldsymbol H)^*$

How do I get to the expression above? Do I need to use some properties? I am trying to do that deriving each term separately.

Bruno A
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