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I'm trying to understand the derivation of LS algorithm for channel estimation in OFDM.

Could anyone explain why do we need complex conj transpose in the below equation? LS

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Because when a quantity can be complex, and even when it is just real, the absolute squared difference $|f-g|^2$ can be expressed in both domain (complex and real) as:

$$|f-g|^2 = (f-g)^H(f-g)$$ and of course this is correct as well for reals. This setting is often related to Hilbert spaces.

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