Cross-correlation maximum in frequency domain

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I need to compute the complex cross-correlation between two signals a and b and the take only the maximum value of the cross-correlation, regardless of the lag time where this occurs. I can do it either in time domain or in frequency domain. This needs to be later incorporated in a FPGA, so I want to be efficient.
An alternative is to go to frequency domain correlation, but I would need to do
which is probably computationally costly. Is there a way to avoid going back and forth twice to the frequency and time domain and still compute the maximum cross-correlation?

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