  The measurement of the cross-correlation function is crucial to assess
magnification bias in galaxy surveys. Previous works used mini-tile
subsampling, but accurately determining the integral constraint (IC) correction
for unbiased estimation is challenging due to various factors. We present a new
methodology for estimating the cross-correlation function, utilizing full field
area and reducing statistical uncertainty. Covariance matrices were estimated
by dividing each field into at least five patches using a k-mean clustering
algorithm. Robustness was assessed by comparing spectroscopic and photometric
lens samples, yielding compatible results. Cross-correlation and
auto-correlation analyses in the GAMA fields revealed a stronger signal in
GAMA15, likely due to rare large-scale structure combinations. Our findings
highlight the robustness of the new methodology and suggest sample-specific
effects. Subsequent papers in this series will explore other aspects of
magnification bias and address potential biases from the GAMA15 signal on
cosmological parameter constraints.
