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We have been studying a user-centric radio access network (RAN) for the realization of uniform radio quality “anywhere anytime” with Cell-free massive MIMO (CF-mMIMO) technology. In user-centric RAN, the central processing unit (CPU) that processes CF-mMIMO signals is assumed to be deployed in multiple sites to address the scalability problem for large-scale CF-mMIMO. However, the distributed deployment of CPUs results in radio quality degradation due to interference between UEs connected to CPUs at different sites. To address this problem, multiple CPU cooperation methods between CPUs at different sites are being studied. However, for cooperation, conventional methods require the exchange of radio signals and channel state information between CPUs, which significantly increases the transmission load on the backhaul connecting the sites. To resolve this issue, we propose an inter-site CPU cooperation method that maintains high radio quality while reducing the amount of data transmitted between sites to suppress inter-site interference. The proposed method is realized by deploying a channel estimation processing function for inter-site interference at each site and suppressing inter-site interference independently. Furthermore, we introduce optimization management that adjusts the degree of cooperation among CPUs based on the proposed method according to the required radio quality and computation and transmission resources in the area. We evaluate the proposed method by computational simulation. We show that the proposed method can reduce the transmission load by 53% with the same area throughput compared to the existing CPU cooperation schemes.