Block-Diagonal Belief-Propagation Detection for

Cell-Free Massive MIMO (CF-mMIMO) is a promising technology owing to its high user spectrum efficiency. However, CF-mMIMO faces the challenges of baseband signal processing, especially for uplink data detection. In this paper, Gaussian interference of approximation (GAI) Belief Propagation (BP) detection is utilized for CF-mMIMO systems to achieve near-optimal performance. Based on the natural feature of the block-diagonal (BD) channel matrix, a reduced-complexity GAI-BP, which is named BD-GAI-BP, is proposed to save the computational complexity while maintaining the performance merits. Numerical results show that compared with the state-of-the-art data detection algorithm, the GAI-BP detection supports 28.93% more UEs with $BER =10^{-3}$. The proposed BD-GAI-BP saves 10.94% computational costs while achieving comparable performance with the GAI-BP.