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This paper investigates the system model and the transmit beamforming designfor the Cell-Free massive multi-input multi-output (MIMO) integrated sensingand communication (ISAC) system. The impact of the uncertainty of the targetlocations on the propagation of wireless signals is considered during bothuplink and downlink phases, and especially, the main statistics of the MIMOchannel estimation error are theoretically derived in the closed-form fashion.A fundamental performance metric, termed communication-sensing (C-S) region, isdefined for the considered system via three cases, i.e., the sensing-only case,the communication-only case and the ISAC case. The transmit beamforming designproblems for the three cases are respectively carried out through differentreformulations, e.g., the Lagrangian dual transform and the quadraticfractional transform, and some combinations of the block coordinate descentmethod and the successive convex approximation method. Numerical resultspresent a 3-dimensional C-S region with a dynamic number of access points toillustrate the trade-off between communication and radar sensing. The advantagefor radar sensing of the Cell-Free massive MIMO system is also studied via acomparison with the traditional cellular system. Finally, the efficacy of theproposed beamforming scheme is validated in comparison with zero-forcing andmaximum ratio transmission schemes.

Communication-Sensing Region for Cell-Free Massive MIMO ISAC Systems