Optimal Antenna Cluster Size in Cell-Free Large-Scale Distributed Antenna Systems With Imperfect CSI and Intercluster Interference

In cell-free large-scale distributed antenna systems (L-DASs), the antennas are distributed over the intended coverage area. Introducing cooperation among the antennas can significantly improve the system throughput. However, only finite-cluster-size (limited) cooperation with L-DAS antenna clusters is realistic due to practical limitations. In this paper, the impact of antenna cluster size on the downlink sum rate of frequency-division duplex (FDD) cell-free L-DASs is analyzed, considering imperfect channel state information (CSI) and intercluster interference (ICLI). We investigate the optimal cluster size in terms of maximizing the downlink sum rate with respect to the overhead of imperfect channel training and feedback. When the number of users is sufficiently large, closed-form lower bounds of the ergodic sum capacity, which are leveraged to analyze the system performance, are derived by constructing different rate-achieving user-scheduling schemes. Both analog and digital feedback schemes are considered to evaluate the imperfect channel feedback. Based on these, closed-form expressions of the optimal cluster size for 1-D antenna topology systems and the corresponding achievable rates are derived. The scaling law of the optimal cluster size for 2-D antenna topology systems is also given. Numerical results demonstrate the impact of the signal-to-noise ratio (SNR) and the block length on the achievable rates and the optimal cluster size, which agree with our analytical results.