Cell-Free Massive MIMO-OFDM: Asynchronous Reception and Performance Analysis

Cell-free massive multiple-input–multiple-output (CF mMIMO) is a promising technology to enhance the spectrum efficiency in future wireless systems by leveraging distributed access points (APs) to jointly serve the users over the same time-frequency resource. However, for uplink communications under orthogonal frequency division multiplexing (OFDM), the signals received at different APs from different users are generally asynchronous, due to the varying distances between the APs and users. In this article, we study the performance of CF mMIMO-OFDM wireless system under asynchronous signal reception in terms of uplink channel estimation and achievable spectral efficiency. In particular, we devise the minimum mean square error (MMSE) channel estimation under asynchronous reception and reveal how the phase shift, intersymbol interference, and intercarrier interference introduced by asynchronous reception destroy the orthogonality between different pilot sequences at the APs. In addition, given the imperfect channel state information caused by pilot contamination and asynchronous reception, we obtain closed-form expressions for the uplink achievable rate for both centralized and distributed operations. We show that for both operations, the uplink achievable rates under asynchronous reception are much smaller than those under synchronous reception due to the phase shift caused by asynchronous reception. Last, numerical results demonstrate that under asynchronous reception, the maximum sum-rate loss with MMSE and maximum ratio (MR) combining in centralized and distributed operations reach 29.5%, 4%, 45.4%, and 8%, respectively. This indicates that while MMSE combining is much more sensitive to asynchronous reception than MR combining, it still achieves a higher achievable rate.