Design and Optimization of Cell-Free Systems: Channel Estimation, Duplexing Scheme, and Synchronization

Abstract

Cell-free massive multiple-input multiple-output (CF-mMIMO) systems, where multiple access points (APs) jointly and coherently serve a large number of user-equipments (UEs) in a geographical area, offer multi-fold improvement in spectral efficiency (SE) compared to cellular mMIMO systems. This is because of its unique ability to convert multi-cell interference of a cellular system to useful information-bearing signals while performing joint data processing at the central processing unit (CPU). Further, the proximity of the UEs and the distributed APs improves macro-diversity and link reliability, which in turn provides a uniform quality of service (QoS) to all the UEs while maintaining a high peak data rate. However, several signal processing challenges need to be thoroughly understood and addressed, in order to make CF-mMIMO practically viable. In this regard, this thesis addresses three problems in CF-mMIMO systems: channel estimation, enabling dynamic time division duplexing (DTDD), and synchronization.

In CF-mMIMO systems, a natural UE grouping by the serving base stations (BSs) does not exist, unlike a cellular mMIMO system. Also, in cellular mMIMO, only the serving BS aims to estimate the channel from a given UE, while in a CF-mMIMO system, all the APs in the vicinity of a given UE need to obtain good channel estimates. Therefore, there is a need to revisit the allocation of pilot sequences across UEs to mitigate pilot contamination in CF-mMIMO systems. We address the problem of channel estimation from three different viewpoints: (i) design of quasi-orthogonal pilots, (ii) development of a low complexity algorithm for pilot allocation, and (iii) pilot length minimization while ensuring that physically proximal UEs do not suffer from pilot contamination. We first develop a clustering algorithm for APs and UEs and propose a novel mutually unbiased orthonormal bases (MUOB)-based pilot (quasi-orthogonal) design, where the pilots are orthogonal within a cluster of APs and UEs and minimally correlated across clusters. Theoretically, we show that pilot sets forming MUOB minimize inter- and intra-cluster pilot contamination. The key advantage of MUOB is that, once these AP-UE clusters are formed, the effect of pilot contamination on the channel estimates is allocation-agnostic due to the constant correlation properties of the MUOB pilots. We also develop iterative algorithms for pilot allocation where clustering of APs and UEs is not required. Now, the preceding two schemes are for a predetermined length of pilot sequences. Hence, we next formulate a pilot length minimization problem and propose a novel pilot design and allocation algorithm that ensures no pilot contamination among any pair of UEs that are proximal to a common AP, and this is guaranteed at all APs. Further, our algorithm procures the pilot allocation with a minimum number of orthogonal pilots being reused across the UEs. We numerically validate the superiority of the proposed algorithms over several existing schemes in the literature and also provide a comparative study of our proposed algorithms.

We next analyze the performance of DTDD-enabled CF-mMIMO systems, where the uplink (UL) reception and downlink (DL) transmission modes of the half-duplex (HD) APs can be scheduled based on the local UL/DL traffic load. Thus, a DTDD-enabled CF system operates like a virtual full-duplex (FD) system that can concurrently serve UL and DL UEs; however, with HD hardware. However, the sum UL-DL SE is limited by inter-AP interference (InAI) and inter-UE interference~(InUI), commonly referred to as cross-link interferences (CLIs). We analyze the effects of CLIs on the sum UL-DL SE of DTDD CF systems. We also develop greedy AP scheduling algorithms and UL-DL power allocation strategies to maximize the sum UL-DL SE. Our algorithms come with closed-form update equations and are shown to converge to local optima. Numerical experiments illustrate that sum SE with DTDD can match and even \emph{outperform} an FD CF system and also an FD cellular system with similar antenna density. This is because DTDD can schedule the APs in UL or DL based on the localized traffic load and achieve better array gain for a given antenna density. Further, in DTDD, CF has better InAI suppression capability as only the subset of APs that are operating in DL interferes with the subset of APs that are operating in UL. In contrast, all the APs contribute to InAI in an FD CF system. Hence, although DTDD and FD enable the CF system to concurrently serve UL and DL UEs, DTDD is preferable because it can meet and even outperform FD without requiring IrAI cancellation hardware.

We next address the synchronization issues in a UL CF-mMIMO system using orthogonal frequency division multiplexing (OFDM). The distributed nature of the CF system results in different propagation delays in the signals received at the APs. This delay in receiving signals from different UEs can exceed the cyclic prefix duration, leading to interference from adjacent subcarriers and consecutive OFDM symbols. We develop a mathematical framework to analyze the impact of inter-carrier and inter-symbol interference (ICI and ISI) in the UL SE of the CF-mMIMO OFDM system. Our analysis shows that ignoring this crucial aspect leads to a gross overestimation of the achievable UL SE. We also develop an interference-aware combining scheme to alleviate ISI and ICI in addition to multi-UE interference. We then account for the scenario in which each UE performs a timing-advance with respect to its nearest AP. Numerically, we illustrate that ICI and ISI can significantly limit the achievable SE, but their impact can be significantly mitigated by employing the nearest AP-based timing advance and interference-aware combining. In fact, in many scenarios, the performance is close to that of a time-aligned CF-mMIMO system.

In summary, in this thesis, we address three aspects of CF-mMIMO systems: channel estimation, DTDD, and UL synchronization. Overall, the key takeaways are as follows:

1. We develop novel pilot design and allocation algorithms for CF-mMIMO systems. In particular, our algorithm based on vertex-coloring ensures no contamination among the UEs that are being served by one or more common AP(s) and, at the same time, procures an optimal allocation with the least number of orthogonal pilots. 2. We analyze the sum UL-DL SE of DTDD-enabled CF systems and develop algorithms for APs' UL/DL mode scheduling and UL-DL power allocation. Our \emph{major} finding is that DTDD-enabled CF is more resilient to CLIs and can even outperform FD cellular as well as FD CF systems with similar antenna densities. 3. Finally, we develop a theoretical framework to analyze the effects of asynchronous reception on the UL SE of the CF-mMIMO systems. Our analysis and experiments underscore the importance of the proposed interference-aware combining scheme that is able to mitigate the resulting ICI and ISI considerably, obtaining a near synchronous/ideal performance.

For all the above cases, we benchmark the performances of our proposed schemes with several existing comparable methods and validate the superiority of the developed algorithms in terms of achievable SE, complexity, and convergence.