Average cell density (D) Spectral ef f iciency (SE) Volume = Area throughput Definition (Area throughput) The area throughput of a cellular network is measured in bit/s/km 2. Area throughput = B [Hz] • D [cells/km 2 ] • SE [bit/s/Hz/cell]

Abstract-Assume that a multi-user multiple-input multipleoutput (MIMO) system is designed from scratch to uniformly cover a given area with maximal energy efficiency (EE). What are the optimal number of antennas, active users, and transmit power? The aim of this paper is to answer this fundamental question. We consider jointly the uplink and downlink with different processing schemes at the base station and propose a new realistic power consumption model that reveals how the above parameters affect the EE. Closed-form expressions for the EE-optimal value of each parameter, when the other two are fixed, are provided for zero-forcing (ZF) processing in single-cell scenarios. These expressions prove how the parameters interact. For example, in sharp contrast to common belief, the transmit power is found to increase (not to decrease) with the number of antennas. This implies that energy-efficient systems can operate in high signalto-noise ratio regimes in which interference-suppressing signal processing is mandatory. Numerical and analytical results show that the maximal EE is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve a relatively large number of users using ZF processing. The numerical results show the same behavior under imperfect channel state information and in symmetric multi-cell scenarios.

Cell-free Massive MIMO is considered as a promising technology for satisfying the increasing number of users and high rate expectations in beyond-5G networks. The key idea is to let many distributed access points (APs) communicate with all users in the network, possibly by using joint coherent signal processing. The aim of this paper is to provide the first comprehensive analysis of this technology under different degrees of cooperation among the APs. Particularly, the uplink spectral efficiencies of four different cell-free implementations are analyzed, with spatially correlated fading and arbitrary linear processing. It turns out that it is possible to outperform conventional Cellular Massive MIMO and small cell networks by a wide margin, but only using global or local minimum mean-square error (MMSE) combining. This is in sharp contrast to the existing literature, which advocates for maximum-ratio combining. Also, we show that a centralized implementation with optimal MMSE processing not only maximizes the SE but largely reduces the fronthaul signaling compared to the standard distributed approach. This makes it the preferred way to operate Cell-free Massive MIMO networks. Non-linear decoding is also investigated and shown to bring negligible improvements. ). same time-frequency resource [8]. The characteristic feature of mMIMO, compared to traditional multi-user MIMO, is that each BS has many more antennas than UEs in the cell. Signal processing methods, such as minimum mean-squared error (MMSE) combining in the uplink, can be used individually at each BS to suppress interference from both the same and other cells [3], [9], [10], without the need for any BS cooperation. The mMIMO theory also supports deployments with spatially distributed arrays in each cell [11], [12], as also illustrated in Fig. 1(a). This setup is essentially the same as the Distributed Antenna System (DAS) setup in [13] and Coordinated Multi-Point (CoMP) with static, disjoint cooperation clusters [14], [15]. These are all different embodiments of cellular networks.An alternative network infrastructure was considered in [16], [17] under the name of Cell-free mMIMO. The idea is to deploy a large number of distributed single-antenna access points (APs), which are connected to a central processing unit (CPU), also known as an edge-cloud processor [18] or C-RAN (cloud radio access network) data center [19]. The CPU operates the system in a Network MIMO fashion, with no cell boundaries, to jointly serve the UEs by coherent joint transmission and reception [15], [20]-[23]. Compared to traditional Network MIMO, the outstanding aspect of Cellfree mMIMO is the operating regime with many more APs than UEs [16]. From an analytical perspective, an important novelty was that imperfect channel state information (CSI) was considered in the performance analysis, while perfect CSI was often assumed in the past [15]. The paper [16] advocated the use of maximum ratio (MR) processing (a.k.a. matched filtering or conjugate beamforming) locally at each AP, whil...

The capacity of cellular networks can be improved by the unprecedented array gain and spatial multiplexing offered by Massive MIMO. Since its inception, the coherent interference caused by pilot contamination has been believed to create a finite capacity limit, as the number of antennas goes to infinity. In this paper, we prove that this is incorrect and an artifact from using simplistic channel models and suboptimal precoding/combining schemes. We show that with multicell MMSE precoding/combining and a tiny amount of spatial channel correlation or large-scale fading variations over the array, the capacity increases without bound as the number of antennas increases, even under pilot contamination. More precisely, the result holds when the channel covariance matrices of the contaminating users are asymptotically linearly independent, which is generally the case. If also the diagonals of the covariance matrices are linearly independent, it is sufficient to know these diagonals (and not the full covariance matrices) to achieve an unlimited asymptotic capacity.

Imagine a coverage area with many wireless access points that cooperate to jointly serve the users, instead of creating autonomous cells. Such a cell-free network operation can potentially resolve many of the interference issues that appear in current cellular networks. This ambition was previously called Network MIMO (multiple-input multiple-output) and has recently reappeared under the name Cell-Free Massive MIMO. The main challenge is to achieve the benefits of cell-free operation in a practically feasible way, with computational complexity and fronthaul requirements that are scalable to large networks with many users. We propose a new framework for scalable Cell-Free Massive MIMO systems by exploiting the dynamic cooperation cluster concept from the Network MIMO literature. We provide algorithms for initial access, pilot assignment, cluster formation, precoding, and combining that are proved to be scalable. Interestingly, the proposed scalable precoding and combining outperform conventional maximum ratio processing and also performs closely to the best unscalable alternatives. Index TermsCell-Free Massive MIMO, scalable implementation, centralized and distributed algorithms, dynamic cooperation clustering, user-centric networking. 2 impractical, assumptions that lead to immense fronthaul signaling for CSI and data sharing, respectively, as well as huge computational complexity. Fortunately, [9] proved that Network MIMO can operate without CSI sharing, by sacrificing the ability for the APs to jointly cancel interference. Moreover, to limit data sharing and computational complexity, each UE can be served only by an AP subset [10]. Initially, a network-centric approach was taken by dividing the APs into non-overlapping (disjoint) cooperation clusters in which the APs are sharing data (and potentially CSI) to serve only the UEs residing in the joint coverage area [11]-[13]. This approach was considered in 4G but provides small practical gains [14]. One key reason is that many UEs will be located at the edges of the clusters and, thus, will observe substantial intercluster interference from the neighboring clusters [15].The alternative is to take a user-centric approach where each UE is served by the AP subset providing the best channel conditions. Since these subsets are generally different for every UE, it is not possible to divide the network into non-overlapping cooperation clusters. Instead, each AP needs to cooperate with different APs when serving different UEs, over the same time and frequency resource [16]-[18]. 1 A general user-centric cooperation framework was proposed in [17] under the name dynamic cooperation clustering (DCC) and was further described and analyzed in the textbook [10]. The word dynamic refers to the adaptation to time-variant characteristics such as channel properties and UE locations (to name a few). The practical feasibility of DCCs was experimentally verified by the pCell technology [21], but the combination of Network MIMO and DCC didn't gain much interest at the time it was prop...

Abstract-How would a cellular network designed for maximal energy efficiency look like? To answer this fundamental question, tools from stochastic geometry are used in this paper to model future cellular networks and obtain a new lower bound on the average uplink spectral efficiency. This enables us to formulate a tractable uplink energy efficiency (EE) maximization problem and solve it analytically with respect to the density of base stations (BSs), the transmit power levels, the number of BS antennas and users per cell, and the pilot reuse factor. The closedform expressions obtained from this general EE maximization framework provide valuable insights on the interplay between the optimization variables, hardware characteristics, and propagation environment. Small cells are proved to give high EE, but the EE improvement saturates quickly with the BS density. Interestingly, the maximal EE is achieved by also equipping the BSs with multiple antennas and operate in a "massive MIMO" fashion, where the array gain from coherent detection mitigates interference and the multiplexing of many users reduces the energy cost per user.

A realistic performance assessment of any wireless technology requires the use of a channel model that reflects its main characteristics. The independent and identically distributed Rayleigh fading channel model has been (and still is) the basis of most theoretical research on multiple antenna technologies in scattering environments. This letter shows that such a model is not physically appearing when using a reconfigurable intelligent surface (RIS) with rectangular geometry and provides an alternative physically feasible Rayleigh fading model that can be used as a baseline when evaluating RIS-aided communications. The model is used to revisit the basic RIS properties, e.g., the rank of spatial correlation matrices and channel hardening.

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