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In this paper, we focus on the coverage probability of a double-intelligent reflecting surface (IRS) assisted wireless network and study the impact of multiplicative beamforming gain and correlated Rayleigh fading. In particular, we obtain a novel closed-form expression of the coverage probability of a single-input single-output (SISO) system assisted by two large IRSs while being dependent on the corresponding arbitrary reflecting beamforming matrices (RBMs) and large-scale statistics in terms of correlation matrices. Taking advantage of the large-scale statistics, i.e., statistical channel state information (CSI), we perform optimization of the RBMs of both IRSs once per several coherence intervals rather than at each interval. Hence, we achieve a reduction of the computational complexity, otherwise increased in multi-IRS-assisted networks during their RBM optimization. Numerical results validate the analytical expressions even for small IRSs, confirm enhanced performance over the conventional single-IRS counterpart, and reveal insightful properties., Comment: accepted in IEEE Wireless Communications Letters

Standard cell-free (CF) multiple-input-multiple-output (mMIMO) systems is a promising technology to cover the demands for higher data rates in fifth-generation (5G) networks and beyond. These systems assume a large number of distributed access points (APs) using joint coherent transmission to communicate with the users. However, CF mMIMO systems present an increasing computational complexity as the number of users increases. Scalable cell-free CF (SCF) systems have been proposed to face this challenge. Given that the cost-efficient deployment of such large networks requires low-cost transceivers, which are prone to unavoidable hardware imperfections, realistic evaluations of SCF mMIMO systems should take them into account before implementation. Hence, in this work, we focus on the impact of hardware impairments (HWIs) on the SCF mMIMO systems through a general model accounting for both additive and multiplicative impairments. Notably, there is no other work in the literature studying the impact of phase noise (PN) in the local oscillators (LOs) of CF mMIMO systems or in general the impact of any HWIs in SCF mMIMO systems. In particular, we derive upper and lower bounds on the uplink capacity accounting for HWIs. Moreover, we obtain the optimal hardware-aware (HA) partial minimum mean-squared error (PMMSE) combiner. Especially, the lower bound is derived in closed-form using the theory of deterministic equivalents (DEs). Among the interesting findings, we observe that separate LOs (SLOs) outperform a common LO (CLO), and the additive transmit distortion degrades more the performance than the additive receive distortion., Comment: Accepted in IEEE TVT, 15 pages, 5 figures

This paper suggests the use of multiple distributed intelligent reflecting surfaces (IRSs) towards a smarter control of the propagation environment. Notably, we also take into account the inevitable correlated Rayleigh fading in IRS-assisted systems. In particular, in a single-input and single-output (SISO) system, we consider and compare two insightful scenarios, namely, a finite number of large IRSs and a large number of finite size IRSs to show which implementation method is more advantageous. In this direction, we derive the coverage probability in closed-form for both cases contingent on statistical channel state information (CSI) by using the deterministic equivalent (DE) analysis. Next, we obtain the optimal coverage probability. Among others, numerical results reveal that the addition of more surfaces outperforms the design scheme of adding more elements per surface. Moreover, in the case of uncorrelated Rayleigh fading, statistical CSI-based IRS systems do not allow the optimization of the coverage probability., Comment: 6 pages, 2 figures. This work is submitted to the IEEE for possible publication

We consider a two-way half-duplex decode-and-forward (DF) relaying system with multiple pairs of single-antenna users assisted by a cell-free (CF) massive multiple-input multiple-output (mMIMO) architecture with multiple-antenna access points (APs). Under the practical constraint of imperfect channel state information (CSI), we derive the achievable sum spectral efficiency (SE) for a finite number of APs with maximum ratio (MR) linear processing for both reception and transmission in closed-form. Notably, the proposed CF mMIMO relaying architecture, exploiting the spatial diversity, and providing better coverage, outperforms the conventional collocated mMIMO deployment. Moreover, we shed light on the power-scaling laws maintaining a specific SE as the number of APs grows. A thorough examination of the interplay between the transmit powers per pilot symbol and user/APs takes place, and useful conclusions are extracted. Finally, differently to the common approach for power control in CF mMIMO systems, we design a power allocation scheme maximizing the sum SE., Comment: 15 pages, 8 figures, This work was accepted in IEEE Trans. Green Commun. Net

Most works in IRS-assisted systems have ignored the impact of the inevitable residual hardware impairments (HWIs) at both the transceiver hardware and the IRS while any relevant works have addressed only simple scenarios, e.g., with single-antenna network nodes and/or without taking the randomness of phase noise at the IRS into account. In this work, we aim at filling up this gap by considering a general IRS-assisted multi-user (MU) multiple-input single-output (MISO) system with imperfect CSI and correlated Rayleigh fading. In parallel, we present a general computationally efficient methodology for IRS reflect beamforming (RB) optimization. Specifically, we introduce an advantageous channel estimation (CE) method for such systems accounting for the HWIs. Moreover, we derive the uplink achievable spectral efficiency (SE) with maximal-ratio combining (MRC) receiver, displaying three significant advantages being: 1) its closed-form expression, 2) its dependence only on large-scale statistics, and 3) its low training overhead. Notably, by exploiting the first two benefits, we achieve to perform optimization with respect to the reflect beamforming matrix (RBM) that can take place only at every several coherence intervals, and thus, reduces significantly the computational cost compared to other methods which require frequent phase optimization. Among the insightful observations, we highlight that uncorrelated Rayleigh fading does not allow optimization of the SE, which makes the application of an IRS ineffective. Also, in the case that the phase drifts, describing the distortion of the phases in the RBM, are uniformly distributed, the presence of an IRS provides no advantage. The analytical results outperform previous works and are verified by Monte-Carlo (MC) simulations., Comment: 30 pages, 5 figures, accepted in IEEE TWC

Cell-free (CF) massive multiple-input-multiple-output (MIMO) has emerged as an alternative deployment for conventional cellular massive MIMO networks. Prior works relied on the strong assumption (quite idealized) that the APs are uniformly distributed, and actually, this randomness was considered during the simulation and not in the analysis. However, in practice, ongoing and future networks become denser and increasingly irregular. Having this in mind, we consider that the AP locations are modeled by means of a Poisson point process (PPP) which is a more realistic model for the spatial randomness than a grid or uniform deployment. In particular, by virtue of stochastic geometry tools, we derive both the downlink coverage probability and achievable rate. Notably, this is the only work providing the coverage probability and shedding light on this aspect of CF massive MIMO systems. Focusing on the extraction of interesting insights, we consider small-cells (SCs) as a benchmark for comparison. Among the findings, CF massive MIMO systems achieve both higher coverage and rate with comparison to SCs due to the properties of favorable propagation, channel hardening, and interference suppression. Especially, we showed for both architectures that increasing the AP density results in a higher coverage which saturates after a certain value and increasing the number of users decreases the achievable rate but CF massive MIMO systems take advantage of the aforementioned properties, and thus, outperform SCs. In general, the performance gap between CF massive MIMO systems and SCs is enhanced by increasing the AP density. Another interesting observation concerns that a higher path-loss exponent decreases the rate while the users closer to the APs affect more the performance in terms of the rate., Comment: 14 pages, accepted in IEEE TVT

Motivated by the ever-growing demand for \emph{green} wireless communications and the advantages of \emph{cell-free} (CF) massive multiple-input multiple-output (MIMO) systems, we focus on the design of their downlink for optimal \emph{energy efficiency} (EE). To address this fundamental topic, we assume that each access point (AP) is deployed with multiple antennas and serves multiple users on the same time-frequency resource while the APs are Poisson point process (PPP) distributed, which approaches realistically their opportunistic spatial randomness. Relied on tools from stochastic geometry, we derive a lower bound on the downlink average achievable spectral efficiency (SE). Next, we consider a realistic power consumption model for CF massive MIMO systems. These steps enable the formulation of a tractable optimization problem concerning the downlink EE per unit area, which results in the analytical determination of the optimal pilot reuse factor, the AP density, and the number of AP antennas and users that maximize the EE. Notably, the EE per unit area and not just the EE is the necessary metric to describe CF systems, where we meet multi-point transmission. Hence, we provide useful design guidelines for CF massive MIMO systems relating to fundamental system variables towards optimal EE. Among the results, we observe that a lower pilot reuse factor enables a decrease of the interference, and subsequently, higher EE up to a specific value. Overall, it is shown that the CF massive MIMO technology is a promising candidate for next-generation networks achieving simultaneously high SE and EE per unit area., Comment: 15 pages, 7 figures, accepted in IEEE TGCN

Small-cell densification is a strategy enabling the offloading of users from macro base stations (MBSs), in order to alleviate their load and increase the coverage, especially, for cell-edge users. In parallel, as the network increases in density, the BS cooperation emerges as an efficient design method towards the demands for drastic improvement of the system performance against the detrimental overall interference. In addition, the tiers are enhanced with cell association policies by introducing the concept of the association probability. Above this and motivated by the advantages of cooperation among BSs, the small base stations (SBSs) are enriched with this property in their design. SBS cooperation allows shedding light into its impact on the cell selection rules in multi-antenna HetNets. Under these settings, software-defined networking (SDN) is introduced smoothly to play the leading role in the orchestration of the network. {In particular, heavy operations such as the coordination and the cell association are undertaken by virtue of an SDN controller performing and managing efficiently the corresponding computations due to its centralized adaptability and dynamicity towards the enhancement and potential scalability of the network}. In this context, we derive the coverage probability and the mean achievable rate. Not only we show the outperformance of BS cooperation over uncoordinated BSs, but we also demonstrate that the SBS cooperation enables the admittance of more users from the macro-cell BSs (MBSs). Moreover, we investigate the performance of different transmission techniques, and we identify the optimal bias in each case when SBSs cooperate. Finally, we depict that the SBS densification is beneficial until a specific density value since a further increase does not increase the coverage probability., Comment: Accepted in IEEE TWC