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Standard cell-free (CF) massive 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. [ABSTRACT FROM AUTHOR]

In Massive MIMO base stations (BSs), the hardware design needs to balance high spectral efficiency (SE) with low complexity. The level of hardware impairments (HWIs) indicates how strong the signal distortion introduced by hardware imperfections is. In particular, the analog-to-digital converters (ADCs) have an important impact on signal distortion and power consumption. This article addresses the fundamental problem of selecting the optimal hardware quality in the Massive MIMO space. In particular, we examine the optimal HWI and ADC bit allocation per BS antenna to maximize the SE. The results show that in co-located arrays with low channel gain variations across antennas, equal ADC bit allocation is optimal. In contrast, cell-free Massive MIMO systems benefit the most from optimizing the ADC bit allocation achieving improvements in the order of 2 [bit-per-channel-use] per user equipment when using regularized zero-forcing (RZF). In addition, when including the impact of power consumption in cell-free Massive MIMO with RZF, allocating low values of mixed ADC bit resolutions across the BS antennas can increase the energy efficiency up to 30% compared to equal ADC bit allocation. [ABSTRACT FROM AUTHOR]

Many of the systems in various signal processing applications are nonlinear due to, for example, hardware impairments, such as nonlinear amplifiers and finite-resolution quantization. The Bussgang decomposition is a popular tool used when analyzing the performance of systems that involve such nonlinear components. In a nutshell, the decomposition provides an exact probabilistic relationship between the output and the input of a nonlinearity: the output is equal to a scaled version of the input plus uncorrelated distortion. The decomposition can be used to compute either exact performance results or lower bounds, where the uncorrelated distortion is treated as independent noise. This lecture note explains the basic theory, provides key examples, extends the theory to complex-valued vector signals, and clarifies some potential misconceptions. [ABSTRACT FROM AUTHOR]

We consider backward crosstalk in $2\times 2$ transmitters, which is caused by crosstalk from the outputs of the transmitter to the inputs or by the combination of output crosstalk and impedance mismatch. We analyze its impact via feedback networks together with third-order power amplifier non-linearities. We utilize the Bussgang decomposition to express the distorted output signals of the transmitter as a linear transformation of the input plus uncorrelated distortion. The normalized mean-square errors (NMSEs) between the distorted and desired amplified signals are expressed analytically and the optimal closed-form power back-off that minimizes the worst NMSE of the two branches is derived. In the second part of the paper, an achievable spectral efficiency (SE) is presented for the communication from this “dirty” transmitter to another single-antenna receiver. The SE-maximizing precoder is optimally found by exploiting the hardware characteristics. Furthermore, the optimal power back-off is analyzed for two sub-optimal precoders, which either do not exploit any hardware knowledge or only partial knowledge. The simulation results show that the performance of these sub-optimal precoders is close-to-optimal. We also discuss how the analysis in this paper can be extended to transmitters with an arbitrary number of antenna branches. [ABSTRACT FROM AUTHOR]

In this paper, we consider how the uplink transmission of a spatially correlated massive multiple-input multiple-output (MIMO) system can be protected from a jamming attack. To suppress the jamming, we propose a novel framework including a new optimal linear estimator in the training phase and a bilinear equalizer in the data phase. The proposed estimator is optimal in the sense of maximizing the spectral efficiency of the legitimate system attacked by a jammer, and its implementation needs the statistical knowledge about the jammer’s channel. We derive an efficient algorithm to estimate the jamming information needed for implementation of the proposed framework. Furthermore, we demonstrate that optimized power allocation at the legitimate users can improve the performance of the proposed framework regardless of the jamming power optimization. Our proposed framework can be exploited to combat jamming in scenarios with either ideal or non-ideal hardware at the legitimate users and the jammer. Numerical results reveal that using the proposed framework, the jammer cannot dramatically affect the performance of the legitimate system. [ABSTRACT FROM AUTHOR]

The use of base stations (BSs) and access points (APs) with a large number of antennas, called Massive MIMO (multiple-input multiple-output), is a key technology for increasing the capacity of 5G networks and beyond. While originally conceived for conventional sub-6 GHz frequencies, Massive MIMO (mMIMO) is also ideal for frequency bands in the range 30-300 GHz, known as millimeter wave (mmWave). Despite conceptual similarities, the way in which mMIMO can be exploited in these bands is radically different, due to their specific propagation behaviors and hardware characteristics. This article reviews these differences and their implications, while dispelling common misunderstandings. Building on this foundation, we suggest appropriate signal processing schemes and use cases to efficiently exploit mMIMO in both frequency bands. [ABSTRACT FROM AUTHOR]

This paper analyzes how the distortion created by hardware impairments in a multiple-antenna base station affects the uplink spectral efficiency (SE), with a focus on massive multiple input multiple output (MIMO). This distortion is correlated across the antennas but has been often approximated as uncorrelated to facilitate (tractable) SE analysis. To determine when this approximation is accurate, basic properties of distortion correlation are first uncovered. Then, we separately analyze the distortion correlation caused by third-order non-linearities and by quantization. Finally, we study the SE numerically and show that the distortion correlation can be safely neglected in massive MIMO when there are sufficiently many users. Under independent identically distributed Rayleigh fading and equal signal-to-noise ratios (SNRs), this occurs for more than five transmitting users. Other channel models and SNR variations have only minor impact on the accuracy. We also demonstrate the importance of taking the distortion characteristics into account in the receive combining. [ABSTRACT FROM AUTHOR]

Transceiver hardware impairments (e.g., phase noise, in-phase/quadrature-phase imbalance, amplifier nonlinearities, and quantization errors) have obvious degradation effects on the performance of wireless communications. While prior works have improved our knowledge of the influence of hardware impairments of single-user multiple-input multiple-output (MIMO) systems over Rayleigh fading channels, an analysis encompassing the Rician fading channel is not yet available. In this paper, we pursue a detailed analysis of regular and large-scale (LS) MIMO systems over Rician fading channels by deriving new closed-form expressions for the achievable rate to provide several important insights for practical system design. More specifically, for regular MIMO systems with hardware impairments, there is always a finite achievable rate ceiling, which is irrespective of the transmit power and fading conditions. For LS-MIMO systems, it is interesting to find that the achievable rate loss depends on the Rician $K$- factor, which reveals that the favorable propagation in LS-MIMO systems can remove the influence of hardware impairments. However, we show that the nonideal LS-MIMO system can still achieve high spectral efficiency due to its huge degrees of freedom. [ABSTRACT FROM PUBLISHER]

What 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 closed-form 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. [ABSTRACT FROM PUBLISHER]

Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas, deployed on co-located or distributed arrays. Huge spatial degrees-of-freedom are achieved by coherent processing over these massive arrays, which provide strong signal gains, resilience to imperfect channel knowledge, and low interference. This comes at the price of more infrastructure; the hardware cost and circuit power consumption scale linearly/affinely with the number of BS antennas $N$. Hence, the key to cost-efficient deployment of large arrays is low-cost antenna branches with low circuit power, in contrast to today's conventional expensive and power-hungry BS antenna branches. Such low-cost transceivers are prone to hardware imperfections, but it has been conjectured that the huge degrees-of-freedom would bring robustness to such imperfections. We prove this claim for a generalized uplink system with multiplicative phase-drifts, additive distortion noise, and noise amplification. Specifically, we derive closed-form expressions for the user rates and a scaling law that shows how fast the hardware imperfections can increase with N$ while maintaining high rates. The connection between this scaling law and the power consumption of different transceiver circuits is rigorously exemplified. This reveals that one can make the circuit power increase as \sqrt{N} , instead of linearly, by careful circuit-aware system design. [ABSTRACT FROM PUBLISHER]

The use of large-scale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain. Recent works in the field of massive multiple-input multiple-output (MIMO) show that the user channels decorrelate when the number of antennas at the base stations (BSs) increases, thus strong signal gains are achievable with little interuser interference. Since these results rely on asymptotics, it is important to investigate whether the conventional system models are reasonable in this asymptotic regime. This paper considers a new system model that incorporates general transceiver hardware impairments at both the BSs (equipped with large antenna arrays) and the single-antenna user equipments (UEs). As opposed to the conventional case of ideal hardware, we show that hardware impairments create finite ceilings on the channel estimation accuracy and on the downlink/uplink capacity of each UE. Surprisingly, the capacity is mainly limited by the hardware at the UE, while the impact of impairments in the large-scale arrays vanishes asymptotically and interuser interference (in particular, pilot contamination) becomes negligible. Furthermore, we prove that the huge degrees of freedom offered by massive MIMO can be used to reduce the transmit power and/or to tolerate larger hardware impairments, which allows for the use of inexpensive and energy-efficient antenna elements. [ABSTRACT FROM PUBLISHER]

Physical transceivers have hardware impairments that create distortions which degrade the performance of communication systems. The vast majority of technical contributions in the area of relaying neglect hardware impairments and, thus, assume ideal hardware. Such approximations make sense in low-rate systems, but can lead to very misleading results when analyzing future high-rate systems. This paper quantifies the impact of hardware impairments on dual-hop relaying, for both amplify-and-forward and decode-and-forward protocols. The outage probability (OP) in these practical scenarios is a function of the effective end-to-end signal-to-noise-and-distortion ratio (SNDR). This paper derives new closed-form expressions for the exact and asymptotic OPs, accounting for hardware impairments at the source, relay, and destination. A similar analysis for the ergodic capacity is also pursued, resulting in new upper bounds. We assume that both hops are subject to independent but non-identically distributed Nakagami-m fading. This paper validates that the performance loss is small at low rates, but otherwise can be very substantial. In particular, it is proved that for high signal-to-noise ratio (SNR), the end-to-end SNDR converges to a deterministic constant, coined the SNDR ceiling, which is inversely proportional to the level of impairments. This stands in contrast to the ideal hardware case in which the end-to-end SNDR grows without bound in the high-SNR regime. Finally, we provide fundamental design guidelines for selecting hardware that satisfies the requirements of a practical relaying system. [ABSTRACT FROM AUTHOR]