Since the introduction of fifth-generation new radio (5G-NR) in Third Generation Partnership Project (3GPP) Release 15, swift progress has been made to evolve 5G with 3GPP Release 18 emerging. A critical aspect is the design of massive multiple-input multiple-output (MIMO) technology. In this line, this paper makes several important contributions: We provide a comprehensive overview of the evolution of standardized massive MIMO features from 3GPP Release 15 to 17 for both time/frequency-division duplex operation across frequency range in (FR)-1 and FR 2-1. We analyze the progress on channel state information (CSI) frameworks, beam management frameworks and present enhancements for uplink CSI. We shed light on emerging 3GPP Release 18 problems requiring imminent attention. These include advanced codebook design and sounding reference signal design for coherent joint transmission (CJT) with multiple transmission/reception points (multi TRPs). We discuss advancements in uplink demodulation reference signal design, enhancements for mobility to provide accurate CSI estimates, and unified transmission configuration indicator framework tailored for FR 2–1 bands. For each concept, we provide system level simulation results to highlight their performance benefits. Via field trials in an outdoor environment at Shanghai Jiaotong University, we demonstrate the gains of multi-TRP CJT relative to single TRP at 3.7 GHz.

We provide a simple, yet general and accurate framework for analyzing zero-forcing (ZF) precoding performance for a full-dimensional massive multiple-input multiple-output system. Exploiting an order two Neumann series, our framework approximates the expected (average) ZF signal-to-noise ratio and ergodic sum spectral efficiency, while catering for a finite multipath propagation model, as well as correlated and uncorrelated user equipment (UE) positions in both azimuth and elevation domains. The analysis provides clear insights on the influence of propagation and system parameters on ZF performance. We identify how far UEs must lie in azimuth and elevation for the ZF precoder to approach uncorrelated channels. Our framework is useful for predicting the ZF performance degradation arising from channel correlation. For optimal performance, UEs could be separated by around 30° in azimuth and 15° in elevation - conditions which are difficult to meet in reality.

Mobile communications have been undergoing a generational change every ten years or so. However, the time difference between the so-called “G's” is also decreasing. While fifth-generation (5G) systems are becoming a commercial reality, there is already significant interest in systems beyond 5G, which we refer to as the sixth generation (6G) of wireless systems. In contrast to the already published papers on the topic, we take a top-down approach to 6G. More precisely, we present a holistic discussion of 6G systems beginning with lifestyle and societal changes driving the need for next-generation networks. This is followed by a discussion into the technical requirements needed to enable 6G applications, based on which we dissect key challenges and possibilities for practically realizable system solutions across all layers of the Open Systems Interconnection stack (i.e., from applications to the physical layer). Since many of the 6G applications will need access to an order-of-magnitude more spectrum, utilization of frequencies between 100 GHz and 1 THz becomes of paramount importance. As such, the 6G ecosystem will feature a diverse range of frequency bands, ranging from below 6 GHz up to 1 THz. We comprehensively characterize the limitations that must be overcome to realize working systems in these bands and provide a unique perspective on the physical and higher layer challenges relating to the design of next-generation core networks, new modulation and coding methods, novel multiple-access techniques, antenna arrays, wave propagation, radio frequency transceiver design, and real-time signal processing. We rigorously discuss the fundamental changes required in the core networks of the future, such as the redesign or significant reduction of the transport architecture that serves as a major source of latency for time-sensitive applications. This is in sharp contrast to the present hierarchical network architectures that are not suitable to realize many of the anticipated 6G services. While evaluating the strengths and weaknesses of key candidate 6G technologies, we differentiate what may be practically achievable over the next decade, relative to what is possible in theory. Keeping this in mind, we present concrete research challenges for each of the discussed system aspects, providing inspiration for what follows.

With the potential to provide a clean break from massive multiple-input multiple-output, large intelligent surfaces (LISs) have recently received a thrust of research interest. Various proposals have been made in the literature to define the exact functionality of LISs, ranging from fully active to largely passive solutions. Nevertheless, almost all studies in the literature investigate the fundamental spectral efficiency performance of these architectures. In stark contrast, this paper investigates the implementation aspects of LISs. Using the fully active LIS as the basis of our exposition, we first present a rigorous discussion on the relative merits and disadvantages of possible implementation architectures from a radio-frequency circuits and real-time processing viewpoints. We then show that a distributed architecture based on a common module interfacing a smaller number of antennas can be scalable. To avoid severe losses with analog signal distribution, multiple common modules can be interconnected via a digital nearest-neighbor network. Furthermore, we show that with such a design, the maximum backplane throughput scales with the number of served user terminals, instead of the number of antennas across the surface. The discussions in the paper can serve as a guideline toward the real-time design and development of LISs.

Massive multiple-input multiple-output (MIMO) has gained a tremendous amount of attention as a key enabler of fifth-generation cellular systems. The majority of the vast literature on massive MIMO is based on fully digital processing, where each antenna element in the massive array is equipped with an up/down-conversion chain. Unlike previous works, we present a suite of greedy algorithms using pure analog processing which approach the performance of uplink digital zero-forcing (ZF) combining. Based on successive nulling and amplification processing (SNAP), the proposed techniques are evaluated in a multi-user context over a range of heterogeneous channel models. Rigorous comparisons are then made to other benchmark analog techniques, digital ZF and an upper bound on analog processing. The most promising approach is shown to have very low-complexity and robustness against a variety of channel conditions, while providing useful performance gains.

Fifth-generation (5G) new radio (NR) deployments are being rolled out in both the C-band (3.3 - 5.0 GHz) and millimeter-wave (mmWave) band (24.5 - 29.5 GHz). For outdoor scenarios, the C-band is expected to provide wide area coverage and throughput uniformity, whereas the mmWave band is expected to provide ultra-high throughput to dedicated areas within the C-band coverage. Due to the differences in the frequency bands, both systems are expected to be designed with different transmit and receive parameters, naturally resulting in performance variations proportional to the chosen parameters. Unlike many previous works, this paper presents measurement evaluations in central Auckland, New Zealand, from a pre-commercial deployment of a single-user, single-cell 5G-NR system operating in both bands. The net throughput, coverage reliability, and channel rank are analyzed across the two bands with baseband and analog beamforming. Our results show that the C-band coverage is considerably better than mmWave, with a consistently higher channel rank. Furthermore, the spatial stationarity region (SSR) for the azimuth angles-of-departure (AODs) is characterized, and a model derived from the measured beam identities is presented. The SSR of azimuth AODs is seen to closely follow a gamma distribution.

Massive multiple-input multiple-output (MIMO) promises significantly higher performance relative to conventional multiuser systems. However, the promised gains of massive MIMO systems rely heavily on the accuracy of the absolute frontend calibration, as well as quality of channel estimates at the base station (BS). In this paper, we analyze user equipment-aided calibration mechanism to estimate the amplitude scaling and phase drift at each radio-frequency chain connected to the BS array. Assuming a uniform linear array at the BS and Ricean fading, we obtain the estimation parameters with moment-based (amplitude, phase) and maximum-likelihood (phase-only) estimation techniques. In stark contrast to previous works, we mathematically articulate the equivalence of the two approaches for phase estimation. Furthermore, we rigorously derive a Cramér-Rao lower bound to characterize the accuracy of the two estimators. Via numerical simulations, we evaluate the estimator performance with varying dominant line-of-sight powers, dominant angles-of-arrival, and signal-to-noise ratios.

We examine the favorable propagation (FP) behavior of a massive multi-user multiple-input-multiple-output (MU-MIMO) system equipped with a uniform linear array (ULA), horizontal uniform rectangular array (HURA) or uniform circular array (UCA) using a ray-based channel model with user cluster sharing. We demonstrate FP for these systems and provide analytical expressions for the mean-squared distance (MSD) of the FP metric from its large-system limit for each of the aforementioned topologies. We use these results to examine the detrimental effects of user cluster sharing on FP behavior, and demonstrate the superior performance of the ULA as compared to the UCA and the HURA with equal inter-element spacing. Although cluster sharing has a negative impact on FP for finite arrays, we additionally examine the asymptotic rate of convergence to FP as a function of array size and show that this rate is unchanged with or without user cluster sharing.

Favorable propagation (FP) and channel hardening (CH) are desired properties in massive multiple-input multiple-output (MIMO) systems. To date, these properties have primarily been analyzed for classical statistical channel models, or ray-based models with very specific angular parameters and distributions. This paper presents a thorough mathematical analysis of the asymptotic system behavior for ray-based channels with arbitrary ray distributions, and considers two types of antenna array structures at the cellular base station: a uniform linear array (ULA) and a uniform planar array (UPA). In addition to FP and channel hardening, we analyze the large system potential (LSP) which measures the asymptotic ratio of the expected power in the desired channel to the expected total interference power when both the antenna and user numbers grow. LSP is said to hold when this ratio converges to a positive constant. The results demonstrate that while FP is guaranteed in ray-based channels, CH may or may not occur depending on the nature of the model. Furthermore, we demonstrate that LSP will not normally hold as the expected interference power grows logarithmically for both ULAs and UPAs relative to the power in the desired channel as the system size increases. Nevertheless, we identify some fundamental and attractive properties of massive MIMO in this limiting regime.

Favorable propagation (FP) and channel hardening are desired properties in massive multiple-input and multiple-output (MIMO) systems, where nearly optimal performance is achieved with linear processing techniques, such as maximal-ratio combining. To date, these properties have primarily been analyzed for statistical channel models, or ray-based models with very specific angular parameters and distributions. This paper presents a thorough mathematical analysis of the asymptotic system behavior for ray-based channels with arbitrary ray distributions and a uniform linear array at the base station. In addition to FP and channel hardening, we analyze the large system potential (LSP) which measures the asymptotic signal-to-interference ratio when both the antenna and user numbers grow at an equal rate. The results demonstrate that while FP is guaranteed in ray-based channels, channel hardening may or may not occur depending on the nature of the model. Furthermore, we demonstrate that LSP will not normally hold as the interference power grows logarithmically relative to the signal as the array size increases. Nevertheless, we identify some fundamental and attractive properties of massive MIMO in this limiting regime.

The performance of linear multi-user multiple-input multiple-output (MU-MIMO) systems has been extensively studied for classical statistical channel models. In contrast, there is little analysis for ray-based models, which are physically motivated, feature prominently in standards and have been experimentally validated. Thus, we present a novel analytical framework for zero forcing (ZF) and maximal ratio combining (MRC) applicable to such models. Specifically, using a central result for averaging in the angular domain, we derive accurate expressions for ZF signal-to-noise ratio and MRC signal, interference and noise powers. The remarkably simple expressions offer the following insights into the effects of the propagation environment. While ZF is robust to parameters such as cluster and subray angular spreads, MRC interference is highly sensitive to them. We show that the performance scales linearly with the number of antennas, and that it degrades with narrow angular spreads and as the propagation moves toward the antenna end-fire. Finally, by evaluating the variance of the MRC interference, we observe that an approximation to the MRC SINR widely used for classical statistical models, is inaccurate in ray-based channels.

In multiuser multiple-input multiple-output (MU-MIMO) systems, channel correlation is detrimental to system performance. We demonstrate that widely used, yet overly simplified, correlation models that generate identical correlation profiles for each terminal tend to severely underestimate the system performance. In sharp contrast, more physically motivated models that capture variations in the power angular spectra across multiple terminals, generate diverse correlation patterns. This has a significant impact on the system performance. Assuming correlated Rayleigh fading and downlink zero-forcing precoding, tight closed-form approximations for the average signal- to-noise-ratio, and ergodic sum spectral efficiency are derived. Our expressions provide clear insights into the impact of diverse correlation patterns on the above performance metrics. Unlike previous works, the correlation models are parameterized with measured data from a recent 2.53 GHz urban macrocellular campaign in Cologne, Germany. Overall, results from this paper can be treated as a timely re-calibration of performance expectations from practical MU-MIMO systems.

In this paper, we take a fundamental look at the interference characteristics of a lens-based millimeter-wave (mmWave) multiuser multiple-input multiple-output system (MU-MIMO) system. We consider a hybrid architecture, implemented via a bank of radio-frequency (RF) switches which perform beam selection followed by low-complexity uplink maximum-ratio combining (MRC) at baseband. Considering a Rotman lens antenna array in line- of-sight (LoS) propagation, we derive tight analytical approximations to the average (expected) interference power of an arbitrary terminal, with and without the presence of RF switching. The analytical expressions show that without RF switching, the Rotman lens losses its benefits and collapses to a conventional uniform linear array. Our numerical results demonstrate that the expected interference power to a given terminal decreases significantly with RF switching, due to beam selection separating the uplink direction-of-arrivals (DoAs), in contrast to the case without RF switching, which relaxes the beam selection constraint and thus allows very similar DoAs. Overall, the results in this paper emphasize the necessity of RF switching in order to obtain superior performance with lens arrays, over conventional phased arrays.

We consider a massive multiple-input multiple- output system with minimum-mean-squared-error processing on the uplink. A novel analytical framework is proposed to approximate the instantaneous signal-to-interference-plus-noise- ratio (SINR) of an arbitrary user terminal, as well as, the system sum spectral efficiency. Unlike previous studies, our methodology considers spatially correlated Ricean fading, with unequal Ricean K-factors, spatial correlation matrices and link gains across all terminals. Under this fully heterogeneous setting, we demonstrate that the SINR of a terminal can be tightly approximated by a linear combination of non-central chi-squared random variables, where the scaling depends on the individual link gains, K-factors, and eigenvalues of the terminal specific correlation matrices. Our approximations remain tight across the considered spatial correlation models, K-factor models, average uplink signal-to-noise-ratios and number of receive antennas. Leveraging the general form of the SINR and sum spectral efficiency, an analytical method to approximate their statistical moments is presented utilizing the moment generating function. The generality of the aforementioned analytical results is demonstrated via several special cases of practical relevance.

Spatial correlation across an antenna array is known to be detrimental to the terminal signal-to- interference-plus-noise-ratio (SINR) and system spectral efficiency. For a downlink multiuser multiple-input multiple-output system (MU-MIMO), we show that the widely used, yet overly simplified, correlation models which generate fixed correlation patterns for all terminals tend to underestimate the system performance. This is in contrast to more sophisticated, yet physically motivated, remote scattering models that generate variations in the correlation structure across multiple terminals. The remote scattering models are parameterized with measured data from a recent 2.53 GHz urban macrocellular channel measurement campaign in Cologne, Germany. Assuming spatially correlated Ricean fading, with maximum-ratio transmission precoding, tight closed-form approximations to the expected (average) SINR, and ergodic sum spectral efficiency are derived. The expressions provide clear insights into the impact of variable correlation patterns on the above performance metrics. Our results demonstrate the sensitivity of the MU-MIMO performance to different correlation models, and provide a cautionary tale of its impact.

Multi-cell wireless systems usually encounter both intra-cell and inter-cell interference, which can be mitigated via coordinated multipoint (CoMP) transmission. Previous works on multi-cell analysis in the microwave band generally consider fully digital beamforming, requiring a complete radio-frequency chain behind each antenna. This is practically infeasible for millimeter-wave (mmWave) systems where large amounts of antennas are necessary to provide sufficient gain and to enable transmission/reception of multiple streams to/from a user. This paper provides a general methodology to analytically compute the expected per-cell spectral efficiency of an mmWave multi-cell single-stream system using phase-shifter-based analog beamforming and regularized zero-forcing digital beamforming. Four analog-digital hybrid beamforming techniques for multi-cell multi-stream mmWave communication are proposed, assuming that base stations in different cells can share channel state information to cooperatively transmit signals to their home-cell users. Spectral efficiency of the proposed hybrid beamforming approaches is investigated and compared using two channel models suitable for fifth-generation cellular systems, namely the 3rd Generation Partnership Project model and the NYUSIM model. Numerical results show that the benefits of base station coordination (as compared with the non-CoMP case) are governed by the underlying propagation model, and the aggregate interference levels proportional to the cell radius and number of users per cell. We show that in sparse channels, non-CoMP approaches exceed CoMP (coordinated beamforming) performance.

Closed-form approximations to the expected perterminal signal-to-interference-plus-noise-ratio (SINR) and ergodic sum spectral efficiency of a large multiuser multiple-input multiple-output system are presented. Our analysis assumes correlated Ricean fading with maximum ratio combining on the uplink, where the base station (BS) is equipped with a uniform linear array (ULA) with physical size restrictions. Unlike previous studies, our model caters for the presence of unequal correlation matrices and unequal Rice factors for each terminal. As the number of BS antennas grows without bound, with a finite number of terminals, we derive the limiting expected perterminal SINR and ergodic sum spectral efficiency of the system. Our findings suggest that with restrictions on the size of the ULA, the expected SINR saturates with increasing operating signal-to-noise-ratio (SNR) and BS antennas. Whilst unequal correlation matrices result in higher performance, the presence of strong line-of-sight (LoS) has an opposite effect. Our analysis accommodates changes in system dimensions, SNR, LoS levels, spatial correlation levels and variations in fixed physical spacings of the BS array.

General analysis of expected per-terminal signal-to-interference-plus-noise-ratio (SINR) and ergodic per-cell sum spectral efficiency for a multi-cellular system with coordinated regularized zero-forcing (RZF) precoding is presented. An application to two-tier small-cell networks is considered, assuming independent and identically distributed (i.i.d.) and semi-correlated Rayleigh fading channels, with spatial correlation at the base station. Our analysis caters for equal and unequal correlation matrices for each terminal. For the i.i.d. case and when each terminal is assigned an equal correlation matrix, our expressions are averaged over the eigenvalue densities of the channel correlation matrices, which follow an uncorrelated and correlated complex central Wishart distribution. With unequal correlation matrices, we exploit the high signal-to-noise-ratio (SNR) convergence of RZF precoding to zero-forcing (ZF) precoding and use a second-order Neumann series expansion to derive closed-form approximations to the expected RZF SINR and ergodic sum spectral efficiency, via the expected ZF SNR and ergodic sum spectral efficiency. Our numerical results show the adverse effects of intercellular interference, along with the improvements in the above-mentioned performance metrics with network-wide coordination over cell-wide and macro-only coordination strategies. The derived expressions are robust to changes in system dimensions, operating SNRs, and correlation levels.

A general framework for the analysis of expected per-user signal-to-interference-plus-noise-ratio (SINR) of a multiuser multiple-input-multiple-output system is presented. Our analysis assumes spatially correlated Rayleigh fading channels with regularized zero-forcing precoding on the downlink. Unlike previous works, our analytical expressions are averaged over the eigenvalue densities of the complex Wishart distributed channel correlation matrix. To aid the derivation of the expected per-user SINR, we derive a closed-form expression for the joint density of two arbitrary eigenvalues of the complex Wishart matrix. In the high signal-to-noise-ratio (SNR) regime, with zero-forcing precoding, we derive analytical expressions to approximate the instantaneous per-user SNR and show that it is approximately gamma distributed. The generality of the approximations is validated with numerical results over a wide range of system dimensions, spatial correlation and SNR levels.

Analytical expressions to approximate the expected per-user signal-to-interference-plus-noise-ratio (SINR) and ergodic sum-rate of a multiuser multiple-input-multiple-output system are presented. Our analysis assumes uncorrelated Ricean fading channels with regularized zero-forcing precoding on the downlink. The derived expressions are averaged with respect to the previously unknown arbitrary eigenvalue densities of the complex non-central Wishart distributed channel correlation matrix. To aid the derivation of the expected SINR, we derive analytical expressions for the joint density of two arbitrary eigenvalues of the complex non-central Wishart matrix. Unlike previous studies, our model caters to the presence of a unique Rice factor for each user terminal, making it suitable for analysis of modern systems, such as small cells and millimeter-wave. Our findings suggest that while the presence of strong line-of-sight has an adverse effect on the expected SINR and ergodic sum-rates, increasing the variability of Rice factors enhances the peak rate performance of the system. Our analysis can be applied to arbitrary system dimensions and is seen to remain tight across the signal-to-noise-ratio range considered.