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Recent developments in Multiple-Input-Multiple-Output (MIMO) technology include packing a large number of antenna elements in a compact array to access the bandwidth benefits provided by higher mutual coupling (MC). The resulting super-wideband (SW) systems require a circuit-theoretic framework to handle the MC and channel models which span extremely large bands. Hence, in this paper, we make two key contributions. First, we develop a physically-consistent Rician channel model for use with SW systems. Secondly, we express the circuit-theoretic models in terms of a standard MIMO model, so that insights into the effects of antenna layouts, MC, and bandwidth can be made using standard communication theory. For example, we show the bandwidth widening resulting from the new channel model. In addition, we show that MC distorts line-of-sight paths which has beamforming implications. We also highlight the interaction between spatial correlation and MC and show that tight coupling reduces spatial correlations at low frequencies., Comment: This paper has been submitted to the IEEE for possible publication

We present a new method to combine multimass equilibrium dynamical models and pulsar timing data to constrain the mass distribution and remnant populations of Milky Way globular clusters (GCs). We first apply this method to 47 Tuc, a cluster for which there exists an abundance of stellar kinematic data and which is also host to a large population of millisecond pulsars. We demonstrate that the pulsar timing data allow us to place strong constraints on the overall mass distribution and remnant populations even without fitting on stellar kinematics. Our models favor a small population of stellar-mass BHs in this cluster (with a total mass of $446^{+75}_{-72} \mathrm{M_\odot}$), arguing against the need for a large ($ > 2000 \ \mathrm{M_\odot}$) central intermediate-mass black hole. We then apply the method to Terzan 5, a heavily obscured bulge cluster which hosts the largest population of millisecond pulsars of any Milky Way GC and for which the collection of conventional stellar kinematic data is very limited. We improve existing constraints on the mass distribution and structural parameters of this cluster and place stringent constraints on its black hole content, finding an upper limit on the mass in BHs of $\sim 4000 \ \mathrm{M_\odot}$. This method allows us to probe the central dynamics of GCs even in the absence of stellar kinematic data and can be easily applied to other GCs with pulsar timing data, for which datasets will continue to grow with the next generation of radio telescopes., Comment: 33 pages, 19 figures. Accepted for publication in ApJ

Motivated by the ideal peak-to-average-power ratio and radar sensing capability of traditional frequency-coded radar waveforms, this paper considers the frequency shift keying (FSK) based waveform for joint communications and radar (JCR). An analysis of the probability distributions of its ambiguity function (AF) sidelobe levels (SLs) and peak sidelobe level (PSL) is conducted to study the radar sensing capability of random FSK. Numerical results show that the independent frequency modulation introduces uncontrollable AF PSLs. In order to address this problem, the initial phases of waveform sub-pulses are designed by solving a min-max optimisation problem. Numerical results indicate that the optimisation-based phase design can effectively reduce the AF PSL to a level close to well-designed radar waveforms while having no impact on the data rate and the receiver complexity. For large numbers of waveform sub-pulses and modulation orders, the impact on the error probability is also insignificant., Comment: Submitted to IEEE Transactions on Wireless Communications, 13 pages, 6 figures

This paper studies the coexistence between a downlink multiuser massive multi-input-multi-output (MIMO) communication system and MIMO radar. The performance of the massive MIMO system with maximum ratio ($\MR$), zero-forcing ($\ZF$), and protective $\ZF$ ($\PZF$) precoding designs is characterized in terms of spectral efficiency (SE) and by taking the channel estimation errors and power control into account. The idea of $\PZF$ precoding relies on the projection of the information-bearing signal onto the null space of the radar channel to protect the radar against communication signals. We further derive closed-form expressions for the detection probability of the radar system for the considered precoding designs. By leveraging the closed-form expressions for the SE and detection probability, we formulate a power control problem at the radar and base station (BS) to maximize the detection probability while satisfying the per-user SE requirements. This optimization problem can be efficiently tackled via the bisection method by solving a linear feasibility problem. Our analysis and simulations show that the $\PZF$ design has the highest detection probability performance among all designs, with intermediate SE performance compared to the other two designs. Moreover, by optimally selecting the power control coefficients at the BS and radar, the detection probability improves significantly., Comment: 10 Figures, IEEE Open Journal of the Communication society

Fluid antennas (FAs) is a promising technology for introducing flexibility and reconfigurability in wireless networks. Recent research efforts have highlighted the potential gains that can be achieved in comparison to conventional antennas. These works assume that the FA has a discrete number of positions that the liquid can take. However, from a practical standpoint, the liquid moves in a continuous fashion to any point inside the FA. In this paper, we focus on a continuous FA system (CFAS) and present a general framework for its design and analytical evaluation. In particular, we derive closed-form analytical expressions for the level crossing rate (LCR) and the average fade duration of the continuous signal-to-interference ratio (SIR) process over the FA's length. Then, by leveraging the LCR expression, we characterize the system's outage performance with a bound on the cumulative distribution function of the SIR's supremum. Our results confirm that the CFAS outperforms its discrete counterpart and thus provides the performance limits of FA-based systems., Comment: IEEE Communications Letters

Populations of stellar-mass black holes (BHs) in globular clusters (GCs) influence their dynamical evolution and have important implications on one of the main formation channels for gravitational wave sources. Inferring the size of these populations remains difficult, however. In this work, multimass models of 34 Milky Way GCs, first presented in Dickson et al., are used to explore the present-day BH populations. Direct constraints on both the total and visible mass components provided by several observables allow these models to accurately determine the distribution of the dark mass (including BHs) within clusters, as we demonstrate in a proof-of-concept fitting of the models to mock observations extracted from Monte Carlo cluster models. New constraints on the BH population retained to the present-day in each cluster are inferred from our models. We find that BH mass fractions ranging from 0 to 1 per cent of the total mass are typically required to explain the observations, except for Omega Cen, for which we infer a mass fraction above 5 per cent, in agreement with previous works. Relationships between the dark remnant populations and other cluster parameters are examined, demonstrating a clear anti-correlation between the amount of BHs and mass segregation between visible stars, as well as a correlation between remnant mass fractions and the dynamical age of clusters. Our inferred BH populations are in good agreement overall with other recent studies using different methodologies, but with notable discrepancies for individual clusters., Comment: 18 pages, 9 figures, MNRAS accepted

We develop an optimal version of a prior two-stage channel estimation protocol for RIS-assisted channels. The new design uses a modified DFT matrix (MDFT) for the training phases at the RIS and is shown to minimize the total channel estimation error variance. In conjunction with interpolation (estimating fewer RIS channels), the MDFT approach accelerates channel estimation even when the channel from base station to RIS is line-of-sight. In contrast, prior two-stage techniques required a full-rank channel for efficient estimation. We investigate the resulting channel estimation errors by comparing different training phase designs for a variety of propagation conditions using a ray-based channel model. To examine the overall performance, we simulate the spectral efficiency with MRC processing for a single-user RIS-assisted system using an existing optimal design for the RIS transmission phases. Results verify the optimality of MDFT while simulations and analysis show that the performance is more dependent on the user-to-RIS channel correlation and the coarseness of the interpolation used, rather than the training phase design. For example, under a scenario with more highly correlated channels, the procedure accelerates channel estimation by a factor of 16, while the improvement is a factor of 5 in a less correlated case. The overall procedure is extremely robust, with a maximum performance loss of 1.5bits/sec/Hz compared to that with perfect channel state information for the considered channel conditions.

The objective of this paper is to develop simple techniques to enhance the performance of multi-user RIS aided wireless systems. Specifically, we develop a novel technique called \textit{channel separation} which provides a better understanding of how the RIS phases affect the uplink sum rate and sum rates for ZF and MMSE linear receivers. Leveraging channel separation, we propose a simple iterative algorithm to improve the uplink sum rate and the sum rates of ZF and MMSE linear receivers when discrete RIS phases are considered. For continuous RIS phases, we derive simple closed form solutions to enhance the uplink sum rate and reduce the total mean square error of the MMSE combiner. The latter metric is a tractable alternative to maximizing sum rates for ZF and MMSE. Numerical simulations are performed for all optimization techniques and the effectiveness of each technique is compared to a full numerical optimization procedure, namely an interior point (IP) algorithm., Comment: arXiv admin note: text overlap with arXiv:2110.02493

In this paper we focus on phase dependent loss (PDL), an important aspect of reconfigurable intelligent surfaces (RIS) where the signals reflected from the RIS elements are attenuated by varying amounts depending on the phase rotation provided by the element. To evaluate the effects of PDL, we analyse the SNR of a SIMO RIS-aided wireless link. We assume that the channel between the base station (BS) and RIS is a rank-1 LOS channel while the user (UE)-BS and UE-RIS are correlated Rayleigh channels. The RIS design is optimal in the absence of PDL and maximizes the SNR in this scenario. Specifically, we derive a closed form expression for the mean SNR in the presence of PDL. The attenuation function used for PDL was developed from a detailed circuit analysis of RIS elements. Leveraging the derived results, we analytically characterise the impact of PDL on the mean SNR. Numerical results are conducted to validate the derived expressions and verify the analysis., Comment: arXiv admin note: text overlap with arXiv:2110.03801

We present an analysis of the optimal uplink (UL) SNR of a SIMO Reconfigurable Intelligent Surface (RIS)-aided wireless link. We assume that the channel between base station (BS) and RIS is a rank-1 LOS channel while the user (UE)-RIS and UE-BS channels are correlated Ricean. For the optimal RIS matrix, we derive an exact closed form expression for the mean SNR and an approximation for the SNR variance leading to an accurate gamma approximation to the distribution of the UL SNR. Furthermore, we analytically characterise the effects of correlation and the Ricean K-factor on SNR, showing that increasing the K-factor and correlation in the UE-BS channel can have negative effects on the mean SNR, while increasing the K-factor and correlation in the UE-RIS channel improves system performance. We also present favourable and unfavourable channel scenarios which provide insight into the sort of environments that improve or degrade the mean SNR. We also show that the relative gain in the mean SNR when transitioning from an unfavourable to a favourable environment saturates to $(4-\pi)/\pi$ as $N \rightarrow \infty $, Comment: reconfigurable intelligent surface, intelligent reflecting surface, optimal RIS SNR analysis. arXiv admin note: text overlap with arXiv:2008.09376

The objective of this paper is to develop simple techniques to bound the optimal uplink sum-rate of multi-user RIS-aided wireless systems. Specifically, we develop a novel technique called \textit{channel separation} which provides a new understanding as to how the RIS phases affect the sum-rate. Leveraging channel separation, we derive upper and lower bounds on the optimal sum-rate. In addition, we propose a low-complexity alternating optimization algorithm to obtain near-optimal sum-rate results. Numerical results demonstrate the tightness of the bounds and show that the alternating optimization approach delivers sum-rate values similar to the results of a full numerical optimization procedure. Furthermore, in practical scenarios where hardware limitations cause the RIS phases to be quantized, our lower bound can still be applied and shows that the sum-rate is robust to quantization, even with low resolution., Comment: reconfigurable intelligent surface, intelligent reflecting surface, RIS, optimal sum rate tight bound, optimal sum rate

We analyse the behaviour of a massive multi-user MIMO (MU-MIMO) system comprising a base station (BS) equipped with one of five different antenna topologies for which the spatial aperture is either unconstrained, or space-constrained. We derive the normalized mean interference (NMI) with a ray-based channel model, as a metric for topology comparison in each of the two cases. Based on the derivation for a horizontal uniform rectangular array (HURA) in [1], we provide closed-form NMI equations for the uniform linear array (ULA) and uniform circular array (UCirA). We then derive the same for a vertical URA (VURA) and uniform cylindrical array (UCylA). Results for the commonly-considered unconstrained case confirm the prior understanding that topologies with wider azimuth footprints aid performance. However, in the space-constrained case performance is dictated by the angular resolution afforded by the topology, particularly in elevation. We confirm the behavioural patterns predicted by the NMI by observing the same patterns in the system SINR with minimum mean-squared error (MMSE) processing., Comment: 5 pages, 3 figures

In this paper, we present an analysis of the optimal uplink SNR of a SIMO Reconfigurable Intelligent Surface (RIS)-aided wireless link. We assume that the channel between base station and RIS is a rank-1 LOS channel while the user (UE)-RIS and UE-base station (BS) channels are correlated Rayleigh. We derive an exact closed form expression for the mean SNR and an approximation for the SNR variance leading to an accurate gamma approximation to the distribution of the UL SNR. Furthermore, we analytically characterise the effects of correlation on SNR, showing that correlation in the UE-BS channel can have negative effects on the mean SNR, while correlation in the UE-RIS channel improves system performance. For systems with a large number of RIS elements, correlation in the UE-RIS channel can cause an increase in the mean SNR of up to 27.32% relative to an uncorrelated channel., Comment: 6 pages, 4 figures. Keywords: Reconfigurable Intelligent Surface (RIS), Intelligent Reflecting Surface (IRS)

We present a flexible family of 3D mobility models suitable for unmanned aerial vehicles (UAV). Based on stochastic differential equations, the models offer a unique property of explicitly incorporating the mobility control mechanism and environmental perturbation, while enabling tractable steady state solutions for properties such as position and connectivity. Specifically, motivated by UAV flight data, for a symmetric mobility model with an arbitrary control mechanism, we derive the steady state distribution of the distance from the target position. We provide closed form expressions for the special cases of the Ornstein-Uhlenbeck (OU) process and on-off control (OC). We extend the model to incorporate imperfect positioning and asymmetric control. For a practically relevant scenario of partial symmetry (such as in the x-y plane), we present steady state position results for the OU control. Building on these results, we derive UAV connectivity probability results based on a SNR criterion in a Rayleigh fading environment., Comment: 6 pages, 6 figures, accepted for publication at IEEE PIMRC 2020

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., Comment: 7 pages, 3 figures, Accepted for publication in IEEE PIMRC 2020

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., Comment: To appear in the Proceedings of IEEE PIMRC 2019, Istanbul, Turkey

Massive multiple-input multiple-output (MIMO) is becoming a mature technology, and has been approved for standardization in the 5G ecosystem. Although there is a large body of papers on the theoretical analysis of massive MIMO, the majority of relevant work assumes the simplified, yet overly idealistic, Kronecker-type model for spatial correlation. Motivated by the deficiencies of the Kronecker model, we invoke a naturally generalized spatial correlation model, that is the Weichselberger model. For this model, we pursue a comprehensive analysis of massive MIMO performance in terms of channel hardening and favorable propagation (FP). We identify a number of scenarios under which massive MIMO may fail, in terms of channel hardening and FP, and discuss their relevance from a practical perspective., Comment: IEEE ICC 2019, submitted

Massive multiple-input multiple-output (MIMO) is now making its way to the standardization exercise of future 5G networks. Yet, there are still fundamental questions pertaining to the robustness of massive MIMO against physically detrimental propagation conditions. On these grounds, we identify scenarios under which massive MIMO can potentially fail in Ricean channels, and characterize them physically, as well as, mathematically. Our analysis extends and generalizes a stream of recent papers on this topic and articulates emphatically that such harmful scenarios in Ricean fading conditions are unlikely and can be compensated using any standard scheduling scheme. This implies that massive MIMO is intrinsically effective at combating interuser interference and, if needed, can avail of the base-station scheduler for further robustness., Comment: IEEE Wireless Communications Letters, accepted

Closed-form approximations of the expected per-terminal signal-to-interference-plus-noise-ratio (SINR) and ergodic sum spectral efficiency of a multiuser multiple-input multiple-output system are presented. Our analysis assumes spatially correlated Ricean fading channels with maximum-ratio combining on the uplink. Unlike previous studies, our model accounts for the presence of unequal correlation matrices, unequal Rice factors, as well as unequal link gains to each terminal. The derived approximations lend themselves to useful insights, special cases and demonstrate the aggregate impact of line-of-sight (LoS) and unequal correlation matrices. Numerical results show that while unequal correlation matrices enhance the expected SINR and ergodic sum spectral efficiency, the presence of strong LoS has an opposite effect. Our approximations are general and remain insensitive to changes in the system dimensions, signal-to-noise-ratios, LoS levels and unequal correlation levels., Comment: 4 pages, 2 figures, accepted for publication in the IEEE Wireless Communications Letters, Vol. 6, 2017

Closed-form approximations to the expected per-terminal 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 per-terminal 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., Comment: 7 pages, 3 figures, accepted for publication in the proceedings of IEEE ICC, to be held in Paris, France, May 2017

We investigate coordinated regularized zero-forcing precoding for limited feedback multicell multiuser multiple-input single-output systems. We begin by deriving an approximation to the expected signal-to-interference-plus-noise ratio for the proposed scheme with perfect channel direction information (CDI) at the base station (BS). We also derive an expected SINR approximation for limited feedback systems with random vector quantization (RVQ) based codebook CDI at the BS. Using the expected interference result for the RVQ based limited feedback CDI, we propose an adaptive feedback bit allocation strategy to minimize the expected interference by partitioning the total number of bits between the serving and out-of-cell interfering channels. Numerical results show that the proposed adaptive feedback bit allocation method offers a spectral efficiency gain over the existing coordinated zero-forcing scheme., Comment: 9 pages, 7 figures, accepted in IEEE Transactions on Vehicular Technology

In this paper we demonstrate the rate gains achieved by two-tier heterogeneous cellular networks (HetNets) with varying degrees of coordination between macrocell and microcell base stations (BSs). We show that without the presence of coordination, network densification does not provide any gain in the sum rate and rapidly decreases the mean per-user signal-to-interference-plus-noise-ratio (SINR). Our results show that coordination reduces the rate of SINR decay with increasing numbers of microcell BSs in the system. Validity of the analytically approximated mean per-user SINR over a wide range of signal-to-noise-ratio (SNR) is demonstrated via comparison with the simulated results., Comment: 7 pages, 8 figures, submitted to IEEE International Conference on Communications (ICC) 4th International Workshop on Small Cells and 5G (SmallNets), London, UK, June 2015

In this paper, we analyze both the rate of convergence and the performance of a matched-filter (MF) precoder in a massive multi-user (MU) multiple-input-multiple-output (MIMO) system, with the aim of determining the impact of distributing the transmit antennas into multiple clusters. We consider cases of transmit spatial correlation, unequal link gains and imperfect channel state information (CSI). Furthermore, we derive a MF signal-to-interference-plus-noise-ratio (SINR) limit as both the number of transmit antennas and the number of users tend to infinity. In our results, we show that both the rate of convergence and performance is strongly dependent on spatial correlation. In the presence of spatial correlation, distributing the antennas into multiple clusters renders significant gains over a co-located antenna array scenario. In uncorrelated scenarios, a co-located antenna cluster has a marginally better mean per-user SINR performance due to its superior single-user signal-to-noise-ratio (SNR) regime, i.e., when a user is close to the base station (BS), the links between the user and all transmit antennas becomes strong., Comment: 26 pages, 9 figures

In this paper we examine a number of deployment issues which arise from practical considerations in massive multiple-input-multiple-output (MIMO) systems. We show both spatial correlation and line-of-sight (LOS) introduce an interference component to the system which causes non-orthogonality between user channels. Distributing the antennas into multiple clusters is shown to reduce spatial correlation and improve performance. Furthermore, due to its ability to minimize interference, zero forcing (ZF) precoding performs well in massive MIMO systems compared to matched filter (MF) precoding which suffers large penalties. However, the noise component in the ZF signal-to-noise-ratio (SNR) increases significantly in the case of imperfect transmit channel state information (CSI)., Comment: 6 pages, 9 figures

Approximate expressions for the spatial correlation of cylindrical and uniform rectangular arrays (URA) are derived using measured distributions of angles of departure (AOD) for both the azimuth and zenith domains. We examine massive multiple-input-multiple-output (MIMO) convergence properties of the correlated channels by considering a number of convergence metrics. The per-user matched filter (MF) signal-to-interference-plus-noise ratio (SINR) performance and convergence rate, to respective limiting values, of the two antenna topologies is also explored., Comment: 6 pages, 6 figures

In this paper we examine convergence properties of massive MIMO systems with the aim of determining the number of antennas required for massive MIMO gains. We consider three characteristics of a channel matrix and study their asymptotic behaviour. Furthermore, we derive ZF SNR and MF SINR for a scenario of unequal receive powers. In our results we include the effects of spatial correlation. We show that the rate of convergence of channel metrics is much slower than that of the ZF/MF precoder properties., Comment: 6 pages, 6 figures, ICC 2014