2618074
Multi-User Massive MIMO Communication Systems Based on Irregular Antenna Arrays
In practical mobile communication engineering applications, surfaces of antenna array deployment regions are usually uneven. Therefore, massive multi-input-multi-output (MIMO) communication systems usually transmit wireless signals by irregular antenna arrays. To evaluate the performance of irregular antenna arrays, the matrix correlation coefficient and the ergodic received gain are defined for massive MIMO communication systems with mutual coupling effects. Furthermore, the lower bound of the ergodic achievable rate, symbol error rate, and average outage probability is first derived for multi-user massive MIMO communication systems using irregular antenna arrays. Asymptotic results are also derived when the number of antennae approaches infinity. Numerical results indicate that there exists a maximum achievable rate when the number of antennae keeps increasing in massive MIMO communication systems using irregular antenna arrays. Moreover, the irregular antenna array outperforms the regular antenna array in the achievable rate of massive MIMO communication systems when the number of antennae is larger than or equal to a given threshold.
5972986
5G Ultra-Dense Cellular Networks
Traditional ultra-dense wireless networks are recommended as a complement for cellular networks and are deployed in partial areas, such as hotspot and indoor scenarios. Based on the massive multiple-input multi-output antennas and the millimeter wave communication technologies, the 5G ultra-dense cellular network is proposed to deploy in overall cellular scenarios. Moreover, a distribution network architecture is presented for 5G ultra-dense cellular networks. Furthermore, the backhaul network capacity and the backhaul energy efficiency of ultra-dense cellular networks are investigated to answer an important question, that is, how much densification can be deployed for 5G ultra-dense cellular networks. Simulation results reveal that there exist densification limits for 5G ultra-dense cellular networks with backhaul network capacity and backhaul energy efficiency constraints.
2874658
Mutual coupling in MIMO wireless systems: a rigorous network theory analysis
A new framework for the analysis of multiple-input multiple-output (MIMO) wireless systems is introduced to account for mutual coupling effects in the antenna arrays. The multiport interactions at transmit and receive are characterized by representing the channel using a scattering parameter matrix. A new power constraint that limits the average radiated power is also introduced. The capacity of the MIMO system with mutual coupling is defined as the maximum mutual information of the transmit and receive vectors over all possible transmit signaling and receive loading. Full-wave electromagnetic antenna simulations combined with a simple path-based channel model are used to demonstrate the utility of the method.
17201716
Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas
A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval. Time-division duplex operation combined with reverse-link pilots enables the base station to estimate the reciprocal forward- and reverse-link channels. The conjugate-transpose of the channel estimates are used as a linear precoder and combiner respectively on the forward and reverse links. Propagation, unknown to both terminals and base station, comprises fast fading, log-normal shadow fading, and geometric attenuation. In the limit of an infinite number of antennas a complete multi-cellular analysis, which accounts for inter-cellular interference and the overhead and errors associated with channel-state information, yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve. In particular the effects of uncorrelated noise and fast fading vanish, throughput and the number of terminals are independent of the size of the cells, spectral efficiency is independent of bandwidth, and the required transmitted energy per bit vanishes. The only remaining impairment is inter-cellular interference caused by re-use of the pilot sequences in other cells (pilot contamination) which does not vanish with unlimited number of antennas.
3332631
Energy and Spectral Efficiency of Very Large Multiuser MIMO Systems
A multiplicity of autonomous terminals simultaneously transmits data streams to a compact array of antennas. The array uses imperfect channel-state information derived from transmitted pilots to extract the individual data streams. The power radiated by the terminals can be made inversely proportional to the square-root of the number of base station antennas with no reduction in performance. In contrast if perfect channel-state information were available the power could be made inversely proportional to the number of antennas. Lower capacity bounds for maximum-ratio combining (MRC), zero-forcing (ZF) and minimum mean-square error (MMSE) detection are derived. An MRC receiver normally performs worse than ZF and MMSE. However as power levels are reduced, the cross-talk introduced by the inferior maximum-ratio receiver eventually falls below the noise level and this simple receiver becomes a viable option. The tradeoff between the energy efficiency (as measured in bits/J) and spectral efficiency (as measured in bits/channel use/terminal) is quantified for a channel model that includes small-scale fading but not large-scale fading. It is shown that the use of moderately large antenna arrays can improve the spectral and energy efficiency with orders of magnitude compared to a single-antenna system.
9494098
Closed-Loop Beam Alignment for Massive MIMO Channel Estimation
Training sequences are designed to probe wireless channels to obtain channel state information for block-fading channels. Optimal training sounds the channel using orthogonal beamforming vectors to find an estimate that optimizes some cost function, such as mean square error. As the number of transmit antennas increases, however, the training overhead becomes significant. This creates a need for alternative channel estimation schemes for increasingly large transmit arrays. In this work, we relax the orthogonal restriction on sounding vectors. The use of a feedback channel after each forward channel use during training enables closed-loop sounding vector design. A misalignment cost function is introduced, which provides a metric to sequentially design sounding vectors. In turn, the structure of the sounding vectors aligns the transmit beamformer with the true channel direction, thereby increasing beamforming gain. This beam alignment scheme for massive MIMO is shown to improve beamforming gain over conventional orthogonal training for a MISO channel.
13296398
MIMO systems with mutual coupling: How many antennas to pack into fixed-length arrays?
For multiple-input multiple-output wireless systems, we investigate the important question of how many antennas to place in fixed-length arrays, accounting for both spatial correlation and mutual coupling at the transmitter and receiver. We show that there is an optimal antenna configuration yielding the highest capacity which depends strongly on the array length and the transmission wavelength, but does not depend strongly on the signal to noise ratio (SNR). Moreover, we show that ignoring the effect of mutual coupling gives misleading results, yielding unbounded capacity growth. As another key finding, we demonstrate the surprising result that if the optimal antenna configuration is employed, then further optimizing the transmission based on the channel statistics gives very little benefit over simple equal-power spatial multiplexing. By deriving an expression for the capacity at low SNR, we provide a straightforward method for estimating the optimal number of antennas.
8537889
Large-Scale MIMO Transmitters in Fixed Physical Spaces: The Effect of Transmit Correlation and Mutual Coupling
We explore the performance of multiple input multiple output (MIMO) transmitters in correlated channels where increasing numbers of antenna elements are fitted in a fixed physical space. As well investigated in the literature, two main effects emerge in such a design: transmit spatial correlation and mutual antenna coupling. In contrast to the literature however, here we investigate the combined effect of reducing the distance between the antenna elements with increasing the number of elements in a fixed transmitter space. In other words, towards the implementation of large-scale MIMO transmitters in limited physical spaces, we investigate the joint effect of two contradicting phenomena: the reduction of spatial diversity due to reducing the separation between antennas and the increase in transmit diversity by increasing the number of elements. Within this context, we analytically approximate the performance of two distinct linear precoding designs. The theoretical analysis and simulations show the somewhat surprising result that for a given number of receivers the improved transmit diversity dominates the performance of practical linear precoders. Consequently, important benefits in the system sum rate can be gleaned by fitting more antenna elements in a fixed space by employing separations smaller than the wavelength of the transmit frequency.
39809258
Mutual coupling effects in multi-user massive MIMO base stations
We analyze the effects of mutual coupling and spatial correlation on the performance of multi-user MIMO systems having a large number of antenna elements at the base station (`large-scale' MIMO or `massive' MIMO). We show that these effects set a practical limit on the maximum number of antennas that can be packed into any given physical base station size, above which no further spectral efficiency gain is achieved. Different antenna elements such as dipoles, patches and dual-polarized patches are considered.
206454719
Five disruptive technology directions for 5G
New research directions will lead to fundamental changes in the design of future fifth generation (5G) cellular networks. This article describes five technologies that could lead to both architectural and component disruptive design changes: device-centric architectures, millimeter wave, massive MIMO, smarter devices, and native support for machine-to-machine communications. The key ideas for each technology are described, along with their potential impact on 5G and the research challenges that remain.
63117909
Conformal Array Antenna Theory And Design
Thank you for downloading conformal array antenna theory and design. As you may know, people have look hundreds times for their favorite books like this conformal array antenna theory and design, but end up in malicious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they are facing with some harmful virus inside their laptop. conformal array antenna theory and design is available in our digital library an online access to it is set as public so you can get it instantly. Our books collection hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the conformal array antenna theory and design is universally compatible with any devices to read.
122874812
PATTERN SYNTHESIS OF CONFORMAL ANTENNA ARRAY BY THE HYBRID GENETIC ALGORITHM
Desired far-field radiation patterns of 5 × 11 conformal antenna array are synthesized using a hybrid genetic algorithm (HGA), which combines the simplified quadratic interpolation (SQI) method and the real-coded genetic algorithm (RCGA). This hybrid genetic algorithm is shown to outperform standard genetic algorithm (GA) when used to synthesize amplitude weights of the elements to satisfy specified deep notches, nulls and average sidelobe level constraints. The HGA procedure appears to be a high effective means to compensate the mutual coupling effects on the individual element patterns for the conformal antenna array.
124013117
Synthesis of Sparse Planar Arrays Using Modified Real Genetic Algorithm
In array design, the positions of sparse array elements is an important concern for optimal performance in terms of its ability to achieve minimum peak sidelobe level (SLL). This paper proposes a modified real genetic algorithm (MGA) based on resetting of chromosome for the element position optimization of sparse planar arrays with rectangular boundary. And here the multiple optimization constraints include the number of elements, the aperture and the minimum element spacing. By simplifying the space between the elements from the actual distance to Chebychev distance, the MGA searches a smaller solution space by means of indirect description of individual, and it can avoid infeasible solution during the optimization process by two novel genetic operators. Finally, the simulation results confirming the great efficiency and the robustness of the proposed method are shown in this paper
42483036
Sparse antenna array configurations in large aperture synthesis radio telescopes
This paper presents the trade-offs between sparse versus dense and regular versus irregular arrays for the station configuration of the LOFAR low band antenna. The relation between these parameters and the element patterns, station beam patterns, effective area, receiver noise temperature, tapering opportunities and the field of view (or beam width) are presented. A method is proposed and evaluated to suppress the peak grating lobe level in an aperture synthesis telescope consisting of regular sparse stations
1898025
Distance Distributions in Finite Uniformly Random Networks: Theory and Applications
In wireless networks, knowledge of internode distances is essential for performance analysis and protocol design. When determining distance distributions in random networks, the underlying nodal arrangement is almost universally taken to be a stationary Poisson point process. While this may be a good approximation in some cases, there are also certain shortcomings to this model, such as the fact that, in practical networks, the number of nodes in disjoint areas is not independent. This paper considers a more-realistic network model where a known and fixed number of nodes are independently distributed in a given region and characterizes the distribution of the Euclidean internode distances. The key finding is that, when the nodes are uniformly randomly placed inside a ball of arbitrary dimensions, the probability density function (pdf) of the internode distances follows a generalized beta distribution. This result is applied to study wireless network characteristics such as energy consumption, interference, outage, and connectivity.
55575843
Handbook of spatial statistics
Introduction Historical Introduction, Peter J. Diggle Continuous Spatial Variation Continuous Parameter Stochastic Process Theory, Tilmann Gneiting and Peter Guttorp Classical Geostatistical Methods, Dale L. Zimmerman and Michael Stein Likelihood-Based Methods, Dale L. Zimmerman Spectral Domain, Montserrat Fuentes and Brian Reich Asymptotics for Spatial Processes, Michael Stein Hierarchical Modeling with Spatial Data, Christopher K. Wikle Low Rank Representations for Spatial Processes, Christopher K. Wikle Constructions for Nonstationary Spatial Processes, Paul D. Sampson Monitoring Network Design, James V. Zidek and Dale L. Zimmerman Non-Gaussian and Nonparametric Models for Continuous Spatial Data, Mark F.J. Steel and Montserrat Fuentes Discrete Spatial Variation Discrete Spatial Variation, Havard Rue and Leonard Held Conditional and Intrinsic Autoregressions, Leonhard Held and Havard Rue Disease Mapping, Lance Waller and Brad Carlin Spatial Econometrics, R. Kelley Pace and James LeSage Spatial Point Patterns Spatial Point Process Theory, Marie-Colette van Lieshout Spatial Point Process Models, Valerie Isham Nonparametric Methods, Peter J. Diggle Parametric Methods, Jesper Moller Modeling Strategies, Adrian Baddeley Multivariate and Marked Point Processes, Adrian Baddeley Point Process Models and Methods in Spatial Epidemiology, Lance Waller Spatio-Temporal Processes Continuous Parameter Spatio-Temporal Processes, Tilmann Gneiting and Peter Guttorp Dynamic Spatial Models Including Spatial Time Series, Dani Gamerman Spatio-Temporal Point Processes, Peter J. Diggle and Edith Gabriel Modeling Spatial Trajectories, David R. Brillinger Data Assimilation, Douglas W. Nychka and Jeffrey L. Anderson Additional Topics Multivariate Spatial Process Models, Alan E. Gelfand and Sudipto Banerjee Misaligned Spatial Data: The Change of Support Problem, Alan E. Gelfand Spatial Aggregation and the Ecological Fallacy, Jonathan Wakefield and Hilary Lyons Spatial Gradients and Wombling, Sudipto Banerjee Index
2026673
The Multicell Multiuser MIMO Uplink with Very Large Antenna Arrays and a Finite-Dimensional Channel
We consider multicell multiuser MIMO systems with a very large number of antennas at the base station (BS). We assume that the channel is estimated by using uplink training. We further consider a physical channel model where the angular domain is separated into a finite number of distinct directions. We analyze the so-called pilot contamination effect discovered in previous work, and show that this effect persists under the finite-dimensional channel model that we consider. In particular, we consider a uniform array at the BS. For this scenario, we show that when the number of BS antennas goes to infinity, the system performance under a finite-dimensional channel model with P angular bins is the same as the performance under an uncorrelated channel model with P antennas. We further derive a lower bound on the achievable rate of uplink data transmission with a linear detector at the BS. We then specialize this lower bound to the cases of maximum-ratio combining (MRC) and zero-forcing (ZF) receivers, for a finite and an infinite number of BS antennas. Numerical results corroborate our analysis and show a comparison between the performances of MRC and ZF in terms of sum-rate.
4774663
Correlation and capacity of MIMO systems and mutual coupling, radiation efficiency, and diversity gain of their antennas: simulations and measurements in a reverberation chamber
MIMO systems are characterized by their maximum available capacity, which is reduced if there is correlation between the signals on different channels. The correlation is primarily caused by mutual coupling between the elements of the antenna arrays on both the receiving and transmitting sides. Similarly, diversity antennas can be characterized by a diversity gain that also is affected by mutual coupling between the antennas. We explain how such MIMO and diversity antennas with mutual coupling can be analyzed by classical embedded element patterns that can be computed by standard computer codes. In the MIMO example under investigation, the mutual coupling reduces both correlation, which increases the capacity, and radiation efficiency, which decreases it, and the combined effect is a net capacity reduction. We also explain how the radiation efficiency, diversity gain, correlation, and channel capacity can be measured in a reverberation chamber. The measurements show good agreement with simulations.
7517522
Capacity scaling in MIMO Wireless systems under correlated fading
Previous studies have shown that single-user systems employing n-element antenna arrays at both the transmitter and the receiver can achieve a capacity proportional to n, assuming independent Rayleigh fading between antenna pairs. We explore the capacity of dual-antenna-array systems under correlated fading via theoretical analysis and ray-tracing simulations. We derive and compare expressions for the asymptotic growth rate of capacity with n antennas for both independent and correlated fading cases; the latter is derived under some assumptions about the scaling of the fading correlation structure. In both cases, the theoretic capacity growth is linear in n but the growth rate is 10-20% smaller in the presence of correlated fading. We analyze our assumption of separable transmit/receive correlations via simulations based on a ray-tracing propagation model. Results show that empirical capacities converge to the limit capacity predicted from our asymptotic theory even at moderate n = 16. We present results for both the cases when the transmitter does and does not know the channel realization.
109557562
Antenna Theory: Analysis and Design
The most-up-to-date resource available on antenna theory and design. Expanded coverage of design procedures and equations makes meeting ABET design requirements easy and prepares readers for authentic situations in industry. New coverage of microstrip antennas exposes readers to information vital to a wide variety of practical applications.Computer programs at end of each chapter and the accompanying disk assist in problem solving, design projects and data plotting.-- Includes updated material on moment methods, radar cross section, mutual impedances, aperture and horn antennas, and antenna measurements.-- Outstanding 3-dimensional illustrations help readers visualize the entire antenna radiation pattern.
122959444
Effect of mutual coupling on the performance of adaptive arrays
The effect of mutual coupling between array elements on the performance of adaptive arrays is examined. The study includes both steady state and transient performance. An expression for the steady state output signal-to-interference-plus-noise ratio (SINR) of adaptive arrays, taking into account the mutual coupling between the array elements, is derived. The expression is used to assess the steady state performance of adaptive arrays. The transient response is studied by computing the eigenvalues associated with the signal covariance matrix. The steering vector required to maximize the output SINR of Applebaum-type adaptive arrays in the presence of mutual coupling is also given.
27893269
Effect of element mutual coupling on the capacity of fixed length linear arrays
The effect of element mutual coupling on the capacity of multiple-input-multiple-output (MIMO) antenna systems is demonstrated by considering a fixed-length linear array of half-wave dipoles. Mutual coupling between elements, which influences both the spatial correlation and the received signal-to-noise ratio (SNR), is taken into account by means of the impedance matrix. Monte Carlo simulations are performed for both single-sided (i.e., transmitting end or receiving end) and double-sided fading correlations. It is shown that mutual coupling results in substantially lower capacity and, hence, in reduced degrees of freedom.
647004
Capacity of MIMO channels with one-sided correlation
We present closed-form expressions for the marginal density distribution of the unordered eigenvalues of HFH* where F is an input covariance and H is a matrix representing a MIMO (multi-input multi-output) Rayleigh-faded channel with one-sided correlation at either end of the link, transmitter or receiver, with no constraints on the numbers of antennas therein. Using the foregoing distribution, we then derive analytical expressions for the capacity. The expressions found are evaluated through several examples conducted with correlation structures of practical interest.
17873814
ZF Detectors over Correlated K Fading MIMO Channels
This paper provides a systematic characterization of Zero-Forcing (ZF) detectors over multiple-input multiple-output (MIMO) channels that experience both small and large-scale fading. In particular, we consider the generic K distribution (Rayleigh/gamma distribution) to model the composite fading fluctuations and also assume the general case of semi-correlated small-scale fading. In the following, novel exact analytical expressions for the achievable sum rate are derived, followed by asymptotic expressions in the high and low Signal-to-Noise ratio (SNR) regimes. In these limiting cases, two common and insightful affine expansions are studied followed by new, closed-form upper and lower bounds on the sum rate that remain tight for all SNRs. In the second part of the paper, we present exact tractable expressions along with first-order expansions for the symbol error rate (SER) and outage probability; we also quantify the performance of ZF detectors in terms of diversity order and array (or coding) gain. The implications of the model parameters on the ZF detector performance are investigated via Monte-Carlo simulations which also validate the theoretical analysis.
12701744
Beamforming via Large and Dense Antenna Arrays Above a Clutter
The paper sheds light on the beamforming (BF) performance of large (potentially unconstrained in size) as well as dense (but physically constrained in size) antenna arrays when equipped with arbitrarily many elements. Two operational modes are investigated: Single-layer BF and multi-layer BF. In the first mode, a realistic BF criterion namely the average BF gain is revisited and employed to understand the far-field and the near-field effects on the BF performance of large-scale antennas above a clutter. The diminishing throughput returns in a single-layer BF mode versus the number of antennas necessitate multi-layering. In the multi-layer BF mode, the RF coverage is divided into a number of directive non-overlapping sector-beams in a deterministic manner within a multi-user multi-input multi-output (MIMO) system. The optimal number of layers that maximizes the user's sum-rate given a constrained antenna array is found as a compromise between the multiplexing gain (associated with the number of sector-beams) and the inter-beam interference, represented by the side lobe level (SLL).
6467090
Ergodic Capacity Analysis of Amplify-and-Forward MIMO Dual-Hop Systems
This paper presents an analytical characterization of the ergodic capacity of amplify-and-forward (AF) MIMO dual-hop relay channels, assuming that the channel state information is available at the destination terminal only. In contrast to prior results, our expressions apply for arbitrary numbers of antennas and arbitrary relay configurations. We derive an expression for the exact ergodic capacity, simplified closed-form expressions for the high SNR regime, and tight closed-form upper and lower bounds. These results are made possible by employing recent tools from finite-dimensional random matrix theory, which are used to derive new closed-form expressions for various statistical properties of the equivalent AF MIMO dual-hop relay channel, such as the distribution of an unordered eigenvalue and certain random determinant properties. Based on the analytical capacity expressions, we investigate the impact of the system and channel characteristics, such as the antenna configuration and the relay power gain. We also demonstrate a number of interesting relationships between the dual-hop AF MIMO relay channel and conventional point-to-point MIMO channels in various asymptotic regimes.
20463198
Pattern Synthesis of Conformal Array Antenna in the Presence of Platform Using Differential Evolution Algorithm
A synthesis method based on differential evolution algorithm is proposed for conformal antenna arrays in the presence of platform. With the desired phase weights determined by the scan angle and array geometry, the amplitude weights of elements are optimized by differential evolution algorithm to drive down the side-lobes. Both the effect of platform on radiation pattern of conformal array and the mutual coupling between the elements are taken into account by calculating the antenna array and platform simultaneously using the method of moment. Application of adaptive integral method reduces the storage and computation time needed by the method of moments.
9555781
Sparse Antenna Array Optimization With the Cross-Entropy Method
The interest in sparse antenna arrays is growing, mainly due to cost concerns, array size limitations, etc. Formally, it can be shown that their design can be expressed as a constrained multidimensional nonlinear optimization problem. Generally, through lack of convex property, such a multiextrema problem is very tricky to solve by usual deterministic optimization methods. In this article, a recent stochastic approach, called Cross-Entropy method, is applied to the continuous constrained design problem. The method is able to construct a random sequence of solutions which converges probabilistically to the optimal or the near-optimal solution. Roughly speaking, it performs adaptive changes to probability density functions according to the Kullback-Leibler cross-entropy. The approach efficiency is illustrated in the design of a sparse antenna array with various requirements.
13652874
Energy efficiency of small cell backhaul networks based on Gauss-Markov mobile models
To satisfy the recent growth of mobile data usage, small cells are recommended to deploy into conventional cellular networks. However, the massive backhaul traffic is a troublesome problem for small cell networks, especial in wireless backhaul transmission links. In this study, backhaul traffic models are first presented considering the Gauss–Markov mobile models of mobile stations in small cell networks. Furthermore, an energy efficiency model of small cell backhaul networks with Gauss–Markov mobile models has been proposed. Numerical results indicate that the energy efficiency of small cell backhaul networks can be optimised by trade-off the number and radius of small cells in cellular networks.
9745860
Spatial Spectrum and Energy Efficiency of Random Cellular Networks
It is a great challenge to evaluate the network performance of cellular mobile communication systems. In this paper, we propose new spatial spectrum and energy efficiency models for Poisson-Voronoi tessellation (PVT) random cellular networks. To evaluate the user access to the network, a Markov chain based wireless channel access model is first proposed for PVT random cellular networks. On that basis, the outage probability and blocking probability of PVT random cellular networks are derived, which can be computed numerically. Furthermore, taking into account the call arrival rate, the path loss exponent and the base station (BS) density in random cellular networks, spatial spectrum and energy efficiency models are proposed and analyzed for PVT random cellular networks. Numerical simulations are conducted to evaluate the network spectrum and energy efficiency in PVT random cellular networks.
1343383
Massive MIMO in the UL/DL of Cellular Networks: How Many Antennas Do We Need?
We consider the uplink (UL) and downlink (DL) of non-cooperative multi-cellular time-division duplexing (TDD) systems, assuming that the number N of antennas per base station (BS) and the number K of user terminals (UTs) per cell are large. Our system model accounts for channel estimation, pilot contamination, and an arbitrary path loss and antenna correlation for each link. We derive approximations of achievable rates with several linear precoders and detectors which are proven to be asymptotically tight, but accurate for realistic system dimensions, as shown by simulations. It is known from previous work assuming uncorrelated channels, that as N→∞ while K is fixed, the system performance is limited by pilot contamination, the simplest precoders/detectors, i.e., eigenbeamforming (BF) and matched filter (MF), are optimal, and the transmit power can be made arbitrarily small. We analyze to which extent these conclusions hold in the more realistic setting where N is not extremely large compared to K. In particular, we derive how many antennas per UT are needed to achieve η% of the ultimate performance limit with infinitely many antennas and how many more antennas are needed with MF and BF to achieve the performance of minimum mean-square error (MMSE) detection and regularized zero-forcing (RZF), respectively.