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Massive MIMO in the UL/DL of cellular networks: How many antennas do we need?
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2013
"... We consider the uplink (UL) and downlink (DL) of noncooperative multicellular timedivision 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 con ..."
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Cited by 109 (13 self)
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We consider the uplink (UL) and downlink (DL) of noncooperative multicellular timedivision 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 meansquare error (MMSE) detection and regularized zeroforcing (RZF), respectively.
Argos: Practical ManyAntenna Base Stations
"... Multiuser multipleinput multipleoutput theory predicts manyfold capacity gains by leveraging many antennas on wireless base stations to serve multiple clients simultaneously through multiuser beamforming (MUBF). However, realizing a base station with a large number antennas is nontrivial,andhasy ..."
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Cited by 47 (6 self)
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Multiuser multipleinput multipleoutput theory predicts manyfold capacity gains by leveraging many antennas on wireless base stations to serve multiple clients simultaneously through multiuser beamforming (MUBF). However, realizing a base station with a large number antennas is nontrivial,andhasyettobeachievedintherealworld. We present the design, realization, and evaluation of Argos, the first reported base station architecture that is capable of serving many terminals simultaneously through MUBF with a large number of antennas (M ≫ 10). Designed for extreme flexibility and scalability, Argos exploits hierarchical and modular design principles, properly partitions baseband processing, and holistically considers realtime requirements of MUBF. Argos employs a novel, completely distributed, beamforming technique, as well as an internal calibration procedure to enable implicit beamforming with channel estimation cost independent of the number of base station antennas. We report an Argos prototype with 64 antennas and capable of serving 15 clients simultaneously. We experimentally demonstrate that by scaling from 1 to 64 antennas the prototype can achieve up to 6.7 fold capacity gains while using a mere 1/64thofthetransmissionpower.
Performance of conjugate and zeroforcing beamforming in largescale antenna systems
 IEEE Journal on Selected Areas in Communications
, 2013
"... Abstract—LargeScale Antenna Systems (LSAS) is a form of multiuser MIMO technology in which unprecedented numbers of antennas serve a significantly smaller number of autonomous terminals. We compare the two most prominent linear precoders, conjugate beamforming and zeroforcing, with respect to net ..."
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Cited by 33 (1 self)
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Abstract—LargeScale Antenna Systems (LSAS) is a form of multiuser MIMO technology in which unprecedented numbers of antennas serve a significantly smaller number of autonomous terminals. We compare the two most prominent linear precoders, conjugate beamforming and zeroforcing, with respect to net spectralefficiency and radiated energyefficiency in a simplified singlecell scenario where propagation is governed by independent Rayleigh fading, and where channelstate information (CSI) acquisition and data transmission are both performed during a short coherence interval. An effectivenoise analysis of the precoded forward channel yields explicit lower bounds on net capacity which account for CSI acquisition overhead and errors as well as the suboptimality of the precoders. In turn the bounds generate tradeoff curves between radiated energyefficiency and net spectralefficiency. For high spectralefficiency and low energyefficiency zeroforcing outperforms conjugate beamforming, while at low spectralefficiency and high energyefficiency the opposite holds. Surprisingly, in an optimized system, the total LSAScritical computational burden of conjugate beamforming may be greater than that of zeroforcing. Conjugate beamforming may still be preferable to zeroforcing because of its greater robustness, and because conjugate beamforming lends itself to a decentralized architecture and decentralized signal processing. Index Terms—Largescale antenna system, capacity, energy efficiency, spectral efficiency, spatial multiplexing, beamforming, precoder, computational burden I.
Massive MIMO Systems with NonIdeal Hardware: Energy Efficiency, Estimation, and Capacity Limits
, 2014
"... The use of largescale 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 multipleinput multipleoutput (MIMO) show that the user channels dec ..."
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Cited by 29 (6 self)
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The use of largescale 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 multipleinput multipleoutput (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 singleantenna 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 largescale 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 energyefficient antenna elements.
Perantenna constant envelope precoding for large multiuser MIMO systems,” arXiv:1111.3752v1
, 2012
"... N.B.: When citing this work, cite the original article. ©2013 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to ..."
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Cited by 17 (5 self)
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N.B.: When citing this work, cite the original article. ©2013 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Downlink training techniques for FDD massive MIMO systems: openloop and closedloop training with memory
 IEEE Journal of Selected Topics in Signal Processing
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The Multicell Multiuser MIMO Uplink with Very Large Antenna Arrays and a FiniteDimensional Channel
, 2013
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Optimal Design of EnergyEfficient MultiUser MIMO Systems: Is Massive MIMO the Answer?
"... Assume that a multiuser multipleinput multipleoutput (MIMO) system is designed from scratch to uniformly cover a given area with maximal energy efficiency (EE). What are the optimal number of antennas, active users, and transmit power? The aim of this paper is to answer this fundamental question ..."
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Cited by 14 (6 self)
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Assume that a multiuser multipleinput multipleoutput (MIMO) system is designed from scratch to uniformly cover a given area with maximal energy efficiency (EE). What are the optimal number of antennas, active users, and transmit power? The aim of this paper is to answer this fundamental question. We consider jointly the uplink and downlink with different processing schemes at the base station and propose a new realistic power consumption model that reveals how the above parameters affect the EE. Closedform expressions for the EEoptimal value of each parameter, when the other two are fixed, are provided for zeroforcing (ZF) processing in singlecell scenarios. These expressions prove how the parameters interact. For example, in sharp contrast to common belief, the transmit power is found to increase (not to decrease) with the number of antennas. This implies that energyefficient systems can operate in high signaltonoise ratio regimes in which interferencesuppressing signal processing is mandatory. Numerical and analytical results show that the maximal EE is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve a relatively large number of users using ZF processing. The numerical results show the same behavior under imperfect channel state information and in symmetric multicell scenarios.
Designing multiuser MIMO for energy efficiency: When is massive MIMO the answer
 in Proc. IEEE Wireless Commun. and Networking Conf. (WCNC
, 2014
"... Abstract—Assume that a multiuser multipleinput multipleoutput (MIMO) communication system must be designed to cover a given area with maximal energy efficiency (bits/Joule). What are the optimal values for the number of antennas, active users, and transmit power? By using a new model that describ ..."
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Cited by 13 (7 self)
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Abstract—Assume that a multiuser multipleinput multipleoutput (MIMO) communication system must be designed to cover a given area with maximal energy efficiency (bits/Joule). What are the optimal values for the number of antennas, active users, and transmit power? By using a new model that describes how these three parameters affect the total energy efficiency of the system, this work provides closedform expressions for their optimal values and interactions. In sharp contrast to common belief, the transmit power is found to increase (not decrease) with the number of antennas. This implies that energy efficient systems can operate at high signaltonoise ratio (SNR) regimes in which the use of interferencesuppressing precoding schemes is essential. Numerical results show that the maximal energy efficiency is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve relatively many users using interferencesuppressing regularized zeroforcing precoding. I.