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109
Energy and spectral efficiency of very large multiuser MIMO systems
 IEEE TRANS. COMMUN
, 2013
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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.
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.
Pilot beam pattern design for channel estimation in massive MIMO systems
 IEEE J. Sel. Topics Signal Process
, 2014
"... Abstract—In this paper, the problem of pilot beam pattern design for channel estimation in massive multipleinput multipleoutput systems with a large number of transmit antennas at the base station is considered, and a new algorithm for pilot beam pattern design for optimal channel estimation is p ..."
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Cited by 11 (8 self)
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Abstract—In this paper, the problem of pilot beam pattern design for channel estimation in massive multipleinput multipleoutput systems with a large number of transmit antennas at the base station is considered, and a new algorithm for pilot beam pattern design for optimal channel estimation is proposed under the assumption that the channel is a stationary GaussMarkov random process. The proposed algorithm designs the pilot beam pattern sequentially by exploiting the properties of Kalman filtering and the associated prediction error covariance matrices and also the channel statistics such as spatial and temporal channel correlation. The resulting design generates a sequentiallyoptimal sequence of pilot beam patterns with low complexity for a given set of system parameters. Numerical results show the effectiveness of the proposed algorithm. Index Terms—Channel estimation, massive MIMO systems, spatiotemporal correlation, training signal design. I.
Spatial Modulation for Generalized MIMO: Challenges, Opportunities and Implementation
, 2013
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Linear precoding based on polynomial expansion: Reducing complexity . . .
 IEEE J. SEL. TOPICS SIGNAL PROCESS
, 2014
"... Massive multipleinput multipleoutput (MIMO) techniques have the potential to bring tremendous improvements in spectral efficiency to future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal non ..."
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Cited by 10 (5 self)
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Massive multipleinput multipleoutput (MIMO) techniques have the potential to bring tremendous improvements in spectral efficiency to future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal nonlinear precoding are solved moreorless automatically by enlarging system dimensions. However, the computational precoding complexity grows with the system dimensions. For example, the closetooptimal and relatively “antennaefficient ” regularized zeroforcing (RZF) precoding is very complicated to implement in practice, since it requires fast inversions of large matrices in every coherence period. Motivated by the high performance of RZF, we propose to replace the matrix inversion and multiplication by a truncated polynomial expansion (TPE), thereby obtaining the new TPE precoding scheme which is more suitable for realtime hardware implementation and significantly reduces the delay to the first transmitted symbol. The degree of the matrix polynomial can be adapted to the available hardware resources and enables smooth transition between simple maximum ratio transmission and more advanced RZF. By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signaltointerferenceandnoise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closedform expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed peruser rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signaltonoise ratio.
Uplink performance of timereversal MRC in massive MIMO systems subject to phase noise,”
 IEEE Trans. Wirel. Commun.,
, 2015
"... AbstractMultiuser multipleinput multipleoutput (MUMIMO) cellular systems with an excess of base station (BS) antennas (Massive MIMO) offer unprecedented multiplexing gains and radiated energy efficiency. Oscillator phase noise is introduced in the transmitter and receiver radio frequency chain ..."
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Cited by 8 (0 self)
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AbstractMultiuser multipleinput multipleoutput (MUMIMO) cellular systems with an excess of base station (BS) antennas (Massive MIMO) offer unprecedented multiplexing gains and radiated energy efficiency. Oscillator phase noise is introduced in the transmitter and receiver radio frequency chains and severely degrades the performance of communication systems. We study the effect of oscillator phase noise in frequencyselective Massive MIMO systems with imperfect channel state information (CSI). In particular, we consider two distinct operation modes, namely when the phase noise processes at the M BS antennas are identical (synchronous operation) and when they are independent (nonsynchronous operation). We analyze a linear and lowcomplexity timereversal maximumratio combining (TRMRC) reception strategy. For both operation modes we derive a lower bound on the sumcapacity and we compare their performance. Based on the derived achievable sumrates, we show that with the proposed receive processing an O( √ M ) array gain is achievable. Due to the phase noise drift the estimated effective channel becomes progressively outdated. Therefore, phase noise effectively limits the length of the interval used for data transmission and the number of scheduled users. The derived achievable rates provide insights into the optimum choice of the data interval length and the number of scheduled users. Index TermsReceiver algorithns, MUMIMO, phase noise.