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116
Outdoor MIMO wireless channels: Models and performance prediction,”
 IEEE Trans. Commun.,
, 2002
"... AbstractWe present a new model for multipleinput multipleoutput (MIMO) outdoor wireless fading channels which is more general and realistic than the usual i.i.d. model. The proposed model allows to investigate the behavior of channel capacity as a function of parameters such as the local scatter ..."
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Cited by 206 (10 self)
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AbstractWe present a new model for multipleinput multipleoutput (MIMO) outdoor wireless fading channels which is more general and realistic than the usual i.i.d. model. The proposed model allows to investigate the behavior of channel capacity as a function of parameters such as the local scattering radius at the transmitter and the receiver, the distance between the transmit and receive arrays, and the antenna beamwidths and spacing. We show that capacity is driven by the spatial fading correlation and the condition number of the MIMO channel matrix through specific sets of propagation parameters. We use the new model to point out the existence of "pinhole" channels which exhibit low fading correlation between antennas but still have poor rank properties and hence low capacity. We suggest guidelines for predicting high rank (and hence high capacity) in MIMO channels. We also show that even at long ranges high channel rank can easily be obtained under mild scattering conditions. Finally, we validate our results by simulations using ray tracing techniques.
Performance analysis of the VBLAST algorithm: an analytical approach
 IEEE Transactions on Wireless Communications
, 2004
"... Abstract—An analytical approach to the performance analysis of the VBLAST algorithm is presented in this paper, which is based on the analytical model of the GrammSchmidt process. Closedform analytical expressions of the vector signal at ith processing step and its power are presented. A rigorou ..."
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Cited by 56 (17 self)
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Abstract—An analytical approach to the performance analysis of the VBLAST algorithm is presented in this paper, which is based on the analytical model of the GrammSchmidt process. Closedform analytical expressions of the vector signal at ith processing step and its power are presented. A rigorous proof that the diversity order at ith step (without optimal ordering) is (nm+i) is given. It is shown that the optimal ordering is based on the least correlation criterion and that the afterprocessing signal power is determined by the channel correlation matrices in a fashion similar to the channel capacity. Index Terms—MIMO, VBLAST, multiantenna system, fading 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.
A single coefficient spatial correlation model for multipleinput multipleoutput (mimo) radio channels
 in Proc. URSI XXVIIth General Assembly
, 2002
"... Spatial fading correlation is one of the impairments practical MultipleInput MultipleOutput (MIMO) wireless communication systems have to cope with. The designer of such systems should take into account that the system performance can substantially degrade when correlation is present. Therefore, w ..."
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Cited by 27 (1 self)
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Spatial fading correlation is one of the impairments practical MultipleInput MultipleOutput (MIMO) wireless communication systems have to cope with. The designer of such systems should take into account that the system performance can substantially degrade when correlation is present. Therefore, we introduce an easytouse single parameter MIMO spatial correlation model that nevertheless reflects the relevant characteristics of the reallife propagation phenomena appropriately. We demonstrate how an excellent match between the BER performance based on measurements and that based on the introduced model can be achieved, as well as its flexibility to model a wide range of propagation environments. 1
Capacity bounds and estimates for the finite scatterers MIMO wireless channel
 IEEE Journ. Sel. Areas in Commun
, 2003
"... Abstract—We consider the limits to the capacity of the multipleinput–multipleoutput wireless channel as modeled by the finite scatterers channel model, a generic model of the multipath channel which accounts for each individual multipath component. We assume a normalization that allows for the arr ..."
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Cited by 24 (1 self)
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Abstract—We consider the limits to the capacity of the multipleinput–multipleoutput wireless channel as modeled by the finite scatterers channel model, a generic model of the multipath channel which accounts for each individual multipath component. We assume a normalization that allows for the array gain due to multiple receive antenna elements and, hence, can obtain meaningful limits as the number of elements tends to infinity. We show that the capacity is upper bounded by the capacity of an identity channel of dimension equal to the number of scatterers. Because this bound is not very tight, we also determine an estimate of the capacity as the number of transmit/receive elements tends to infinity which is asymptotically accurate. Index Terms—Finite scatterers channel model, multipleinput– multipleoutput (MIMO) capacity. I.
On the condition number distribution of complex wishart matrices
, 2010
"... Abstract—This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multipleinput m ..."
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Cited by 20 (1 self)
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Abstract—This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multipleinput multipleoutput (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and noncentral Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closedform expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semicorrelated Rayleigh fading and Ricean fading. Index Terms—MIMO systems, complex Wishart matrices, condition number, joint eigenvalue distribution.
Optimal design of source and relay pilots for MIMO relay channel estimation
 IEEE Trans. Signal Process
, 2011
"... Abstract—In this paper, we consider a channel estimation scheme for a twohop nonregenerative MIMO relay system without the direct link between source and destination. This scheme has two phases. In the first phase, the source does not transmit while the relay transmits and the destination receives. ..."
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Cited by 20 (1 self)
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Abstract—In this paper, we consider a channel estimation scheme for a twohop nonregenerative MIMO relay system without the direct link between source and destination. This scheme has two phases. In the first phase, the source does not transmit while the relay transmits and the destination receives. In the second phase, the source transmits, the relay amplifies and forwards, and the destination receives. At the destination, the data received in the first phase are used to estimate the relaytodestination channel, and the data received in the second phase are used to estimate the sourcetorelay channel. The linear minimum meansquare error estimation (LMMSE) is used for channel estimation, which allows the use of prior knowledge of channel correlations. For phase 1, an algorithm is developed to compute the optimal source pilot matrix for use at the relay. For phase 2, an algorithm is developed to compute the optimal source pilot matrix for use at the source and the optimal relay pilot matrix for use at the relay. Index Terms—Convex optimization, MIMO wireless relays, nonconvex optimization, pilot waveform design, relay channel estimation. I.
A DiscreteTime Model for Triply Selective MIMO Rayleigh Fading Channels
"... Abstract—A statistical discretetime model is proposed for simulating wideband multipleinput multipleoutput (MIMO) fading channels which are triply selective due to angle spread, Doppler spread, and delay spread. The new discretetime MIMO channel model includes the combined effects of the transmi ..."
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Cited by 18 (13 self)
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Abstract—A statistical discretetime model is proposed for simulating wideband multipleinput multipleoutput (MIMO) fading channels which are triply selective due to angle spread, Doppler spread, and delay spread. The new discretetime MIMO channel model includes the combined effects of the transmit filter, physical MIMO multipath channel fading, and receive filter, and it has the same sampling period as that of the MIMO receiver. This leads to very efficient simulation of physical continuoustime MIMO channels. A new method is also presented to efficiently generate the MIMO channel stochastic coefficients. The statistical accuracy of the discretetime MIMO channel model is rigorously verified through theoretical analysis and extensive simulations in different conditions. The high computational efficiency of the discretetime MIMO channel model is illustrated by comparing it to that of the continuoustime MIMO channel model. The new model is further employed to evaluate the channel capacity of MIMO systems in a triply selective Rayleigh fading environment. The simulation results reveal some interesting effects of spatial correlations, multipaths, and number of antennas on the MIMO channel capacity. Index Terms—Discretetime channel model, multipleinput multipleoutput (MIMO) channel, multipleinput multipleoutput multipath channel capacity, Rayleigh fading, triply selective fading, widesense stationary uncorrelated scattering (WSSUS) multipath channel. I.
Spatial Degrees of Freedom of Large Distributed MIMO Systems and Wireless Ad hoc Networks
"... Abstract — We consider a large distributed MIMO system where wireless users with single transmit and receive antenna cooperate in clusters to form distributed transmit and receive antenna arrays. We characterize how the capacity of the distributed MIMO transmission scales with the number of cooperat ..."
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Cited by 17 (2 self)
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Abstract — We consider a large distributed MIMO system where wireless users with single transmit and receive antenna cooperate in clusters to form distributed transmit and receive antenna arrays. We characterize how the capacity of the distributed MIMO transmission scales with the number of cooperating users, the area of the clusters and the separation between them, in a lineofsight propagation environment. We use this result to answer the following question: can distributed MIMO provide significant capacity gain over traditional multihop in large adhoc networks with n sourcedestination pairs randomly distributed over an area A? Two diametrically opposite answers [24] and [26] have emerged in the current literature. We show that neither of these two results are universal and their validity depends on the relation between the number of users n and √ A/λ, which we identify as the spatial degrees of freedom in the network. λ is the carrier wavelength. When √ A/λ ≥ n, there are n degrees of freedom in the network and distributed MIMO with hierarchical cooperation can achieve a capacity scaling linearly in n as in [24], while capacity of multihop scales only as √ n. On the other hand, when √ A/λ ≤ √ n as in [26], there are only √ n degrees of freedom in the network and they can be readily achieved by multihop. Our results also reveal a third regime where √ n ≤ √ A/λ ≤ n. Here, the number of degrees of freedom are smaller than n but larger than what can be achieved by multihop. We construct scaling optimal architectures for this intermediate regime. I.