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54
Degrees of freedom region of the MIMO . . .
, 2008
"... We provide achievability as well as converse results for the degrees of freedom region of a multipleinput multipleoutput (MIMO) X channel, i.e., a system with two transmitters, two receivers, each equipped with multiple antennas, where independent messages need to be conveyed over fixed channels fr ..."
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Cited by 91 (19 self)
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We provide achievability as well as converse results for the degrees of freedom region of a multipleinput multipleoutput (MIMO) X channel, i.e., a system with two transmitters, two receivers, each equipped with multiple antennas, where independent messages need to be conveyed over fixed channels from each transmitter to each receiver. The inner and outer bounds on the degrees of freedom region are tight whenever integer degrees of freedom are optimal for each message. With M =1antennas at each node, we find that the total (sum rate) degrees of freedom are bounded above and below as 1? 4 X.IfM>1 and channel
Multiantenna capacity of sparse multipath channels
 IEEE TRANS. INFORM. THEORY
, 2006
"... Existing results on multiinput multioutput (MIMO) channel capacity implicitly assume a rich scattering environment in which the channel power scales quadratically with the number of antennas, resulting in linear capacity scaling with the number of antennas. While this assumption may be justified ..."
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Cited by 23 (6 self)
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Existing results on multiinput multioutput (MIMO) channel capacity implicitly assume a rich scattering environment in which the channel power scales quadratically with the number of antennas, resulting in linear capacity scaling with the number of antennas. While this assumption may be justified in systems with few antennas, it leads to violation of fundamental power conservation principles in the limit of large number of antennas. Furthermore, recent measurement results have shown that physical MIMO channels exhibit a sparse multipath structure, even for relatively few antenna dimensions. Motivated by these observations, we propose a framework for modeling sparse channels and study the coherent capacity of sparse MIMO channels from two perspectives: 1) capacity scaling with the number of antennas, and 2) capacity as a function of transmit SNR for a fixed number of antennas. The statistically independent degrees of freedom (DoF) in sparse channels are less than the number of signalspace dimensions and, as a result, sparse channels afford a fundamental new degree of freedom over which channel capacity can be optimized: the distribution of the DoF’s in the available signalspace dimensions. Our investigation is based on a family of sparse channel configurations whose capacity admits a simple and intuitive closedform approximation and reveals a new tradeoff between the multiplexing gain and the received SNR. We identify an ideal channel
of matching network on bandwidth of compact antenna arrays
 IEEE Trans. Antennas Propagat
, 2006
"... We analyze the impact of the matching network on compact multipleinput multipleoutput systems. Existing studies have found that the matching network has a significant influence on the performance of multiple antenna systems when the antennas are in close proximity. However, none has examined the w ..."
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Cited by 20 (4 self)
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We analyze the impact of the matching network on compact multipleinput multipleoutput systems. Existing studies have found that the matching network has a significant influence on the performance of multiple antenna systems when the antennas are in close proximity. However, none has examined the wideband case. In this paper, we investigate the wideband performance of four different matching networks for multiple dipole antennas. The performance of the matching networks is given in terms of the bandwidths of correlation and matching efficiency, which are extensions of the singleantenna concept of bandwidth to multiple antenna systems. We also investigate the impact of the propagation conditions on the matching and bandwidth. For a uniform twodimensional (2D) angular power spectrum, we find that while individualport matching can achieve in excess of 3 % fractional correlation bandwidth for envelope correlation of 0.5 at an antenna separation of 0.01lambda, multiport matching is required for efficiency bandwidth to exist for a return loss of6 dB. Moreover, even with multiport matching, both correlation and efficiency bandwidths decrease drastically at small antenna separations. At 0.01lambda, the correlation and efficiency bandwidths are 0.4 % and 0.2%, respectively. Similar evaluations were performed for measured outdoortoindoor channels with moderate to small 2D angular spreads. We find that the efficiency advantage of multiport matching over individualport matching diminishes with decreasing angular spread IEEE Transactions on Antennas and propagation
On diversity and multiplexing gain of multiple antennas systems with transmitter channel information
 in Proc. Annu. Allerton Conf. Communication, Control, Computing
, 2004
"... We quantify the multiplexingdiversity tradeoff of a multipleinput multipleoutput (MIMO) system, when the channel state information (CSI) is known perfectly at the receiver and partially at the transmitter. The partial knowledge of CSI at the transmitter consists of the quantized value of one of t ..."
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Cited by 18 (2 self)
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We quantify the multiplexingdiversity tradeoff of a multipleinput multipleoutput (MIMO) system, when the channel state information (CSI) is known perfectly at the receiver and partially at the transmitter. The partial knowledge of CSI at the transmitter consists of the quantized value of one of the eigenvalues and perfect knowledge of eigenvectors of the channel matrix. The key result is that while multiplexing gain cannot be increased beyond minimum number of transmit and receive antennas, diversity order for each multiplexing gain can be substantially increased by using only a few bits of feedback at the transmitter. For example, with 1 bit of feedback in a 2 × 3 system, for multiplexing gains of 0, 1, and 2, diversity gains of 42, 6, and 2 can be achieved, respectively. Thus, while the tradeoff between diversity advantage and multiplexing gain is still present, its behavior is significantly changed by channel knowledge at the transmitter. The major reason for this different tradeoff can be attributed to addition of longterm power control, which allows the transmitter to switch between modes for reducing outage and increasing throughput based on signal to noise ratio along different eigenvalues. 1
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.
MIMO diversity in the presence of double scattering
 IEEE Trans. Inform. Theory
"... Abstract—The potential benefits of multipleantenna systems may be limited by two types of channel degradations—rank deficiency and spatial fading correlation of the channel. In this paper, we assess the effects of these degradations on the diversity performance of multipleinput multipleoutput (MI ..."
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Cited by 15 (4 self)
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Abstract—The potential benefits of multipleantenna systems may be limited by two types of channel degradations—rank deficiency and spatial fading correlation of the channel. In this paper, we assess the effects of these degradations on the diversity performance of multipleinput multipleoutput (MIMO) systems, with an emphasis on orthogonal space–time block codes (OSTBC), in terms of the symbol error probability (SEP), the effective fading figure (EFF), and the capacity at low signaltonoise ratio (SNR). In particular, we consider a general family of MIMO channels known as doublescattering channels—i.e., Rayleigh product MIMO channels—which encompasses a variety of propagation environments from independent and identically distributed (i.i.d.) Rayleigh to degenerate keyhole or pinhole cases by embracing both rankdeficient and spatial correlation effects. It is shown that a MIMO system with transmit and receive antennas achieves the diversity of order
Indoor millimeter wave mimo: Feasibility and performance
 Wireless Communications, IEEE Transactions on
, 2011
"... Abstract—In this paper, we investigate spatial multiplexing at millimeter (mm) wave carrier frequencies for shortrange indoor applications by quantifying fundamental limits in lineofsight (LOS) environments and then investigating performance in the presence of multipath and LOS blockage. Our cont ..."
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Cited by 11 (2 self)
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Abstract—In this paper, we investigate spatial multiplexing at millimeter (mm) wave carrier frequencies for shortrange indoor applications by quantifying fundamental limits in lineofsight (LOS) environments and then investigating performance in the presence of multipath and LOS blockage. Our contributions are summarized as follows. For linear arrays with constrained form factor, an asymptotic analysis based on the properties of prolate spheroidal wave functions shows that a sparse array producing a spatially uncorrelated channel matrix effectively provides the maximum number of spatial degrees of freedom in a LOS environment, although substantial beamforming gains can be obtained by using denser arrays. This motivates our proposed mmwave MIMO architecture, which utilizes arrays of subarrays to provide both directivity and spatial multiplexing gains. System performance is evaluated in a simulated indoor environment using a raytracing model that incorporates multipath effects and potential LOS blockage. Eigenmode transmission with waterfilling power allocation serves as a performance benchmark, and is compared to the simpler scheme of beamsteering transmission with MMSE reception and a fixed signal constellation. Our numerical results provide insight into the spatial variations of attainable capacity within a room, and the combinations of beamsteering and spatial multiplexing used in different scenarios. Index Terms—Millimeter wave communication, MIMO, channel capacity, antenna arrays. I.
Impact of scattering on the capacity, diversity and propagation range of multiple antenna channels
 IEEE Trans. on Information Theory
, 2004
"... Abstract — The impact of scattering condition and array configuration on performances are inseparable in early analyses of multipleantenna systems. An arrayindependent scattering model is introduced where three basic scattering mechanisms are modeled. Performance results become more intrinsic prop ..."
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Cited by 9 (1 self)
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Abstract — The impact of scattering condition and array configuration on performances are inseparable in early analyses of multipleantenna systems. An arrayindependent scattering model is introduced where three basic scattering mechanisms are modeled. Performance results become more intrinsic property of the scattering channel itself. For linear arrays of length L in an environment of total angle spread Ω, the ergodic capacity is shown to increase linearly with LΩ  for large arrays. When antenna arrays reduce to practical sizes, the capacity scaling depends on the SNR as well. This implies that the number of antennas used should also depend on the SNR. In terms of outage capacity, the tradeoff between spatial multiplexing gain and diversity gain is shown to be very sensitive to the underlying scattering mechanisms. Finally, as Ω  varies with the propagation range, the tradeoff among multiplexing gain, diversity gain, and propagation range is studied. Index Terms — Multiple antennas, multipleinput multipleoutput (MIMO) systems, physical channel modeling, antenna
Why Does the Kronecker Model Result in Misleading Capacity Estimates?
, 808
"... Many recent works that study the performance of multiinput multioutput (MIMO) systems in practice assume a Kronecker model where the variances of the channel entries, upon decomposition on to the transmit and the receive eigenbases, admit a separable form. Measurement campaigns, however, show tha ..."
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Cited by 6 (4 self)
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Many recent works that study the performance of multiinput multioutput (MIMO) systems in practice assume a Kronecker model where the variances of the channel entries, upon decomposition on to the transmit and the receive eigenbases, admit a separable form. Measurement campaigns, however, show that the Kronecker model results in poor estimates for capacity. Motivated by these observations, a channel model that does not impose a separable structure has been recently proposed and shown to fit the capacity of measured channels better. In this work, we show that this recently proposed modeling framework can be viewed as a natural consequence of channel decomposition on to its canonical coordinates, the transmit and/or the receive eigenbases. Using tools from random matrix theory, we then establish the theoretical basis behind the Kronecker mismatch at the low and the highSNR extremes: 1) Sparsity of the dominant statistical degrees of freedom (DoF) in the true channel at the lowSNR extreme, and 2) Nonregularity of the sparsity structure (disparities in the distribution of the DoF across the rows and the columns) at the highSNR extreme. Index Terms Correlation, fading channels, information rates, MIMO systems, multiplexing, random matrix theory, sparse systems. I.
Inverse source problem in an oblate spheroidal geometry
 IEEE Trans. Antennas Propagat
, 2006
"... The canonical inverse source problem of reconstructing an unknown source whose region of support is describable as a spheroidal (oblate or prolate) volume from knowledge of the farfield radiation pattern it generates is formulated and solved within the framework of the inhomogeneous scalar Helmholt ..."
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Cited by 6 (3 self)
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The canonical inverse source problem of reconstructing an unknown source whose region of support is describable as a spheroidal (oblate or prolate) volume from knowledge of the farfield radiation pattern it generates is formulated and solved within the framework of the inhomogeneous scalar Helmholtz equation via a linear inversion framework in Hilbert spaces. Particular attention is paid to the analysis and computer illustration of flat, aperturelike sources whose support is approximated by an oblate spheroidal volume. Key words: Inverse source problem, minimum energy source, nonradiating source, spheroidal wave. 1 1