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## Capacity scaling and spectral efficiency in wide-band correlated MIMO channels (2003)

Venue: | IEEE Trans. Inform. Theory |

Citations: | 36 - 9 self |

### Citations

7717 |
Matrix Analysis
- Horn, Johnson
- 1990
(Show Context)
Citation Context ...ecomposition of is given by (113) where is a unitary matrix and is a diagonal matrix with nonnegative diagonal entries. Denoting , one has (114) where the last step follows from Hadamard’s inequality =-=[30]-=- and is the th diagonal entry in . Then it follows from Jensen’s inequality that (115) where . Then is a scaled doubly stochastic matrix with scale by Lemma 1. The general upper bound then follows fro... |

2919 | Capacity of multi-antenna gaussian channels
- Telatar
- 1999
(Show Context)
Citation Context ...d by B. Hassibi, Associate Editor for Communications. Digital Object Identifier 10.1109/TIT.2003.817446 narrow-band multiple-input multiple-output (MIMO) systems with the number of antennas (see [1], =-=[2]-=-). However, these studies are based on an idealized channel model, representing a rich scattering environment, that assumes independent and identically distributed (i.i.d.) Gaussian entries for the ch... |

2425 | On limits of wireless communications in a fading environment when using multiple antennas
- Gans
- 1998
(Show Context)
Citation Context ...icated by B. Hassibi, Associate Editor for Communications. Digital Object Identifier 10.1109/TIT.2003.817446 narrow-band multiple-input multiple-output (MIMO) systems with the number of antennas (see =-=[1]-=-, [2]). However, these studies are based on an idealized channel model, representing a rich scattering environment, that assumes independent and identically distributed (i.i.d.) Gaussian entries for t... |

1434 |
Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas
- Foschini
- 1996
(Show Context)
Citation Context ...s (119) Note that the effective two-dimensional MIMO channel matrix is a lower triangular matrix with entries in the main diagonal being complex Gaussian distributed. Similar to BLAST-type processing =-=[32]-=-, [33], successive decoding and interference cancellation can be used to construct two parallel Rayleigh-fading subchannels. More specifically, the first subchannel corresponding to the first received... |

1330 | Probability: theory and examples
- Durrett
- 1996
(Show Context)
Citation Context ...mma 4, channel capacity is lower-bounded by (62) where is a unit variance chi-square random variable with two degrees of freedom. Note pointwise Since by and , the dominated convergence theorem (DCT) =-=[21]-=- implies that (63) Therefore, (64) which completes the proof. 2) Low-Power Regime: We write to emphasize capacity as a function of transmit power . Theorem 2—Capacity Scaling: For fixed and , the capa... |

585 |
Real Analysis: Modern Techniques and Their Applications, 2nd edition
- Folland
- 1999
(Show Context)
Citation Context ...tween ESD and distribution of eigenvalues, which sets a rigorous ground for our channel capacity investigation. Theorem 3: Let be as in (69). Assume the set of nonnegative functions is equicontinuous =-=[23]-=-, that is, if for every , there is a neighborhood of such that for all and all . Suppose that converges to pointwise and that the ESDs converge pointwise as to a deterministic almost surely, written a... |

550 | Fading correlation and its effect on the capacity of multielement antenna systems - Shiu, Foschini, et al. - 2000 |

494 | Capacity of a mobile multipleantenna communication link in Rayleigh flat fading - Marzetta, Hochwald - 1999 |

453 | Spectral analysis of large dimensional random matrices
- Bai, Silverstein
- 2009
(Show Context)
Citation Context ... Random Matrices: The essential mathematical tool we will be using in studying the infinite connectivity case is the so-called spectral analysis of random matrices. Interested readers are referred to =-=[22]-=- for an excellent review on this subject. In the following, we make a brief introduction and clarify some common misconceptions in applying the random matrix theory. Definition 4: Let be an Hermitian ... |

426 | Fading channels: information-theoretic and communications aspects
- Biglieri, Proakis, et al.
- 1998
(Show Context)
Citation Context ...in increasing beyond the number of paths. In the wide-band case, we show that frequency selectivity does not affect ergodic capacity, which is consistent with known results in the single-antenna case =-=[15]-=-. In fact, wide-band capacity is solely governed by spatial channel characteristics via appropriate scaling with . The most conspicuous effect of increasing bandwidth is that it tightens the capacity ... |

393 | Spectral efficiency in the wideband regime
- Verdú
- 2002
(Show Context)
Citation Context ...ral efficiency of wide-band MIMO channels and provide explicit characterizations of the minimum energy per bit (required for reliable communication) and the wide-band slope recently proposed by Verdú =-=[16]-=-. The rest of this paper is organized as follows. In the next section, we present a general physical model for wide-band MIMO channels, review the virtual representation and its relation to the physic... |

277 |
Nonlinear Programming
- Mangasarian
- 1969
(Show Context)
Citation Context ...iven by (117) Setting partial derivatives to zero we get (118) Observe is a solution to (118). It is also easy to check that this solution together with associated satisfies the Kuhn–Tucker condition =-=[31]-=-, and thus achieves the maximum which turns out to be . APPENDIX II PROOF OF LEMMA 4 Proof: We illustrate the idea by an example shown in Fig. 11 where and . If the information is only transmitted at ... |

261 | Capacity scaling of MIMO wireless systems under correlated fading
- Chuah, Tse, et al.
- 2002
(Show Context)
Citation Context ...f correlated channels, analogous to the role of i.i.d. channel matrix in the idealized model. To our knowledge, the most recent work addressing the issue of capacity scaling in correlated channels is =-=[13]-=-. The channel model used in [13] is a generalization of the i.i.d. model and still predicts linear capacity growth with the number of antennas, albeit with a smaller slope compared to i.i.d. channels.... |

234 |
Space-time processing for wireless communications,”
- Paulraj, Papadias
- 1997
(Show Context)
Citation Context ... models that describe the channel via signal propagation over multiple paths, each path associated with an angle of departure (AoD), an angle of arrival (AoA), a delay and a path gain (see, e.g., [7]–=-=[9]-=-, [4], [10]). While quite accurate, such models depend on physical AoAs, AoDs, and delays in a nonlinear fashion making it rather difficult to incorporate them in system design or analytical calculati... |

201 | Space-time transmit precoding with imperfect feedback,” - Visotsky, Madhow - 2001 |

175 | On the capacity of OFDMbased spatial multiplexing systems
- Bolckei, Gesbert, et al.
- 2002
(Show Context)
Citation Context ...and MIMO channels. Thus, whether we have a small or large delay spread does not affect the ergodic capacity, just as in the single-antenna case [15]. Note that some recent results suggested otherwise =-=[25]-=-. However, a correct interpretation of the results in [25] is consistent with Theorem 6.8 Recent experimental measurements support the conclusions of Theorem 6 as well. Remark 1: Note that (81) is ide... |

156 | Deconstructing multi-antenna fading channels,”
- Sayeed
- 2002
(Show Context)
Citation Context ...ractically feasible antenna spacings. Several experimental and analytical studies have shown that the capacity of realistic MIMO channels can be significantly less than that of i.i.d. models (see [3]–=-=[6]-=-). Idealized statistical models, such as those used in [1], [2], represent one extreme in existing modeling approaches. On the other extreme are detailed physical (ray-tracing) models that describe th... |

138 |
On the Asymptotic Eigenvalue Distribution of Toeplitz Matrices,”
- Gray
- 1972
(Show Context)
Citation Context ...ess a Toeplitz structure consistent with the stationary spatial statistics for ULAs identified in Section II-D. It is well known that Toeplitz matrices are diagonalized by DFT matrices asymptotically =-=[26]-=-. Thus, for large and (110) where and are diagonal matrices consisting of the nonnegative eigenvalues of and . Substituting (110) in (109) we get (111) where is also an i.i.d. matrix since and are uni... |

89 |
Unified channel model for mobile radio systems with smart antennas,”
- Fuhl, Molisch, et al.
- 1998
(Show Context)
Citation Context ...at describe the channel via signal propagation over multiple paths, each path associated with an angle of departure (AoD), an angle of arrival (AoA), a delay and a path gain (see, e.g., [7]–[9], [4], =-=[10]-=-). While quite accurate, such models depend on physical AoAs, AoDs, and delays in a nonlinear fashion making it rather difficult to incorporate them in system design or analytical calculations. Indeed... |

83 | Channel capacity and beamforming for multiple transmit and receive antennas with covariance feedback,” in
- Jafar, Vishwanath, et al.
- 2001
(Show Context)
Citation Context ...ed otherwise. An obstacle in analyzing capacity of realistic MIMO channels is the optimal input distribution in (56). Except for diagonal channels , i.i.d. channels , and a few other correlated cases =-=[18]-=-–[20], the optimal is unknown, which limits the strength of capacity results for these channels. The 2512 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 49, NO. 10, OCTOBER 2003 doubly stochastic struc... |

75 |
Capacity of MIMO systems based on measured wireless channels,”
- Molisch, Steinbauer, et al.
- 2002
(Show Context)
Citation Context ...ls that describe the channel via signal propagation over multiple paths, each path associated with an angle of departure (AoD), an angle of arrival (AoA), a delay and a path gain (see, e.g., [7]–[9], =-=[4]-=-, [10]). While quite accurate, such models depend on physical AoAs, AoDs, and delays in a nonlinear fashion making it rather difficult to incorporate them in system design or analytical calculations. ... |

68 | WiSE design of indoor wireless systems: practical computation and optimization, - Fortune, Gay, et al. - 1995 |

67 |
Transmit signal design of optimal estimation of correlated MIMO channels
- Kotecha, Sayeed
- 2004
(Show Context)
Citation Context ...pealing interpretation of physical scattering afforded by the virtual representation can be fruitfully exploited in many other aspects, including space–time code design [27], [28], channel estimation =-=[29]-=-, and channel simulation. APPENDIX I ALTERNATIVE PROOF OF LEMMA 2 Proof: Starting with arbitrary , the eigen-decomposition of is given by (113) where is a unitary matrix and is a diagonal matrix with ... |

62 |
Capacity of the discrete-time Gaussian channel with intersymbol interference
- Hirt, Massey
- 1988
(Show Context)
Citation Context ...maximization is over a family of input Gaussian covariance matrices that satisfy the total power constraint (80) The above definition of wide-band ergodic capacity is consistent with that obtained in =-=[24]-=- for single-antenna frequency selective additive white Gaussian noise (AWGN) channels. Since the integrand in (79) in nonnegative, finding the optimal family is equivalent to finding the optimal at ea... |

40 |
On a moment theorem for complex Gaussian processes,”
- Reed
- 1961
(Show Context)
Citation Context ...since entries of are uncorrelated. Thus, if , one has Moreover, since the entries of , and, thus, , are from a proper complex Gaussian joint distribution, the Gaussian moment-factoring theorem (GMFT) =-=[34]-=- implies that Therefore, (138) where Lemma 1 is used in the last step. Next, consider the terms like for . The coefficient due to the first row in is (139) Use GMFT to break the sum into two parts as ... |

36 | Spectral analysis of networks with random topologies.
- Grenander, Silverstein
- 1977
(Show Context)
Citation Context ...nd the total transmit power. The analysis in the large antenna regime is greatly facilitated by a fortuitous connection between the -connected model and some earlier work of Grenander and Silverstein =-=[14]-=- on the limiting empirical eigenvalue distribution of a class of random matrices. We show that for large , exhibits linear growth with if grows linearly with as well. This, in turn, implies that linea... |

23 | Essential degrees of freedom in space-time fading channels,” in
- Sayeed, Veeravalli
- 2002
(Show Context)
Citation Context ...channel is unknown at the transmitter but perfectly known at the receiver. The workhorse of our analysis is a recently introduced virtual representation of narrow-band [6] and wide-band MIMO channels =-=[11]-=-, [12] that provides an intuitive and tractable characterization of realistic physical models and yields useful insights into the effects of scattering characteristics on channel capacity. The virtual... |

22 | Spatial multiplexing in correlated fading via the virtual channel representation
- Hong, Liu, et al.
- 2003
(Show Context)
Citation Context ...t the simple and intuitively appealing interpretation of physical scattering afforded by the virtual representation can be fruitfully exploited in many other aspects, including space–time code design =-=[27]-=-, [28], channel estimation [29], and channel simulation. APPENDIX I ALTERNATIVE PROOF OF LEMMA 2 Proof: Starting with arbitrary , the eigen-decomposition of is given by (113) where is a unitary matrix... |

21 | Wireless indoor channel modeling: statistical agreement of ray tracing simulations and channel sounding measurements,” in
- German, Spencer, et al.
- 2001
(Show Context)
Citation Context ...th practically feasible antenna spacings. Several experimental and analytical studies have shown that the capacity of realistic MIMO channels can be significantly less than that of i.i.d. models (see =-=[3]-=-–[6]). Idealized statistical models, such as those used in [1], [2], represent one extreme in existing modeling approaches. On the other extreme are detailed physical (ray-tracing) models that describ... |

16 |
Initial estimation of communication efficiency of indoor wireless channel
- Foschini, Valenzuela
- 1997
(Show Context)
Citation Context ... incorporate them in system design or analytical calculations. Indeed, most capacity studies based on physical models have relied on numerical simulation for capacity assessment (see, e.g., [4], [7], =-=[8]-=-). The goal of this paper is to investigate capacity scaling in realistic correlated MIMO channels. We consider both narrow-band and wide-band channels and explore scaling behavior of ergodic capacity... |

10 | A virtual representation for time- and frequencyselective correlated MIMO channels,” - Sayeed - 2003 |

7 | On the capacity of correlated MIMO channels - Kotecha, Sayeed |

6 | Sayeed, “Space-time D-block codes via the virtual MIMO channel representation
- Liu, M
(Show Context)
Citation Context ...simple and intuitively appealing interpretation of physical scattering afforded by the virtual representation can be fruitfully exploited in many other aspects, including space–time code design [27], =-=[28]-=-, channel estimation [29], and channel simulation. APPENDIX I ALTERNATIVE PROOF OF LEMMA 2 Proof: Starting with arbitrary , the eigen-decomposition of is given by (113) where is a unitary matrix and i... |

4 |
virtual representation for time- and frequency-selective correlated mimo channels
- “A
- 2003
(Show Context)
Citation Context ...ly follows from (38) by substituting . Thus, the spatial statistics of are determined by the statistics of the narrow-band matrix (or, equivalently, ). The total channel power is distributed as [11], =-=[12]-=- (39) E. -Diagonal Virtual Model for Narrow-Band MIMO Channels We now motivate a simple model—the -diagonal virtual model—for correlated narrow-band MIMO channels that plays a key role in the scaling ... |

3 |
Improved layered space-time processing in multiple antenna systems
- Liu, Sayeed
- 2001
(Show Context)
Citation Context ...) Note that the effective two-dimensional MIMO channel matrix is a lower triangular matrix with entries in the main diagonal being complex Gaussian distributed. Similar to BLAST-type processing [32], =-=[33]-=-, successive decoding and interference cancellation can be used to construct two parallel Rayleigh-fading subchannels. More specifically, the first subchannel corresponding to the first received anten... |

1 | Sayeed, “Optimal estimation of correlated MIMO channels,” submitted to the - Kotecha, M - 2002 |

1 |
On the capacity of correlated MIMO channels,” Univ
- Kotecha, Sayeed
- 2002
(Show Context)
Citation Context ...herwise. An obstacle in analyzing capacity of realistic MIMO channels is the optimal input distribution in (56). Except for diagonal channels , i.i.d. channels , and a few other correlated cases [18]–=-=[20]-=-, the optimal is unknown, which limits the strength of capacity results for these channels. The 2512 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 49, NO. 10, OCTOBER 2003 doubly stochastic structure ... |