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## Capacity Limits of MIMO Channels (2003)

Venue: | IEEE J. Select. Areas Commun |

Citations: | 3 - 0 self |

### Citations

12164 |
Elements of Information Theory
- Cover, Thomas
- 1991
(Show Context)
Citation Context ...tant Channel: The capacity of any MAC can be written as the convex closure of the union of rate regions corresponding to every product input distribution satisfying the user-by-user power constraints =-=[18]-=-. For the Gaussian MIMO MAC, however, it has been shown that it is sufficient to consider only Gaussian inputs and that the convex hull operation is not needed [11], [86]. For any set of powers , the ... |

2858 | Capacity of multi-antenna Gaussian channels
- Telatar
- 1995
(Show Context)
Citation Context ...ed. However, another domain can be exploited to significantly increase channel capacity: the use of multiple transmit and receive antennas. Pioneering work by Winters [81], Foschini [20], and Telatar =-=[69]-=- ignited much interest in this area by predicting remarkable spectral efficiencies for wireless systems with multiple antennas when the channel exhibits rich scattering and its variations can be accur... |

2351 | On limits of wireless communication in a fading environment using multiple antennas
- Foschini, Gans
- 1998
(Show Context)
Citation Context ...s, the fading MIMO channel capacity assuming perfect channel knowledge at both transmitter and receiver is (5) Tr 2) Capacity With Perfect CSIR and CDIT: ZMSW Model: Seminal work by Foschini and Gans =-=[22]-=- and Telatar [69] addressed the case of perfect CSIR and a ZMSW channel distribution at the transmitter. Recall that in this case, the channel matrix is assumed to have i.i.d. complex Gaussian entries... |

1403 |
Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas
- Foschini
- 1996
(Show Context)
Citation Context ...d complexity limited. However, another domain can be exploited to significantly increase channel capacity: the use of multiple transmit and receive antennas. Pioneering work by Winters [81], Foschini =-=[20]-=-, and Telatar [69] ignited much interest in this area by predicting remarkable spectral efficiencies for wireless systems with multiple antennas when the channel exhibits rich scattering and its varia... |

1024 |
Writing on Dirty Paper
- Costa
- 1983
(Show Context)
Citation Context ...egion: An achievable region for the MIMO BC was first obtained for the case by Caire and Shamai [9] and later extended to the multiple-receive antenna case by Yu and Cioffi [83] using the idea of DPC =-=[17]-=-. The basic premise of DPC is as follows. If the transmitter (but not the receiver) has perfect, noncausal knowledge of additive Gaussian interference in the channel, then the capacity of the channel ... |

797 | R.Laroia, “Opportunistic Beamforming using Dumb Antennas
- Viswanath
- 2002
(Show Context)
Citation Context ...lly understood. Although in this paper we focus on the physical layer, smart schemes to handle CDIT can also be found at higher layers. An interesting example is the idea of opportunistic beamforming =-=[78]-=-. In the absence of CSIT, the transmitter randomly chooses the beamforming weights. With enough users in the system, it becomes very likely that these weights will be nearly optimal for one of the use... |

529 | Fading correlation and its effect on the capacity of multielement antenna systems
- Shiu, Foschini, et al.
- 2000
(Show Context)
Citation Context ...nments [26]. Antenna correlation varies drastically as a function of the scattering environment, the distance between transmitter and receiver, the antenna configurations, and the Doppler spread [1], =-=[65]-=-. As we shall see, the effect of channel correlation on capacity depends on what is known about the channel at the transmitter and receiver: correlation sometimes increases capacity and sometimes redu... |

499 | How much training is needed in multiple-antenna wireless links
- Hassibi, Hochwald
- 2000
(Show Context)
Citation Context ... no time for data transmission before the channel changes. So the key question to ask is how much training is needed in multiple-antenna wireless links. This question itself is the title of the paper =-=[29]-=- by Hassibi and Hochwald where they compute a lower bound on the capacity of a channel that is learned by training and maximize the bound as a function of the receive SNR, fading coherence time, and n... |

489 | Capacity of mobile multiple-antenna communication link in Rayleigh flat fading
- Hochwald, Marzetta
- 1999
(Show Context)
Citation Context ...tter) is of particular interest. In this section, we summarize some MIMO capacity results in this area. One of the first papers to address the MIMO capacity with CDIR and CDIT under the ZMSW model is =-=[53]-=- by Marzetta and Hochwald. They model the channel matrix components as i.i.d. complex Gaussian random variables that remain constant for a coherence interval of symbol periods after which they change ... |

407 | Spatio-temporal coding for wireless communication
- Raleigh, Cioffi
- 1998
(Show Context)
Citation Context ...ial is on memoryless channels (flat-fading), the results can also be extended to channels with memory (ISI) using well-known methods for incorporating the channel delay spread into the channel matrix =-=[59]-=-, as will be discussed in the next section. Many practical MIMO techniques have been developed to capitalize on the theoretical capacity gains predicted by Shannon theory. A major focus of such work i... |

390 | Spectral efficiency in the wideband regime
- Verdú
- 2002
(Show Context)
Citation Context ...IMO techniques described herein are applicable to any channel described by a matrix. Matrix channels describe not only multiantenna systems but also channels with crosstalk [85] and wideband channels =-=[72]-=-. While the focus of this tutorial is on memoryless channels (flat-fading), the results can also be extended to channels with memory (ISI) using well-known methods for incorporating the channel delay ... |

358 | From theory to practice: An overview of MIMO space-time coded wireless systems
- Gesbert, Shafi, et al.
- 2003
(Show Context)
Citation Context ...ng [3], space–time CDMA [14], [34], and space–time OFDM [50], [52], [82]. An overview of the recent advances in these areas and other practical techniques along with their performance can be found in =-=[25]-=-. The remainder of this paper is organized as follows. In Section II, we discuss the capacity of single-user MIMO systems under different assumptions about channel state and distribution information a... |

276 | Sum capacity of Gaussian vector broadcast channels
- Yu, Cioffi
- 2004
(Show Context)
Citation Context ...y is achievable using DPC. The sum-rate optimality of DPC was extended to the multiuser channel with by Viswanath and Tse [79] and to the more general case by Vishwanath et al. [74] and Yu and Cioffi =-=[84]-=-. It has also recently been conjectured that the DPC rate region is the actual capacity region of the multiple-antenna broadcast channel. Significant progress toward proving this conjecture is made in... |

256 | Capacity scaling in MIMO wireless systems under correlated fading
- Chuah, Tse, et al.
- 2002
(Show Context)
Citation Context ...itter knows the channel perfectly (perfect CSIT) or only knows its distribution (CDIT). The proportionality constant of this linear increase, called the rate of growth, has also been characterized in =-=[15]-=-, [31], [68], [69]. Chuah et al. [15] show that with perfect CSIR and CSIT, the rate of growth of capacity with is reduced by channel fading correlations at high SNR but is increased at low SNR. They ... |

222 |
On the capacity of radio communication systems with diversity in a rayleigh fading environment
- Winters
- 1987
(Show Context)
Citation Context ..., bandwidth, and complexity limited. However, another domain can be exploited to significantly increase channel capacity: the use of multiple transmit and receive antennas. Pioneering work by Winters =-=[81]-=-, Foschini [20], and Telatar [69] ignited much interest in this area by predicting remarkable spectral efficiencies for wireless systems with multiple antennas when the channel exhibits rich scatterin... |

204 | Wornell, “Efficient use of side information in multiple-antenna data transmission over fading channels
- Narula, Lopez, et al.
- 1998
(Show Context)
Citation Context ...antennas reduces the average sum capacity. (8) matrix. Key results on the capacity of such channels have been recently obtained by several authors including Madhow and Visotsky [76], Trott and Narula =-=[58]-=-, [57], Jafar and Goldsmith [42], [40], [38], Jorsweick and Boche [45], [46], and Simon and Moustakas [56], [66]. Mathematically the problem is defined by (6) and (7), with the distribution on determi... |

199 | Transmit beam-forming and power control for cellular wireless systems
- Rashid-Farrokhi, Liu, et al.
- 1998
(Show Context)
Citation Context ...DPC is a very powerful capacity-achieving scheme, but it appears quite difficult to implement in practice. Thus, non-DPC multiuser transmissions schemes for the downlink (such as downlink beamforming =-=[60]-=-) are also of practical relevance. IV. MULTICELL MIMO The MAC and the BC are information theoretic abstractions of the uplink and the downlink of a single cell in a cellular system. However, a cellula... |

196 | Space-time transmit precoding with imperfect feedback
- Visotsky, Madhow
- 2001
(Show Context)
Citation Context ...erm channel statistics (the feedback model of Fig. 1) is referred to by many names including mean and covariance feedback, imperfect feedback and partial CSI [38], [40], [42], [45], [46], [56], [66], =-=[76]-=-. • The feedback channel is assumed to be free from noise. This makes the CDIT a deterministic function of the CDIR and allows optimal codes to be constructed directly over the input alphabet [8]. • F... |

194 | R.L.: Systematic design of unitary space-time constellations
- Hochwald, Marzetta, et al.
- 1962
(Show Context)
Citation Context ...ins predicted by Shannon theory. A major focus of such work is space-time coding: recent work in this area is summarized in [21]. Other techniques for MIMO systems include space–time modulation [30], =-=[33]-=-, adaptive modulation and coding [10], space–time 1 Note that an outage under perfect CSI at the receiver only is different than an outage when both transmitter and receiver have perfect CSI. Under re... |

186 | Capacity and optimal resource allocation for fading broadcast channels. I. Ergodic capacity
- Li, Goldsmith
- 2001
(Show Context)
Citation Context ...arying channels under different transmitter and receiver CSI and CDI assumptions extend to the capacity region of the multiple-access channel (MAC) and broadcast channel (BC) in the obvious way [28], =-=[48]-=-, [49], [70]. However, these MIMO multiuser capacity regions, even for time-invariant channels, are difficult to find. Few capacity results exist for timevarying multiuser MIMO channels, especially un... |

186 | Diversity-multiplexing tradeoff in multiple-access channels
- Tse, Viswanath, et al.
- 2004
(Show Context)
Citation Context ...ltiple antennas. Multiple antennas can be used not only to enhance the capacity of the system but also to drive down the probability of error through diversity combining. Recent work by Zheng and Tse =-=[88]-=- unravels a fundamental diversity versus multiplexing tradeoff in MIMO systems. Also, instead of using isotropic transmit antennas on the downlink and transmitting to many users, it may be simpler to ... |

184 |
On the capacity of some channels with channel state information
- Caire, Shamai
- 1999
(Show Context)
Citation Context ...6], [76]. • The feedback channel is assumed to be free from noise. This makes the CDIT a deterministic function of the CDIR and allows optimal codes to be constructed directly over the input alphabet =-=[8]-=-. • For each realization of the conditional average transmit power is constrained as . • The ergodic capacity of the system in Fig. 1 is the capacity averaged over the different realizations where is ... |

167 | On the capacity of OFDM-based spatial multiplexing systems
- Bolcskei, Gesbert, et al.
- 2002
(Show Context)
Citation Context ...SISO frequency selective fading channels can be represented by the MIMO system model (1) in this manner [59]. For MIMO systems, the matrix channel model is derived by Bolcskei, Gesbert and Paulraj in =-=[5]-=- based on an analysis of the capacity behavior of OFDM-based MIMO channels in broadband fading environments. Under the assumption of perfect CSIR and CDIT for the ZMSW model, their results show that i... |

155 | Multiple-antenna channel hardening and its implications for rate feedback and scheduling
- Hochwald, Marzetta, et al.
- 2004
(Show Context)
Citation Context ...knows the channel perfectly (perfect CSIT) or only knows its distribution (CDIT). The proportionality constant of this linear increase, called the rate of growth, has also been characterized in [15], =-=[31]-=-, [68], [69]. Chuah et al. [15] show that with perfect CSIR and CSIT, the rate of growth of capacity with is reduced by channel fading correlations at high SNR but is increased at low SNR. They also s... |

145 | Capacity bounds via duality with applications to multiple-antenna systems on flat-fading channels
- Lapidoth, Moser
- 2003
(Show Context)
Citation Context ...es beyond some lag , called the correlation time of the fading, then it is shown in [54] that increasing the number of transmit antennas beyond antennas does not increase capacity. Lapidoth and Moser =-=[47]-=- explored the channel capacity of this CDIT/CDIR model for the ZMSW distribution at high SNR without the block fading assumption. In contrast to the results of Zheng and Tse for block fading, Lapidoth... |

142 |
Multiaccess fading channels-part i: polymatroid structure,optimal resource allocation and throughput capacities,” Information Theory
- Tse, Hanly
- 1998
(Show Context)
Citation Context ...ermore, the corner point should correspond to successive decoding in order of increasing priority, i.e., the user with the highest priority should be decoded last and, therefore, sees no interference =-=[70]-=-, [73]. Thus, the problem of finding the boundary point on the capacity region associated with priorities assumed to be in descending order (users can be arbitrarily re-numbered to satisfy this condit... |

136 | Sum power iterative water-filling for multi-antenna Gaussian broadcast channels
- Jindal, Jafar, et al.
- 2002
(Show Context)
Citation Context ...specialized algorithm to find the optimal MAC covariances can be found in [35]. An algorithm based on the iterative waterfilling algorithm [86] that finds the sum rate optimal covariances is given in =-=[43]-=-. The dirty paper rate region is shown in Fig. 9 for a channel with two-users, and . Notice that the dirty paper rate region shown in Fig. 9 is actually a union of MAC regions, where each MAC region c... |

128 |
Enhancing the cellular downlink capacity via co-processing at the transmitter end
- Shamai, Zaidel
- 2001
(Show Context)
Citation Context ...(i.e., across base stations) in a straightforward manner. The application of DPC to a multiple-cell environment with cooperation between base stations is pioneered in recent work by Shamai and Zaidel =-=[64]-=-. For one antenna at each user and each base station, they show that a relatively simple application of DPC can enhance the capacity of the cellular downlink. While capacity computations are not the f... |

114 | On the duality of Gaussian multiple-access and broadcast channels
- Jindal, Vishwanath, et al.
- 2004
(Show Context)
Citation Context ...per result we find that are uncorrelated, which implies This is the multiple-antenna extension of the previously established duality between the scalar Gaussian broadcast and multiple-access channels =-=[44]-=-. In addition to the relationship between the two rate regions, for any set of covariance matrices in the MAC/BC (and the corresponding rate vector), [74] provides an explicit set of transformations t... |

110 | Keyholes, correlations, and capacities of multielement transmit and receive antennas
- Chizhik, Foschini, et al.
- 2002
(Show Context)
Citation Context ... it [16]. Moreover, channels with very low correlation between antennas can still exhibit a “keyhole” effect where the rank of the channel gain matrix is very small, leading to limited capacity gains =-=[12]-=-. Fortunately, this effect is not prevalent in most environments. The impact of channel statistics in the low-power (wideband) regime has interesting properties as well: recent results in this area ca... |

108 | Gaussian multiaccess channels with ISI: capacity region and multiuser water-filling
- Cheng, Verdu
- 1993
(Show Context)
Citation Context ... the user-by-user power constraints [18]. For the Gaussian MIMO MAC, however, it has been shown that it is sufficient to consider only Gaussian inputs and that the convex hull operation is not needed =-=[11]-=-, [86]. For any set of powers , the capacity of the MIMO MAC is shown in (12), at the bottom of the next page. The th user transmits a zero-mean Gaussian with spatial covariance matrix . Each set of c... |

105 | Information-theoretic considerations for symmetric, cellular, multiple-access fading channels—Part II
- Shamai, Wyner
- 1997
(Show Context)
Citation Context ... algorithm of [86] easily extends to this case, with joint space and time waterfilling. The capacity region of a MAC with perfect CSIR and CDIT under the ZMSW distribution model was found in [23] and =-=[63]-=-. In this case, Gaussian inputs are optimal and the ergodic capacity region is equal to the time average of the capacity obtained at each fading instant with a constant transmit policy (i.e., a consta... |

103 | A space-time correlation model for multielement antenna systems in mobile fading channels
- Abdi, Kaveh
- 2002
(Show Context)
Citation Context ...nvironments [26]. Antenna correlation varies drastically as a function of the scattering environment, the distance between transmitter and receiver, the antenna configurations, and the Doppler spread =-=[1]-=-, [65]. As we shall see, the effect of channel correlation on capacity depends on what is known about the channel at the transmitter and receiver: correlation sometimes increases capacity and sometime... |

100 |
Capacity and lattice strategies for canceling known interference
- Erez, Shamai, et al.
- 2005
(Show Context)
Citation Context ...a way that the transmit power is not increased. A more practical (and more general) technique to perform this presubtraction is the cancelling for known interference technique found by Erez et al. in =-=[19]-=-. In the MIMO BC, DPC can be applied at the transmitter when choosing codewords for different receivers. The transmitter first picks a codeword (i.e., ) for receiver 1. The transmitter then chooses a ... |

100 |
Downlink capacity evaluation of cellular networks with known interference cancellation
- Viswanathan, Venkatesan, et al.
- 2003
(Show Context)
Citation Context ...techniques and then transformed to the corresponding optimal BC covariances using the MAC-BC transformations given in [74]. A specialized algorithm to find the optimal MAC covariances can be found in =-=[35]-=-. An algorithm based on the iterative waterfilling algorithm [86] that finds the sum rate optimal covariances is given in [43]. The dirty paper rate region is shown in Fig. 9 for a channel with two-us... |

91 |
Adaptive modulation and MIMO coding for broadband wireless data networks
- Catreux, Erceg, et al.
- 2002
(Show Context)
Citation Context ...jor focus of such work is space-time coding: recent work in this area is summarized in [21]. Other techniques for MIMO systems include space–time modulation [30], [33], adaptive modulation and coding =-=[10]-=-, space–time 1 Note that an outage under perfect CSI at the receiver only is different than an outage when both transmitter and receiver have perfect CSI. Under receiver CSI only an outage occurs when... |

91 |
An outer bound to the capacity region of broadcast channels
- Sato
- 1978
(Show Context)
Citation Context ...(17) 3) Optimality of DPC: DPC was first shown to achieve the sum-rate capacity of the MIMO BC for the two-user, , channel by Caire and Shamai [9]. This was shown by proving that the Sato upper bound =-=[61]-=- on the broadcast channel sum-rate capacity is achievable using DPC. The sum-rate optimality of DPC was extended to the multiuser channel with by Viswanath and Tse [79] and to the more general case by... |

84 |
Multiaccess fading channels–Part II: Delaylimited capacities
- Hanly, Tse
- 1998
(Show Context)
Citation Context ...time-varying channels under different transmitter and receiver CSI and CDI assumptions extend to the capacity region of the multiple-access channel (MAC) and broadcast channel (BC) in the obvious way =-=[28]-=-, [48], [49], [70]. However, these MIMO multiuser capacity regions, even for time-invariant channels, are difficult to find. Few capacity results exist for timevarying multiuser MIMO channels, especia... |

81 | Channel capacity and beamforming for multiple transmit and receive antennas with covariance feedback
- Jafar, Vishwanath, et al.
- 2001
(Show Context)
Citation Context ...ture adaptation to the short-term channel statistics (the feedback model of Fig. 1) is referred to by many names including mean and covariance feedback, imperfect feedback and partial CSI [38], [40], =-=[42]-=-, [45], [46], [56], [66], [76]. • The feedback channel is assumed to be free from noise. This makes the CDIT a deterministic function of the CDIR and allows optimal codes to be constructed directly ov... |

80 | Performance limits of coded diversity methods for transmitter antenna arrays
- Narula, Trott, et al.
- 1999
(Show Context)
Citation Context ...as reduces the average sum capacity. (8) matrix. Key results on the capacity of such channels have been recently obtained by several authors including Madhow and Visotsky [76], Trott and Narula [58], =-=[57]-=-, Jafar and Goldsmith [42], [40], [38], Jorsweick and Boche [45], [46], and Simon and Moustakas [56], [66]. Mathematically the problem is defined by (6) and (7), with the distribution on determined by... |

80 | Asymptotically optimal water-filling in vector multiple-access channels,”IEEE Trans
- Viswanath, Tse, et al.
- 2001
(Show Context)
Citation Context ...ptotic results on the sum capacity of MIMO MAC channels with the number of receive antennas and the number of transmitters increasing to infinity were obtained by Telatar [69] and by Viswanath et al. =-=[80]-=-. MIMO MAC sum capacity with perfect CSIR and CDIT under the ZMSW distribution model (i.e., each transmitter’s channel is distributed as ) is found to grow linearly with [69]. Thus, for systems with l... |

73 |
MIMO-OFDM for wireless communications: signal detection with enhanced channel estimation
- Li, Winters, et al.
- 2002
(Show Context)
Citation Context ...LE I TABLE OF ABBREVIATIONS Fig. 1. MIMO channel with perfect CSIR and distribution feedback. equalization [2], [51], space–time signal processing [3], space–time CDMA [14], [34], and space–time OFDM =-=[50]-=-, [52], [82]. An overview of the recent advances in these areas and other practical techniques along with their performance can be found in [25]. The remainder of this paper is organized as follows. I... |

72 |
Introduction to Convex Optimization with Engineering Applications
- Boyd, Vandenberghe
- 1995
(Show Context)
Citation Context ...ful feature of the optimization problem above is that the objective function is concave in the covariance matrices. Thus, efficient convex optimization tools exist that solve this problem numerically =-=[7]-=-. A more efficient numerical technique to find the sum-rate maximizing (i.e., ) covariance matrices, called iterative waterfilling, was developed by Yu et al. [86]. This technique is based on the Karu... |

71 |
Capacity of MIMO systems based on measured wireless channels
- Molisch, Steinbauer, et al.
- 2002
(Show Context)
Citation Context ...e need to estimate the capacity gains of BLAST for practical systems in the presence of channel fade correlations and frequency selective fading sparked off measurement campaigns reported in [24] and =-=[55]-=-. The measured capacities are found to be about 30% smaller than would be anticipated from an idealized model. However, the capacity gains over single antenna systems are still overwhelming. 3) Capaci... |

61 | On a Gaussian approximation to the capacity of wireless MIMO systems
- Smith, Shafi
- 2002
(Show Context)
Citation Context ...the channel perfectly (perfect CSIT) or only knows its distribution (CDIT). The proportionality constant of this linear increase, called the rate of growth, has also been characterized in [15], [31], =-=[68]-=-, [69]. Chuah et al. [15] show that with perfect CSIR and CSIT, the rate of growth of capacity with is reduced by channel fading correlations at high SNR but is increased at low SNR. They also show th... |

60 |
Fading channels: Information theoretic and communications aspects
- Biglieri, Proakis, et al.
- 1998
(Show Context)
Citation Context ...obability associated with it and capacity is measured relative to outage probability1 (capacity CDF) [20]. An excellent tutorial on fading channel capacity for single antenna channels can be found in =-=[4]-=-. For single-user MIMO channels with perfect transmitter and receiver CSI the ergodic and outage capacity calculations are straightforward since the capacity is known for every channel state. Thus, fo... |

60 |
Channel capacity and capacity-range of beamforming in MIMO wireless systems under correlated fading with covariance feedback
- Jorswieck, Boche
- 2004
(Show Context)
Citation Context ...daptation to the short-term channel statistics (the feedback model of Fig. 1) is referred to by many names including mean and covariance feedback, imperfect feedback and partial CSI [38], [40], [42], =-=[45]-=-, [46], [56], [66], [76]. • The feedback channel is assumed to be free from noise. This makes the CDIT a deterministic function of the CDIR and allows optimal codes to be constructed directly over the... |

59 | Trellis precoding for the broadcast channel
- Yu, Cioffi
- 2001
(Show Context)
Citation Context ...ing (DPC) Achievable Rate Region: An achievable region for the MIMO BC was first obtained for the case by Caire and Shamai [9] and later extended to the multiple-receive antenna case by Yu and Cioffi =-=[83]-=- using the idea of DPC [17]. The basic premise of DPC is as follows. If the transmitter (but not the receiver) has perfect, noncausal knowledge of additive Gaussian interference in the channel, then t... |

56 | Space-time multiple access: linear growth in the sum rate
- Hochwald, Vishwanath
- 2002
(Show Context)
Citation Context ...is expectation involving Laguerre polynomials is derived in [69]. If and simultaneously become large, capacity is seen to grow linearly with . Expressions for the growth rate constant can be found in =-=[32]-=- and [69]. Telatar [69] conjectures that the optimal input covariance matrix that maximizes capacity versus outage is a diagonal matrix with the power equally distributed among a subset of the transmi... |

55 |
Moustakas, “Optimizing MIMO antenna systems with channel covariance feedback
- Simon, L
- 2003
(Show Context)
Citation Context ...hort-term channel statistics (the feedback model of Fig. 1) is referred to by many names including mean and covariance feedback, imperfect feedback and partial CSI [38], [40], [42], [45], [46], [56], =-=[66]-=-, [76]. • The feedback channel is assumed to be free from noise. This makes the CDIT a deterministic function of the CDIR and allows optimal codes to be constructed directly over the input alphabet [8... |

52 | On the capacity of multiple input multiple output broadcast channels
- Vishwanath, Jindal, et al.
- 2002
(Show Context)
Citation Context ...ar channels, but this equivalence does not hold for MIMO channels. It has been shown [36] that the achievable region with successive decoding is contained within the DPC region. 2) MAC-BC Duality: In =-=[74]-=-, Vishwanath, Jindal, and Goldsmith showed that the dirty paper rate region of the multiantenna BC with power constraint is equal to the union of capacity regions of the dual MAC, where the union is t... |

49 | Sum capacity of the multiple antenna Gaussian broadcast channel and uplink-downlink duality”, submitted to
- Viswanath, Tse
- 2002
(Show Context)
Citation Context ...oving that the Sato upper bound [61] on the broadcast channel sum-rate capacity is achievable using DPC. The sum-rate optimality of DPC was extended to the multiuser channel with by Viswanath and Tse =-=[79]-=- and to the more general case by Vishwanath et al. [74] and Yu and Cioffi [84]. It has also recently been conjectured that the DPC rate region is the actual capacity region of the multiple-antenna bro... |

47 | Analysis and performance of some basic space-time architectures
- Foschini, Chizhik, et al.
- 2003
(Show Context)
Citation Context ... techniques have been developed to capitalize on the theoretical capacity gains predicted by Shannon theory. A major focus of such work is space-time coding: recent work in this area is summarized in =-=[21]-=-. Other techniques for MIMO systems include space–time modulation [30], [33], adaptive modulation and coding [10], space–time 1 Note that an outage under perfect CSI at the receiver only is different ... |

44 | Phantomnet: exploring optimal multicellular multiple antenna systems
- Jafar, Foschini, et al.
- 2004
(Show Context)
Citation Context ...erference cancellation by the receiver instead of the transmitter) are completely equivalent capacity-wise for scalar channels, but this equivalence does not hold for MIMO channels. It has been shown =-=[36]-=- that the achievable region with successive decoding is contained within the DPC region. 2) MAC-BC Duality: In [74], Vishwanath, Jindal, and Goldsmith showed that the dirty paper rate region of the mu... |

38 |
On optimality of beamforming for multiple antenna systems with imperfect feedback
- Jafar, Goldsmith
- 2001
(Show Context)
Citation Context ...literature adaptation to the short-term channel statistics (the feedback model of Fig. 1) is referred to by many names including mean and covariance feedback, imperfect feedback and partial CSI [38], =-=[40]-=-, [42], [45], [46], [56], [66], [76]. • The feedback channel is assumed to be free from noise. This makes the CDIT a deterministic function of the CDIR and allows optimal codes to be constructed direc... |

37 | Multiple-antenna capacity in correlated Rayleigh fading with channel covariance information
- Jafar, Goldsmith
- 2005
(Show Context)
Citation Context ...a nonzero mean or a nonwhite covariance. Thus, if these distribution parameters can be tracked, the channel distribution corresponds to either the CMI or CCI model. Recent work by Jafar and Goldsmith =-=[37]-=- addresses the MIMO channel capacity with CDIT and CDIR under the CCI distribution model. The channel matrix components are modeled as spatially correlated complex Gaussian random variables that remai... |

31 | Packing spheres in the Grassmann manifold: A geometric approach to the noncoherent multi-antenna channel
- Zheng, Tse
- 1999
(Show Context)
Citation Context ...pacity does not increase at all as the number of transmit antennas is increased beyond the length of the coherence interval . The MIMO capacity for this model was further explored by Zheng and Tse in =-=[89]-=-. They show that at high SNRs capacity is achieved using no more than transmit antennas. In particular, having more transmit antennas than receive antennas does not provide any capacity increase at hi... |

29 | Layered space-time receivers for frequency-selective wireless channels
- Lozano, Papadias
- 2002
(Show Context)
Citation Context ...ply.686 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 21, NO. 5, JUNE 2003 TABLE I TABLE OF ABBREVIATIONS Fig. 1. MIMO channel with perfect CSIR and distribution feedback. equalization [2], =-=[51]-=-, space–time signal processing [3], space–time CDMA [14], [34], and space–time OFDM [50], [52], [82]. An overview of the recent advances in these areas and other practical techniques along with their ... |

27 | Optimum power and rate allocation strategies for multiple access fading channels
- Vishwanath, Jafar, et al.
- 2000
(Show Context)
Citation Context ..., the corner point should correspond to successive decoding in order of increasing priority, i.e., the user with the highest priority should be decoded last and, therefore, sees no interference [70], =-=[73]-=-. Thus, the problem of finding the boundary point on the capacity region associated with priorities assumed to be in descending order (users can be arbitrarily re-numbered to satisfy this condition) c... |

24 |
Iterative Receivers for Space–Time Block-Coded OFDM Systems in Dispersive Fading Channels
- Lu, Wang, et al.
- 2002
(Show Context)
Citation Context ...ABLE OF ABBREVIATIONS Fig. 1. MIMO channel with perfect CSIR and distribution feedback. equalization [2], [51], space–time signal processing [3], space–time CDMA [14], [34], and space–time OFDM [50], =-=[52]-=-, [82]. An overview of the recent advances in these areas and other practical techniques along with their performance can be found in [25]. The remainder of this paper is organized as follows. In Sect... |

24 |
Iterative Water-filling for Vector Multiple Access Channels
- Yu, Rhee, et al.
(Show Context)
Citation Context ...ser-by-user power constraints [18]. For the Gaussian MIMO MAC, however, it has been shown that it is sufficient to consider only Gaussian inputs and that the convex hull operation is not needed [11], =-=[86]-=-. For any set of powers , the capacity of the MIMO MAC is shown in (12), at the bottom of the next page. The th user transmits a zero-mean Gaussian with spatial covariance matrix . Each set of covaria... |

23 |
Overview and comparison of equalization schemes for space time coded signals with application to EDGE
- Al-Dhahir
- 2002
(Show Context)
Citation Context ...ns apply.686 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 21, NO. 5, JUNE 2003 TABLE I TABLE OF ABBREVIATIONS Fig. 1. MIMO channel with perfect CSIR and distribution feedback. equalization =-=[2]-=-, [51], space–time signal processing [3], space–time CDMA [14], [34], and space–time OFDM [50], [52], [82]. An overview of the recent advances in these areas and other practical techniques along with ... |

21 |
Multiple Antennas in Cellular CDMA Systems
- Huang, Viswanathan, et al.
(Show Context)
Citation Context .... 21, NO. 5, JUNE 2003 TABLE I TABLE OF ABBREVIATIONS Fig. 1. MIMO channel with perfect CSIR and distribution feedback. equalization [2], [51], space–time signal processing [3], space–time CDMA [14], =-=[34]-=-, and space–time OFDM [50], [52], [82]. An overview of the recent advances in these areas and other practical techniques along with their performance can be found in [25]. The remainder of this paper ... |

20 |
Outdoor BLAST measurement system at 2.44 GHz: Calibration and initial results
- Gans, Amitay, et al.
- 2002
(Show Context)
Citation Context ...ivity. The need to estimate the capacity gains of BLAST for practical systems in the presence of channel fade correlations and frequency selective fading sparked off measurement campaigns reported in =-=[24]-=- and [55]. The measured capacities are found to be about 30% smaller than would be anticipated from an idealized model. However, the capacity gains over single antenna systems are still overwhelming. ... |

20 | Optimal Power Control in Multiple Access Fading Channels - Yu, Rhee, et al. - 2001 |

19 |
Transmitter optimization for multiple antenna cellular systems
- Jafar, Goldsmith
- 2002
(Show Context)
Citation Context ...ownlink. While capacity computations are not the focus of [64], they do show that their scheme is asymptotically optimal at high SNRs. The MIMO downlink capacity is explored by Jafar and Goldsmith in =-=[39]-=-. Note that the multicell downlink can be solved in a similar way as the uplink. But this requires perfect data and power cooperation between the base stations. If we let represent the transmit vector... |

18 |
An inequality on the capacity region of multiaccess fading channels,” Communications and Cryptography-Two sides of one Tapestry
- Gallager
- 1994
(Show Context)
Citation Context ...erfilling algorithm of [86] easily extends to this case, with joint space and time waterfilling. The capacity region of a MAC with perfect CSIR and CDIT under the ZMSW distribution model was found in =-=[23]-=- and [63]. In this case, Gaussian inputs are optimal and the ergodic capacity region is equal to the time average of the capacity obtained at each fading instant with a constant transmit policy (i.e.,... |

16 | An adaptive multiuser power control algorithm for VDSL Global Telecommunications Conference, 2001. GLOBECOM ’01
- Yu, Ginis, et al.
(Show Context)
Citation Context ...ssumptions. Note that the MIMO techniques described herein are applicable to any channel described by a matrix. Matrix channels describe not only multiantenna systems but also channels with crosstalk =-=[85]-=- and wideband channels [72]. While the focus of this tutorial is on memoryless channels (flat-fading), the results can also be extended to channels with memory (ISI) using well-known methods for incor... |

15 |
Optimizing multi-transmitter singlereceiver (MISO) antenna systems with partial channel knowledge
- Moustakas, Simon
- 2003
(Show Context)
Citation Context ... the short-term channel statistics (the feedback model of Fig. 1) is referred to by many names including mean and covariance feedback, imperfect feedback and partial CSI [38], [40], [42], [45], [46], =-=[56]-=-, [66], [76]. • The feedback channel is assumed to be free from noise. This makes the CDIT a deterministic function of the CDIR and allows optimal codes to be constructed directly over the input alpha... |

15 |
Multiuser capacity in block fading with no channel state information
- Shamai, Marzetta
- 2002
(Show Context)
Citation Context ...e transmitter or receiver under the CMI or CCI distribution models. Some results on the optimum distribution for the single antenna case with CDIT and CDIR under the ZMSW distribution can be found in =-=[62]-=-. With perfect CSIR and CSIT the system can be viewed as a set of parallel non interfering MIMO MACs (one for each fading state) sharing a common power constraint. Thus, the ergodic capacity region ca... |

14 |
Multiple input multiple output measurements and modeling
- Chizhik
(Show Context)
Citation Context ...mpletely general, this simple correlation model has been validated through recent field measurements as a sufficiently accurate representation of the fade correlations seen in actual cellular systems =-=[13]-=-. Under CMI the channel mean and the variance of the estimation error are assumed known and under CCI the transmit and receive covariance matrices and are assumed known. 2) CDIT and CDIR: In highly mo... |

13 |
The Use of Diversity Antennas in High-Speed Wireless Systems: Capacity Gains, Fairness Issues, Multiuser Scheduling,” Bell Labs. Tech. Memo, 2001; download from http://mars.bell-labs.com [7
- Borst, Whiting
- 2002
(Show Context)
Citation Context ...distribution feedback of the channel mean or covariance 2 The capacity for high outage probabilities becomes relevant for schemes that transmit only to the best user. For such schemes, it is shown in =-=[6]-=- that increasing the number of transmit antennas reduces the average sum capacity. (8) matrix. Key results on the capacity of such channels have been recently obtained by several authors including Mad... |

13 |
optimal resource allocation for fading broadcast channels .II. Outage capacity
- “Capacity
- 2001
(Show Context)
Citation Context ... channels under different transmitter and receiver CSI and CDI assumptions extend to the capacity region of the multiple-access channel (MAC) and broadcast channel (BC) in the obvious way [28], [48], =-=[49]-=-, [70]. However, these MIMO multiuser capacity regions, even for time-invariant channels, are difficult to find. Few capacity results exist for timevarying multiuser MIMO channels, especially under th... |

11 |
Space-time processing for broadband wireless access Communications
- Al-Dhahir, N, et al.
- 2002
(Show Context)
Citation Context ...REAS IN COMMUNICATIONS, VOL. 21, NO. 5, JUNE 2003 TABLE I TABLE OF ABBREVIATIONS Fig. 1. MIMO channel with perfect CSIR and distribution feedback. equalization [2], [51], space–time signal processing =-=[3]-=-, space–time CDMA [14], [34], and space–time OFDM [50], [52], [82]. An overview of the recent advances in these areas and other practical techniques along with their performance can be found in [25]. ... |

10 | Outer bounds for multi-antenna broadcast channels - Vishwanath, Kramer, et al. - 2002 |

10 |
Sum capacity of the multi-antenna broadcast channel
- Viswanath, Tse
- 2002
(Show Context)
Citation Context ...lso recently been conjectured that the DPC rate region is the actual capacity region of the multiple-antenna broadcast channel. Significant progress toward proving this conjecture is made in [75] and =-=[77]-=-. 4) Fading Channels: Most of the capacity problems for fading MIMO BCs are still open, with the exception of sum-rate capacity with perfect CSIR and CSIT. In this case, as for the MIMO MAC, the MIMO ... |

8 |
Multiuser decision-feedback receivers for the general Gaussian multiple-access channel
- Guess, Varanasi
- 1996
(Show Context)
Citation Context ...nterference from user 1) and decoding user 1 last (without interference from user 2). Successive decoding can reduce a complex multiuser detection problem into a series of single-user detection steps =-=[27]-=-. The capacity region of a MIMO MAC for the single transmit antenna case ( ) is shown in Fig. 7. When , the covariance matrix of each transmitter is a scalar equal to the transmitted power. Clearly, e... |

8 | Giannakis, “High-rate space-time layered OFDM
- Xin, B
- 2002
(Show Context)
Citation Context ...F ABBREVIATIONS Fig. 1. MIMO channel with perfect CSIR and distribution feedback. equalization [2], [51], space–time signal processing [3], space–time CDMA [14], [34], and space–time OFDM [50], [52], =-=[82]-=-. An overview of the recent advances in these areas and other practical techniques along with their performance can be found in [25]. The remainder of this paper is organized as follows. In Section II... |

7 |
space-time modulation for multiple-antenna communications in Rayleigh flat fading
- “Unitary
- 2000
(Show Context)
Citation Context ...3], [89] assume block fading models, i.e., the channel fade coefficients are assumed to be constant for a block of symbol durations. Hochwald and Marzetta extend their results to continuous fading in =-=[54]-=- where, within each independent -symbol block, the fading coefficients have an arbitrary time correlation. If the correlation vanishes beyond some lag , called the correlation time of the fading, then... |

6 |
Channel and propagation models for wireless systems design
- Greenstein, Andersen, et al.
- 2002
(Show Context)
Citation Context ...ions of the channel. Recent work has developed both analytical and measurement-based MIMO channel models along with the corresponding capacity calculations for typical indoor and outdoor environments =-=[26]-=-. Antenna correlation varies drastically as a function of the scattering environment, the distance between transmitter and receiver, the antenna configurations, and the Doppler spread [1], [65]. As we... |

5 |
differential unitary space-time codes
- “Cayley
- 2002
(Show Context)
Citation Context ...ity gains predicted by Shannon theory. A major focus of such work is space-time coding: recent work in this area is summarized in [21]. Other techniques for MIMO systems include space–time modulation =-=[30]-=-, [33], adaptive modulation and coding [10], space–time 1 Note that an outage under perfect CSI at the receiver only is different than an outage when both transmitter and receiver have perfect CSI. Un... |

4 |
achievable rates in a multi-antenna broadcast downlink
- “On
- 2000
(Show Context)
Citation Context ...as more than one antenna, the Gaussian broadcast channel is generally nondegraded. 3 The capacity region of general nondegraded broadcast channels is unknown, but the seminal work of Caire and Shamai =-=[9]-=- and subsequent research on this problem have shed a great deal of light on this channel and the sum capacity of the MIMO BC has been found. In subsequent sections, we focus mainly on the constant cha... |

4 |
Capacity of multi-antenna channels in the low-power regime
- Tulino, Lozano, et al.
- 2002
(Show Context)
Citation Context ... this effect is not prevalent in most environments. The impact of channel statistics in the low-power (wideband) regime has interesting properties as well: recent results in this area can be found in =-=[71]-=-. We focus on MIMO channel capacity in the Shannon theoretic sense. The Shannon capacity of a single-user time-invariant channel is defined as the maximum mutual information between the channel input ... |

3 |
The performance of a space-time spreading CDMA system with channel estimation errors
- Chong, Milstein
- 2002
(Show Context)
Citation Context ...S, VOL. 21, NO. 5, JUNE 2003 TABLE I TABLE OF ABBREVIATIONS Fig. 1. MIMO channel with perfect CSIR and distribution feedback. equalization [2], [51], space–time signal processing [3], space–time CDMA =-=[14]-=-, [34], and space–time OFDM [50], [52], [82]. An overview of the recent advances in these areas and other practical techniques along with their performance can be found in [25]. The remainder of this ... |

3 |
optimization and optimality of beamforming for multiple antenna systems with imperfect feedback
- “Transmitter
(Show Context)
Citation Context ...n the literature adaptation to the short-term channel statistics (the feedback model of Fig. 1) is referred to by many names including mean and covariance feedback, imperfect feedback and partial CSI =-=[38]-=-, [40], [42], [45], [46], [56], [66], [76]. • The feedback channel is assumed to be free from noise. This makes the CDIT a deterministic function of the CDIR and allows optimal codes to be constructed... |

2 |
mac capacity region with covariance feedback
- “Vector
- 2001
(Show Context)
Citation Context ...e power constraint, then the optimal covariances are scaled versions of the identity matrix [69]. There has also been some work on capacity with perfect CSIR and CDIT under the CCI distribution model =-=[41]-=-. In this paper, Jafar and Goldsmith determine the optimal transmit covariance matrices when there is transmit antenna correlation that is known at the transmitters. This topic has yet to be fully inv... |

2 |
transmission with imperfect channel state information at the transmit antenna array,” Wireless Personal Commun., submitted for publication
- “Optimal
(Show Context)
Citation Context ...ion to the short-term channel statistics (the feedback model of Fig. 1) is referred to by many names including mean and covariance feedback, imperfect feedback and partial CSI [38], [40], [42], [45], =-=[46]-=-, [56], [66], [76]. • The feedback channel is assumed to be free from noise. This makes the CDIT a deterministic function of the CDIR and allows optimal codes to be constructed directly over the input... |