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673
Grassmannian beamforming for multipleinput multipleoutput wireless systems
 IEEE TRANS. INFORM. THEORY
, 2003
"... Transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multipleinput and multipleoutput (MIMO) wireless systems. Unfortunately, optimal performance requires either complete channel knowledge or knowledge of the optimal beamformi ..."
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Cited by 329 (39 self)
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Transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multipleinput and multipleoutput (MIMO) wireless systems. Unfortunately, optimal performance requires either complete channel knowledge or knowledge of the optimal beamforming vector which are not always realizable in practice. In this correspondence, a quantized maximum signaltonoise ratio (SNR) beamforming technique is proposed where the receiver only sends the label of the best beamforming vector in a predetermined codebook to the transmitter. By using the distribution of the optimal beamforming vector in independent identically distributed Rayleigh fading matrix channels, the codebook design problem is solved and related to the problem of Grassmannian line packing. The proposed design criterion is flexible enough to allow for side constraints on the codebook vectors. Bounds on the codebook size are derived to guarantee full diversity order. Results on the density of Grassmannian line packings are derived and used to develop bounds on the codebook size given a capacity or SNR loss. Monte Carlo simulations are presented that compare the probability of error for different quantization strategies.
On the optimality of multiantenna broadcast scheduling using zeroforcing beamforming
 IEEE J. SELECT. AREAS COMMUN
, 2006
"... Although the capacity of multipleinput/multipleoutput (MIMO) broadcast channels (BCs) can be achieved by dirty paper coding (DPC), it is difficult to implement in practical systems. This paper investigates if, for a large number of users, simpler schemes can achieve the same performance. Specifica ..."
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Cited by 302 (4 self)
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Although the capacity of multipleinput/multipleoutput (MIMO) broadcast channels (BCs) can be achieved by dirty paper coding (DPC), it is difficult to implement in practical systems. This paper investigates if, for a large number of users, simpler schemes can achieve the same performance. Specifically, we show that a zeroforcing beamforming (ZFBF) strategy, while generally suboptimal, can achieve the same asymptotic sum capacity as that of DPC, as the number of users goes to infinity. In proving this asymptotic result, we provide an algorithm for determining which users should be active under ZFBF. These users are semiorthogonal to one another and can be grouped for simultaneous transmission to enhance the throughput of scheduling algorithms. Based on the user grouping, we propose and compare two fair scheduling schemes in roundrobin ZFBF and proportionalfair ZFBF. We provide numerical results to confirm the optimality of ZFBF and to compare the performance of ZFBF and proposed fair scheduling schemes with that of various MIMO BC strategies.
Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit
, 2006
"... Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NPhard in general. We show here that for systems with ‘typical’/‘random ’ Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our pr ..."
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Cited by 278 (23 self)
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Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NPhard in general. We show here that for systems with ‘typical’/‘random ’ Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our proposal, Stagewise Orthogonal Matching Pursuit (StOMP), successively transforms the signal into a negligible residual. Starting with initial residual r0 = y, at the sth stage it forms the ‘matched filter ’ Φ T rs−1, identifies all coordinates with amplitudes exceeding a speciallychosen threshold, solves a leastsquares problem using the selected coordinates, and subtracts the leastsquares fit, producing a new residual. After a fixed number of stages (e.g. 10), it stops. In contrast to Orthogonal Matching Pursuit (OMP), many coefficients can enter the model at each stage in StOMP while only one enters per stage in OMP; and StOMP takes a fixed number of stages (e.g. 10), while OMP can take many (e.g. n). StOMP runs much faster than competing proposals for sparse solutions, such as ℓ1 minimization and OMP, and so is attractive for solving largescale problems. We use phase diagrams to compare algorithm performance. The problem of recovering a ksparse vector x0 from (y, Φ) where Φ is random n × N and y = Φx0 is represented by a point (n/N, k/n)
An overview of limited feedback in wireless communication systems
 IEEE J. SEL. AREAS COMMUN
, 2008
"... It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channe ..."
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Cited by 199 (41 self)
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It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finiterate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, singleuser, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.
An Overview of MIMO Communications: A Key to Gigabit Wireless
 Proc. IEEE
, 2004
"... High data rate wireless communications, nearing 1 Gigabit/second (Gbps) transmission rates, is of interest in emerging Wireless Local Area Networks (WLANs) and home Audio/Visual (A/V) networks. Designing very high speed wireless links that offer good QualityofService (QoS) and range capability in ..."
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Cited by 165 (0 self)
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High data rate wireless communications, nearing 1 Gigabit/second (Gbps) transmission rates, is of interest in emerging Wireless Local Area Networks (WLANs) and home Audio/Visual (A/V) networks. Designing very high speed wireless links that offer good QualityofService (QoS) and range capability in NonLineofSight (NLOS) environments constitutes a significant research and engineering challenge. Ignoring fading in NLOS environments, we can, in principle, meet the 1Gbps data rate requirement with a singletransmit singlereceive antenna wireless system if the product of bandwidth (measured in Hz) and spectral efficiency (measured in bps/Hz) is equal to 10 9. As we shall outline in this paper, a variety of cost, technology and regulatory constraints make such a brute force solution unattractive if not impossible. The use of multiple antennas at transmitter and receiver, popularly known as multipleinput multipleoutput (MIMO) wireless is an emerging costeffective technology that offers substantial leverages in making 1Gbps wireless links a reality. This paper provides an overview of MIMO wireless technology covering channel models, performance limits, coding, and transceiver design.
Multiantenna downlink channels with limited feedback and user selection
 IEEE J. Select. Areas Commun
, 2007
"... Abstract — We analyze the sumrate performance of a multiantenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to ..."
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Cited by 117 (2 self)
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Abstract — We analyze the sumrate performance of a multiantenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to directional information, information regarding the quality of each channel. Such information should reflect both the channel magnitude and the quantization error. Expressions for the SINR distribution and the sumrate are derived, and tradeoffs between the number of feedback bits, the number of users, and the SNR are observed. In particular, for a target performance, having more users reduces feedback load. Index Terms — MIMO, quantized feedback, limited feedback, zeroforcing beamforming, multiuser diversity, broadcast channel,
Capacity and power allocation for fading MIMO channels with channel estimation error
 IEEE Transactions on Information Theory
, 2006
"... Abstract—In this correspondence, we investigate the effect of channel estimation error on the capacity of multipleinput–multipleoutput (MIMO) fading channels. We study lower and upper bounds of mutual information under channel estimation error, and show that the two bounds are tight for Gaussian i ..."
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Cited by 103 (0 self)
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Abstract—In this correspondence, we investigate the effect of channel estimation error on the capacity of multipleinput–multipleoutput (MIMO) fading channels. We study lower and upper bounds of mutual information under channel estimation error, and show that the two bounds are tight for Gaussian inputs. Assuming Gaussian inputs we also derive tight lower bounds of ergodic and outage capacities and optimal transmitter power allocation strategies that achieve the bounds under perfect feedback. For the ergodic capacity, the optimal strategy is a modified waterfilling over the spatial (antenna) and temporal (fading) domains. This strategy is close to optimum under small feedback delays, but when the delay is large, equal powers should be allocated across spatial dimensions. For the outage capacity, the optimal scheme is a spatial waterfilling and temporal truncated channel inversion. Numerical results show that some capacity gain is obtained by spatial power allocation. Temporal power adaptation, on the other hand, gives negligible gain in terms of ergodic capacity, but greatly enhances outage performance. Index Terms—Capacity, channel estimation error, feedback delay, multipleinput–multipleoutput (MIMO), mutual information, outage capacity, power allocation, waterfilling. I.
Networked MIMO with Clustered Linear Precoding
, 2008
"... A clustered base transceiver station (BTS) coordination strategy is proposed for a large cellular MIMO network, which includes full intracluster coordination–to enhance the sum rate–and limited intercluster coordination–to reduce interference for the cluster edge users. Multicell block diagonaliz ..."
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Cited by 90 (19 self)
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A clustered base transceiver station (BTS) coordination strategy is proposed for a large cellular MIMO network, which includes full intracluster coordination–to enhance the sum rate–and limited intercluster coordination–to reduce interference for the cluster edge users. Multicell block diagonalization is used to coordinate the transmissions across multiple BTSs in the same cluster. To satisfy perBTS power constraints, three combined precoder and power allocation algorithms are proposed with different performance and complexity tradeoffs. For intercluster coordination, the coordination area is chosen to balance fairness for edge users and the achievable sum rate. It is shown that a small cluster size (about 7 cells) is sufficient to obtain most of the sum rate benefits from clustered coordination while greatly relieving channel feedback requirement. Simulations show that the proposed coordination strategy efficiently reduces interference and provides a considerable sum rate gain for cellular MIMO networks.