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35
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 205 (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.
Antenna combining for the MIMO downlink channel,” To appear
 IEEE Trans. Wireless Commun
, 2007
"... A multiple antenna downlink channel where limited channel feedback is available to the transmitter is considered. In a vector downlink channel (single antenna at each receiver), the transmit antenna array can be used to transmit separate data streams to multiple receivers only if the transmitter has ..."
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Cited by 25 (3 self)
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A multiple antenna downlink channel where limited channel feedback is available to the transmitter is considered. In a vector downlink channel (single antenna at each receiver), the transmit antenna array can be used to transmit separate data streams to multiple receivers only if the transmitter has very accurate channel knowledge, i.e., if there is highrate channel feedback from each receiver. In this work it is shown that channel feedback requirements can be significantly reduced if each receiver has a small number of antennas and appropriately combines its antenna outputs. A combining method that minimizes channel quantization error at each receiver, and thereby minimizes multiuser interference, is proposed and analyzed. This technique is shown to outperform traditional techniques such as maximumratio combining because minimization of interference power is more critical than maximization of signal power in the multiple antenna downlink. Analysis is provided to quantify the feedback savings, and the technique is seen to work well with user selection and is also robust to receiver estimation error. I.
The degrees of freedom region of twouser and certain threeuser MIMO broadcast channel with delayed CSI
 IEEE Trans. Inf. Theory
"... The degrees of freedom (DoF) region of the fastfading MIMO (multipleinput multipleoutput) Gaussian broadcast channel (BC) is studied when there is delayed channel state information at the transmitter (CSIT). In this setting, the channel matrices are assumed to vary independently across time and t ..."
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Cited by 21 (1 self)
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The degrees of freedom (DoF) region of the fastfading MIMO (multipleinput multipleoutput) Gaussian broadcast channel (BC) is studied when there is delayed channel state information at the transmitter (CSIT). In this setting, the channel matrices are assumed to vary independently across time and the transmitter is assumed to know the channel matrices with some arbitrary finite delay. An outerbound to the DoF region of the general Kuser MIMO BC (with an arbitrary number of antennas at each terminal) is derived. This outerbound is then shown to be tight for two classes of MIMO BCs, namely, (a) the twouser MIMO BC with arbitrary number of antennas at all terminals, and (b) for certain threeuser MIMO BCs where all three receivers have an equal number of antennas and the transmitter has no more than twice the number of antennas present at each receivers. The achievability results are obtained by developing an interference alignment scheme that optimally accounts for multiple, and possibly distinct, number of antennas at the receivers. Index Terms Broadcast channel, degrees of freedom, delayed CSIT, interference alignment, outer bound.
MISO Broadcast Channels with Delayed FiniteRate Feedback: Predict or Observe?
"... Abstract—Most multiuser precoding techniques require accurate channel state information at the transmitter (CSIT) to maintain orthogonality between the users. Such techniques have proven quite fragile in timevarying channels because the CSIT is inherently imperfect due to quantization error and fe ..."
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Cited by 10 (2 self)
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Abstract—Most multiuser precoding techniques require accurate channel state information at the transmitter (CSIT) to maintain orthogonality between the users. Such techniques have proven quite fragile in timevarying channels because the CSIT is inherently imperfect due to quantization error and feedback delay. An alternative approach recently proposed by MaddahAli and Tse (MAT) allows for significant multiplexing gain in the multiinput singleoutput (MISO) broadcast channel (BC) even with CSIT that is “completely stale”, i.e., uncorrelated with the current channel state. With K users, their scheme claims to lose only a log(K) factor relative to the full K degrees of freedom (DoF) attainable in the MISO BC with perfect CSIT for large K. However, their result does not consider the cost of the feedback, which is potentially very large in high mobility (short channel coherence time). In this paper, we more closely examine the MAT scheme and compare its maximum net DoF gain to single user transmission (which always achieves 1 DoF) and partial CSIT linear precoding (which achieves up to K). In particular, assuming the channel coherence time isN symbol periods and the feedback delay is Nfd, we show that when N < (1+o(1))K logK (short coherence time), single user transmission performs best, whereas for N> (1+o(1))(Nfd+K / logK)(1−log−1K)−1 (long coherence time), zeroforcing precoding outperforms the other two. The MAT scheme is optimal for intermediate coherence times, which for practical parameter choices is indeed quite a large and significant range, even accounting for the feedback cost. Index Terms—MIMO, channel state information, quantization. I.
Mode switching for MIMO broadcast channel based on delay and channel quantization,” submitted to
 EURASIP Special Issue on Multiuser MIMO Transmission with Limited Feedback, Cooperation, and Coordination
, 2008
"... Imperfect channel state information degrades the performance of multipleinput multipleoutput (MIMO) communications; its effect on singleuser (SU) and multiuser (MU) MIMO transmissions are quite different. In particular, MUMIMO suffers from residual interuser interference due to imperfect chann ..."
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Cited by 9 (4 self)
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Imperfect channel state information degrades the performance of multipleinput multipleoutput (MIMO) communications; its effect on singleuser (SU) and multiuser (MU) MIMO transmissions are quite different. In particular, MUMIMO suffers from residual interuser interference due to imperfect channel state information while SUMIMO only suffers from a power loss. This paper compares the throughput loss of both SU and MU MIMO on the downlink due to delay and channel quantization. Accurate closedform approximations are derived for the achievable rates for both SU and MU MIMO. It is shown that SUMIMO is relatively robust to delayed and quantized channel information, while MUMIMO with zeroforcing precoding loses spatial multiplexing gain with a fixed delay or fixed codebook size. Based on derived achievable rates, a mode switching algorithm is proposed that switches between SU and MU MIMO modes to improve the spectral efficiency, based on the average signaltonoise ratio (SNR), the normalized Doppler frequency, and the channel quantization codebook size. The operating regions for SU and MU modes with different delays and codebook sizes are determined, which can be used to select the preferred mode. It is shown that the MU mode is active only when the normalized Doppler frequency is very small and the codebook size is large. Index Terms Multiuser MIMO, adaptive transmission, mode switching, imperfect channel state information at the transmitter (CSIT), zeroforcing precoding.
A scalable limited feedback design for network MIMO using percell product codebook
 IEEE Trans. Wirel. Commun
, 2010
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User scheduling for heterogeneous multiuser mimo systems: A subspace viewpoint,” Vehicular Technology
 IEEE Transactions on
, 2011
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Receive Combining vs. MultiStream Multiplexing in Downlink Systems with MultiAntenna Users
"... Abstract—In downlink multiantenna systems with many users, the multiplexing gain is strictly limited by the number of transmit antennas N and the use of these antennas. Assuming that the total number of receive antennas at the multiantenna users is much larger than N, the maximal multiplexing gain ..."
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Cited by 3 (1 self)
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Abstract—In downlink multiantenna systems with many users, the multiplexing gain is strictly limited by the number of transmit antennas N and the use of these antennas. Assuming that the total number of receive antennas at the multiantenna users is much larger than N, the maximal multiplexing gain can be achieved with many different transmission/reception strategies. For example, the excess number of receive antennas can be utilized to schedule users with effective channels that are nearorthogonal, for multistream multiplexing to users with wellconditioned channels, and/or to enable interferenceaware receive combining. In this paper, we try to answer the question if the N data streams should be divided among few users (many streams per user) or many users (few streams per user, enabling receive combining). Analytic results are derived to show how user selection, spatial correlation, heterogeneous user conditions, and imperfect channel acquisition (quantization or estimation errors) affect the performance when sending the maximal number of streams or one stream per scheduled user—the two extremes in data stream allocation. While contradicting observations on this topic have been reported in prior works, we show that selecting many users and allocating one stream per user (i.e., exploiting receive combining) is the best candidate under realistic conditions. This is explained by the provably stronger resilience towards spatial correlation and the larger benefit from multiuser diversity. This fundamental result has positive implications for the design of downlink systems as it reduces the hardware requirements at the user devices and simplifies the throughput optimization. Index Terms—Multiuser MIMO, channel estimation, limited feedback, blockdiagonalization, zeroforcing, receive combining.
Differential feedback of channel Gram matrices for block diagonalized multiuser MIMO systems
 in Proc. 2010 IEEE Intl. Conf. on Communications
"... Abstract—This paper proposes a differential quantization strategy to be used in the feedback link of a multiinputmultioutput (MIMO) multiuser broadcast communication system. This strategy is based on an algorithm presented for single user MIMO, and is applied to broadcast systems where the transm ..."
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Cited by 2 (2 self)
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Abstract—This paper proposes a differential quantization strategy to be used in the feedback link of a multiinputmultioutput (MIMO) multiuser broadcast communication system. This strategy is based on an algorithm presented for single user MIMO, and is applied to broadcast systems where the transmitter design is based on block diagonalization, i.e., the transmissions are optimized so as not to produce multiuser interference at the receive terminals, which are using more than one antenna each. The algorithm is applied to the channel Gram matrices exploiting geodesic curves and the intrinsic geometry of positive definite Hermitian matrices. Furthermore, the differential nature of the algorithm exploits the correlation in time present in real channels. Simulation results in the paper show that the proposed algorithm outperforms other techniques based on the direct quantization of the channel matrix. Index Terms—MIMO systems, multiuser systems, broadcast channels, feedback communication, quantization, differential geometry. I.