Results 1  10
of
118
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 ..."
Abstract

Cited by 205 (41 self)
 Add to MetaCart
(Show Context)
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.
Multiuser MIMO Achievable Rates with Downlink Training and Channel State Feedback
"... We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and it is provided to the transmitter by channel state feedback. Unquantized (analog) and quantized (digital) channel state feedback sche ..."
Abstract

Cited by 114 (8 self)
 Add to MetaCart
We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and it is provided to the transmitter by channel state feedback. Unquantized (analog) and quantized (digital) channel state feedback schemes are analyzed and compared under various assumptions. Digital feedback is shown to be potentially superior when the feedback channel uses per channel state coefficient is larger than 1. Also, we show that by proper design of the digital feedback link, errors in the feedback have a minor effect even if simple uncoded modulation is used on the feedback channel. We discuss first the case of an unfaded AWGN feedback channel with orthogonal access and then the case of fading MIMO multiaccess (MIMOMAC). We show that by exploiting the MIMOMAC nature of the uplink channel, a much better scaling of the feedback channel resource with the number of base station antennas can be achieved. Finally, for the case of delayed feedback, we show that in the realistic case where the fading process has (normalized) maximum Doppler frequency shift 0 ≤ F < 1/2, a fraction 1 − 2F of the optimal multiplexing gain is achievable. The general conclusion of this work is that very significant downlink throughput is achievable with simple and efficient channel state feedback, provided that the feedback link is properly designed.
Capacity of a multipleantenna fading channel with a quantized precoding matrix
 IEEE Trans. Inf. Theory
, 2009
"... channel, feedback from the receiver can be used to specify a transmit precoding matrix, which selectively activates the strongest channel modes. Here we analyze the performance of Random Vector Quantization (RVQ), in which the precoding matrix is selected from a random codebook containing independen ..."
Abstract

Cited by 35 (8 self)
 Add to MetaCart
(Show Context)
channel, feedback from the receiver can be used to specify a transmit precoding matrix, which selectively activates the strongest channel modes. Here we analyze the performance of Random Vector Quantization (RVQ), in which the precoding matrix is selected from a random codebook containing independent, isotropically distributed entries. We assume that channel elements are i.i.d. and known to the receiver, which relays the optimal (ratemaximizing) precoder codebook index to the transmitter using B bits. We first derive the large system capacity of beamforming (rankone precoding matrix) as a function of B, where large system refers to the limit as B and the number of transmit and receive antennas all go to infinity with fixed ratios. RVQ for beamforming is asymptotically optimal, i.e., no other quantization scheme can achieve a larger asymptotic rate. We subsequently consider a precoding matrix with arbitrary rank, and approximate the asymptotic RVQ performance with optimal and linear receivers (matched filter and Minimum Mean Squared Error (MMSE)). Numerical examples show that these approximations accurately predict the performance of finitesize systems of interest. Given a target spectral efficiency, numerical examples show that the amount of feedback required by the linear MMSE receiver is only slightly more than that required by the optimal receiver, whereas the matched filter can require significantly more feedback. Index Terms—Beamforming, large system analysis, limited feedback, MultiInput MultiOutput (MIMO), precoding, vector quantization. I.
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 ..."
Abstract

Cited by 25 (3 self)
 Add to MetaCart
(Show Context)
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.
Multimode transmission for the MIMO broadcast channel with imperfect channel state information
 IEEE Transactions on Communications
"... This paper proposes a multimode transmission strategy to improve the spectral efficiency achieved by the multipleinput multipleoutput (MIMO) broadcast channel with delayed and quantized channel state information. It adaptively adjusts the number of active users, denoted as the transmission mode, ..."
Abstract

Cited by 25 (10 self)
 Add to MetaCart
(Show Context)
This paper proposes a multimode transmission strategy to improve the spectral efficiency achieved by the multipleinput multipleoutput (MIMO) broadcast channel with delayed and quantized channel state information. It adaptively adjusts the number of active users, denoted as the transmission mode, to balance transmit array gain, spatial division multiplexing gain, and residual interuser interference. Accurate closedform approximations are derived for the achievable rates for different modes, which are used to select the active mode that maximizes the ergodic throughput. User scheduling algorithms based on multimode transmission are then proposed for the network with a large number of users, to reduce the overall amount of feedback. It is shown that the proposed algorithms provide throughput gains at moderate yet practically relevant signaltonoise ratio. Index Terms MIMO systems, space division multiplexing, broadcast channels, scheduling, feedback, delay effects, adaptive systems. I.
Multiuser MIMO Downlink Made Practical: Achievable Rates with Simple Channel State Estimation and Feedback Schemes
"... We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and explicit channel feedback is performed to provide transmitter channel state information (CSIT). Both “analog” and quantized (digital) ..."
Abstract

Cited by 22 (6 self)
 Add to MetaCart
We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and explicit channel feedback is performed to provide transmitter channel state information (CSIT). Both “analog” and quantized (digital) channel feedback are analyzed, and digital feedback is shown to be potentially superior when the feedback channel uses per channel coefficient is larger than 1. Also, we show that by proper design of the digital feedback link, errors in the feedback have a relatively minor effect even if simple uncoded modulation is used on the feedback channel. We extend our analysis to the case of fading MIMO Multiaccess Channel (MIMOMAC) in the feedback link, as well as to the case of a timevarying channel and feedback delay. We show that by exploiting the MIMOMAC nature of the uplink channel, a fully scalable system with both downlink multiplexing gain and feedback redundancy proportional to the number of base station antennas can be achieved. Furthermore, the feedback strategy is optimized by a nontrivial combination of timedivision and spacedivision multipleaccess. For the case of delayed feedback, we show that in the realistic case where the fading process has (normalized) maximum Doppler frequency shift 0 ≤ F < 1/2, a fraction 1 − 2F of the optimal multiplexing gain is achievable. The general conclusion of this work is that very significant downlink throughput is achievable with simple and efficient channel state feedback, provided that the feedback link is properly designed.
Degrees of Freedom of the Network MIMO Channel With Distributed CSI
, 2013
"... Abstract—In this work, we discuss the joint precoding with finite rate feedback in the socalled network MIMO where the TXs share the knowledge of the data symbols to be transmitted. We introduce a distributed channel state information (DCSI) model where each TX has its own local estimate of the ove ..."
Abstract

Cited by 16 (6 self)
 Add to MetaCart
Abstract—In this work, we discuss the joint precoding with finite rate feedback in the socalled network MIMO where the TXs share the knowledge of the data symbols to be transmitted. We introduce a distributed channel state information (DCSI) model where each TX has its own local estimate of the overall multiuser MIMO channel and must make a precoding decision solely based on the available local CSI. We refer to this channel as the DCSIMIMO channel and the precoding problem as distributed precoding. We extend to the DCSI setting the work from Jindal in [1] for the conventional MIMO Broadcast Channel (BC) in which the number of Degrees of Freedom (DoFs) achieved by Zero Forcing (ZF) was derived as a function of the scaling in the logarithm of the SignaltoNoise Ratio (SNR) of the number of quantizing bits. Particularly, we show the seemingly pessimistic result that the number of DoFs at each user is limited by the worst CSI across all users and across all TXs. This is in contrast to the conventional MIMO BC where the number of DoFs at one user is solely dependent on the quality of the estimation of his own feedback. Consequently, we provide precoding schemes improving on the achieved number of DoFs. For the twouser case, the derived novel precoder achieves a number of DoFs limited by the best CSI accuracy across the TXs instead of the worst with conventional ZF. We also advocate the use of hierarchical quantization of the CSI, for which we show that considerable gains are possible. Finally, we use the previous analysis to derive the DoFs optimal allocation of the feedback bits to the various TXs under a constraint on the size of the aggregate feedback in the network, in the case where conventional ZF is used.
Bit Allocation Laws for MultiAntenna Channel Feedback Quantization: MultiUser Case
"... This paper addresses the optimal design of limitedfeedback downlink multiuser spatial multiplexing systems. A multipleantenna basestation is assumed to serve multiple singleantenna users, who quantize and feed back their channel state information (CSI) through a shared ratelimited feedback cha ..."
Abstract

Cited by 15 (5 self)
 Add to MetaCart
This paper addresses the optimal design of limitedfeedback downlink multiuser spatial multiplexing systems. A multipleantenna basestation is assumed to serve multiple singleantenna users, who quantize and feed back their channel state information (CSI) through a shared ratelimited feedback channel. The optimization problem is cast in the form of minimizing the average transmission power at the basestation subject to users’ target signaltointerferenceplusnoise ratios (SINR) and outage probability constraints. The goal is to derive the feedback bit allocations among the users and the corresponding channel magnitude and direction quantization codebooks in a highresolution quantization regime. Toward this end, this paper develops an optimization framework using approximate analytical closedform solutions, the accuracy of which is then verified by numerical results. The results show that, for channels in the real space, the number of channel direction quantization bits should be (M−1) times the number of channel magnitude quantization bits, where M is the number of basestation antennas. Moreover, users with higher requested qualityofservice (QoS), i.e. lower target outage probabilities, and higher requested downlink rates, i.e. higher target SINR’s, should use larger shares of the feedback rate. It is also shown that, for the target QoS parameters to be feasible, the total feedback bandwidth should scale logarithmically with the geometric mean of the target SINR values and the geometric mean of the inverse target outage probabilities. In particular, the minimum required feedback rate is shown to increase if the users ’ target parameters deviate from the corresponding geometric means. Finally, the paper shows that, as the total number of feedback bits B increases, the performance of the limitedfeedback system approaches the perfectCSI system as 2 −B/M2
1 MultiUser Diversity vs. Accurate Channel State Information in MIMO Downlink Channels
"... In a multiple transmit antenna, single antenna per receiver downlink channel with limited channel state feedback, we consider the following question: given a constraint on the total systemwide feedback load, is it preferable to get lowrate/coarse channel feedback from a large number of receivers o ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
(Show Context)
In a multiple transmit antenna, single antenna per receiver downlink channel with limited channel state feedback, we consider the following question: given a constraint on the total systemwide feedback load, is it preferable to get lowrate/coarse channel feedback from a large number of receivers or highrate/highquality feedback from a smaller number of receivers? Acquiring feedback from many receivers allows multiuser diversity to be exploited, while highrate feedback allows for very precise selection of beamforming directions. We show that there is a strong preference for obtaining highquality feedback, and that obtaining nearperfect channel information from as many receivers as possible provides a significantly larger sum rate than collecting a few feedback bits from a large number of users. I.
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 ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
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.