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Optimization of Training and Feedback Overhead for Beamforming over Block Fading Channels
, 2009
"... We examine the capacity of beamforming over a singleuser, multiantenna link taking into account the overhead due to channel estimation and limited feedback of channel state information. Multiinput singleoutput (MISO) and multiinput multioutput (MIMO) channels are considered subject to block Ra ..."
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Cited by 17 (0 self)
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We examine the capacity of beamforming over a singleuser, multiantenna link taking into account the overhead due to channel estimation and limited feedback of channel state information. Multiinput singleoutput (MISO) and multiinput multioutput (MIMO) channels are considered subject to block Rayleigh fading. Each coherence block contains L symbols, and is spanned by T training symbols, B feedback bits, and the data symbols. The training symbols are used to obtain a Minimum Mean Squared Error estimate of the channel matrix. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing 2B i.i.d. random vectors, and sends the corresponding B bits back to the transmitter. We derive bounds on the beamforming capacity for MISO and MIMO channels and characterize the optimal (ratemaximizing) training and feedback overhead (T and B) as L and the number of transmit antennas Nt both become large. The optimal Nt is limited by the coherence time, and increases as L / logL. For the MISO channel the optimal T/L and B/L (fractional overhead due to training and feedback) are asymptotically the same, and tend to zero at the rate 1 / logNt. For the MIMO channel the optimal feedback overhead B/L tends to zero faster (as 1 / log² Nt).
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 ..."
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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.
Capacity of Beamforming with Limited Training and Feedback
"... We examine the capacity of beamforming over a MultiInput/SingleOutput block Rayleigh fading channel with finite training for channel estimation and limited feedback. A fixedlength packet is assumed, which is spanned by ¢ training symbols, £ feedback bits, and the data symbols. The training symb ..."
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Cited by 11 (5 self)
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We examine the capacity of beamforming over a MultiInput/SingleOutput block Rayleigh fading channel with finite training for channel estimation and limited feedback. A fixedlength packet is assumed, which is spanned by ¢ training symbols, £ feedback bits, and the data symbols. The training symbols are used to obtain a Minimum Mean Squared Error (MMSE) estimate of the channel vector. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing ¤¦ ¥ i.i.d. random vectors, and relays the corresponding £ bits back to the transmitter. We derive bounds on the capacity and show that for a large number of transmit antennas §© ¨ , the optimal ¢ and £ , which maximize the bounds, are approximately equal and both increase as §�¨������¦��§© ¨. We conclude that with limited training and feedback, the optimal number of antennas to activate also increases as § ¨ �����¦�� § ¨.
Interference alignment with quantized Grassmannian feedback in the Kuser constant MIMO interference channel,” Submitted to
 IEEE Trans. Inf. Theory
, 2013
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CSIT sharing over finite capacity backhaul for spatial interference alignment,” to appear
 in IEEE International Symposium on Information Theory (ISIT). [Online]. Available: http://arxiv.org/pdf/1302.1008v1.pdf
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Limited Feedback for Interference Alignment in the Kuser MIMO Interference Channel
"... Abstract—A simple limited feedback scheme is proposed for interference alignment on the Kuser MultipleInputMultipleOutput Interference Channel (MIMOIC). The scaling of the number of feedback bits with the transmit power required to preserve the multiplexing gain that can be achieved using perfe ..."
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Cited by 4 (1 self)
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Abstract—A simple limited feedback scheme is proposed for interference alignment on the Kuser MultipleInputMultipleOutput Interference Channel (MIMOIC). The scaling of the number of feedback bits with the transmit power required to preserve the multiplexing gain that can be achieved using perfect channel state information (CSI) is derived. This result is obtained through a reformulation of the interference alignment problem in order to exploit the benefits of quantization on the Grassmann manifold, which is well investigated in the singleuser MIMO channel. Furthermore, through simulations we show that the proposed scheme outperforms the naive feedback scheme consisting in independently quantizing the channel matrices, in the sense that it yields a better sum rate performance for the same number of feedback bits. I.
Subcarrier Clustering for MISOOFDM Channels with Quantized Beamforming
"... Abstract—We consider a transmit beamforming for an OFDM channel with multiple transmit antennas and single receive antenna. With channel information, a receiver selects and quantizes transmit beamforming vector for each subcarrier. The quantized beamformers are then relayed to the transmitter via a ..."
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Cited by 3 (3 self)
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Abstract—We consider a transmit beamforming for an OFDM channel with multiple transmit antennas and single receive antenna. With channel information, a receiver selects and quantizes transmit beamforming vector for each subcarrier. The quantized beamformers are then relayed to the transmitter via a ratelimited feedback channel. We propose to reduce the required number of feedback bits by applying a common transmit beamformer for a cluster of adjacent subcarriers. The sum capacity over all subcarriers depends on a cluster size, the number of feedback bits, and the number of channel taps. Approximation of the optimal cluster size that maximizes the sum rates is derived and is shown to predict simulation results very well. Numerical results show that operating with the optimal cluster size can achieve significant performance gain. I.
The multiplexing gain of a twocell MIMO channel with unequal CSI
 in Proc. IEEE International Symposium on Information Theory (ISIT
, 2011
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Optimal Feedback Interval for TemporallyCorrelated Multiantenna Channel
"... Abstract—Assuming perfect channel state information (CSI), the receiver in a pointtopoint multiantenna channel can compute the optimal transmit beamforming vector that maximizes channel capacity. The transmitter, which is not able to estimate the CSI, obtains the quantized transmit beamforming vec ..."
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Cited by 2 (0 self)
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Abstract—Assuming perfect channel state information (CSI), the receiver in a pointtopoint multiantenna channel can compute the optimal transmit beamforming vector that maximizes channel capacity. The transmitter, which is not able to estimate the CSI, obtains the quantized transmit beamforming vector via a ratelimited feedback channel. We assume that time evolution of both MIMO and MISO channels can be modeled as the firstorder autoregressive process parameterized by a temporalcorrelation coefficient. For a limited number of feedback bits, we would like to find out how often the feedback update should take place. Applying a large system limit and random vector quantization (RVQ), we derive the integer optimization problem, which determines the optimal feedback interval that maximizes the average capacity. The analytical results show that the optimal feedback interval depends on the temporal correlation coefficient, available feedback, and the number of transmit and receive antennas. I.
Trellisextended codebooks and successive phase adjustment: A path from LTEAdvanced to FDD massive MIMO systems
 IEEE Transactions on Wireless Communications
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