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163
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 finite-rate 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, single-user, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.
What Is the Value of Limited Feedback for MIMO Channels?
, 2004
"... Feedbackinacommunicationssystemcan enablethetransmittertoexploitchannelcondi - tionsandavoidinterference.Inthecaseofa multiple-inputmultiple-outputchannel,feedback canbeusedtospecifyaprecodingmatrixatthe transmitter,whichactivatesthestrongestchan - nelmodes.Insituationswherethefeedbackis severelylim ..."
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Cited by 176 (31 self)
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Feedbackinacommunicationssystemcan enablethetransmittertoexploitchannelcondi - tionsandavoidinterference.Inthecaseofa multiple-inputmultiple-outputchannel,feedback canbeusedtospecifyaprecodingmatrixatthe transmitter,whichactivatesthestrongestchan - nelmodes.Insituationswherethefeedbackis severelylimited,importantissuesarehowto quantizetheinformationneededatthetransmitterandhowmuchimprovementinassociated performancecanbeobtainedasafunctionof theamountoffeedbackavailable.Wegivean overviewofsomerecentworkinthisarea.Meth - odsarepresentedforconstructingasetofpossibleprecodingmatrices, fromwhichaparticular choicecanberelayedtothetransmitter.Perfor - manceresultsshowthatevenafewbitsoffeedbackcanprovideperformanceclosetothatwith fullchannelknowledgeatthetransmitter.
Limited feedback unitary precoding for spatial multiplexing systems
- IEEE Trans. Info. Theory
, 2005
"... Abstract—Multiple-input multiple-output (MIMO) wireless systems use antenna arrays at both the transmitter and receiver to provide communication links with substantial diversity and capacity. Spatial multiplexing is a common space–time modulation technique for MIMO communication systems where indepe ..."
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Cited by 125 (18 self)
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Abstract—Multiple-input multiple-output (MIMO) wireless systems use antenna arrays at both the transmitter and receiver to provide communication links with substantial diversity and capacity. Spatial multiplexing is a common space–time modulation technique for MIMO communication systems where independent information streams are sent over different transmit antennas. Unfortunately, spatial multiplexing is sensitive to illconditioning of the channel matrix. Precoding can improve the resilience of spatial multiplexing at the expense of full channel knowledge at the transmitter—which is often not realistic. This correspondence proposes a quantized precoding system where the optimal precoder is chosen from a finite codebook known to both receiver and transmitter. The index of the optimal precoder is conveyed from the receiver to the transmitter over a low-delay feedback link. Criteria are presented for selecting the optimal precoding matrix based on the error rate and mutual information for different receiver designs. Codebook design criteria are proposed for each selection criterion by minimizing a bound on the average distortion assuming a Rayleigh-fading matrix channel. The design criteria are shown to be equivalent to packing subspaces in the Grassmann manifold using the projection two-norm and Fubini–Study distances. Simulation results showthat the proposed system outperforms antenna subset selection and performs close to optimal unitary precoding with a minimal amount of feedback. Index Terms—Diversity methods, Grassmannian subspace packing, multiple-input multiple-output (MIMO) systems, quantized precoding, Rayleigh channels, spatial multiplexing, vertical Bell Labs layered space– time (V-BLAST) architecture. I.
Network beamforming using relays with perfect channel information
- IEEE Trans. Inform. Theory
, 2009
"... This paper is on beamforming in wireless relay networks with perfect channel information at relays, the receiver, and the transmitter if there is a direct link between the transmitter and receiver. It is assumed that every node in the network has its own power constraint. A two-step amplify-and-forw ..."
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Cited by 87 (10 self)
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This paper is on beamforming in wireless relay networks with perfect channel information at relays, the receiver, and the transmitter if there is a direct link between the transmitter and receiver. It is assumed that every node in the network has its own power constraint. A two-step amplify-and-forward protocol is used, in which the transmitter and relays not only use match filters to form a beam at the receiver but also adaptively adjust their transmit powers according to the channel strength information. For a network with any number of relays and no direct link, the optimal power control is solved analytically. The complexity of finding the exact solution is linear in the number of relays. Our results show that the transmitter should always use its maximal power and the optimal power used at a relay is not a binary function. It can take any value between zero and its maximum transmit power. Also, surprisingly, this value depends on the quality of all other channels in addition to the relay’s own channels. Despite this coupling fact, distributive strategies are proposed in which, with the aid of a low-rate broadcast from the receiver, a relay needs only its own channel information to implement the optimal power control. Simulated performance shows that network beamforming achieves the maximal diversity and outperforms other existing schemes. ∗This work was supported in part by ARO under the Multi-University Research Initiative (MURI) grant #W911NF-04-1-0224. 1 Then, beamforming in networks with a direct link are considered. We show that when the direct link exists during the first step only, the optimal power control at the transmitter and relays is the same as that of networks with no direct link. For networks with a direct link during the second step only and both steps, recursive numerical algorithms are proposed to solve the power control problem. Simulation shows that by adjusting the transmitter and relays ’ powers adaptively, network performance is significantly improved. 1
On the design of MIMO block-fading channels with feedback-link capacity constraint,”
- IEEE Trans. Commun.,
, 2004
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Design and analysis of transmitbeamforming based on limited-rate feedback
, 2006
"... This paper deals with design and performance analysis of transmit beamformers for multiple-input multiple-output (MIMO) systems based on bandwidth-limited information that is fed back from the receiver to the transmitter. By casting the design of transmit beamforming based on limited-rate feedback ..."
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Cited by 75 (1 self)
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This paper deals with design and performance analysis of transmit beamformers for multiple-input multiple-output (MIMO) systems based on bandwidth-limited information that is fed back from the receiver to the transmitter. By casting the design of transmit beamforming based on limited-rate feedback as an equivalent sphere vector quantization (SVQ) problem, multiantenna beamformed transmissions through independent and identically distributed (i.i.d.) Rayleigh fading channels are first considered. The rate-distortion function of the vector source is upper-bounded, and the operational rate-distortion performance achieved by the generalized Lloyd’s algorithm is lower-bounded. Although different in nature, the two bounds yield asymptotically equivalent performance analysis results. The average signal-to-noise ratio (SNR) performance is also quantified. Finally, beamformer codebook designs are studied for correlated Rayleigh fading channels, and a low-complexity codebook design that achieves near-optimal performance is derived.
Quantifying the Power Loss when Transmit Beamforming Relies on Finite Rate Feedback
, 2003
"... Transmit beamforming achieves optimal performance in systems with multiple transmit-antennas and a single receive-antenna, from both the capacity and the received signalto -noise ratio (SNR) perspectives, but ideally requires perfect channel knowledge at the transmitter. In practical systems where t ..."
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Cited by 67 (9 self)
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Transmit beamforming achieves optimal performance in systems with multiple transmit-antennas and a single receive-antenna, from both the capacity and the received signalto -noise ratio (SNR) perspectives, but ideally requires perfect channel knowledge at the transmitter. In practical systems where the feedback link can only convey a finite number of bits, transmit-beamformer designs have been extensively investigated using either the outage probability, or the average SNR, as the figure of merit. In this paper, we study the symbol error rate (SER) for transmit beamforming with finite-rate feedback, in a multi-input single-output (MISO) setting. We derive a SER lower bound, which is tight for good beamformer designs. Comparing this bound with the SER corresponding to the ideal case, we quantify the power loss due to the finite rate constraint, across the entire SNR range.
How Accurate Channel Prediction needs to be for Transmit-Beamforming with Adaptive Modulation over Rayleigh MIMO Channels?
, 2004
"... Adaptive modulation improves the system throughput considerably by matching transmitter parameters to timevarying wireless fading channels. Crucial to adaptive modulation is the quality of channel state information (CSI) at the transmitter. In this paper, we first present a channel predictor based o ..."
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Cited by 57 (3 self)
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Adaptive modulation improves the system throughput considerably by matching transmitter parameters to timevarying wireless fading channels. Crucial to adaptive modulation is the quality of channel state information (CSI) at the transmitter. In this paper, we first present a channel predictor based on pilot symbol assisted modulation (PSAM) for multi-input multioutput (MIMO) Rayleigh fading channels. We then analyze the impact of the channel prediction error on the bit error rate (BER) performance of a transmit-beamformer with adaptive modulation that treats the predicted channels as perfect. Our numerical results reveal the critical value of the normalized prediction error, below which the predicted channels can be treated as perfect by the adaptive modulator; otherwise, explicit consideration of the channel imperfection must be accounted for at the transmitter.
Limited feedback unitary precoding for orthogonal space-time block codes
- IEEE Trans. Signal Processing
, 2005
"... Abstract—Orthogonal space-time block codes (OSTBCs) are a class of easily decoded space-time codes that achieve full diversity order in Rayleigh fading channels. OSTBCs exist only for certain numbers of transmit antennas and do not provide array gain like diversity techniques that exploit transmit c ..."
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Cited by 56 (7 self)
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Abstract—Orthogonal space-time block codes (OSTBCs) are a class of easily decoded space-time codes that achieve full diversity order in Rayleigh fading channels. OSTBCs exist only for certain numbers of transmit antennas and do not provide array gain like diversity techniques that exploit transmit channel information. When channel state information is available at the transmitter, though, precoding the space-time codeword can be used to support different numbers of transmit antennas and to improve array gain. Unfortunately, transmitters in many wireless systems have no knowledge about current channel conditions. This motivates limited feedback precoding methods such as channel quantization or antenna subset selection. This paper investigates a limited feedback approach that uses a codebook of precoding matrices known a priori to both the transmitter and receiver. The receiver chooses a matrix from the codebook based on current channel conditions and conveys the optimal codebook matrix to the transmitter over an error-free, zero-delay feedback channel. A criterion for choosing the optimal precoding matrix in the codebook is proposed that relates directly to minimizing the probability of symbol error of the precoded system. Low average distortion codebooks are derived based on the optimal codeword selection criterion. The resulting design is found to relate to the famous applied mathematics problem of subspace packing in the Grassmann manifold. Codebooks designed by this method are proven to provide full diversity order in Rayleigh fading channels. Monte Carlo simulations show that limited feedback precoding performs better than antenna subset selection. Index Terms—Diversity methods, Grassmannian subspace packing, MIMO systems, orthogonal space-time block coding,
Interpolation based transmit beamforming for MIMO-OFDM with limited feedback,” in
- Proc. IEEE Int. Conf. on Communications,
, 2004
"... Abstract-Transmit beamforming with receive combining is a simple method for exploiting the significant diversity provided by multiple-input multiple-output (MIMO) systems, and the use of orthogonal frequency division multiplexing (OFDM) enables low complexity implementation of this scheme over freq ..."
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Cited by 53 (4 self)
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Abstract-Transmit beamforming with receive combining is a simple method for exploiting the significant diversity provided by multiple-input multiple-output (MIMO) systems, and the use of orthogonal frequency division multiplexing (OFDM) enables low complexity implementation of this scheme over frequency selective MIMO channels. This paper proposes a beamforming technique that reduces feedback requirements for optimal beamforming. In the proposed architecture, the receiver sends back quantized versions of select beamforming vectors and the transmitter reconstructs the missing beamforming vectors through interpolation. Since a beamforming vector is phase invariant and has unit norm, a new spherical linear interpolator is proposed that exploits additional parameters for phase rotation. These parameters are determined at the receiver in the sense of maximizing the minimum channel gain or capacity, and sent back to the transmitter along with the quantized beamforming vectors. Simulation results show that the proposed beamforming method requires much less feedback information than optimal beamforming with only slight diversity loss.
