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33
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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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.
Recursive and trellisbased feedback reduction for MIMOOFDM with ratelimited feedback
 IEEE Trans. Wireless Commun
, 2006
"... Abstract — We investigate an adaptive MIMOOFDM system with a feedback link that can only convey a finite number of bits. We consider three different transmitter configurations: i) beamforming applied per OFDM subcarrier, ii) precoded spatial multiplexing applied per subcarrier, and iii) precoded or ..."
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Abstract — We investigate an adaptive MIMOOFDM system with a feedback link that can only convey a finite number of bits. We consider three different transmitter configurations: i) beamforming applied per OFDM subcarrier, ii) precoded spatial multiplexing applied per subcarrier, and iii) precoded orthogonal space time block coding applied per subcarrier. Depending on the channel realization, the receiver selects the optimal beamforming vector or precoding matrix from a finitesize codebook on each subcarrier, and informs the transmitter through finiterate feedback. Exploiting the fact that the channel responses across OFDM subcarriers are correlated, we propose two methods to reduce the amount of feedback. One is recursive feedback encoding that selects the optimal beamforming/precoding choices sequentially across the subcarriers, and adopts a smallersize timevarying codebook per subcarrier depending on prior decisions. The other is trellisbased feedback encoding that selects the optimal decisions for all subcarriers at once along a trellis structure via the Viterbi algorithm. Our methods are applicable to different transmitter configurations in a unified fashion. Simulation results demonstrate that the trellisbased approach outperforms the recursive method as well as an existing interpolationbased alternative at high signaltonoiseratio, as the latter suffers from “diversity loss.” Index Terms — Finiterate feedback, multiinput multioutput (MIMO), OFDM, recursive vector quantization, trellis coded quantization. I.
Bit allocation and statistical precoding for correlated MIMO channels with limited feedback
 IEEE Trans. Veh. Technol
, 2012
"... Abstract—In this paper, we jointly consider statistical precoding and feedback of bit allocation (BA) for multipleinput– multipleouput (MIMO) systems over correlated channels. The proposed system will be termed a BA system. We assume that the statistics of the channel is known to the transmitter ..."
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Cited by 7 (6 self)
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Abstract—In this paper, we jointly consider statistical precoding and feedback of bit allocation (BA) for multipleinput– multipleouput (MIMO) systems over correlated channels. The proposed system will be termed a BA system. We assume that the statistics of the channel is known to the transmitter and a reverse link of very low rate is available so that the receiver can send back the quantized BA. Based on the statistics of the channel, we derive the statistical precoder so that bounds of the error rate averaged over the random correlated channel are minimized. Due to statistical precoding, the distribution of the BA is highly nonuniform. Treating BA as a vector signal, we quantize it using vector quantization (VQ), which is known to be particularly useful for quantizing signals with nonuniform distributions. As the distribution of BA is taken into consideration in the codebook design, a good tradeoff between performance and feedback rate can be achieved. Simulations show that the combination of statistical precoding and VQbased quantization for BA leads to good performance with a small number of feedback bits. Index Terms—Bit allocation, correlated channel, MIMO, precoding, VQ.
Interpolationbased multimode precoding for MIMOOFDM systems
 in EURASIP Proc. EUSIPCO
, 2005
"... Abstract — Spatial multiplexing with multimode precoding provides a means to achieve both high capacity and high reliability in multipleinput multipleoutput orthogonal frequencydivision multiplexing (MIMOOFDM) systems. Multimode precoding uses linear transmit precoding that adapts the number of ..."
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Cited by 6 (1 self)
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Abstract — Spatial multiplexing with multimode precoding provides a means to achieve both high capacity and high reliability in multipleinput multipleoutput orthogonal frequencydivision multiplexing (MIMOOFDM) systems. Multimode precoding uses linear transmit precoding that adapts the number of spatial multiplexing data streams or modes, according to the transmit channel state information (CSI). As such, it typically requires complete knowledge of the multimode precoding matrices for each subcarrier at the transmitter. In practical scenarios where the CSI is acquired at the receiver and fed back to the transmitter through a lowrate feedback link, this requirement may entail a prohibitive feedback overhead. In this paper, we propose to reduce the feedback requirement by combining codebookbased precoder quantization, to efficiently quantize and represent the optimal precoder on each subcarrier, and multimode precoder frequency downsampling and interpolation, to efficiently reconstruct the precoding matrices on all subcarriers based on the feedback of the indexes of the quantized precoders only on a fraction of the subcarriers. To enable this efficient interpolationbased quantized multimode precoding solution, we introduce (1) a novel precoder codebook design that lends itself to precoder interpolation, across subcarriers, followed by mode selection, (2) a new precoder interpolator and, finally, (3) a clustered mode selection approach that significantly reduces the feedback overhead related to the mode information on each subcarrier. MonteCarlo biterror rate (BER) performance simulations demonstrate the effectiveness of the proposed quantized multimode precoding solution, at reasonable feedback overhead. Index Terms — Multipleinput multipleoutput (MIMO), OFDM, limited feedback, vector quantization, mode selection, linear precoding, matrix interpolation under a unitary constraint. I.
Feedback Quantization for Linear Precoded Spatial Multiplexing
, 2008
"... This paper gives an overview and a comparison of recent feedback quantization schemes for linear precoded spatial multiplexing systems. In addition, feedback compression methods are presented that exploit the time correlation of the channel. These methods can be roughly divided into two classes. The ..."
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Cited by 6 (0 self)
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This paper gives an overview and a comparison of recent feedback quantization schemes for linear precoded spatial multiplexing systems. In addition, feedback compression methods are presented that exploit the time correlation of the channel. These methods can be roughly divided into two classes. The first class tries to minimize the data rate on the feedback link while keeping the performance constant. This class is novel and relies on entropy coding. The second class tries to optimize the performance while using the maximal data rate on the feedback link. This class is presented within the welldeveloped framework of finitestate vector quantization. Within this class, existing as well as novel methods are presented and compared.
Feedback reduction for spatial multiplexing with linear precoding
 in Proc., IEEE Int. Conf. Acoust., Speech and Sig. Proc
, 2007
"... This paper presents two novel methods to optimally compress the feedback for spatial multiplexing with linear precoding. The methods exploit the time correlation of the channel and the knowledge of the previously fed back precoder matrices to estimate the conditional probabilities of the different p ..."
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This paper presents two novel methods to optimally compress the feedback for spatial multiplexing with linear precoding. The methods exploit the time correlation of the channel and the knowledge of the previously fed back precoder matrices to estimate the conditional probabilities of the different possible feedback indices. These probabilities are then used to losslessly compress the actual feedback using variablelength codes. Two compression schemes are presented, one for a nondedicated feedback channel and one for a dedicated feedback channel. Index Terms — MIMO systems, linear precoding, partial CSI feedback 1.
Minimizing transmit power for coherent communications in wireless sensor networks with finiterate feedback
 IEEE Trans. Signal Process
, 2008
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Power Allocation for the Fading Relay Channel with Limited Feedback
 in Proc. IEEE ICC2010
, 2006
"... Abstract—It has been shown that channel state information (CSI) at transmitter can significantly increase the performance of a relay system. However, most of the existing designs assume perfect CSI at the transmitters. Since most practical systems can only obtain partial CSI at the transmitters, it ..."
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Cited by 3 (2 self)
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Abstract—It has been shown that channel state information (CSI) at transmitter can significantly increase the performance of a relay system. However, most of the existing designs assume perfect CSI at the transmitters. Since most practical systems can only obtain partial CSI at the transmitters, it is necessary to analyze the relay channels with limited CSI feedback. Our objective in this paper is to find the optimal power allocation strategy for relay channel under different levels of transmitter CSI, with the system outage probability constraint. We consider a DecodeandForward (DF) cooperative diversity model where one source node communicates with one destination node assisted by one half duplex relay. The Lloyd Algorithm is employed to quantize the CSI at receiver and construct the codebook, whose copies are also equipped on the source and the relay nodes. Each code in the codebook is a power allocation vector. Simulation results show that a few feedback bits can significantly improve the system performance.
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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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.
QUANTIZED FEEDBACK AND FEEDBACK REDUCTION FOR PRECODED SPATIAL MULTIPLEXING MIMO SYSTEMS Invited Paper
"... In this paper, we discuss different options for quantized feedback and feedback reduction for a precoded spatialmultiplexing multipleinput multipleoutput (MIMO) system in a timevarying channel. The novel contributions of this paper are a quantized feedback strategy based on the biterrorrate (B ..."
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In this paper, we discuss different options for quantized feedback and feedback reduction for a precoded spatialmultiplexing multipleinput multipleoutput (MIMO) system in a timevarying channel. The novel contributions of this paper are a quantized feedback strategy based on the biterrorrate (BER) of a linear receiver, and two new feedback reduction strategies for a timevarying channel. Both these feedback reduction schemes exploit the time correlation of the MIMO channel. They basically can be viewed as an optimized generalization of existing feedback reduction strategies. 1.