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40
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 43 (8 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.
Multiantenna downlink channels with limited feedback and user selection
 IEEE J. Select. Areas Commun
, 2007
"... Abstract — We analyze the sumrate performance of a multiantenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to ..."
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Cited by 36 (2 self)
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Abstract — We analyze the sumrate performance of a multiantenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to directional information, information regarding the quality of each channel. Such information should reflect both the channel magnitude and the quantization error. Expressions for the SINR distribution and the sumrate are derived, and tradeoffs between the number of feedback bits, the number of users, and the SNR are observed. In particular, for a target performance, having more users reduces feedback load. Index Terms — MIMO, quantized feedback, limited feedback, zeroforcing beamforming, multiuser diversity, broadcast channel,
Robust power allocation designs for multiuser and multiantenna downlink communication systems through convex optimization
 IEEE J. Sel. Areas Commun
, 2007
"... Abstract — In this paper, we study the design of the transmitter in the downlink of a multiuser and multiantenna wireless communications system, considering the realistic scenario where only an imperfect estimate of the actual channel is available at both communication ends. Precisely, the actual ch ..."
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Cited by 16 (1 self)
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Abstract — In this paper, we study the design of the transmitter in the downlink of a multiuser and multiantenna wireless communications system, considering the realistic scenario where only an imperfect estimate of the actual channel is available at both communication ends. Precisely, the actual channel is assumed to be inside an uncertainty region around the channel estimate, which models the imperfections of the channel knowledge that may arise from, e.g., estimation Gaussian errors, quantization effects, or combinations of both sources of errors. In this context, our objective is to design a robust power allocation among the information symbols that are to be sent to the users such that the total transmitted power is minimized, while maintaining the necessary quality of service to obtain reliable communication links between the base station and the users for any possible realization of the actual channel inside the uncertainty region. This robust power allocation is obtained as the solution to a convex optimization problem, which, in general, can be numerically solved in a very efficient way, and even for a particular case of the uncertainty region, a quasiclosed form solution can be found. Finally, the goodness of the robust proposed transmission scheme is presented through numerical results. Index Terms — Robust designs, imperfect CSI, multiantenna systems, broadcast channel, convex optimization.
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 ..."
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Cited by 11 (6 self)
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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.
Performance of Orthogonal Beamforming for SDMA with Limited Feedback
 IEEE TRANS. VEHICULAR TECHNOLOGY
, 2007
"... On the multiantenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. Optimal multiuser transmission, known as dirty paper coding, requires noncausal channel state information (CSI) and extreme complexity and is hence not directly realizable. A ..."
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Cited by 10 (2 self)
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On the multiantenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. Optimal multiuser transmission, known as dirty paper coding, requires noncausal channel state information (CSI) and extreme complexity and is hence not directly realizable. A more practical design, named per user unitary and rate control (PU2RC), has been proposed for emerging cellular standards. PU2RC supports multiuser simultaneous transmission, enables limited feedback, and is capable of exploiting multiuser diversity. Its key feature is an orthogonal beamforming (or precoding) constraint, where each user selects a beamformer (or precoder) from a codebook of multiple orthonormal bases. In this paper, the asymptotic throughput scaling laws for PU2RC with a large user pool are derived for different regimes. In the interferencelimited regime, the throughput of PU2RC is shown to scale logarithmically with the number of users. In the normal and noiselimited regimes, the throughput is found to scale double logarithmically with the number of users and also linearly with the number of antennas at the base station. In addition, numerical results show that PU2RC achieves higher throughput and is more robust against CSI quantization errors than the popular alternative of zeroforcing beamforming if the number of users is sufficiently large.
On the Tradeoff Between Feedback and Capacity in Measured MUMIMO Channels
, 2009
"... In this work we study the capacity of multiuser multipleinput multipleoutput (MUMIMO) downlink channels with codebookbased limited feedback using real measurement data. Several aspects of MUMIMO channels are evaluated. Firstly, we compare the sum rate of different MUMIMO precoding schemes in ..."
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Cited by 6 (3 self)
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In this work we study the capacity of multiuser multipleinput multipleoutput (MUMIMO) downlink channels with codebookbased limited feedback using real measurement data. Several aspects of MUMIMO channels are evaluated. Firstly, we compare the sum rate of different MUMIMO precoding schemes in various channel conditions. Secondly, we study the effect of different codebooks on the performance of limited feedback MUMIMO. Thirdly, we relate the required feedback rate with the achievable rate on the downlink channel. Real multiuser channel measurement data acquired with the Eurecom MIMO OpenAir Sounder (EMOS) is used. To the best of our knowledge, these are the first measurement results giving evidence of how MUMIMO precoding schemes depend on the precoding scheme, channel characteristics, user separation, and codebook. For example, we show that having a large user separation as well as codebooks adapted to the second order statistics of the channel gives a sum rate close to the theoretical limit. A small user separation due to bad scheduling or a poorly adapted codebook on the other hand can impair the gain brought by MUMIMO. The tools and the analysis presented in this paper allow the system designer to tradeoff downlink rate with feedback rate by carefully choosing the codebook.
How many users should be turned on in a multiantenna broadcast channel
 IEEE J. Select. Areas Commun
, 2008
"... Abstract—This paper considers broadcast channels with L antennas at the base station and m singleantenna users, where L and m are typically of the same order. We assume that only partial channel state information is available at the base station through a finite rate feedback. Our key observation i ..."
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Cited by 5 (3 self)
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Abstract—This paper considers broadcast channels with L antennas at the base station and m singleantenna users, where L and m are typically of the same order. We assume that only partial channel state information is available at the base station through a finite rate feedback. Our key observation is that the optimal number of onusers (users turned on), say s, is a function of signaltonoise ratio (SNR) and feedback rate. In support of this, an asymptotic analysis is employed where L, m and the feedback rate approach infinity linearly. We derive the asymptotic optimal feedback strategy as well as a realistic criterion to decide which users should be turned on. The corresponding asymptotic throughput per antenna, which we define as the spatial efficiency, turns out to be a function of the number of onusers s, and therefore s must be chosen appropriately. Based on the asymptotics, a scheme is developed for systems with finite many antennas and users. Compared with other studies in which s is presumed constant, our scheme achieves a significant gain. Furthermore, our analysis and scheme are valid for heterogeneous systems where different users may have different path loss coefficients and feedback rates. Index Terms—Broadcast channels, feedback, MIMO systems, throughput. I.
Structure of channel quantization codebook for multiuser spatial multiplexing systems
 Proc. IEEE International Conference on Communications (ICC), Cape Town, South Africa
, 2010
"... Abstract—This paper studies the structure of the channel quantization codebook for multiuser MISO systems with limited channel state information at the basestation. The problem is cast in the form of minimizing the sum power subject to the worstcase SINR constraints over spherical channel uncertai ..."
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Cited by 4 (4 self)
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Abstract—This paper studies the structure of the channel quantization codebook for multiuser MISO systems with limited channel state information at the basestation. The problem is cast in the form of minimizing the sum power subject to the worstcase SINR constraints over spherical channel uncertainty regions. This paper adopts a zeroforcing approach for beamforming vectors design, and uses a robust optimization technique via semidefinite programming (SDP) for power control as the benchmark performance measure. We then present an alternative less complex and practically feasible method for computing the power values and present sufficient conditions on the uncertainty radius so that the resulting sum power remains close to the SDP solution. The proposed conditions guarantee that the interference caused by the channel uncertainties can be effectively controlled. Based on these conditions, we study the structure of the channel quantization codebooks and show that the quantization codebook has a product form that involves spatially uniform quantization of the channel direction, and independent channel magnitude quantization which is uniform in dB scale. The structural insight obtained by our analysis also gives a bitsharing law for dividing the quantization bits between the two codebooks. We finally show that the total number of quantization bits should increase as log(SINRtarget) as the target SINR increases. I.
TwoStage Channel Feedback for Beamforming and Scheduling in Network MIMO Systems
"... Abstract—This paper proposes an efficient twostage beamforming and scheduling algorithm for the limitedfeedback cooperative multipoint (CoMP) systems. The system includes multiple basestations cooperatively transmitting data to a pool of users, which share a ratelimited feedback channel for sen ..."
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Cited by 4 (3 self)
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Abstract—This paper proposes an efficient twostage beamforming and scheduling algorithm for the limitedfeedback cooperative multipoint (CoMP) systems. The system includes multiple basestations cooperatively transmitting data to a pool of users, which share a ratelimited feedback channel for sending back the channel state information (CSI). The feedback mechanism is divided into two stages that are used separately for scheduling and beamforming. In the first stage, the users report their best channel gain from all the basestation antennas and the basestations schedule the best user for each of their antennas. The scheduled users are then polled in the second stage to feedback their quantized channel vectors. The paper proposes an analytical framework to derive the bit allocation between the two feedback stages and the bit allocation for quantizing each user’s CSI. For a total number of feedback bits B, it is shown that the number of bits assigned to the second feedback stage should scale as log B. Furthermore, in quantizing channel vectors from different basestations, each user should allocate its feedback budget in proportion to the logarithm of the corresponding channel gains. These bit allocation are then used to show that the overall system performance scales doublelogarithmically with B and logarithmically with the transmit SNR. The paper further presents several numerical results to show that, in comparison with other beamformingscheduling algorithms in the literature, the proposed scheme provides a consistent improvement in downlink sum rate and network utility. Such improvements, in particular, are achieved in spite of a significant reduction in the beamformingscheduling computational complexity, which makes the proposed scheme an attractive solution for practical system implementations. I.