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189
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.
Multi-antenna downlink channels with limited feedback and user selection
- IEEE J. Select. Areas Commun
, 2007
"... Abstract — We analyze the sum-rate 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 119 (2 self)
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Abstract — We analyze the sum-rate 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 sum-rate 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, zero-forcing beamforming, multiuser diversity, broadcast channel,
Pilot contamination and precoding in multi-cell TDD systems
- LU et al.: OVERVIEW OF MASSIVE MIMO: BENEFITS AND CHALLENGES 757
, 2011
"... Abstract—This paper considers a multi-cell multiple antenna system with precoding used at the base stations for downlink transmission. Channel state information (CSI) is essential for precoding at the base stations. An effective technique for ob-taining this CSI is time-division duplex (TDD) operati ..."
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Cited by 76 (6 self)
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Abstract—This paper considers a multi-cell multiple antenna system with precoding used at the base stations for downlink transmission. Channel state information (CSI) is essential for precoding at the base stations. An effective technique for ob-taining this CSI is time-division duplex (TDD) operation where uplink training in conjunction with reciprocity simultaneously provides the base stations with downlink as well as uplink channel estimates. This paper mathematically characterizes the impact that uplink training has on the performance of such multi-cell multiple antenna systems. When non-orthogonal training sequences are used for uplink training, the paper shows that the precoding matrix used by the base station in one cell becomes corrupted by the channel between that base station and the users in other cells in an undesirable manner. This paper analyzes this fundamental problem of pilot contamination in multi-cell systems. Furthermore, it develops a new multi-cell MMSE-based precoding method that mitigates this problem. In addition to being linear, this precoding method has a simple closed-form expression that results from an intuitive optimization. Numerical results show significant performance gains compared to certain popular single-cell precoding methods. Index Terms—Time-division duplex systems, uplink training, pilot contamination, MMSE precoding. I.
Large system analysis of linear precoding in correlated MISO broadcast channels under limited feedback
- IEEE TRANS. INF. THEORY
, 2012
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Interference Alignment Under Limited Feedback for MIMO Interference Channels
- ARXIV PREPRINT ARXIV:0911.5509, 2009. [ONLINE]. AVAILABLE: HTTP://ARXIV.ORG/ABS/0911.5509
, 2009
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Capacity of a multiple-antenna 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 35 (8 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 (rate-maximizing) precoder codebook index to the transmitter using B bits. We first derive the large system capacity of beamforming (rank-one 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 finite-size 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, Multi-Input Multi-Output (MIMO), precoding, vector quantization. I.
Limited feedback beamforming over temporally-correlated channels
- IEEE Trans. Signal Process
, 2009
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Performance of Orthogonal Beamforming for SDMA with Limited Feedback
- IEEE TRANS. VEHICULAR TECHNOLOGY
, 2007
"... On the multi-antenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. Optimal multi-user transmission, known as dirty paper coding, requires non-causal channel state information (CSI) and extreme complexity and is hence not directly realizable. A ..."
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Cited by 33 (6 self)
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On the multi-antenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. Optimal multi-user transmission, known as dirty paper coding, requires non-causal 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 multi-user simultaneous transmission, enables limited feedback, and is capable of exploiting multi-user 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 interference-limited regime, the throughput of PU2RC is shown to scale logarithmically with the number of users. In the normal and noise-limited 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 zero-forcing beamforming if the number of users is sufficiently large.
Large System Analysis of Linear Precoding in MISO Broadcast Channels with Limited Feedback
, 2010
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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 24 (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 quasi-closed 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.
