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18
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 104 (17 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.
Multiuser diversity vs. accurate channel feedback for mimo broadcast channel”, submitted to
 IEEE ICC
, 2008
"... Abstract — A multiple transmit antenna, single receive antenna (per receiver) downlink channel with limited channel feedback is considered. Given a constraint on the total systemwide channel feedback, the following question is considered: is it preferable to get lowrate feedback from a large numbe ..."
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Cited by 15 (2 self)
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Abstract — A multiple transmit antenna, single receive antenna (per receiver) downlink channel with limited channel feedback is considered. Given a constraint on the total systemwide channel feedback, the following question is considered: is it preferable to get lowrate feedback from a large number of receivers or to receive highrate/highquality feedback from a smaller number of (randomly selected) receivers? Acquiring feedback from many users allows multiuser diversity to be exploited, while highrate feedback allows for very precise selection of beamforming directions. It is shown that systems in which a limited number of users feedback highrate channel information significantly outperform lowrate/many user systems. While capacity increases only double logarithmically with the number of users, the marginal benefit of channel feedback is very significant up to the point where the CSI is essentially perfect. I.
1 MultiUser Diversity vs. Accurate Channel State Information in MIMO Downlink Channels
"... In a multiple transmit antenna, single antenna per receiver downlink channel with limited channel state feedback, we consider the following question: given a constraint on the total systemwide feedback load, is it preferable to get lowrate/coarse channel feedback from a large number of receivers o ..."
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Cited by 8 (0 self)
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In a multiple transmit antenna, single antenna per receiver downlink channel with limited channel state feedback, we consider the following question: given a constraint on the total systemwide feedback load, is it preferable to get lowrate/coarse channel feedback from a large number of receivers or highrate/highquality feedback from a smaller number of receivers? Acquiring feedback from many receivers allows multiuser diversity to be exploited, while highrate feedback allows for very precise selection of beamforming directions. We show that there is a strong preference for obtaining highquality feedback, and that obtaining nearperfect channel information from as many receivers as possible provides a significantly larger sum rate than collecting a few feedback bits from a large number of users. I.
Bit Allocation Laws for MultiAntenna Channel Feedback Quantization: MultiUser Case
"... This paper addresses the optimal design of limitedfeedback downlink multiuser spatial multiplexing systems. A multipleantenna basestation is assumed to serve multiple singleantenna users, who quantize and feed back their channel state information (CSI) through a shared ratelimited feedback cha ..."
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Cited by 7 (3 self)
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This paper addresses the optimal design of limitedfeedback downlink multiuser spatial multiplexing systems. A multipleantenna basestation is assumed to serve multiple singleantenna users, who quantize and feed back their channel state information (CSI) through a shared ratelimited feedback channel. The optimization problem is cast in the form of minimizing the average transmission power at the basestation subject to users’ target signaltointerferenceplusnoise ratios (SINR) and outage probability constraints. The goal is to derive the feedback bit allocations among the users and the corresponding channel magnitude and direction quantization codebooks in a highresolution quantization regime. Toward this end, this paper develops an optimization framework using approximate analytical closedform solutions, the accuracy of which is then verified by numerical results. The results show that, for channels in the real space, the number of channel direction quantization bits should be (M−1) times the number of channel magnitude quantization bits, where M is the number of basestation antennas. Moreover, users with higher requested qualityofservice (QoS), i.e. lower target outage probabilities, and higher requested downlink rates, i.e. higher target SINR’s, should use larger shares of the feedback rate. It is also shown that, for the target QoS parameters to be feasible, the total feedback bandwidth should scale logarithmically with the geometric mean of the target SINR values and the geometric mean of the inverse target outage probabilities. In particular, the minimum required feedback rate is shown to increase if the users ’ target parameters deviate from the corresponding geometric means. Finally, the paper shows that, as the total number of feedback bits B increases, the performance of the limitedfeedback system approaches the perfectCSI system as 2 −B/M2
A limitedfeedback scheduling and beamforming scheme for multiuser multiantenna systems
 in Proc. Global Telecommun. Conf. (GLOBECOM
, 2011
"... Abstract—This paper proposes an efficient twostage limitedfeedback beamforming and scheduling scheme for multipleantenna cellular communication systems. The system model includes a basestation with M antennas and a large pool of users with a total feedback rate of B bits per fading block. The feed ..."
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Abstract—This paper proposes an efficient twostage limitedfeedback beamforming and scheduling scheme for multipleantenna cellular communication systems. The system model includes a basestation with M antennas and a large pool of users with a total feedback rate of B bits per fading block. The feedback process is divided into two stages. In the first stage, the users measure their channel gains from each antenna and feedback the index of the antenna with the highest channel gain along with the gain itself. Based on this information, the basestation schedules M users with the highest channel gains from its M antennas and polls those users for explicit quantization of their vector channels in the second stage. Based on these quantized channels, the basestation then forms zeroforcing beamforming vectors for downlink transmission. This paper presents an approximate analysis for the proposed scheme which is used to optimize the bit allocation between the two feedback stages. It is shown that for a total number of feedback bits B, the number of feedback bits assigned to the second stage, B2, should scale as M(M−1)log(SNR × B). In particular, the fraction B2/B behaves as logB/B in the asymptotic regime where B → ∞. Further, the approximate downlink sum rate is shown to scale as M log SNR + M loglogB, suggesting that both multiuser multiplexing and multiuser diversity gains are realized. As the numerical results verify, the proposed feedback scheme, in spite of its low complexity, performs very close to the more complicated beamforming and scheduling schemes in the literature and in fact outperforms such schemes in the highSNR regime. I.
Kerdock Codes for Limited Feedback Precoded MIMO Systems
, 2008
"... A codebook based limited feedback strategy is a practical way to obtain partial channel state information at the transmitter in a precoded multipleinput multipleoutput (MIMO) wireless system. Conventional codebook designs use Grassmannian packing, equiangular frames, vector quantization, or Fourie ..."
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Cited by 2 (0 self)
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A codebook based limited feedback strategy is a practical way to obtain partial channel state information at the transmitter in a precoded multipleinput multipleoutput (MIMO) wireless system. Conventional codebook designs use Grassmannian packing, equiangular frames, vector quantization, or Fourier based constructions. While the capacity and error rate performance of conventional codebook constructions have been extensively investigated, constructing these codebooks is notoriously difficult relying on techniques such as nonlinear search or iterative algorithms. Further, the resulting codebooks may not have a systematic structure to facilitate storage of the codebook and low search complexity. In this paper, we propose a new systematic codebook design based on Kerdock codes and mutually unbiased bases. The proposed Kerdock codebook consists of multiple mutually unbiased unitary bases matrices with quaternary entries and the identity matrix. We propose to derive the beamforming and precoding codebooks from this base codebook, eliminating the requirement to store multiple codebooks. The propose structure requires little memory to store and, as we show, the quaternary structure facilitates codeword search. We derive the chordal distance for two antenna and four antenna codebooks, showing that the proposed codebooks compare favorably with prior designs. Monte Carlo simulations are used to compare achievable rates and error rates for different codebooks sizes.
Deterministic Equivalents for the Performance Analysis of Isometric Random Precoded Systems
"... Abstract—We consider a general wireless channel model for different types of codedivision multiple access (CDMA) and spacedivision multipleaccess (SDMA) systems with isometric random signature/precoding matrices over frequencyselective and flat fading channels. We derive deterministic approximat ..."
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Abstract—We consider a general wireless channel model for different types of codedivision multiple access (CDMA) and spacedivision multipleaccess (SDMA) systems with isometric random signature/precoding matrices over frequencyselective and flat fading channels. We derive deterministic approximations of the Stieltjes transform, the mutual information and the signaltointerferenceplusnoise ratio (SINR) at the output of the minimummeansquareerror (MMSE) receiver and provide a simple fixedpoint algorithm for their computation, which is proved to converge. The deterministic approximations are asymptotically tight, almost surely, but shown by simulations to be very accurate for even small system dimensions. Our analysis requires neither arguments from free probability theory nor the asymptotic freeness or the convergence of the spectral distribution of the involved matrices. The results presented in this work are, therefore, also a novel contribution to the field of random matrix theory and might be useful to further applications involving isometric random matrices. I.
1Random Beamforming over QuasiStatic and Fading Channels: A Deterministic Equivalent Approach
"... In this work, we study the performance of random isometric precoding over quasistatic and correlated fading channels. We derive deterministic approximations of the mutual information and the signaltointerferenceplusnoise ratio (SINR) at the output of the minimummeansquareerror (MMSE) receive ..."
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In this work, we study the performance of random isometric precoding over quasistatic and correlated fading channels. We derive deterministic approximations of the mutual information and the signaltointerferenceplusnoise ratio (SINR) at the output of the minimummeansquareerror (MMSE) receiver and provide simple provably converging fixedpoint algorithms for their computation. Although the deterministic approximations are only asymptotically exact, almost surely, we show by simulations that they are very accurate for small system dimensions. The analysis is based on the Stieltjes transform method which enables the derivation of deterministic equivalents of functionals of largedimensional random matrices. In contrast to previous works, our analysis does not rely on arguments from free probability theory which allows us to consider random matrix models for which asymptotic freeness does not hold. Thus, the results of this work are also a novel contribution to the field of random matrix theory and are shown to be applicable to a wide spectrum of practical systems. In this article, we specifically characterize the performance of multicellular communication systems, multipleinput multipleoutput multipleaccess channels (MIMOMAC), and MIMO interference channels.
doi:10.1155/2010/919072 Research Article Crystallized Rate Regions for MIMO Transmission
"... which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. When considering the multiuser SISO interference channel, the allowable rate region is not convex and the maximization of the aggregated rate of all the users by the means of t ..."
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which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. When considering the multiuser SISO interference channel, the allowable rate region is not convex and the maximization of the aggregated rate of all the users by the means of transmission power control becomes inefficient. Hence, a concept of the crystallized rate regions has been proposed, where the timesharing approach is considered to maximize the sumrate.In this paper, we extend the concept of crystallized rate regions from the simple SISO interference channel case to the MIMO/OFDM interference channel. As a first step, we extend the timesharing convex hull from the SISO to the MIMO channel case. We provide a noncooperative gametheoretical approach to study the achievable rate regions, and consider the VickreyClarkeGroves (VCG) mechanism design with a novel cost function. Within this analysis, we also investigate the case of OFDM channels, which can be treated as the special case of MIMO channels when the channel transfer matrices are diagonal. In the second step, we adopt the concept of correlated equilibrium into the case of twouser MIMO/OFDM, and we introduce a regretmatching learning algorithm for the system to converge to the equilibrium state. Moreover, we formulate the linear programming problem to find the aggregated rate of all users and solve it using the Simplex method. Finally, numerical results are provided to confirm our theoretical claims and show the improvement provided by this approach. 1.
Nature: R Total Effort Spent: 15 PM Dissemination Level: Public
"... Version: 1 This deliverable provides the final report with the summary of the activities carried out in NEWCOM++ WPR9, with a particular focus on those obtained during the last year. They address on the one hand RRM and JRRM strategies in heterogeneous scenarios and, on the other hand, spectrum mana ..."
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Version: 1 This deliverable provides the final report with the summary of the activities carried out in NEWCOM++ WPR9, with a particular focus on those obtained during the last year. They address on the one hand RRM and JRRM strategies in heterogeneous scenarios and, on the other hand, spectrum management and opportunistic spectrum access to achieve an efficient spectrum usage. Main outcomes of the workpackage as well as integration indicators are also summarised.