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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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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
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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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.
High Resolution Quantization Codebook Design for MultipleAntenna Fading Channels
"... Abstract—This paper investigates the asymptotic structure of the channel vector quantization codebook for limitedfeedback multipleinput singleoutput fading channels. The design criteria is to minimize the average transmission power subject to a target outage probability. First, we consider the de ..."
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Abstract—This paper investigates the asymptotic structure of the channel vector quantization codebook for limitedfeedback multipleinput singleoutput fading channels. The design criteria is to minimize the average transmission power subject to a target outage probability. First, we consider the design of scalar channel magnitude quantization codebook and prove that the asymptotically optimal quantization levels are uniformly spaced in dB scale. Such optimality does not depend on the the channel magnitude distribution, as long as some regularity conditions are satisfied. It is shown that the gradient of the objective function (the average transmission power) with respect to such quantization levels diminishes as Np −3/2 as the number of the levels Np tends to infinity. We then form a product channel vector quantization codebook comprising a uniform (in dB) channel magnitude quantization codebook and a spatially uniform channel direction quantization codebook and derive the optimal bitsharing law between the two codebooks. It is shown that the asymptotically optimal number of direction quantization bits is M−1 times the number of channel magnitude quantization bits, where M is the number of base station antennas. The paper also shows that as the target outage probability decreases, more bits should be allocated to magnitude quantization. I.
High Resolution Channel Quantization Rules for Multiuser Spatial Multiplexing Systems
"... Abstract—This paper addresses the optimal channel quantization codebook design for limited feedback multipleantenna multiuser channels. The base station is equipped with M antennas and serves M singleantenna users, which share a total feedback rate B. We assume real space channels for convenience; ..."
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Abstract—This paper addresses the optimal channel quantization codebook design for limited feedback multipleantenna multiuser channels. The base station is equipped with M antennas and serves M singleantenna users, which share a total feedback rate B. We assume real space channels for convenience; the extension of the analysis to complex space is straightforward. The codebook optimization problem is cast in form of minimizing the average downlink transmission power subject to the users ’ outage probability constraints. This paper adopts a product codebook structure for channel quantization comprising a uniform (in dB) channel magnitude quantization codebook and a spatially uniform channel direction quantization codebook. We first formulate a robust power control problem that minimizes the sum power subject to the worstcase SINR constraints over the channel quantization regions. By using an upper bound solution to this problem, we then optimize the quantization codebooks given the target outage probabilities and the target SINR’s. In the asymptotic regime of B → ∞, the optimal number of channel direction quantization bits is shown to be M−1 times the number of channel magnitude quantization bits. It is further shown that the users with higher requested QoS (lower target outage probabilities) and higher requested downlink rates (higher target SINR’s) should receive larger shares of the feedback rate. The paper also shows that, for the target parameters to be feasible, the total feedback bandwidth should scale logarithmically with ¯γ, the geometric mean of the target SINR values, and 1/¯q, the geometric mean of the inverse target outage probabilities. Moreover, the minimum required feedback rate increases if the users ’ target parameters deviate from the average parameters ¯γ and ¯q. Finally, we show that, asB increases, the multiuser system performance approaches the performance B of the perfect channel state information system as 1/¯q ·2
Limited Feedback MultiAntenna Quantization Codebook Design  Part I Singleuser Channels
"... In this twopart paper, we study the design and optimization of limited feedback singleuser and multiuser systems with a multipleantenna base station and singleantenna users. The design problem is cast in form of minimizing the average transmission power at the base station subject to the outage ..."
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In this twopart paper, we study the design and optimization of limited feedback singleuser and multiuser systems with a multipleantenna base station and singleantenna users. The design problem is cast in form of minimizing the average transmission power at the base station subject to the outage probability constraints at the users ’ side. The optimization is over the users ’ channel quantization codebooks and the transmission power control function at the base station. Our approach is based on fixing the outage scenarios in advance and transforming the design problem into a robust system design problem. The first part of the paper addresses the singleuser system and the second part studies the multiuser case. For the singleuser case, we start by showing that uniformly quantizing the channel magnitude in dB scale is asymptotically optimal, regardless of the magnitude distribution function. We derive the optimal uniform (in dB) channel magnitude codebook and combine it with a spatially uniform channel direction codebook to achieve a product channel quantization codebook. We then optimize such a product structure in the asymptotic regime of B → ∞, where B is the total number of quantization feedback bits. The paper shows that for channels in the real space, the asymptotically optimal number of direction quantization bits should be (M−1)/2 times the number of magnitude quantization bits, where M is the number of base station antennas. We also show that the designed system approaches the performance of the perfect channel state 2B information system as 2 M+1.
On Codebook Design for Distributed Relay Beamforming Network
"... Abstract — We study the problem of codebook design for quantized distributed relay beamforming under individual relay power constraint in a cooperative relay network. The received SNR is used as the design metric. We study two types of codebook design: phaseonly codebook where each relay uses full ..."
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Abstract — We study the problem of codebook design for quantized distributed relay beamforming under individual relay power constraint in a cooperative relay network. The received SNR is used as the design metric. We study two types of codebook design: phaseonly codebook where each relay uses full power, and codebook with power control where relay power and phase need to be jointly considered. For the former, we adopt Grassmannian line packing criterion under equal gain constraint, and compare the performance with that under the generalized Lloyd Algorithm for optimal codebook design. For codebook with power control, the generalized Lloyd Algorithm can be used for the optimal codebook design, but incurs high complexity. We propose a lowcomplexity suboptimal method, which can directly use the optimal power control solution for perfect channel knowledge under the individual power constraint. Through simulation study, it is found that it is more beneficial to use codebook with power control over codebook without power control when relays are closer to destination, instead of the source. I.