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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 34 (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 (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.
Training and Feedback Optimization for Multiuser MIMO Downlink
, 2009
"... We consider a MIMO fading broadcast channel where the fading channel coefficients are constant over timefrequency blocks that span a coherent time × a coherence bandwidth. In closedloop systems, channel state information at transmitter (CSIT) is acquired by the downlink training sent by the base s ..."
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Cited by 32 (2 self)
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We consider a MIMO fading broadcast channel where the fading channel coefficients are constant over timefrequency blocks that span a coherent time × a coherence bandwidth. In closedloop systems, channel state information at transmitter (CSIT) is acquired by the downlink training sent by the base station and an explicit feedback from each user terminal. In openloop systems, CSIT is obtained by exploiting uplink training and channel reciprocity. We use a tight closedform lower bound on the ergodic achievable rate in the presence of CSIT errors in order to optimize the overall system throughput, by taking explicitly into account the overhead due to channel estimation and channel state feedback. Based on three timefrequency block models inspired by actual systems, we provide some useful guidelines for the overall system optimization. In particular, digital (quantized) feedback is found to offer a substantial advantage over analog (unquantized) feedback.
How Much Training and Feedback are Needed in MIMO Broadcast Channels?
"... Abstract — We consider a MIMO fading broadcast channel where channel state information is acquired at user terminals via downlink training and explicit analog feedback is used to provide transmitter channel state information (CSIT) to the base station. The feedback channel (the corresponding uplink) ..."
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Cited by 11 (3 self)
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Abstract — We consider a MIMO fading broadcast channel where channel state information is acquired at user terminals via downlink training and explicit analog feedback is used to provide transmitter channel state information (CSIT) to the base station. The feedback channel (the corresponding uplink) is modeled as a MIMO multiple access channel. Under the assumption that data transmission, downlink training, and feedback are performed within the same channel coherence interval of length T symbols, the optimization of a lower bound on the achievable ergodic rate sum yields a nontrivial resource allocation tradeoff. We solve this tradeoff and provide the optimal training and feedback resource allocation for the case of zeroforcing beamforming. When the same power level is used during all stages, it is found that the optimal length of the training + feedback phases increases as O ( √ T) for large T. On the other hand, when different power levels can be used for different stages, for sufficiently large T it is optimal to use the minimum number of symbols for training + feedback but to use power of order O ( √ T). I.
Optimization of training and feedback for beamforming over a MIMO channel
 in Proc. IEEE Wireless Commun. and Networking Conf. (WCNC). Hong Kong
, 2007
"... Abstract — We examine the capacity of beamforming over a block Rayleigh fading MultiInput/MultiOutput (MIMO) channel with finite training for channel estimation and limited feedback. A fixedlength packet is assumed, which is spanned by T training symbols, B feedback bits, and the data symbols. Th ..."
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Cited by 7 (4 self)
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Abstract — We examine the capacity of beamforming over a block Rayleigh fading MultiInput/MultiOutput (MIMO) channel with finite training for channel estimation and limited feedback. A fixedlength packet is assumed, which is spanned by T training symbols, B feedback bits, and the data symbols. The training symbols are used to obtain a Minimum Mean Squared Error (MMSE) estimate of the channel matrix. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing 2 B i.i.d. random vectors, and relays the corresponding Bbit index back to the transmitter. We derive bounds on the large system capacity, i.e., as the number of transmit antennas Nt → ∞ and receive antennas Nr → ∞ with fixed ratio Nt/Nr. The bounds are used to show that the optimal T, which maximizes the capacity, increases as Nt / log Nt, whereas the optimal B increases as Nt / log 2 Nt. I.
Application Driven Joint UplinkDownlink Optimization
 in ITG/IEEE Workshop on Smart Antennas (WSA’10
, 2010
"... Abstract — This paper introduces a new mathematical framework which is used to derive joint uplink/downlink achievable rate regions for multiuser spatial multiplexing between one base station and multiple terminals. The framework consists of two models: the first one is a simple transmission model ..."
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Abstract — This paper introduces a new mathematical framework which is used to derive joint uplink/downlink achievable rate regions for multiuser spatial multiplexing between one base station and multiple terminals. The framework consists of two models: the first one is a simple transmission model for uplink (UL) and downlink (DL), which is capable to give a lower bound on the capacity for the case that the transmission is subject to imperfect channel state information (CSI). A detailed model for concrete channel estimation and feedback schemes provides the parameter input to the former model and covers the most important aspects such as pilot design optimization, linear channel estimation, feedback delay, and feedback quantization. We apply this framework to determine optimal pilot densities and CSI feedback quantity, given that a weighted sum of UL and DL throughput is to be maximized for a certain user velocity. We show that for low speed, and if DL throughput is of particular importance, a significant portion of the UL should be invested into CSI feedback. At higher velocity, however, DL performance becomes mainly affected by CSI feedback delay, and hence CSI feedback brings little gain considering the inherent sacrifice of UL capacity. We further show that for high velocities, it becomes beneficial to use no CSI feedback at all, but apply random beamforming in the DL and operate in timedivision multiplex.
Overhead and Spectral Efficiency of PilotAssisted Interference Alignment in TimeSelective Fading Channels
"... Abstract—The spectral efficiency achievable by IA (interference alignment) in a Kuser MIMO (multipleinput multipleoutput) interference channel is studied in the face of timeselective continuous fading explicitly estimated through pilotsymbol observations. The robustness of IA in such operation ..."
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Abstract—The spectral efficiency achievable by IA (interference alignment) in a Kuser MIMO (multipleinput multipleoutput) interference channel is studied in the face of timeselective continuous fading explicitly estimated through pilotsymbol observations. The robustness of IA in such operationally relevant conditions is assessed through a joint optimization of the pilot overhead and the IA update interval, which are characterized—in highpower conditions—as solutions of a fixedpoint equation. Variations of the formulation are given for both FDD (frequencydivision duplexing) and TDD (timedivision duplexing), the former requiring explicit feedback of the fading estimates and the latter relying on fading reciprocity. For the FDD variation, analog feedback is considered. In addition to arbitrary numbers of users and antennas, and arbitrary temporal fading correlation functions, the derivations accommodate forward and reverse links with asymmetric power levels. Index Terms—Interference alignment, timeselective fading, pilotassisted transmission, spectral efficiency, pilot overhead, precoder update interval. I.
Signature Quantization in Fading CDMA With Limited Feedback
, 2009
"... In this paper, we analyze the performance of a signature quantization scheme for reverselink Direct Sequence (DS) Code Division Multiple Access (CDMA). Assuming perfect estimates of channel and interference covariance, the receiver selects the signature that maximizes signaltointerference plus n ..."
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Cited by 1 (0 self)
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In this paper, we analyze the performance of a signature quantization scheme for reverselink Direct Sequence (DS) Code Division Multiple Access (CDMA). Assuming perfect estimates of channel and interference covariance, the receiver selects the signature that maximizes signaltointerference plus noise ratio (SINR) for a desired user from a signature codebook. The codebook index corresponding to the optimal signature is then relayed to the user with finite number of bits via a feedback channel. Previously, we showed that a Random Vector Quantization (RVQ) codebook, which contains independent isotropically distributed vectors, is optimal (i.e., maximizes SINR) in a large system limit in which number of interfering users, processing gain, and feedback bits tend to infinity with fixed ratios. Dai et al. have analyzed the large system SINR for a matched filter with nonfading channel. Here we extend the results to linear minimum mean squared error (MMSE) receiver and multipath fading channel. Numerical examples show that the derived large system results give a good approximation to the performance of finitesize system. Index Terms Random Vector Quantization, large system limit, signature quantization, limited feedback, multipath
ROBUST DOWNLINK SINR BALANCING BASED ON MMSE OPTIMAL CSI FEEDBACK
"... A robust signaltointerferenceplusnoise ratio (SINR) design is proposed that is based on fed back channel state information (CSI). The channel estimator, the quantizer, and the rankreduction basis are jointly optimized to get a minimum mean square error (MMSE) optimal CSI feedback. Based on the ..."
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A robust signaltointerferenceplusnoise ratio (SINR) design is proposed that is based on fed back channel state information (CSI). The channel estimator, the quantizer, and the rankreduction basis are jointly optimized to get a minimum mean square error (MMSE) optimal CSI feedback. Based on the CSI feedback, the transmitter can compute the conditional covariance matrices of the different channels that enable a balancing of the different SINRs on average. The robust SINR balancing algorithm shows good balancing properties also for the instantaneous SINR and clearly outperforms the nonrobust SINR balancing approach. 1.
Large System Performance of Signature 1 Quantization in CDMA
, 2009
"... In this paper, we analyze the performance of a signature quantization scheme for reverselink Direct Sequence (DS) Code Division Multiple Access (CDMA). Assuming perfect estimates of channel and interference covariance, the receiver selects the signature that maximizes signaltointerference plus n ..."
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In this paper, we analyze the performance of a signature quantization scheme for reverselink Direct Sequence (DS) Code Division Multiple Access (CDMA). Assuming perfect estimates of channel and interference covariance, the receiver selects the signature that maximizes signaltointerference plus noise ratio (SINR) for a desired user from a signature codebook. The codebook index corresponding to the optimal signature is then relayed to the user with finite number of bits via a feedback channel. Previously, we showed that a Random Vector Quantization (RVQ) codebook, which contains independent isotropically distributed vectors, is optimal (i.e., maximizes SINR) in a large system limit in which number of interfering users, processing gain, and feedback bits tend to infinity with fixed ratios. Dai et al. have analyzed the large system SINR for a matched filter with nonfading channel. Here we extend the results to linear minimum mean squared error (MMSE) receiver and multipath fading channel. Numerical examples show that the derived large system results give a good approximation to the performance of finitesize system. Index Terms Random Vector Quantization, large system limit, signature quantization, limited feedback, multipath