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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 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.
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 6 (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 4 (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.
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 2 (1 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.
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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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
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
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.
Research Article On the Problem of Bandwidth Partitioning in FDD BlockFading SingleUser MISO/SIMO Systems
, 2008
"... division duplex, multiinput singleoutput communication systems, into subbands for the uplink, the downlink, and the feedback. In the downlink, the transmitter applies coherent beamforming based on quantized channel information which is obtained by feedback from the receiver. As feedback takes away ..."
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division duplex, multiinput singleoutput communication systems, into subbands for the uplink, the downlink, and the feedback. In the downlink, the transmitter applies coherent beamforming based on quantized channel information which is obtained by feedback from the receiver. As feedback takes away resources from the uplink, which could otherwise be used to transfer payload data, it is highly desirable to reserve the “right ” amount of uplink resources for the feedback. Under the assumption of random vector quantization, and a frequency flat, independent and identically distributed blockfading channel, we derive closedform expressions for both the feedback quantization and bandwidth partitioning which jointly maximize the sum of the average payload data rates of the downlink and the uplink. While we do introduce some approximations to facilitate mathematical tractability, the analytical solution is asymptotically exact as the number of antennas approaches infinity, while for systems with few antennas, it turns out to be a fairly accurate approximation. In this way, the obtained results are meaningful for practical communication systems, which usually can only employ a few antennas. Copyright © 2008 M. T. Ivrlač and J. A. Nossek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.