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91
SpatioTemporal Coding for Wireless Communications
 IEEE Transaction on Communications
, 1998
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Joint TxRx beamforming design for multicarrier MIMO channels: a unified framework for convex optimization
 IEEE TRANS. SIGNAL PROCESSING
, 2003
"... This paper addresses the joint design of transmit and receive beamforming or linear processing (commonly termed linear precoding at the transmitter and equalization at the receiver) for multicarrier multipleinput multipleoutput (MIMO) channels under a variety of design criteria. Instead of consid ..."
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Cited by 155 (17 self)
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This paper addresses the joint design of transmit and receive beamforming or linear processing (commonly termed linear precoding at the transmitter and equalization at the receiver) for multicarrier multipleinput multipleoutput (MIMO) channels under a variety of design criteria. Instead of considering each design criterion in a separate way, we generalize the existing results by developing a unified framework based on considering two families of objective functions that embrace most reasonable criteria to design a communication system: Schurconcave and Schurconvex functions. Once the optimal structure of the transmitreceive processing is known, the design problem simplifies and can be formulated within the powerful framework of convex optimization theory, in which a great number of interesting design criteria can be easily accommodated and efficiently solved, even though closedform expressions may not exist. From this perspective, we analyze a variety of design criteria, and in particular, we derive optimal beamvectors in the sense of having minimum average bit error rate (BER). Additional constraints on the peaktoaverage ratio (PAR) or on the signal dynamic range are easily included in the design. We propose two multilevel waterfilling practical solutions that perform very close to the optimal in terms of average BER with a low implementation complexity. If cooperation among the processing operating at different carriers is allowed, the performance improves significantly. Interestingly, with carrier cooperation, it turns out that the exact optimal solution in terms of average BER can be obtained in closed form.
Redundant Filterbank Precoders and Equalizers  Part I: Unification and Optimal Designs
 IEEE TRANS. SIGNAL PROCESSING
, 1999
"... Transmitter redundancy introduced using filterbank precoders generalizes existing modulations including OFDM, DMT, TDMA, and CDMA schemes encountered with single and multiuser communications. Sufficient conditions are derived to guarantee that with FIR filterbank precoders FIR channels are equalize ..."
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Cited by 141 (28 self)
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Transmitter redundancy introduced using filterbank precoders generalizes existing modulations including OFDM, DMT, TDMA, and CDMA schemes encountered with single and multiuser communications. Sufficient conditions are derived to guarantee that with FIR filterbank precoders FIR channels are equalized perfectly in the absence of noise by FIR zeroforcing equalizer filterbanks, irrespective of the channel zero locations. Multicarrier transmissions through frequencyselective channels can thus be recovered even when deep fades are present. Jointly optimal transmitterreceiver filterbank designs are also developed, based on maximum output SNR and minimum meansquare error criteria under zeroforcing and fixed transmitted power constraints. Analytical performance results are presented for the zeroforcing filterbanks and are compared with meansquare error and ideal designs using simulations.
Optimal Designs for SpaceTime Linear Precoders and Decoders
 IEEE Trans. Signal Processing
, 2001
"... In this paper we introduce a new paradigm for the design of transmitter spacetime coding that we refer to as linear precoding. It leads to simple closed form solutions for transmission over frequency selective multipleinput multipleoutput (MIMO) channels, which are scalable with respect to the nu ..."
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Cited by 127 (5 self)
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In this paper we introduce a new paradigm for the design of transmitter spacetime coding that we refer to as linear precoding. It leads to simple closed form solutions for transmission over frequency selective multipleinput multipleoutput (MIMO) channels, which are scalable with respect to the number of antennas, size of the coding block and transmit average/peak power. The scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension. The specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses, under average and peak power constraints. The solutions are shown to convert the MIMO channel with memory into a set of parallel flat fading subchannels, regardless of the design criterion, while appropriate power/bits loading on the subchannels is the specific signature of the different designs. The proposed designs are compared in terms of various performance measures such as information rate, BER and symbol mean square error.
Generalized linear precoder and decoder design for MIMO channels using the weighted MMSE criterion
 IEEE Transactions on Communications
, 2001
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Linear precoding via conic optimization for fixed mimo receivers
 IEEE Trans. on Signal Processing
, 2006
"... We consider the problem of designing linear precoders for fixed multiple input multiple output (MIMO) receivers. Two different design criteria are considered. In the first, we minimize the transmitted power subject to signal to interference plus noise ratio (SINR) constraints. In the second, we maxi ..."
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Cited by 58 (2 self)
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We consider the problem of designing linear precoders for fixed multiple input multiple output (MIMO) receivers. Two different design criteria are considered. In the first, we minimize the transmitted power subject to signal to interference plus noise ratio (SINR) constraints. In the second, we maximize the worst case SINR subject to a power constraint. We show that both problems can be solved using standard conic optimization packages. In addition, we develop conditions for the optimal precoder for both of these problems, and propose two simple fixed point iterations to find the solutions which satisfy these conditions. The relation to the well known downlink uplink duality in the context of joint downlink beamforming and power control is also explored. Our precoder design is general, and as a special case it solves the beamforming problem. In contrast to most of the existing precoders, it is not limited to full rank systems. Simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders. 1
Transceiver optimization for multiuser MIMO systems
 IEEE Tran. on Signal Processing, 52(1):214 – 226
, 2004
"... Abstract—We consider the uplink of a multiuser system where the transmitters as well as the receiver are equipped with multiple antennas. Each user multiplexes its symbols by a linear precoder through its transmit antennas. We work with the systemwide mean squared error as the performance measure a ..."
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Cited by 47 (9 self)
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Abstract—We consider the uplink of a multiuser system where the transmitters as well as the receiver are equipped with multiple antennas. Each user multiplexes its symbols by a linear precoder through its transmit antennas. We work with the systemwide mean squared error as the performance measure and propose algorithms to find the jointly optimum linear precoders at each transmitter and linear decoders at the receiver. We first work with the case where the number of symbols to be transmitted by each user is given. We then investigate how the symbol rate should be chosen for each user with optimum transmitters and receivers. The convergence analysis of the algorithms is given, and numerical evidence that supports the analysis is presented. Index Terms—MMSE receivers, multiuser MIMO system, receiver beamforming, transmitter beamforming.
Gradient of mutual information in linear vector Gaussian channels
 IEEE Trans. Inf. Theory
, 2006
"... Abstract — This paper considers a general linear vector Gaussian channel with arbitrary signaling and pursues two closely related goals: i) closedform expressions for the gradient of the mutual information with respect to arbitrary parameters of the system, and ii) fundamental connections between i ..."
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Cited by 44 (11 self)
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Abstract — This paper considers a general linear vector Gaussian channel with arbitrary signaling and pursues two closely related goals: i) closedform expressions for the gradient of the mutual information with respect to arbitrary parameters of the system, and ii) fundamental connections between information theory and estimation theory. Generalizing the fundamental relationship recently unveiled by Guo, Shamai, and Verdú [1], we show that the gradient of the mutual information with respect to the channel matrix is equal to the product of the channel matrix and the error covariance matrix of the estimate of the input given the output. I.
Filterbank transceivers optimizing information rate in block transmissions over dispersive channels
 IEEE TRANS. INFORM. THEORY
, 1999
"... Optimal finite impulse response (FIR) transmit and receive filterbanks are derived for blockbased data transmissions over frequencyselective additive Gaussian noise (AGN) channels by maximizing mutual information subject to a fixed transmitpower constraint. Both FIR and polezero channels are cons ..."
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Cited by 44 (4 self)
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Optimal finite impulse response (FIR) transmit and receive filterbanks are derived for blockbased data transmissions over frequencyselective additive Gaussian noise (AGN) channels by maximizing mutual information subject to a fixed transmitpower constraint. Both FIR and polezero channels are considered. The inherent flexibility of the proposed transceivers is exploited to derive, as special cases, zeroforcing (ZF) and minimum meansquare error receive filterbanks. The transmit filterbank converts transmission over a frequencyselective fading channel, affected by additive colored noise, into a set of independent flat fading subchannels with uncorrelated noise samples. Two loading algorithms are also developed to distribute transmit power and number of bits across the usable subchannels, while adhering to an upper bound on the bit error rate (BER). Reduction of the signaltonoise ratio (SNR) margin required to satisfy the prescribed BER is achieved by coding each subchannel’s bit stream. The potential of the proposed transceivers is illustrated and compared to discrete multitone (DMT) with simulated examples.
Optimum power allocation for parallel Gaussian channels with arbitrary input distributions
 IEEE TRANS. INF. THEORY
, 2006
"... The mutual information of independent parallel Gaussiannoise channels is maximized, under an average power constraint, by independent Gaussian inputs whose power is allocated according to the waterfilling policy. In practice, discrete signaling constellations with limited peaktoaverage ratios (m ..."
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Cited by 39 (9 self)
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The mutual information of independent parallel Gaussiannoise channels is maximized, under an average power constraint, by independent Gaussian inputs whose power is allocated according to the waterfilling policy. In practice, discrete signaling constellations with limited peaktoaverage ratios (mPSK, mQAM, etc.) are used in lieu of the ideal Gaussian signals. This paper gives the power allocation policy that maximizes the mutual information over parallel channels with arbitrary input distributions. Such policy admits a graphical interpretation, referred to as mercury/waterfilling, which generalizes the waterfilling solution and allows retaining some of its intuition. The relationship between mutual information of Gaussian channels and nonlinear minimum meansquare error (MMSE) proves key to solving the power allocation problem.