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136
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 55 (3 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
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 45 (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.
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 35 (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.
Optimal linear precoding strategies for wideband noncooperative systems based on game theory – Part II: Algorithms
 IEEE Trans. Signal Process
, 2008
"... In this twoparts paper we propose a decentralized strategy, based on a gametheoretic formulation, to find out the optimal precoding/multiplexing matrices for a multipointtomultipoint communication system composed of a set of wideband links sharing the same physical resources, i.e., time and band ..."
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Cited by 30 (3 self)
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In this twoparts paper we propose a decentralized strategy, based on a gametheoretic formulation, to find out the optimal precoding/multiplexing matrices for a multipointtomultipoint communication system composed of a set of wideband links sharing the same physical resources, i.e., time and bandwidth. We assume, as optimality criterion, the achievement of a Nash equilibrium and consider two alternative optimization problems: 1) the competitive maximization of mutual information on each link, given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies; and 2) the competitive maximization of the transmission rate, using finite order constellations, under the same constraints as above, plus a constraint on the average error probability. In Part I of the paper, we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies. Then, we prove that the optimal precoding/multiplexing scheme for both games leads to a channel diagonalizing structure, so that both matrixvalued problems can be recast in a simpler unified vector power control game, with no performance penalty. Thus, we study this simpler game and derive sufficient conditions ensuring the uniqueness of the Nash equilibrium. Interestingly, although derived under stronger constraints,
Joint transceiver design for MIMO communications using geometric mean decomposition
 IEEE Trans. Signal Process
, 2005
"... Abstract—In recent years, considerable attention has been paid to the joint optimal transceiver design for multiinput multioutput (MIMO) communication systems. In this paper, we propose a joint transceiver design that combines the geometric mean decomposition (GMD) with either the conventional zer ..."
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Cited by 28 (5 self)
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Abstract—In recent years, considerable attention has been paid to the joint optimal transceiver design for multiinput multioutput (MIMO) communication systems. In this paper, we propose a joint transceiver design that combines the geometric mean decomposition (GMD) with either the conventional zeroforcing VBLAST decoder or the more recent zeroforcing dirty paper precoder (ZFDP). Our scheme decomposes a MIMO channel into multiple identical parallel subchannels, which can make it rather convenient to design modulation/demodulation and coding/decoding schemes. Moreover, we prove that our scheme is asymptotically optimal for (moderately) high SNR in terms of both channel throughput and bit error rate (BER) performance. This desirable property is not shared by any other conventional schemes. We also consider the subchannel selection issues when some of the subchannels are too poor to be useful. Our scheme can also be combined with orthogonal frequency division multiplexing (OFDM) for intersymbol interference (ISI) suppression. The effectiveness of our approaches has been validated by both theoretical analyses and numerical simulations. Index Terms—Channel capacity, dirty paper precoding, intersymbol interference suppression, joint transceiver design, matrix
Optimum linear joint transmitreceive processing for MIMO channels with QoS constraints
 IEEE Transactions on Signal Processing
, 2004
"... Abstract—This paper considers vector communications through multipleinput multipleoutput (MIMO) channels with a set of quality of service (QoS) requirements for the simultaneously established substreams. Linear transmitreceive processing (also termed linear precoder at the transmitter and linear ..."
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Cited by 26 (3 self)
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Abstract—This paper considers vector communications through multipleinput multipleoutput (MIMO) channels with a set of quality of service (QoS) requirements for the simultaneously established substreams. Linear transmitreceive processing (also termed linear precoder at the transmitter and linear equalizer at the receiver) is designed to satisfy the QoS constraints with minimum transmitted power (the exact conditions under which the problem becomes unfeasible are given). Although the original problem is a complicated nonconvex problem with matrixvalued variables, with the aid of majorization theory, we reformulate it as a simple convex optimization problem with scalar variables. We then propose a practical and efficient multilevel waterfilling algorithm to optimally solve the problem for the general case of different QoS requirements. The optimal transmitreceive processing is shown to diagonalize the channel matrix only after a very specific prerotation of the data symbols. For situations in which the resulting transmit power is too large, we give the precise way to relax the QoS constraints in order to reduce the required power based on a perturbation analysis. We also propose a robust design under channel estimation errors that has an important interest for practical systems. Numerical results from simulations are given to support the mathematical development of the problem. Index Terms—Array signal processing, beamforming, joint transmitreceive equalization, linear precoding, MIMO channels, spacetime filtering, waterfilling. I.
Capacityachieving input covariance for singleuser multiantenna channels
 IEEE Trans. Wireless Commun
, 2006
"... Abstract — We characterize the capacityachieving input covariance for multiantenna channels known instantaneously at the receiver and in distribution at the transmitter. Our characterization, valid for arbitrary numbers of antennas, encompasses both the eigenvectors and the eigenvalues. The eigenv ..."
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Cited by 24 (9 self)
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Abstract — We characterize the capacityachieving input covariance for multiantenna channels known instantaneously at the receiver and in distribution at the transmitter. Our characterization, valid for arbitrary numbers of antennas, encompasses both the eigenvectors and the eigenvalues. The eigenvectors are found for zeromean channels with arbitrary fading profiles and a wide range of correlation and keyhole structures. For the eigenvalues, in turn, we present necessary and sufficient conditions as well as an iterative algorithm that exhibits remarkable properties: universal applicability, robustness and rapid convergence. In addition, we identify channel structures for which an isotropic input achieves capacity. Index Terms — Capacity, MIMO, input optimization, fading, antenna correlation, Ricean fading, keyhole channel.
Uniform channel decomposition for MIMO communications
 IEEE Transactions on Signal Processing
, 2005
"... Abstract—Assuming the availability of the channel state information at the transmitter (CSIT) and receiver (CSIR), we consider the joint optimal transceiver design for multiinput multioutput (MIMO) communication systems. Using the geometric mean decomposition (GMD), we propose a transceiver design ..."
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Cited by 18 (5 self)
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Abstract—Assuming the availability of the channel state information at the transmitter (CSIT) and receiver (CSIR), we consider the joint optimal transceiver design for multiinput multioutput (MIMO) communication systems. Using the geometric mean decomposition (GMD), we propose a transceiver design that can decompose, in a strictly capacity lossless manner, a MIMO channel into multiple subchannels with identical capacities. This uniform channel decomposition (UCD) scheme has two implementation forms. One is the combination of a linear precoder and a minimum meansquarederror VBLAST (MMSEVBLAST) detector, which is referred to as UCDVBLAST, and the other includes a dirty paper (DP) precoder and a linear equalizer followed by a DP decoder, which we refer to as UCDDP. The UCD scheme can provide much convenience for the modulation/demodulation and coding/decoding procedures due to obviating the need for bit allocation. We also show that UCD can achieve the maximal diversity gain. The simulation results show that the UCD scheme exhibits excellent performance, even without the use of any error correcting codes. Index Terms—Channel capacity, DBLAST, dirty paper precoder, diversity gain, geometric mean decomposition, joint transceiver
Robust design of linear MIMO transceivers
 IEEE Journal on Selected Areas in Communications
, 2005
"... This paper considers the robust design of a linear transceiver with imperfect channel state information (CSI) at the transmitter of a MIMO link. The framework embraces the design problem when CSI at the transmitter consists of the channel mean and covariance matrix or, equivalently, the channel esti ..."
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Cited by 16 (1 self)
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This paper considers the robust design of a linear transceiver with imperfect channel state information (CSI) at the transmitter of a MIMO link. The framework embraces the design problem when CSI at the transmitter consists of the channel mean and covariance matrix or, equivalently, the channel estimate and the estimation error covariance matrix. The design of the linear MIMO transceiver is based on a general cost function covering several well known performance criteria. In particular, two families are considered in detail: Schurconvex and Schurconcave functions. Approximations are used in the low SNR and high SNR regimes separately to obtain simple optimization problems that can be readily solved. Numerical examples show gains compared to other suboptimal methods. 1.
A framework for designing MIMO systems with decision feedback equalization or TomlinsonHarashima precoding
 Proc. of the ICASSP
, 2007
"... We consider joint transceiver design for general MultipleInput MultipleOutput communication systems that implement interference (pre)subtraction, such as those based on Decision Feedback Equalization (DFE) or TomlinsonHarashima precoding (THP). We develop a unified framework for joint transceive ..."
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Cited by 14 (1 self)
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We consider joint transceiver design for general MultipleInput MultipleOutput communication systems that implement interference (pre)subtraction, such as those based on Decision Feedback Equalization (DFE) or TomlinsonHarashima precoding (THP). We develop a unified framework for joint transceiver design by considering design criteria that are expressed as functions of the Mean Square Error (MSE) of the individual data streams. By deriving two inequalities that involve the logarithms of the individual MSEs, we obtain optimal designs for two classes of communication objectives, namely those that are Schurconvex and Schurconcave functions of these logarithms. For Schurconvex objectives, the optimal design results in data streams with equal MSEs. This design simultaneously minimizes the total MSE and maximizes the mutual information for the DFEbased model. For Schurconcave objectives, the optimal DFE design results in linear equalization and the optimal THP design results in linear precoding. The proposed framework embraces a wide range of design objectives and can be regarded as a counterpart of the existing framework of linear transceiver design.