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22
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 50 (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
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 29 (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,
Robust power allocation designs for multiuser and multiantenna downlink communication systems through convex optimization
 IEEE J. Sel. Areas Commun
, 2007
"... Abstract — In this paper, we study the design of the transmitter in the downlink of a multiuser and multiantenna wireless communications system, considering the realistic scenario where only an imperfect estimate of the actual channel is available at both communication ends. Precisely, the actual ch ..."
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Cited by 16 (1 self)
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Abstract — In this paper, we study the design of the transmitter in the downlink of a multiuser and multiantenna wireless communications system, considering the realistic scenario where only an imperfect estimate of the actual channel is available at both communication ends. Precisely, the actual channel is assumed to be inside an uncertainty region around the channel estimate, which models the imperfections of the channel knowledge that may arise from, e.g., estimation Gaussian errors, quantization effects, or combinations of both sources of errors. In this context, our objective is to design a robust power allocation among the information symbols that are to be sent to the users such that the total transmitted power is minimized, while maintaining the necessary quality of service to obtain reliable communication links between the base station and the users for any possible realization of the actual channel inside the uncertainty region. This robust power allocation is obtained as the solution to a convex optimization problem, which, in general, can be numerically solved in a very efficient way, and even for a particular case of the uncertainty region, a quasiclosed form solution can be found. Finally, the goodness of the robust proposed transmission scheme is presented through numerical results. Index Terms — Robust designs, imperfect CSI, multiantenna systems, broadcast channel, convex optimization.
Convex conic formulations of robust downlink precoder designs with quality of service constraints
 IEEE J. Select. Topics Signal Processing
, 2007
"... We consider the design of linear precoders (beamformers) for broadcast channels with Quality of Service (QoS) constraints for each user, in scenarios with uncertain channel state information (CSI) at the transmitter. We consider a deterministicallybounded model for the channel uncertainty of each u ..."
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Cited by 11 (1 self)
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We consider the design of linear precoders (beamformers) for broadcast channels with Quality of Service (QoS) constraints for each user, in scenarios with uncertain channel state information (CSI) at the transmitter. We consider a deterministicallybounded model for the channel uncertainty of each user, and our goal is to design a robust precoder that minimizes the total transmission power required to satisfy the users ’ QoS constraints for all channels within a specified uncertainty region around the transmitter’s estimate of each user’s channel. Since this problem is not known to be computationally tractable, we will derive three conservative design approaches that yield convex and computationallyefficient restrictions of the original design problem. The three approaches yield semidefinite program (SDP) formulations that offer different tradeoffs between the degree of conservatism and the size of the SDP. We will also show how these conservative approaches can be used to derive efficientlysolvable quasiconvex restrictions of some related design problems, including the robust counterpart to the problem of maximizing the minimum signaltointerferenceplusnoiseratio (SINR) subject to a given power constraint. Our simulation results indicate that in the presence of uncertain CSI the proposed approaches can satisfy the users ’ QoS requirements for a significantly larger set of uncertainties than existing methods, and require less transmission power to do so.
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 11 (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.
Tunable channel decomposition for MIMO communications using channel state information
 IEEE Transactions on Signal Processing
, 2006
"... Abstract—We consider jointly designing transceivers for multipleinput multipleoutput (MIMO) communications. Assuming the availability of the channel state information (CSI) at the transmitter (CSIT) and receiver (CSIR), we propose a scheme that can decompose a MIMO channel, in a capacity lossless ..."
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Cited by 6 (0 self)
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Abstract—We consider jointly designing transceivers for multipleinput multipleoutput (MIMO) communications. Assuming the availability of the channel state information (CSI) at the transmitter (CSIT) and receiver (CSIR), we propose a scheme that can decompose a MIMO channel, in a capacity lossless manner, into multiple subchannels with prescribed capacities, or equivalently, signaltointerferenceandnoise ratios (SINRs). We refer to this scheme as the tunable channel decomposition (TCD), which is based on the recently developed generalized triangular decomposition (GTD) algorithm and the closedform representation of minimum meansquarederror VBLAST (MMSEVBLAST) equalizer. The TCD scheme is particularly relevant to the applications where independent data streams with different qualitiesofservice (QoS) share the same MIMO channel. The TCD scheme has two implementation forms. One is the combination of a linear precoder and a minimum meansquarederror VBLAST (MMSEVBLAST) equalizer, which is referred to as TCDVBLAST, and the other includes a dirty paper (DP) precoder and a linear equalizer followed by a DP decoder, which we refer to as TCDDP. We also include the optimal codedivision multipleaccess (CDMA) sequence design as a special case in the framework of MIMO transceiver designs. Hence, our scheme can be directly applied to optimal CDMA sequence design, both in the uplink and downlink scenarios. Index Terms—Channel capacity, channel decomposition, dirty paper (DP) precoding, generalized triangular decomposition, joint transceiver design, multipleinput multipleoutput (MIMO), optimal CDMA sequences, qualityofservice, VBLAST. I.
MIMO Transceivers With Decision Feedback and Bit Loading: Theory and Optimization
, 2010
"... This paper considers MIMO transceivers with linear precoders and decision feedback equalizers (DFEs), with bit allocation at the transmitter. Zeroforcing (ZF) is assumed. Considered first is the minimization of transmitted power, for a given total bit rate and a specified set of error probabilities ..."
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Cited by 5 (4 self)
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This paper considers MIMO transceivers with linear precoders and decision feedback equalizers (DFEs), with bit allocation at the transmitter. Zeroforcing (ZF) is assumed. Considered first is the minimization of transmitted power, for a given total bit rate and a specified set of error probabilities for the symbol streams. The precoder and DFE matrices are optimized jointly with bit allocation. It is shown that the generalized triangular decomposition (GTD) introduced by Jiang, Li, and Hager offers an optimal family of solutions. The optimal linear transceiver (which has a linear equalizer rather than a DFE) with optimal bit allocation is a member of this family. This shows formally that, under optimal bit allocation, linear and DFE transceivers achieve the same minimum power. The DFE transceiver using the geometric mean decomposition (GMD) is another member of this optimal family, and is such that optimal bit allocation yields identical bits for all symbol streams—no bit allocation is necessary—when the specified error probabilities are identical for all streams. The QRbased system used in VBLAST is yet another member of the optimal family and is particularly wellsuited when limited feedback is allowed from receiver to transmitter. Two other optimization problems are then considered: a) minimization of power for specified set of bit rates and error probabilities (the QoS problem), and b) maximization of bit rate for fixed set of error probabilities and power. It is shown in both cases that the GTD yields an optimal family of solutions.
A Hybrid Approach to Spatial Multiplexing in MultiUser MIMO Downlinks
, 2003
"... In the downlink of a Multiuser MIMO (Multiple Input Multiple Output) communication system, intelligent algorithms are needed to choose transmit vectors for spatial multiplexing. ..."
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Cited by 3 (0 self)
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In the downlink of a Multiuser MIMO (Multiple Input Multiple Output) communication system, intelligent algorithms are needed to choose transmit vectors for spatial multiplexing.
Optimum Joint TransmitReceive Linear Processing for Vectored DSL Transmission with QoS Requirements
 in Proc. 36th Asilomar Conference on Signals, Systems & Computers
, 2002
"... This paper considers a DSL system in which a subset of the twistedpair copper wires within a bundle can perform a joint processing at both sides of the communication system (e.g., links between central offices and remote terminals or between central offices and private networks). The DSL channel is ..."
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Cited by 2 (1 self)
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This paper considers a DSL system in which a subset of the twistedpair copper wires within a bundle can perform a joint processing at both sides of the communication system (e.g., links between central offices and remote terminals or between central offices and private networks). The DSL channel is treated as a multiinput multioutput (MIMO) system over which many substreams are established. It is assumed that the signal constellation to be used at each substream is given (possibly after some kind of bit distribution optimization) with a corresponding Quality of Service (QoS) constraint, e.g., to guarantee a certain error probability.
Convex Optimization Theory Applied to Joint TransmitterReceiver Design in MIMO Channels
 in SpaceTime Processing for MIMO Communications, Chapter 8
, 2005
"... Multiantenna MIMO channels have recently become a popular means to increase the spectral efficiency and quality of wireless communications by the use of spatial diversity at both sides of the link [1–4]. In fact, the MIMO concept is much more general and embraces many other scenarios such as wirelin ..."
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Cited by 2 (0 self)
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Multiantenna MIMO channels have recently become a popular means to increase the spectral efficiency and quality of wireless communications by the use of spatial diversity at both sides of the link [1–4]. In fact, the MIMO concept is much more general and embraces many other scenarios such as wireline digital subscriber line (DSL) systems [5] and singleantenna