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58
ProbabilisticallyConstrained Approaches to the Design of the Multiple Antenna Downlink,” in
 Proc. 42nd Asilomar Conference on Signals, Systems and Computers (ACSSC
, 2008
"... AbstractWe consider the downlink of a cellular system in which the base station is equipped with multiple antennas and each user has a single antenna. We study the design of linear precoders with probabilisticallyconstrained Quality of Service (QoS) requirements for each user, in scenarios with u ..."
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AbstractWe consider the downlink of a cellular system in which the base station is equipped with multiple antennas and each user has a single antenna. We study the design of linear precoders with probabilisticallyconstrained Quality of Service (QoS) requirements for each user, in scenarios with uncertain channel state information (CSI) at the transmitter. Our goal is to design the precoder so as to minimize the total transmitted power subject to the satisfaction of the QoS constraints with a maximum allowed outage probability. We consider two stochastic models for the uncertainty in the channel coefficients of each user. The first is a Gaussian model that is appropriate for uncertainty that results from estimation errors. The second one is uniform model that is appropriate for the quantization errors in systems with quantized feedback of channel state information. We formulate the design problem as a chance constrained optimization problem, in which each chance constraint involves randomly perturbed second order cone constraints. We adopt a conservative approach that yields (deterministic) convex and efficientlysolvable design formulations that guarantee the satisfaction of the probabilistic QoS constraints. Furthermore, based on these convex formulations, we propose computationallyefficient algorithms that can reduce the level of conservatism in the initial formulations. Our simulations indicate that the proposed methods can significantly expands the range of QoS requirements that can be satisfied in the presence of uncertainty in the CSI.
Joint beamforming and power control in coordinated multicell: Maxmin duality, effective network and large system transition
 IEEE TRANS. WIRELESS COMMUN
, 2013
"... This paper studies joint beamforming and power control in a coordinated multicell downlink system that serves multiple users per cell to maximize the minimum weighted signaltointerferenceplusnoise ratio. The optimal solution and distributed algorithm with geometrically fast convergence rate are ..."
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Cited by 8 (1 self)
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This paper studies joint beamforming and power control in a coordinated multicell downlink system that serves multiple users per cell to maximize the minimum weighted signaltointerferenceplusnoise ratio. The optimal solution and distributed algorithm with geometrically fast convergence rate are derived by employing the nonlinear PerronFrobenius theory and the multicell network duality. The iterative algorithm, though operating in a distributed manner, still requires instantaneous power update within the coordinated cluster through the backhaul. The backhaul information exchange and message passing may become prohibitive with increasing number of transmit antennas and increasing number of users. In order to derive asymptotically optimal solution, random matrix theory is leveraged to design a distributed algorithm that only requires statistical information. The advantage of our approach is that there is no instantaneous power update through backhaul. Moreover, by using nonlinear PerronFrobenius theory and random matrix theory, an effective primal network and an effective dual network are proposed to characterize and interpret the asymptotic solution.
Relay beamforming strategies for physicallayer security
 in Proc. CISS
, 2010
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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 7 (1 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
Transmit Optimization with Improper Gaussian Signaling for Interference Channels
 IEEE TRANSACTIONS ON SIGNAL PROCESSING, ACCEPTED
, 2013
"... This paper studies the achievable rates of Gaussian interference channels with additive white Gaussian noise (AWGN), when improper or circularly asymmetric complex Gaussian signaling is applied. For the Gaussian multipleinput multipleoutput interference channel (MIMOIC) with the interference tre ..."
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Cited by 6 (2 self)
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This paper studies the achievable rates of Gaussian interference channels with additive white Gaussian noise (AWGN), when improper or circularly asymmetric complex Gaussian signaling is applied. For the Gaussian multipleinput multipleoutput interference channel (MIMOIC) with the interference treated as Gaussian noise, we show that the user’s achievable rate can be expressed as a summation of the rate achievable by the conventional proper or circularly symmetric complex Gaussian signaling in terms of the users ’ transmit covariance matrices, and an additional term, which is a function of both the users ’ transmit covariance and pseudocovariance matrices. The additional degrees of freedom in the pseudocovariance matrix, which is conventionally set to be zero for the case of proper Gaussian signaling, provide an opportunity to further improve the achievable rates of Gaussian MIMOICs by employing improper Gaussian signaling. To this end, this paper proposes widely linear precoding, which efficiently maps proper informationbearing signals to improper transmitted signals at each transmitter for any given pair of transmit covariance and pseudocovariance matrices. In particular, for the case of twouser Gaussian singleinput singleoutput interference channel (SISOIC), we propose a joint covariance and pseudocovariance optimization algorithm with improper Gaussian signaling to achieve the Paretooptimal rates. By utilizing the separable structure of the achievable rate expression, an alternative algorithm with separate covariance and pseudocovariance optimization is also proposed, which guarantees the rate improvement over conventional proper Gaussian signaling.
Robust downlink beamforming using covariance channel state information
 in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP’09
, 2009
"... The problem of multiuser downlink beamforming is studied under the assumption that the transmitter has erroneous covariancebased channel state information (CSI). The goal is to minimize the transmit power under the worstcase qualityofservice (QoS) constraints. Previous convex optimizationbased ..."
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The problem of multiuser downlink beamforming is studied under the assumption that the transmitter has erroneous covariancebased channel state information (CSI). The goal is to minimize the transmit power under the worstcase qualityofservice (QoS) constraints. Previous convex optimizationbased solutions to this problem involve several coarse approximations of the original problem. In our proposed solution, such coarse approximations are avoided and an exact representation of the worstcase solution is obtained using Lagrange duality. The soobtained problem is then converted to a convex form using semidefinite relaxation (SDR). Computer simulations show that the SDR step does not involve any approximation as the resulting solution is always rankone. Simulation results demonstrate substantial performance improvements over earlier worstcase optimizationbased downlink beamforming techniques. Index Terms — Convex optimization, downlink beamforming, user qualityofservice
Coordinate beamforming with relaxed zero forcing: The sequential orthogonal projection combining method and rate control
 Mar. 2012 [Online]. Available: http:// arxiv.org/abs/1203.1758,, ArXiv PrePrint cs.IT/1203.1758
"... Abstract—In this paper, a new beam design paradigm for coordinated beamforming (CB) for current and future cellular networks is proposed based on a relaxed zeroforcing (RZF) constraint. In the conventional zeroforcing (ZF) CB, each cooperating transmitter designs its transmit beamforming matrix t ..."
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Cited by 4 (4 self)
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Abstract—In this paper, a new beam design paradigm for coordinated beamforming (CB) for current and future cellular networks is proposed based on a relaxed zeroforcing (RZF) constraint. In the conventional zeroforcing (ZF) CB, each cooperating transmitter designs its transmit beamforming matrix to null out interference to undesired receivers completely. In the proposed RZF paradigm, however, the ZF constraint is relaxed so that a tolerable amount of interference leakage to undesired receivers is allowed for the beam design at each transmitter. By relaxing the ZF constraint in such a way, transmitters have more degrees of freedom for their beam design to increase the overall data rate of the network. An efficient algorithm for the RZFCB is proposed based on a projected subgradient method. Numerical results show that the proposed RZFCB shows a noticeable gain over the conventional ZFCB. Index Terms—Coordinated beamforming, MIMO system, Zeroforcing, Interference channel, Projected subgradient method.
Beampattern synthesis via a matrix approach for signal power estimation
 IEEE Trans. Signal Process
, 2007
"... Abstract—We present new beampattern synthesis approaches based on semidefinite relaxation (SDR) for signal power estimation. The conventional approaches use weight vectors at the array output for beampattern synthesis, which we refer to as the vector approaches (VA). Instead of this, we use weight ..."
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Abstract—We present new beampattern synthesis approaches based on semidefinite relaxation (SDR) for signal power estimation. The conventional approaches use weight vectors at the array output for beampattern synthesis, which we refer to as the vector approaches (VA). Instead of this, we use weight matrices at the array output, which leads to matrix approaches (MA). We consider several versions of MA, including a (data) adaptive MA (AMA), as well as several dataindependent MA designs. For all of these MA designs, globally optimal solutions can be determined efficiently due to the convex optimization formulations obtained by SDR. Numerical examples as well as theoretical evidence are presented to show that the optimal weight matrix obtained via SDR has few dominant eigenvalues, and often only one. When the number of dominant eigenvalues of the optimal weight matrix is equal to one, MA reduces to VA, and the main advantage offered by SDR in this case is to determine the globally optimal solution efficiently. Moreover, we show that the AMA allows for strict control of mainbeam shape and peak sidelobe level while retaining the capability of adaptively nulling strong interferences and jammers. Numerical examples are also used to demonstrate that better beampattern designs can be achieved via the dataindependent MA than via its VA counterpart. Index Terms—Beamforming, beampattern synthesis, convex optimization, mainbeam shape control, sidelobe control. I.
Multiuser Precoders for Fixed Receivers
 IN PROC. OF IEEE INT. ZURICH SEMINAR (IZS2004
, 2004
"... We consider the problem of designing precoders for multiuser systems using fixed receivers. We first derive a precoder that minimizes the transmitted power subject to signal to interference plus noise ratio (SINR) constraints, and then derive a precoder that maximizes the worst case SINR subject to ..."
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Cited by 3 (1 self)
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We consider the problem of designing precoders for multiuser systems using fixed receivers. We first derive a precoder that minimizes the transmitted power subject to signal to interference plus noise ratio (SINR) constraints, and then derive a precoder that maximizes the worst case SINR subject to a power constraint. We show that both problems can be solved using standard optimization packages. In contrast to most of the existing precoders, our precoder design is not limited to full rank systems, and is applicable to systems in which the number of users is smaller, equal or larger than the processing gain. Simulation results in a multiuser system show that the proposed precoders can significantly outperform existing linear precoders.