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172
Robust minimum variance beamforming
 IEEE Transactions on Signal Processing
, 2005
"... Abstract—This paper introduces an extension of minimum variance beamforming that explicitly takes into account variation or uncertainty in the array response. Sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold. In our method, uncerta ..."
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Cited by 107 (10 self)
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Abstract—This paper introduces an extension of minimum variance beamforming that explicitly takes into account variation or uncertainty in the array response. Sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold. In our method, uncertainty in the array manifold is explicitly modeled via an ellipsoid that gives the possible values of the array for a particular look direction. We choose weights that minimize the total weighted power output of the array, subject to the constraint that the gain should exceed unity for all array responses in this ellipsoid. The robust weight selection process can be cast as a secondorder cone program that can be solved efficiently using Lagrange multiplier techniques. If the ellipsoid reduces to a single point, the method coincides with Capon’s method. We describe in detail several methods that can be used to derive an appropriate uncertainty ellipsoid for the array response. We form separate uncertainty ellipsoids for each component in the signal path (e.g., antenna, electronics) and then determine an aggregate uncertainty ellipsoid from these. We give new results for modeling the elementwise products of ellipsoids. We demonstrate the robust beamforming and the ellipsoidal modeling methods with several numerical examples. Index Terms—Ellipsoidal calculus, Hadamard product, robust beamforming, secondorder cone programming.
MIMO Transceiver Design via Majorization Theory
, 2007
"... and unified representation of different physical communication systems, ranging from multiantenna wireless channels to wireless digital subscriber line systems. They have the key property that several data streams can be simultaneously established. In general, the design of communication systems f ..."
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Cited by 66 (1 self)
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and unified representation of different physical communication systems, ranging from multiantenna wireless channels to wireless digital subscriber line systems. They have the key property that several data streams can be simultaneously established. In general, the design of communication systems for MIMO channels is quite involved (if one can assume the use of sufficiently long and good codes, then the problem formulation simplifies drastically). The first difficulty lies on how to measure the global performance of such systems given the tradeoff on the performance among the different data streams. Once the problem formulation is defined, the resulting mathematical problem is typically too complicated to be optimally solved as it is a matrixvalued nonconvex optimization problem. This design problem has been studied for the past three decades (the first papers
An introduction to convex optimization for communications and signal processing
 IEEE J. SEL. AREAS COMMUN
, 2006
"... Convex optimization methods are widely used in the ..."
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Cited by 56 (2 self)
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Convex optimization methods are widely used in the
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 53 (2 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 robust maximin approach for MIMO communications with imperfect channel state information based on convex optimization
 IEEE Trans. Signal Processing
, 2006
"... Abstract—This paper considers a wireless communication system with multiple transmit and receive antennas, i.e., a multipleinputmultipleoutput (MIMO) channel. The objective is to design the transmitter according to an imperfect channel estimate, where the errors are explicitly taken into account ..."
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Cited by 50 (5 self)
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Abstract—This paper considers a wireless communication system with multiple transmit and receive antennas, i.e., a multipleinputmultipleoutput (MIMO) channel. The objective is to design the transmitter according to an imperfect channel estimate, where the errors are explicitly taken into account to obtain a robust design under the maximin or worst case philosophy. The robust transmission scheme is composed of an orthogonal space–time block code (OSTBC), whose outputs are transmitted through the eigenmodes of the channel estimate with an appropriate power allocation among them. At the receiver, the signal is detected assuming a perfect channel knowledge. The optimization problem corresponding to the design of the power allocation among the estimated eigenmodes, whose goal is the maximization of the signaltonoise ratio (SNR), is transformed to a simple convex problem that can be easily solved. Different sources of errors are considered in the channel estimate, such as the Gaussian noise from the estimation process and the errors from the quantization of the channel estimate, among others. For the case of Gaussian noise, the robust power allocation admits a closedform expression. Finally, the benefits of the proposed design are evaluated and compared with the pure OSTBC and nonrobust approaches. Index Terms—Antenna arrays, beamforming, convex optimization theory, maximum optimization problems, multipleinput multipleoutput (MIMO) systems, saddle point, space–time coding, worstcase robust designs. I.
Robust beamforming for wireless information and power transmission
 IEEE Wireless Commun. Letters
, 2012
"... Abstract—In this letter, we study the robust beamforming problem for the multiantenna wireless broadcasting system with simultaneous information and power transmission, under the assumption of imperfect channel state information (CSI) at the transmitter. Following the worstcase deterministic model ..."
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Cited by 44 (0 self)
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Abstract—In this letter, we study the robust beamforming problem for the multiantenna wireless broadcasting system with simultaneous information and power transmission, under the assumption of imperfect channel state information (CSI) at the transmitter. Following the worstcase deterministic model, our objective is to maximize the worstcase harvested energy for the energy receiver while guaranteeing that the rate for the information receiver is above a threshold for all possible channel realizations. Such problem is nonconvex with infinite number of constraints. Using certain transformation techniques, we convert this problem into a relaxed semidefinite programming problem (SDP) which can be solved efficiently. We further show that the solution of the relaxed SDP problem is always rankone. This indicates that the relaxation is tight and we can get the optimal solution for the original problem. Simulation results are presented to validate the effectiveness of the proposed algorithm. Index Terms—Energy harvesting, beamforming, worstcase robust design, semidefinite programming.
Spectrum Sharing in Wireless Networks via QoSAware Secondary Multicast Beamforming
"... Abstract—Secondary spectrum usage has the potential to considerably increase spectrum utilization. In this paper, qualityofservice (QoS)aware spectrum underlay of a secondary multicast network is considered. A multiantenna secondary access point (AP) is used for multicast (common information) tra ..."
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Cited by 40 (16 self)
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Abstract—Secondary spectrum usage has the potential to considerably increase spectrum utilization. In this paper, qualityofservice (QoS)aware spectrum underlay of a secondary multicast network is considered. A multiantenna secondary access point (AP) is used for multicast (common information) transmission to a number of secondary singleantenna receivers. The idea is that beamforming can be used to steer power towards the secondary receivers while limiting sidelobes that cause interference to primary receivers. Various optimal formulations of beamforming are proposed, motivated by different “cohabitation ” scenarios, including robust designs that are applicable with inaccurate or limited channel state information at the secondary AP. These formulations are NPhard computational problems; yet it is shown how convex approximationbased multicast beamforming tools (originally developed without regard to primary interference constraints) can be adapted to work in a spectrum underlay context. Extensive simulation results demonstrate the effectiveness of the proposed approaches and provide insights on the tradeoffs between different design criteria. Index Terms—Beamforming, multicasting, secondary spectrum usage, semidefinite programming (SDP). I.
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 35 (2 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 Secure Transmission in MISO Channels Based on WorstCase Optimization
 IEEE Trans. Signal Process
, 2012
"... Abstract—This paper studies robust transmission schemes for MISO wiretap channels with imperfect channel state information (CSI) for the eavesdropper link. Both the cases of direct transmission and cooperative jamming with a helper are investigated. The error in the eavesdropper’s CSI is assumed to ..."
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Cited by 27 (5 self)
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Abstract—This paper studies robust transmission schemes for MISO wiretap channels with imperfect channel state information (CSI) for the eavesdropper link. Both the cases of direct transmission and cooperative jamming with a helper are investigated. The error in the eavesdropper’s CSI is assumed to be normbounded, and robust transmit covariance matrices are obtained based on worstcase secrecy rate maximization, under both individual and global power constraints. Numerical results show the advantage of the proposed robust design. In particular, under a global power constraint, although cooperative jamming is not necessary for optimal transmission with perfect eavesdropper’s CSI, we show that robust jamming support can increase the secrecy rate in the presence of channel mismatch. I.
PhasedMIMO Radar: A Tradeoff Between PhasedArray and MIMO Radars
, 2009
"... We propose a new technique for multipleinput multipleoutput (MIMO) radar with colocated antennas which we call phasedMIMO radar. The new technique enjoys the advantages of MIMO radar without sacrificing the main advantage of phasedarray radar which is the coherent processing gain at the transmit ..."
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Cited by 27 (10 self)
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We propose a new technique for multipleinput multipleoutput (MIMO) radar with colocated antennas which we call phasedMIMO radar. The new technique enjoys the advantages of MIMO radar without sacrificing the main advantage of phasedarray radar which is the coherent processing gain at the transmitting side. The essence of the proposed technique is to partition the transmitting array into a number of subarrays that are allowed to overlap. Then, each subarray is used to coherently transmit a waveform which is orthogonal to the waveforms transmitted by other subarrays. Coherent processing gain can be achieved by designing a weight vector for each subarray to form a beam towards a certain direction in space. Moreover, the subarrays are combined jointly to form a MIMO radar resulting in higher resolution capabilities. The substantial improvements offered by the proposed phasedMIMO radar technique as compared to previous techniques are demonstrated analytically and by simulations through analysis of the corresponding beampatterns and achievable output signaltonoiseplusinterference ratios. Both analytical and simulation results validate the effectiveness of the proposed phasedMIMO radar.