Node localization is a difficult task in sensor networks in which the ranging measurements are subject to errors and anchor positions are subject to uncertainty. In this paper, the robust localization problem is formulated using the maximum likelihood criterion under an unbounded uncertainty model for the anchor positions. To overcome the non-convexity of the resulting optimization problem, a convex relaxation leading to second order cone programming (SOCP) is devised. Furthermore, an analysis is performed in order to identify the set of nodes which are accurately positioned using robust SOCP, and to establish a relation between the solution of the proposed robust SOCP optimization and the existing robust optimization using semidefinite programming (SDP). Based on this analysis, a mixed robust SDP-SOCP localization framework is proposed which benefits from the better accuracy of SDP and the lower complexity of SOCP. Since the centralized optimization involves a high computational complexity in large networks, we also derive the distributed implementation of the proposed robust SOCP convex relaxation. Finally, we propose an iterative optimization based on the expectation maximization (EM) algorithm for the cases where anchor uncertainty parameters are unavailable. Simulations confirm that the robust SOCP and mixed robust SDP-SOCP provide tradeoffs between localization accuracy and computational complexity that render them attractive solutions, especially in networks with a large number of nodes.

We consider the design of ultra-wideband (UWB) systems that enable high data rate communications for short-range wireless applications. In particular, we consider the downlink of a direct sequence UWB (DS-UWB) system in which the base station is equipped with multiple antennas and employs pre-rake combining, while each user employs a simple single antenna receiver. We propose the use of multiuser filters for the purpose of pre-equalization at the transmitter in order to mitigate the combined effects of intersymbol interference (ISI) and multiuser interference (MUI) that are generated at the receivers as a result of the wideband nature of the users' channels. For this system, we study the joint design of the transmitter's pre-equalization filters and each receiver's scalar gain under two design criteria. The first design minimizes the total transmitted power from the base station subject to achieving physical layer quality of service requirements of different users. For this design, we show that the calculation of the pre-equalization filters and the receiver gains can be formulated as an efficiently solvable convex optimization problem. In the second design, we consider the minimization of a weighted sum of each user's mean-square error. In order to obtain a computationally tractable solution for this design criterion, we exploit the dual DS-UWB uplink that employs rake combining and post-equalization filters at a central receiver. The numerical studies for each design criterion under realistic models of UWB channel propagation demonstrate the effectiveness of the proposed multiuser pre-equalization filter designs in mitigating ISI and MUI, and thus their ability to enable reliable pre-rake DS-UWB downlink transmission.

In this paper, we study the problem of resource allocation and optimization for multiple-input multiple-output (MIMO) cognitive radio (CR) systems under the assumption of imperfect channel state information (CSI) of the channels between the secondary users (SUs) and the primary users (PUs) at the SUs. We formulate robust design optimization problems for CR systems with one or more SUs communicating over a single or multiple frequency carriers in the presence of multiple PUs. We propose a linear matrix inequality (LMI) transformation that facilitates proper treatment of channel uncertainty at the SU transmitter and we provide solutions to the design problems based on convex optimization and Lagrange dual decomposition techniques. Finally, we demonstrate the importance of the proposed formulations and the implications of ignoring channel uncertainties when designing for CR systems.

We consider the design of ultra-wideband (UWB) systems that provide high capacity communication for short-range wireless applications. The design configuration is a multiuser pre-rake UWB broadcast communication system in which the base station is equipped with multiple antennas to achieve high data rates while each user is equipped with a simple and cost-efficient single antenna receiver. We assume the use of multiuser pre-equalization filters at the base station to mitigate the effect of inter-symbol interference (ISI) and multiuser interference (MUI) at the receivers. For the optimization of these filters we develop an analytical framework that minimizes the total transmission power while satisfying (physical layer) users' quality of service for reliable communications. In particular, the quality of service constraints are expressed in terms of the mean square error (MSE) for each user. We show that the design problem is equivalent to a convex optimization problem that can be solved efficiently. The numerical studies confirm that the proposed design strategy for multiuser pre-equalization filters enables the reduction of the total transmission power to achieve a given set of requested MSE targets.

In this paper, we study design problems for single and multiple-carrier Multiple-Input Multiple-Output (MIMO) Cognitive Radio (CR) systems. We assume imperfect Channel State Information (CSI) of the channels between the Secondary Users (SUs) and the Primary Users (PUs) at the SUs and propose solutions based on a Linear Matrix Inequality transformation that facilitates proper treatment of channel uncertainty at the SU transmitter. We employ convex optimization tools and use a Lagrange dual decomposition approach to solve the optimization problems efficiently. We also present a number of numerical results which clearly demonstrate the robustness and importance of the proposed algorithms.

We consider a broadcast channel with multiple antennas at the base station and single-antenna receivers, and we study transceiver design with quality of service (QoS) requirements in the presence of uncertain channel state information (CSI) at the transmitter. Each user's QoS requirement is formulated as an upper bound on the outage probability of the mean square error (MSE), and we demonstrate that these constraints imply bounds on the outage of the received signal-to-interference-plus-noise-ratio. Using this MSE framework, we provide a unified approach to the design of non-linear and linear transceivers that minimize the transmitted power required to satisfy the QoS constraints. We present three conservative design approaches that yield (deterministic) convex and efficiently-solvable design formulations that guarantee the satisfaction of the QoS constraints, and we propose computationally-efficient algorithms that can reduce the level of conservatism in the initial formulations.

We consider the design of linear precoders for broadcast channels with quality of service (QoS) constraints for each user, in scenarios with uncertain channel state information at the transmitter. Given a total power constraint on the transmission power, our goal is to design a robust fair precoder that maximizes the minimum QoS over all users that can be guaranteed for every channel within a specified uncertainty region around the 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 quasi-convex and computationally-efficient restrictions of the original design problem. The three approaches yield formulations that offer different trade-offs between the degree of conservatism and the size of the design problem. Our simulations indicate that the proposed approaches can significantly increase the minimum QoS of all users when the available channel knowledge at the transmitter is imperfect.

We consider the design of linear transceivers for multiuser communication systems in the presence of uncertain channel state information (CSI), with an emphasis on the downlink. We consider a deterministically-bounded model for the channel uncertainty, and we study the design of robust downlink transceivers that minimize the worst-case MSE over all admissible channels. While we show that the design problem is NP-hard, we also propose an iterative local optimization algorithm that is based on efficiently-solvable convex conic formulations. Our framework is quite flexible, and can incorporate different bounded uncertainty models as well as a variety of power constraints. In particular, we study a "system-wide" uncertainty model, and although the resulting design problem is still NP hard, it does result in a significantly simpler iterative local design algorithm than the "per-user" uncertainty model. Our approaches to the minimax design for the downlink can be extended to the uplink, and we provide explicit formulations for the resulting uplink designs. Simulation results indicate that the proposed designs can significantly reduce the sensitivity of the downlink to uncertain CSI.

We consider joint transceiver design for point-to-point Multiple-Input Multiple-Output communication systems that implement interference (pre-)subtraction; i.e., Decision Feedback Equalization (DFE) or Tomlinson-Harashima precoding (THP). We develop a unified framework for joint transceiver design of these two dual systems by considering design criteria that are expressed as functions of the (logarithm 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 broad classes of communication objectives, namely those that are Schur-convex and Schur-concave functions of these logarithms. These two classes embrace several design criteria for which the optimal transceiver design has remained an open problem. For Schur-convex objectives, the optimal design results in data streams with equal MSEs. In addition to other desirable properties, this design simultaneously minimizes the total MSE and the average bit error rate, and maximizes the Gaussian mutual information; a property that is not achieved by a linear transceiver. Moreover, we show that the optimal design yields objective values that are superior to the corresponding optimal objective value for a linear transceiver. For Schur-concave objectives, the optimal DFE design results in linear equalization and the optimal THP design results in linear precoding. The proposed design framework can be regarded as a counterpart of the existing framework for linear transceiver design.

We consider the design of linear transceivers for multiuser communication systems in the presence of uncertain channel state information (CSI), with an emphasis on downlink systems with a single antenna at each receiver. For systems with uplink-downlink reciprocity, we consider a stochastic model for the channel uncertainty, and we propose an efficient algorithm for the joint design of the linear preceding matrix at the base station and the equalizing gains at the receivers so as to minimize the average mean-square-error (MSE) over the channel uncertainty. The design is based on a generalization, derived herein, of the MSE duality between the broadcast and multiple access channels (MAC) to scenarios with uncertain CSI, and on a convex formulation for the design of robust transceivers for the dual MAC. For systems in which quantized channel feedback is employed, we consider a deterministically-bounded model for the channel uncertainty, and we study the design of robust downlink transceivers that minimize the worst- case MSE over all admissible channels. While we show that the design problem is NP-hard, we also propose an iterative local optimization algorithm that is based on efficiently-solvable convex conic formulations. Our framework is quite flexible, and can incorporate different bounded uncertainty models as well as a variety of power constraints. In particular, we study a "system-wide" uncertainty model, and although the resulting design problem is still NP hard, it does result in a significantly simpler iterative local design algorithm than the "per-user" uncertainty model. Our approaches to the minimax design for the downlink can be extended to the uplink, and we provide explicit formulations for the resulting uplink designs. Simulation results indicate that the proposed approaches to robust linear transceiver design can significantly reduce the sensitivity of the downlink to uncertain CSI, and can provide improved performance over that of existing robust designs.

We consider the design of multiple-input multiple-output communication systems with a linear precoder at the transmitter, zero-forcing decision feedback equalization (ZFDFE) at the receiver, and a low-rate feedback channel that enables communication from the receiver to the transmitter. The channel state information (CSI) available at the receiver is assumed to be perfect, and based on this information the receiver selects a suitable precoder from a codebook and feeds back the index of this precoder to the transmitter. Our approach to the design of the components of this limited feedback scheme is based on the development, herein, of a unified framework for the joint design of the precoder and the ZF-DFE under the assumption that perfect CSI is available at both the transmitter and the receiver. The framework is general and embraces a wide range of design criteria. This framework enables us to characterize the statistical distribution of the optimal precoder in a standard Rayleigh fading environment. Using this distribution, we show that codebooks constructed from Grassmann packings minimize an upper bound on an average distortion measure, and hence are natural candidates for the codebook in limited feedback systems. Our simulation studies show that the proposed limited feedback scheme can provide significantly better performance at a lower feedback rate than existing schemes in which the detection order is fed back to the transmitter.

We consider joint transceiver design for general multiple-input multiple-output communication systems that implement interference (pre-)subtraction, such as those based on decision feedback equalization (DFE) or Tomlinson-Harashima 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 Schur-convex and Schur-concave functions of these logarithms. For Schur-convex 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 DFE-based model. For Schur-concave objectives, the optimal DFE design results in linear equalization and the optimal THP design results in linear preceding. 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.

We consider point-to-point multiple antenna communication systems in which multiple data streams are transmitted simultaneously. We consider systems which use Tomlinson-Harashima (TH) precoding to pre-subtract the interference among these data streams at the transmitter. In a conventional Tomlinson-Harashima precoding system, transmitter feedback and receiver feedforward processing matrices are used for interference pre-subtraction and channel spatial equalization. In addition to these matrices, we consider a transmitter precoding matrix that generalizes the permutation matrix used for ordering the precoded symbols in existing designs. This extra degree of freedom offers the potential for improved performance. In particular, under a mild signal to noise ratio (SNR) constraint, we find an optimum zero-forcing preceding matrix that minimizes the average symbol error rate (SER) of the data streams subject to a transmitter power constraint. We also show that the proposed design is optimal from an average bit error rate (BER) perspective. Simulation studies show significant improvement over conventional zero-forcing Tomlinson-Harashima precoders.

We consider the design of Tomlinson-Harashima (TH) precoders for broadcast channels in the presence of channel uncertainty. For systems in which uplink-downlink reciprocity is used to obtain a channel estimate at the transmitter, we present a robust design based on a statistical model for the channel uncertainty. We provide a convex formulation of the design problem subject to two types of power constraints: a set of constraints on the power transmitted from each antenna and a total power constraint. For the case of the total power constraint, we present a closed-form solution for the robust TH precoder that incurs essentially the same computational cost as the corresponding designs that assume perfect channel knowledge. For systems in which the receivers feed back quantized channel state information to the transmitter, we present a robust design based on a bounded model for the channel uncertainty. We provide a convex formulation for the TH precoder that maximizes the performance under the worst-case channel uncertainty subject to both types of power constraints. We also present a conservative robust design for this type of channel uncertainty that has reduced computational complexity for the case of power constraints on individual antennas and leads to a closed-form solution for the total power constraint case. Simulation studies verify our analytical results and show that the robust TH precoders can significantly reduce the rather high sensitivity of broadcast transmissions to errors in channel state information.

We consider linear precoding for the downlink of a multiuser communication system in the presence of uncertain channel state information (CSI) at the base station. We consider systems in which the base station has multiple antennas and each user has a single antenna and the channel estimate at the receivers is quantized and fed back to the base station. For these systems we propose a deterministically bounded model for the channel uncertainty and a convex optimization formulation for the precoder that maximizes the worst-case performance under constraints on the power transmitted from each antenna. We also derive a closed-form expression for the precoder that maximizes the worst-case performance under a constraint on total transmitted power. The cost of computing this closed-form solution is the same as that of computing the solution to the corresponding method that assumes perfect channel knowledge. An interesting property of the proposed robust precoders is that they do not necessarily use all the allowable transmission power. Our simulations indicate that the proposed approach can significantly reduce the sensitivity of the linearly precoded downlink to uncertainty in the CSI.

We consider linear precoding for the downlink of a multiuser communication system in the presence of uncertain channel state information (CSI) at the base station. We consider systems in which the base station has multiple antennas and each user has a single antenna; i.e. multiple-input single-output (MISO) systems. For systems with uplink-downlink reciprocity we propose a statistical model for the channel uncertainty and provide a convex optimization formulation for the precoder that maximizes an average mean square performance measure. For systems in which the channel measurements are quantized and fed back to the base station we propose a deterministically bounded model for the channel uncertainty and a convex formulation for the precoder that maximizes the worst-case performance. Both formulations allow the incorporation of power constraints on individual antennas in addition to the overall power constraint. Our simulations indicate that the proposed approach can significantly reduce the sensitivity of the linearly preceded downlink to uncertainty in the CSI