Michael Botros Shenouda

A framework for designing mimo systems with decision feedback equalization or tomlinson-harashima precoding

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.

Probabilistically-constrained approaches to the design of the multiple antenna downlink

We 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 probabilistically-constrained 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 efficiently-solvable design formulations that guarantee the satisfaction of the probabilistic QoS constraints. Furthermore, based on these convex formulations, we propose computationally-efficient 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.

Tomlinson-Harashima Precoding for Broadcast Channels with Uncertainty

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.

Dynamic Spectrum Management for Multiple-Antenna Cognitive Radio Systems: Designs with Imperfect CSI

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.

A design framework for limited feedback MIMO systems with zero-forcing DFE

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.

Robust Linear Precoding for Uncertain Miso Broadcast Channels

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

A Framework for Designing MIMO Systems with Decision Feedback Equalization or Tomlinson-Harashima Precoding

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.

Second order cone programming for sensor network localization with anchor position uncertainty

We consider the problem of node localization in sensor networks, and we focus on networks in which the ranging measurements are subject to errors and anchor positions are subject to uncertainty. We consider a statistical model for the uncertainty in the anchor positions and formulate the robust localization problem that finds a maximum likelihood estimation of the node positions. To overcome the non-convexity of the resulting optimization problem, we obtain a convex relaxation that is based on the second order cone programming (SOCP). We also propose a possible distributed implementation using the SOCP convex relaxation. We present numerical studies that compare the presented approach to other existing convex relaxations for the robust localization problem in terms of positioning error and computational complexity.

Single and Multiple Carrier Designs for Cognitive Radio Systems

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.

Outage-based design of robust Tomlinson–Harashima transceivers for the MISO downlink with QoS requirements

Abstract We consider a broadcast channel in which the base station is equipped with multiple antennas and each user has a single antenna, and we study the design of transceivers based on Tomlinson–Harashima precoders with probabilistic quality of service (QoS) requirements for each user, in scenarios with uncertain channel state information (CSI) at the transmitter. Each users QoS requirement is specified as a constraint on the maximum allowed outage probability of the receivers mean square error (MSE) with respect to a specified target MSE, and we demonstrate that these outage constraints are associated with constraints on the outage of the received signal-to-interference-plus-noise-ratio (SINR). We consider four different stochastic models for the channel uncertainty, and we design the downlink transceiver so as to minimize the total transmitted power subject to the satisfaction of the probabilistic QoS constraints. We present three conservative approaches to solving the resulting chance constrained optimization problems. These approaches are based on efficiently solvable deterministic convex design formulations that guarantee the satisfaction of the probabilistic QoS constraints. We also demonstrate how to apply these approaches in order to obtain computationally efficient solutions to some related design problems. Our simulations indicate that the proposed methods can significantly expand the range of QoS requirements that can be satisfied in the presence of uncertainty in the CSI.