Guest Editorial: Nonlinear Optimization of Communication Systems

Linear programming and other classical optimization techniques have found important applications in communication systems for many decades. Recently, there has been a surge in research activities that utilize the latest developments in nonlinear optimization to tackle a much wider scope of work in the analysis and design of communication systems. These activities involve every “layer” of the protocol stack and the principles of layered network architecture itself, and have made intellectual and practical impacts significantly beyond the established frameworks of optimization of communication systems in the early 1990s. These recent results are driven by new demands in the areas of communications and networking, as well as new tools emerging from optimization theory. Such tools include the powerful theories and highly efficient computational algorithms for nonlinear convex optimization, together with global solution methods and relaxation techniques for nonconvex optimization

Highly efficient impulse-radio ultra-wideband cavity-backed slot antenna in stacked air-filled substrate integrated waveguide technology

An impulse-radio ultra-wideband (IR-UWB) cavity-backed slot antenna covering the [5.9803; 6.9989] GHz frequency band of the IEEE 802.15.4a-2011 standard is designed and implemented in an air-filled substrate integrated waveguide (AFSIW) technology for localization applications with an accuracy of at least 3 cm. By relying on both frequency and time-domain optimization, the antenna achieves excellent IR-UWB characteristics. In free-space conditions, an impedance bandwidth of 1.92 GHz (or 29.4%), a total efficiency higher than 89%, a front-to-back ratio of at least 12.1 dB, and a gain higher than 6.3 dBi are measured in the frequency domain. Furthermore, a system fidelity factor larger than 98% and a relative group delay smaller than 100 ps are measured in the time domain within the 3 dB beamwidth of the antenna. As a result, the measured time-of-arrival of a transmitted Gaussian pulse, for different angles of arrival, exhibits variations smaller than 100 ps, corresponding to a maximum distance estimation error of 3 cm. Additionally, the antenna is validated in a real-life worst-case deployment scenario, showing that its characteristics remain stable in a large variety of deployment scenarios. Finally, the difference in frequency-and time-domain performance is studied between the antenna implemented in AFSIW and in dielectric filled substrate integrated waveguide (DFSIW) technology. We conclude that DFSIW technology is less suitable for the envisaged precision IR-UWB localization application

Energy-Efficient Power Control: A Look at 5G Wireless Technologies

This work develops power control algorithms for energy efficiency (EE) maximization (measured in bit/Joule) in wireless networks. Unlike previous related works, minimum-rate constraints are imposed and the signal-to-interference-plus-noise ratio takes a more general expression, which allows one to encompass some of the most promising 5G candidate technologies. Both network-centric and user-centric EE maximizations are considered. In the network-centric scenario, the maximization of the global EE and the minimum EE of the network are performed. Unlike previous contributions, we develop centralized algorithms that are guaranteed to converge, with affordable computational complexity, to a Karush-Kuhn-Tucker point of the considered non-convex optimization problems. Moreover, closed-form feasibility conditions are derived. In the user-centric scenario, game theory is used to study the equilibria of the network and to derive convergent power control algorithms, which can be implemented in a fully decentralized fashion. Both scenarios above are studied under the assumption that single or multiple resource blocks are employed for data transmission. Numerical results assess the performance of the proposed solutions, analyzing the impact of minimum-rate constraints, and comparing the network-centric and user-centric approaches.Comment: Accepted for Publication in the IEEE Transactions on Signal Processin

Filterbank optimization with convex objectives and the optimality of principal component forms

This paper proposes a general framework for the optimization of orthonormal filterbanks (FBs) for given input statistics. This includes as special cases, many previous results on FB optimization for compression. It also solves problems that have not been considered thus far. FB optimization for coding gain maximization (for compression applications) has been well studied before. The optimum FB has been known to satisfy the principal component property, i.e., it minimizes the mean-square error caused by reconstruction after dropping the P weakest (lowest variance) subbands for any P. We point out a much stronger connection between this property and the optimality of the FB. The main result is that a principal component FB (PCFB) is optimum whenever the minimization objective is a concave function of the subband variances produced by the FB. This result has its grounding in majorization and convex function theory and, in particular, explains the optimality of PCFBs for compression. We use the result to show various other optimality properties of PCFBs, especially for noise-suppression applications. Suppose the FB input is a signal corrupted by additive white noise, the desired output is the pure signal, and the subbands of the FB are processed to minimize the output noise. If each subband processor is a zeroth-order Wiener filter for its input, we can show that the expected mean square value of the output noise is a concave function of the subband signal variances. Hence, a PCFB is optimum in the sense of minimizing this mean square error. The above-mentioned concavity of the error and, hence, PCFB optimality, continues to hold even with certain other subband processors such as subband hard thresholds and constant multipliers, although these are not of serious practical interest. We prove that certain extensions of this PCFB optimality result to cases where the input noise is colored, and the FB optimization is over a larger class that includes biorthogonal FBs. We also show that PCFBs do not exist for the classes of DFT and cosine-modulated FBs

LQG Control and Sensing Co-Design

We investigate a Linear-Quadratic-Gaussian (LQG) control and sensing co-design problem, where one jointly designs sensing and control policies. We focus on the realistic case where the sensing design is selected among a finite set of available sensors, where each sensor is associated with a different cost (e.g., power consumption). We consider two dual problem instances: sensing-constrained LQG control, where one maximizes control performance subject to a sensor cost budget, and minimum-sensing LQG control, where one minimizes sensor cost subject to performance constraints. We prove no polynomial time algorithm guarantees across all problem instances a constant approximation factor from the optimal. Nonetheless, we present the first polynomial time algorithms with per-instance suboptimality guarantees. To this end, we leverage a separation principle, that partially decouples the design of sensing and control. Then, we frame LQG co-design as the optimization of approximately supermodular set functions; we develop novel algorithms to solve the problems; and we prove original results on the performance of the algorithms, and establish connections between their suboptimality and control-theoretic quantities. We conclude the paper by discussing two applications, namely, sensing-constrained formation control and resource-constrained robot navigation.Comment: Accepted to IEEE TAC. Includes contributions to submodular function optimization literature, and extends conference paper arXiv:1709.0882