Generalized Design of Diffractive Optical Elements Using Neural Networks

Diffractive optical elements (DOE) utilize diffraction to manipulate light in optical systems. These elements have a wide range of applications including optical interconnects, coherent beam addition, laser beam shaping and refractive optics aberration correction. Due to the wide range of applications, optimal design of DOE has become an important research problem. In the design of the DOEs, existing techniques utilize the Fresnel diffraction theory to compute the phase at the desired location at the output plane. This process involves solving nonlinear integral equations for which various numerical methods along with robust optimization algorithms exist in literature. However all the algorithms proposed so far assume that the size and the spacing of the elements as independent variables in the design of optimal diffractive gratings. Therefore search algorithms need to be called every time the required geometry of the elements changes, resulting in a computationally expensive design procedure for systems utilizing a large number of DOEs. In this work we have developed a novel algorithm that uses neural networks with possibly multiple hidden layers to overcome this limitation and arrives at a general solution for the design of the DOEs for a given application. Inputs to this network are the spacing between the elements and the input/output planes. The network outputs the phase gratings that are required to obtain the desired intensity at the specified location in the output plane. The network was trained using the back-propagation technique. The training set was generated by using GS algorithm approach as described in literature. The mean square error obtained is comparable to conventional techniques but with much lower computational costs

Inter-plane satellite matching in dense LEO constellations

Dense constellations of Low Earth Orbit (LEO) small satellites are envisioned to make extensive use of the inter-satellite link (ISL). Within the same orbital plane, the inter-satellite distances are preserved and the links are rather stable. In contrast, the relative motion between planes makes the inter-plane ISL challenging. In a dense set-up, each spacecraft has several satellites in its coverage volume, but the time duration of each of these links is small and the maximum number of active connections is limited by the hardware. We analyze the matching problem of connecting satellites using the inter-plane ISL for unicast transmissions. We present and evaluate the performance of two solutions to the matching problem with any number of orbital planes and up to two transceivers: a heuristic solution with the aim of minimizing the total cost; and a Markovian solution to maintain the on-going connections as long as possible. The Markovian algorithm reduces the time needed to solve the matching up to 1000x and 10x with respect to the optimal solution and to the heuristic solution, respectively, without compromising the total cost. Our model includes power adaptation and optimizes the network energy consumption as the exemplary cost in the evaluations, but any other QoS-oriented KPI can be used instead

Separation Framework: An Enabler for Cooperative and D2D Communication for Future 5G Networks

Soaring capacity and coverage demands dictate that future cellular networks need to soon migrate towards ultra-dense networks. However, network densification comes with a host of challenges that include compromised energy efficiency, complex interference management, cumbersome mobility management, burdensome signaling overheads and higher backhaul costs. Interestingly, most of the problems, that beleaguer network densification, stem from legacy networks' one common feature i.e., tight coupling between the control and data planes regardless of their degree of heterogeneity and cell density. Consequently, in wake of 5G, control and data planes separation architecture (SARC) has recently been conceived as a promising paradigm that has potential to address most of aforementioned challenges. In this article, we review various proposals that have been presented in literature so far to enable SARC. More specifically, we analyze how and to what degree various SARC proposals address the four main challenges in network densification namely: energy efficiency, system level capacity maximization, interference management and mobility management. We then focus on two salient features of future cellular networks that have not yet been adapted in legacy networks at wide scale and thus remain a hallmark of 5G, i.e., coordinated multipoint (CoMP), and device-to-device (D2D) communications. After providing necessary background on CoMP and D2D, we analyze how SARC can particularly act as a major enabler for CoMP and D2D in context of 5G. This article thus serves as both a tutorial as well as an up to date survey on SARC, CoMP and D2D. Most importantly, the article provides an extensive outlook of challenges and opportunities that lie at the crossroads of these three mutually entangled emerging technologies.Comment: 28 pages, 11 figures, IEEE Communications Surveys & Tutorials 201

Competitive Assessments for HAP Delivery of Mobile Services in Emerging Countries

In recent years, network deployment based on High Altitude Platforms (HAPs) has gained momentum through several initiatives where air vehicles and telecommunications payloads have been adapted and refined, resulting in more efficient and less expensive platforms. In this paper, we study HAP as an alternative or complementary fast-evolving technology to provide mobile services in rural areas of emerging countries, where business models need to be carefully tailored to the reality of their related markets. In these large areas with low user density, mobile services uptake is likely to be slowed by a service profitability which is in turn limited by a relatively low average revenue per user. Through three architectures enabling different business roles and using different terrestrial, HAP and satellite backhaul solutions, we devise how to use in an efficient and profitable fashion these multi-purpose aerial platforms, in complement to existing access and backhauling satellite or terrestrial technologies

Sensor Scheduling for Energy-Efficient Target Tracking in Sensor Networks

In this paper we study the problem of tracking an object moving randomly through a network of wireless sensors. Our objective is to devise strategies for scheduling the sensors to optimize the tradeoff between tracking performance and energy consumption. We cast the scheduling problem as a Partially Observable Markov Decision Process (POMDP), where the control actions correspond to the set of sensors to activate at each time step. Using a bottom-up approach, we consider different sensing, motion and cost models with increasing levels of difficulty. At the first level, the sensing regions of the different sensors do not overlap and the target is only observed within the sensing range of an active sensor. Then, we consider sensors with overlapping sensing range such that the tracking error, and hence the actions of the different sensors, are tightly coupled. Finally, we consider scenarios wherein the target locations and sensors' observations assume values on continuous spaces. Exact solutions are generally intractable even for the simplest models due to the dimensionality of the information and action spaces. Hence, we devise approximate solution techniques, and in some cases derive lower bounds on the optimal tradeoff curves. The generated scheduling policies, albeit suboptimal, often provide close-to-optimal energy-tracking tradeoffs

Solutions to Facility Location–Network Design Problems

This doctoral thesis presents new solution strategies for facility location–network design (FLND) problems. FLND is a combination of facility location and network design: the overall goal is to improve clients’ access to facilities and the means of reaching this goal include both building facilities (as in facility location) and building travelable links (as in network design). We measure clients’ access to facilities by the sum of the travel costs, and our objective is to minimize this sum. FLND problems have facility location problems and network design problems, both of which are NP-hard, as subproblems and are therefore themselves theoretically difficult problems. We approach the search for optimal solutions from both above and below, contributing techniques for finding good upper bounds as well as good lower bounds on an optimal solution. On the upper bound side, we present the first heuristics in the literature for this problem. We have developed a variety of heuristics: simple greedy heuristics, a local search heuristic, metaheuristics including simulated annealing and variable neighborhood search, as well as a custom heuristic based on the problem-specific structure of FLND. Our computational results compare the performance of these heuristics and show that the basic variable neighborhood search performs the best, achieving a solution within 0.6% of optimality on average for our test cases. On the lower bound side, we work with an existing IP formulation whose LP relaxation provides good lower bounds. We present a separation routine for a new class of inequalities that further improve the lower bound, in some cases even obtaining the optimal solution. Putting all this together, we develop a branch-and-cut approach that uses heuristic solutions as upper bounds, and cutting planes for increasing the lower bound at each node of the problem tree, thus reducing the number of nodes needed to solve to optimality. We also present an alternate IP formulation that uses fewer variables than the one accepted in the literature. This formulation allows some problems to be solved more quickly, although its LP relaxation is not as tight. To aid in the visualization of FLND problem instances and their solutions, we have developed a piece of software, FLND Visualizer. Using this application one can create and modify problem instances, solve using a variety of heuristic methods, and view the solutions. Finally, we consider a case study: improving access to health facilities in the Nouna health district of Burkina Faso. We demonstrate the solution techniques developed here on this real-world problem and show the remarkable improvements in accessibility that are possible