Applications of the Internet of Materials: Programmable Wireless Environments

DETERMINISTIC WIRELESS PROPAGATION CONTROL AS A CONCEPT

The Internet of Materials can constitute an effective means for controlling the wireless propagation within a space, introducing programmable wireless environments (PWEs) [92,103]. According to the PWE paradigm, planar objects-such as walls in a floorplan-receive a special coating that can sense impinging waves and actively modify them by applying an electromagnetic (EM) function. All metasurface- enabled wave modifications are possible, including altering the wave’s direction, power, polarization and phase [89]. In this chapter we focus on the network-layer PWE configuration problem, i.e., which functions to deploy at the PWE coatings to serve a set of given user communication objectives within a space.

Apart from metasurfaces, coating technologies for PWEs include relays and phased antenna arrays [95]. Each technology comes with a range of supported functions, environmental applicability and efficiency degrees. Relays are 1 input-N output antenna pairs that can be placed over walls at regular intervals [179]. At each pair, one out of the N outputs can be selected, thereby redirecting the input wave in a partially customizable manner. Phased antenna arrays-also known as intelligent surfaces and reflect arrays [43,152,15G]-are panels commonly comprising a number of patch antennas with half-wavelength size, in a 2D grid arrangement. At each patch, active elements such as PIN diodes are used for altering the phase of the reflected EM wave. Consistent wave steering and absorption is attained at the far field. Metasurfaces have 25 — 100+ times higher density of meta-atoms, allowing allows them to form any surface current distribution over them, thereby producing any EM output due to the Huygens principle [124]. Thus, highly efficient EM functions even in the near field can be attained. Moreover, as discussed in Chapter 4, HyperSurfaces come with the software programming interfaces that allows them to be treated as black-boxes, facilitating their direct integration into applications [99,101], without knowledge of the underlying Physics.

A PWE is created by coating planar objects such as walls and ceilings in an indoor environment-with tiles, i.e., rectangular panels of any aforementioned technology, with inter-networking capabilities [92]. The latter allow a central server to connect to any tile, get its state and set its EM function in an automated manner [93]. This maturity level reached at the physical layer of tiles opens a new research direction at the network level: given a set of users with communication objectives within a PWE, what is the optimal EM function per tile to serve them?

In this chapter we present a solution to this problem, able to handle multiple users, objectives and EM functions. User mobility, multiple objectives per user, multicast groups and partially coated PWEs are supported. The objectives include wireless power transfer and signal- to-interference maximization, as well as eavesdropping and Doppler effect mitigation. In order to achieve these traits, the present chapter details:

■ A systematic way of formulating and combining EM functions for applications.

■ The EM profile of tiles, a novel concept that describes the supported EM functions per tile and their efficiency.

■ A graph-based model to describe PWEs, and a way of transforming communication objectives to graph paths.

Extensive evaluations in multiple floorplans and topologies are presented as examples, yielding important conclusions about the maximum potential of PWEs and their user capacity in terms of maximal supported traffic load. Moreover, while the focus of the examples is wireless communications, the same algorithms can be applied for software-driven manipulation of wireless propagation in any setting.

MODELING, SIMULATING, AND CONFIGURING PWEs—A RAY-ROUTING APPROACH BASED ON GRAPH THEORY

This section provides an abstract model of the Physics behind metasurfaces, leading to a function-centric formulation of their capabilities. This formulation is then used for modeling PWEs as a graph, and describing its workflow and performance objectives as path finding problems.

Persistent notation is summarized in Table 9.1 for ease. (Notation used only locally in the text is omitted).

General Modeling and Properties of HyperSurface Functions

Let Ti denote the set of all HyperSurface tiles deployed within an environment, such as the floorplan of Fig. 9.1. A single tile will be denoted as hH. Let J~k denote all possible EM functions that can be deployed to a tile h. A single function deployed to a tile will be f),Eh-

A function fh is attained by setting the active elements of the HyperSurface accordingly. In this work we will assume that the correspondence between functions and active element states is known, and the reader is redirected to studies on EM Compilers for further details [99,101].

Each function fh receives a nominal input EM field, Ein, (i.e., impinging upon the tile), and then returns a well-defined output Eout (i.e., a reflected, refracted, or no field-in case of perfect absorption), which can be abstracted as:

Table 9.1 Summary of Notation.

Symbol

Explanation

The set of all tiles within an environment.

A single HyperSurface tile.

The set of EM functions supported by a tile h.

A single function, deployed to tile h.

Absorption, Steering and Collimation functions.

EM phase and polarization function modifiers.

Nominal input/output (EM field) of a function.

EM function input/outputs as wave attributes: jfrequency, direction, power, polarity, phases.

Subscripts denoting plain wave and focal wave.

Wave power gain/loss after impinging at tile h.

Graph with tiles 'H and users и G U as nodes, inter tile links Cf, and user-to-tile links Cu.

A path in Q as list of links from node n to n'.

A link in Q from node n to ri .

Link labels denoting intended Tx and Rx users.

A tupple (group) of items.

A list of objects (single items or tupples).

Unintended (not nominal) type of quantity *.

The cardinality of a set *.

Consider the coordinate system over a tile, as shown in Fig. 9.2. In the most generic function case, Ein is defined over the ф = 90° plane on the surface, while Eout contains the output field at any point {г, в. ф} around the tile. It is noted that a function //, also defines the output to any, even unintended input, Ein, which can exemplary arise when EM sources move, without adapting the tile functions accordingly. Therefore, relation (9.1) is generalized as:

We proceed to remark two important properties of the EM functions, stemming from physics:

EM functions fi, are symmetric [89,174]:

D and 2D illustration of the types of links (user links and inter-tile links) and nodes (tiles and users) in a PWE

Figure 9.1 3D and 2D illustration of the types of links (user links and inter-tile links) and nodes (tiles and users) in a PWE.

The symmetry remark can he used for defining a common format for inputs and outputs in Section 9.2.2. It will also he called upon later on, to ensure that communication channels created by tuning HvperSurfaces are bidirectional.

EM functions fh are a linear map of Em —» Eout [89]:

where к is any index, and c. cr- € 7Z.

The linearity property, in conjunction with the symmetry property will he promptly employed to reform the input/output format of Д, without loss of generality.

 
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