# Evaluation Methodology

Figure 8.17 illustrates our methodology to obtain the traffic within the metasurface. MATLAB scripts are employed to simulate the movement and to obtain the corresponding unit cell state matrices. More specifically, we first evaluate the incidence and reflection angles given the positions of the HSF, the illumination source, and the moving target (mobility model). Then, we use Eq. (8.6) to obtain the phase gradients and then Eq. (8.7) to calculate the phase Фтп of each unit cell. Finally, we take the unit cell state that yields the phase that is closer to Ф„ш, this is, we perform the nretasurface coding.

The methods described above allow to obtain the matrix of unit cell states for any incidence and reflection conditions. Iterating over such calculations, we can obtain successive unit cell state matrices corresponding to a given movement with any angular granularity. To model the gateway, we only obtain the unit cell state matrices in steps corresponding to the angular step parameter. A diff operation between adjacent unit cell state matrices describes which unit cells need to be changed and, given our assumptions, which unit cells will receive packets from the gateway.

8.2.2.1 Relevant Inputs

For each type of movement, we collect traces that describe the time instant at which packets are generated as well as their intended destinations. The traces are obtained and classified as a function of the following parameters:

• 1. Metasurface size N x M: The number of unit cells has an impact on the absolute amount of transmitted messages. Observing the impact of the metasurface size on both the required throughput can give design guidelines for HSFs. By default, we take M = N = 50.
• 2. Number of states Ns: The calculations used to assign cell states rounds to the state that yields the phase which is closer to Фи. Higher number of states corresponds to a finer resolution phase gradient that improves the metasurface performance, but possibly at the cost of transmitting more packets. By default, we set Ns = 4.
• 3. Angular step a: Some applications may require tracking objects at very fine-grained angular resolution. In that case, the gateway would probably need to trigger state changes more often. This is modeled via the angular step, whose default value is set to а = 5°.
• 8.2.2.2 Traffic Analysis Metrics

The traffic traces are parsed to obtain the following relevant metrics:

• 1. Percentage of state-changing cells: The comparison between successive HSF state matrices determines the percentage of cells that must be adjusted to accommodate the change in the position of the target or the illumination source.
• 2. Destination matrix: The traffic analysis jdelds a matrix containing the ratio of packets delivered to a given destination with respect to all the transmitted messages.
• 3. Reconfiguration delay: Finally, we are capable of obtaining the delay of distributing the state-changing messages by plugging the traces to an AnyLogic-based custom-made simulator. On the simulator, the Manhattan-like topology described in [128,140] is built. The reconfiguration delay refers to the time between the first message transmission to the last message reception.
• 8.2.2.3 Walkthrough Example

For the sake of exemplification, consider tracking an object moving as in Case B. Figure 8.1G show's snippets of the surface states during the full range of the movement (each shade represents a distinct unit cell state). The starting point is in Fig. 8.16A, where the elevation and azimuth angles of the reflected wave are 6r = фг = 0°. This is also the initial state of the unit cells. The object starts moving in the direction shown in the figure with initial velocity of 30 m/s. When the location of the object changes by more than the angular step a in either the azimuth or elevation planes, the gatew’ay is triggered. From a local data base, the gatew'ay gathers the commands that reconfigure the surface such that the reflected wave arrives to the target at the new location. The commands are then injected into the controller network and for- warded to the individual controllers. Note here that the reconfiguration commands are sent only to the cells that change state. This process is repeated every time the tracked object changes its location by more than a. This process thus generates traces that can be later fed to the AnvLogic simulator to obtain the network delay.

In this section, we employ the methodology proposed above to examine the HSF workload. We start by analyzing the spatio-temporal characteristics of the traffic in Section 8.2.3.1. Then, we examine the effect of varying the parameters of the surface on the network delay and the traffic generated by the different motion scenarios in Sections 8.2.3.2 and 8.2.3.3, respectively.

## Spatio-Temporal Intensity

Here, we analyze the spatio-temporal intensity and rate of updates generated by different types of movements. This is accomplished by showing how often reconfiguration commands are injected to the system. We use this to assess the rate of injection throughout the tracking Figure 8.18 For an object moving according to Case A: (a) Reconfiguration requests during the tracking of the object, (b) Percentage of reconfigured cells versus the azimuth angle of the reflected signal, (c) The number of reconfiguration requests per second.

process. In addition, we visualize the spatial distribution of the required configuration through heat maps that correspond to the surface.

The generation of reconfiguration requests relies on the location of the tracked object, the motion pattern and the angular step. While the HSF can only sense the change in the incident and reflection angles, the latter is an outcome of the distance and the height difference between the tracked object and the surface, and the motion pattern. This is depicted in Fig. 8.18(a) where a motion of Case A is tracked. The markers indicate the time instances when reconfiguration requests are sent from the gateway to the system. Figure 8.18(a) shows that reconfigurations are more frequent as the object moves closer to the surface. For example, more than 88% of the reconfigurations are required within the last third of the motion. This is expected since the reflection angle changes faster when the object is closer to the surface.

Note that not all cells are reconfigured at each request. Rather, a portion of the cells is reconfigured. From Fig. 8.18(b), it is clear that the percentage of reconfigured cells is highly dependent on the preceding and the currently targeted angles. For example, when the tracked object moves from 6r = 25° to 0r = 20°. 70% of the cells are reconfigured. When the change is from 6r = 80° to 6r = 75°, on the other hand, only 28% of the cells are reconfigured in spite of the fact that the change in both cases was 5°. It is worth mentioning here that the initial configuration is excluded from the graph as it does not contribute in showing the trend of change.

When a change in the state of the HSF is required, reconfiguration requests are streamed into the system, which renders the injection inherently bursty (i.e., a burst of reconfiguration commands are injected every time a proper change in the angle occurs). How’ever, the number of reconfiguration requests and the frequency with which the requests are made determine the injection rate. In Fig. 8.18(c), we show how the injection rate significantly increases when the changes in the reflection angle are more frequent. Coincidentally, frequent changes in Case A occur for target angles affecting a higher percentage of unit cells, pushing the injection rate further. This is an important result because excessive injection rates can be an offset of congestion within the controller network.

Another way to evaluate traffic is the spatial distribution of cells to be updated. To visualize this we resort to heat maps, where hotter spots represent the regions of the HSF where controllers receive higher numbers of packets. Figure 8.19 depicts the heat maps corresponding to the three scenarios of movements. Figure 8.19(a) show’s the case of gradual change in 6r where the tracked object follow’s the motion of Case A. Figure 8.19(c), how’ever, show’s the case of arbitrary changes in 6r where the object makes sudden unpredictable leaps, i.e., Case C. The heat maps demonstrate that the traffic is almost evenly distributed over the surface for arbitrary changes. In addition, if compared with the heat maps in Fig. 8.19(b), one can observe the difference in the traffic distribution when the elevation angle of the reflected wave is fixed to 0 (i.e., the HSF is at the same height of the tracked object) and when it is variable. This information can be used in designing the routing mechanism, congestion control techniques and in placing the HSF tiles. Figure 8.19 Spatial distribution of traffic for the three considered movement scenarios.

## Reconfiguration Delay

The effect of changing the number of states on the delay is shown in Fig. 8.20. Since a higher value of Ns produces larger traffic, it is natural for the network delay to increase as observed in the figure.

Furthermore, wre investigate the effect of changing the size of the surface on the relationship between the percentage of the reconfigured cells and the delay as shown in Fig. 8.21. We observe that the linear relationship between the percentage of reconfigured cells and the delay holds for different sizes of the surface. Although varying the size creates a discrepancy in the slopes of the graphs, yet this does not impact the linearity of the relationship. The figure also shows that larger surfaces achieve higher delays which is expected since packets must travel longer paths to change the states of different unit cells. Figure 8.20 Percentage of reconfigured cells vs delay for two values of

Na. Figure 8.21 The linear relationship between the percentage of reconfigured cells and the delay for different sizes of the surface.

## Sensitivity Analysis

Here, we change some of the metasurface parameters, namely the angular step and the number of states and observe the effects on the Figure 8.22 Elevation angle of the reflected signal versus the percentage of state-changing cells for different, values of the angular step for projectile motion.

performance. In the previous results, the angular step was set to 5°. The value of a can be used as an indication of the beam width, such that smaller values of a infer narrower beam widths and higher tracking precision requirements. We investigate the impact of changing a when an object moving according to Case В is tracked. Case В implies that both the azimuth and elevation angles are varied throughout the movement. A reconfiguration is requested every time either of the two angles change by a0.

Figure 8.22 depicts the percentage of state-changing cells corresponding to different values of the elevation angle of the reflected signal for different values of a. An angular step of 2° achieves the smallest percentage of change, and thus traffic, over the entire range of angle variation, which suggests that the HSF may operate faster. However, a small angular step requires a narrow beam which might increase the complexity of the surface fabrication. In addition, as the value of a decreases the rate of updates is expected to increase. The effects of this increase on the injection rate will be investigated in the future. It is worth mentioning here that the movement in Fig. 8.22 is projectile movement. However, for clarity we only show the change in angles in the first half of the motion (until the object reaches the highest point and before dropping). Figure 8.23 Spatial distribution of traffic in the case of projectile motion for values of Ns of Ns = 1 (left). Ns = 8 (middle) and Ns = 16 (right).

The angular step, the smallest change in the angle sensed by the surface, is strongly correlated with the beam width. For instance, a narrow beam implies a small value of a and thus higher tracking resolution. In Fig. 8.22, w’e plot the percentage of updated cells as a function of the elevation angle for different values of a in the case of projectile movement. For clarity, we consider half of the time span of the entire motion range. Note that in this type of motion the azimuth and elevation angles both change as the object moves, thus, a reconfiguration is required whenever either angle changes by a0. The figure show’s that smaller values of a demand more frequent reconfigurations but with a smaller number of reconfigured unit cells at each reconfiguration. While this implies lighter overall traffic and hence a faster operating HSF, it can complicate the surface fabrication due to the narrow beam required for small values of a.

Figure 8.23, on the other hand, show’s the heat maps produced from tracking an object in the projectile movement for different numbers of states of the HSF cells, namely Ns = 4, 8,16. As the number of states increases, the traffic becomes heavier over the entire surface, while for smaller number of states the traffic is lighter especially’ at the bottom- left corner. This might stem from the fact that the bottom-left corner is where the programming starts (initial state is always zero phase). In rather large phase gradients, that area remains largely at the same state.

# Indoor Mobility Scenario

In an indoor scenario, HSFs are envisioned to coat objects like walls and furniture , in which case multiple surfaces can be responsible for the routing configuration of the Non-Line of Sight (NLoS) path between two users. In this section, we consider such a scenario to investigate the generated traffic in a more realistic setting. As such, wre characterize Figure 8.24 Indoor mobility scenario.

the traffic workload on the controller network of five MSs placed in an indoor environment as shown in Fig. 8.24. We assume that a mobile user moves from point A to point В following the trace indicated by the dashed line in the floorplan shown in the figure. In addition, the user is connected to the stationary access point at point В through the NLoS path created via the MS on the walls. The red lines represent the HSF tiles. The user is assumed to emit a very narrow beam at an angle of 55° to the left of the trajectory of the movement. The dimensions of the floor plan and the HSF tiles, and the trajectory of the movement of the user are all fed to an AnyLogic based simulator. The simulator produces the traces of the wave emitted from the user’s mobile device until it reaches point В along with the incident and reflection angles of the wave at each HSF. It is important to note that the wave does not necessarily activate all the surfaces in the room. In the example wave trace shown in Fig. 8.24 (in the black dashed line) for instance, the wave does not activate HSF2 and HSF5. The path of the signal changes as the user changes locations.

The incidence and reflection information at every surface is then treated the same way as in the previous experiments to generate the spatial distribution of traffic and the rate of injection of the reconfiguration requests. Figure 8.25 shows the spatial distribution of traffic within the four tiles. It can be observed that IIS FA is used more than the rest of the surfaces in the considered scenario, whereas HSF 1 is the least used surface. This is due to the fact that the user at point В Figure 8.25 Spatial distribution of traffic in the five surfaces considered in the indoor mobility scenario.

is stationary and because of the narrow beam emitted at a 55° angle, the user can either be reached directly, i.e., through a LOS path or via HSF4. It is important to note that in reality a wider beam is emitted from the user’s device, which is usually simulated as a bundle of narrow beams. Each beam has an additive effect to the incurred traffic. Hence, for ease of exposition we onl}r consider one spatial channel of the beam, represented by a narrow beam emitted at angle 55°.

The rate of injection at each surface is shown in Fig. 8.26. The motion starts at time = 10.sec and lasts for about 14 seconds. Throughout the considered motion, the user loses connectivity for some time, as for example between the 14th and 20th seconds as one can indicate in Fig. 8.26(d). This loss of connectivity occurs due to the narrow beam assumed for the purposes of this simulation. Figure 8.26 shows that the rate of injection does not exceed 3 Mbps for all surfaces. However, due to the location of the tiles, different loads are on each. This information can be useful in designing congestion control algorithms and in placing the tiles.

## CONCLUSIONS

This chapter has provided a metasurface-centric and application- oriented analysis of the prospective capabilities of future HSFs. We Figure 8.26 Rate of injection of reconfiguration requests in bps for the five surfaces considered in the indoor mobility scenario.

have focused on the link between the application requirements (represented as a set of performance metric values) and the metasurface essential characteristics (summarized in a small set of design input parameters) for the case of beam steering. In overall, we have argued and illustrated how this approach allows to dimension the metasurface and navigate the tradeoffs faced in the design process of the complete architecture, in the pathway to deriving useful guidelines of design for future intra-HSF networks.

In Section 8.1, we have presented and applied a methodology to study the scaling trends of HSFs by the order of magnitude. We have concluded that four unit cell states (2 bits) are enough to provide acceptable performance across a wide range of metrics. We also confirmed that large metasurfaces with very small unit cells provide the best performance in most metrics, although it is arguably the most costly solution from a fabrication perspective. Further, to provide unified design guidelines, we proposed performance figures of merit with which we illustrated which design regions can provide close-to-optimal results while minimizing potential cost. Future works could further advance in this aspect by incorporating accurate power and cost models that will allow us to determine the region of optimal solutions in terms of the performance-to-cost ratio, among other explorations.

In Section 8.2, we leveraged the analytical formulations of beam steering coding and, through the definition of typical movements in user-tracking applications and other assumptions, extracted a set of intra-HSF traffic traces. This allows not only to estimate the average communication load, but also to characterize the spatiotemporal features of such load. We have observed that both the amount of state- changing cells and the temporal distribution of requests clearly depend on the instantaneous reflection angle. Moreover, the specific trajectory of the user, understood as the succession of changes in the reflection angle, determines the spatial distribution of unit cell state variations. If the application requires fine-grained tracking, either in time or space, we can expect increases in the amount of traffic to handle through increases of the associated design parameters of the HSF. A further analysis performed in this chapter used traffic traces obtained in this characterization effort to evaluate the delay of prototype HSFs. We have seen, as expected, how the delay is dependent on the reflection angles as they involve more intense exchange of information.