Metasurface-assisted massive backscatter wireless communication with commodity Wi-Fi signals

Conventional wireless communication architecture, a backbone of our modern society, relies on actively generated carrier signals to transfer information, leading to important challenges including limited spectral resources and energy consumption. Backscatter communication systems, on the other hand, modulate an antenna’s impedance to encode information into already existing waves but suffer from low data rates and a lack of information security. Here, we introduce the concept of massive backscatter communication which modulates the propagation environment of stray ambient waves with a programmable metasurface. The metasurface’s large aperture and huge number of degrees of freedom enable unprecedented wave control and thereby secure and high-speed information transfer. Our prototype leveraging existing commodity 2.4 GHz Wi-Fi signals achieves data rates on the order of hundreds of Kbps. Our technique is applicable to all types of wave phenomena and provides a fundamentally new perspective on the role of metasurfaces in future wireless communication.


Supplementary Note 1. The physical model of our MBWC technique
Here, we will elaborate on the physical model of the proposed MBWC. For simplicity, we consider the case of binary information quantization; however, the presented methods can be readily extended for more complicated cases. As shown in Figure 1 in main text, the proposed MBWC system is composed of several modules including a programmable metasurface, two or more coherent receivers, and an information decision module. When the programmable metasurface configured with the coding pattern " (or, # ) is Herein, is a decision threshold, (•) is a real-valued prior-specified nonlinear function, and is the angular frequency of wireless signals. The retrieved information bit is "1" if /01 = 1, corresponding to the case that the control coding pattern # is encoded into the metasurface. Similarly, the retrieved information bit is "0" when the coding pattern " is encoded into the metasurface.
In a nutshell, two critical issues are involved for the proposed MBWC. First, " and # need to be well optimized such that the decision rule (Supplementary Equation 1) can be implemented in a robust way. Second, it is crucial to choose a suitable information decoding scheme, i.e., to choose the nonlinear feature-extraction function (•).
We consider the case that a single unknown wireless source is located somewhere, which represents a typical scenario of local wireless network, for instance, Wi-Fi. Specifically, for a given operational frequency channel, only one Wi-Fi router works at the same time within a relatively local environment. Here, we consider to realize the MBWC by using the programmable metasurface to manipulate the ambient stray wireless waves arising from the unknown wireless source. Without loss of generality, we assume that the unknown wireless source at # emits an unknown radio signal ( ) , as sketched in Supplementary Figure 1a. Then, the echoes received by two coherent receivers reads:  Here, we list three more remarks on Supplementary Equation 5 as following: The "(in)visibility" can be readily achieved by controlling the radiation beam of the metasurface. In particular, the coding patterns, i.e., " or # , can be optimized such that the radiation beam of the metasurface can be focused towards the local spot around the master receiver; in contrast, it has remarkably lower energy around the slavery receiver. In this way, the master receiver is designed for acquiring the stray wireless signal carrying the digital information encoded into the metasurface, while the slavery receiver is only for sampling the wireless signal directly from the non-cooperative wireless source. As such, the passive "carrier" signal can be well reallocated to the Alice and Bobs in a wireless and controllable way.

Remark 2.
In order to achieve the robust information retrieval (i.e., information decoding), it is respectively. Here, we still consider the case that the master receiver at & is "visible" to the metasurface; however, the slavery receiver at ( is "invisible" to the metasurface. As In Supplementary Equation 10, we have explored the fact that 〈 c ( ) k Here, we consider an extreme case that the number of i.i.d. wireless sources tends to be infinity. In this case, we can arrive at the following conclusion in light of the well-known time-reversal theory: where ℎ is a shift-invariant kernel function. Using Supplementary Equation 12 in Supplementary Equation 11 then leads to: Note that the information bit "1" corresponds to the case that the # is chosen such that the stray wireless signal carrying the coding information of the metasurface has its energy focused around & . In contrast, the information bit "0" means that the # is chosen such that the wireless signal acquired by the receiver at & has relatively lower energy level.
In addition, for the cases of "0" and "1", the energies of the stray wireless signals reflected from the metasurface need to be well focused around the receiver at & , i.e., As opposed to the case of binary modulation scheme, the QPSK involves the 4-phase Then, we have Herein, Furthermore, we take the spectral representation of ( ) as following, i.e.,

Supplementary Note 4. Optimization of the information-carrying control coding pattern
We here discuss the inverse-design of the information-carrying control coding patterns of the programmable metasurface. For simplicity, we consider the binary modulation as an illustrative example; however, the reported methods and results can be readily generalized for multi-bit modulation in a straightforward manner.
As discussed in Supplementary Note 1, two "distinguishable" control coding patterns of the metasurface (referred to as pattern-1 " and pattern-2 # ) are optimized such that their associated radiation beams are visible to one receiver (called the master receiver), and meanwhile are invisible to another receiver (called the slavery receiver). Here, we mean by the "distinguishability" that the acquired wireless signals reflected from the metasurface with " can be readily distinguished from those with # by a classifier. Moreover, we mean by "visibility" that the intensity of the wireless signal reflected from the metasurface is focused around the master receiver. In terms of the methods outlined in Supplementary Note 1, we can see that the stray wireless signal carrying the digital information encoded into the metasurface can be readily demodulated, and thus the digital information can be easily decoded.
Formally, we can formulate the inverse-design of the distinguishable control coding pattern of the metasurface for the proposed MBWC into a constrained optimization problem, in particular, The designed programmable metasurface works around 2.412 GHz, consistent with the commodity Wi-Fi frequency. The metasurface is composed of independentlycontrollable 32×24 meta-atoms. Since each meta-atom has a size of 54×54mm 2 , the whole metasurface has size of 1.7×1.3m 2 in total. We remark that the whole metasurface is signal. In our work, the adopted CLK is 50MHz, and the switching time of PIN diode is about 10µs each cycle. Then MCU will send the commands over 24 independent branch channels, leading to almost real-time manipulations of all PIN diodes. In addition, 768 redcolor LEDs are soldiered to indicate the status of the associated PIN diodes, in particular, to indicate clearly whether the PIN diode works well or not.

Supplementary Note 6. Performance of the proposed MBWC
We evaluate the performance of the MBWC prototype by taking the three-channel BASK MBWC as illustrative examples.

Intensity ratio
Here, we define the intensity ratio as | t (→&P1R→&O |, i.e., is = | t (→&P1R→&O | = Here, we give two marks about the intensity ratio. First, the relationship between the intensity ratio and aperture size of metasurface is investigated. Corresponding numerical results are provided in Supplementary Figure 5a. It can be expected that, when the metasurface is configured with suitable coding patterns, the bigger the aperture size of metasurface is, the bigger the intensity ratio is. This does make sense because more energy of the Wi-Fi signals can be well harvested if the metasurface with bigger aperture size is used. Second, we consider the influence of focus locations of metasurface on the intensity ratio. As shown in Supplementary Figure 5b, the focus spots are represented by filled circles and the color of circles denotes the predicted intensity ratio R. It is worth mentioning that we limit the color axis less than 8 to facilitate the display of figure. As expected, the intensity ratio R becomes large when the position of master receiver is away from yoz plane where the direct wave from Wi-Fi source is fairly strong since the Wi-Fi source is polarized along the x direction.

Channel strength
As outlined previously, one of crucial issues to the MBWC is that the master receiver

Channel transmission efficiency
The channel transmission efficiency is defined as the ratio of the total energy within the focusing spot to that in the whole receiving plane. Experimental results have been reported in Supplementary Figure 6. Meanwhile, the corresponding focusing efficiencies of the metasurface have been provided as well. The focusing efficiency of the metasurface is defined as the ratio of the total energy within all focusing spots to that in the receiving plane, which almost keeps constant in all combinations of digital symbols due to the energy conversation. From these experiments, we can clearly see that the highest and lowest channel transmission efficiency are 47.25% and 15.68%, respectively, and that the focusing efficiency of the metasurface is not influenced by the channel number.

Effect on the communication quality from the communication distance
Here, we would like to examine the effect on the quality of the MBWC from the distance