Code-Division Multiplexing Using Space-Time-Coding Metasurface

Code-Division Multiplexing Using Space-Time-Coding Metasurface | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Code-Division Multiplexing Using Space-Time-Coding Metasurface Guo-min Yang, Yuzhen Chen, Xiaoyi Wang, Ya-Qiu Jin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9239883/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 14 You are reading this latest preprint version Abstract Code-division multiplexing (CDM) is essential for supporting massive connectivity in wireless networks, but its implementation typically requires complex and costly radio-frequency (RF) chains. This work presents a simplified, low-cost wireless CDM system based on a space-time-coding metasurface (STCM). By modulating distinct spatial partitions of the metasurface with data streams pre-spread via orthogonal pseudo-random codes, the STCM functions as a distributed parallel modulator. This architecture enables the metasurface to perform simultaneous upconversion while directing modulated reflections from multiple spatial partitions toward either shared or distinct directions. Although these data-carrying waves may physically overlap in the far-field, the inherent orthogonality of the spread codes ensures that the receiver can successfully decorrelate and recover each multiplexed stream. Experimental validation demonstrates three core scenarios: multi-stream transmission to a single direction, single-stream to multiple directions, and multi-stream to multiple directions, all achieved without conventional RF chains. The proposed STCM-based CDM architecture enables simultaneous multi-user communication with a radically simplified RF front-end, paving the way for energy- and cost-efficient high-capacity wireless systems for future wireless networks. Physical sciences/Physics/Electronics, photonics and device physics Physical sciences/Optics and photonics/Applied optics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction The rise of the Internet of things (IoT) and the advent of sixth-generation (6G) networks are intensifying the demand for wireless systems that support massive connectivity 1 , 2 . Code-division multiplexing (CDM) is a pivotal technique for meeting this demand, as it allows multiple users to share the same frequency band simultaneously, thereby boosting network capacity and resilience 3 , 4 . However, conventional CDM relies on intricate radio-frequency (RF) chains, which comprise mixers, filters, amplifiers, and antennas, to generate and process wideband signals. This complexity translates into high power consumption, physical bulk, and elevated cost. These drawbacks become particularly prohibitive at higher frequencies, such as the millimeter-wave bands envisioned for 6G, where the high expense and energy consumption of traditional phased arrays are major impediments 5 . Overcoming the hardware inefficiency of conventional CDM RF systems is therefore a critical step towards making next-generation wireless technology both economically and environmentally sustainable. In the pursuit of more efficient signal processing, metasurfaces as artificially engineered thin-film structures with tailored electromagnetic properties have emerged as a disruptive platform 6 – 8 . Their inherently low-profile and cost-effective nature, combined with an exceptional ability to manipulate electromagnetic waves in real-time, positions them as a foundational technology for future wireless systems 9 – 13 . Current applications already demonstrate their utility in dynamic coverage enhancement 14 – 16 , wireless power transfer 17 , 18 , and holographic multiple-input multiple-output (MIMO) systems 19 – 22 , showcasing a paradigm shift from circuit-based to free-space-based signal processing. The recent advancement of space-time-coding metasurfaces (STCMs) has unlocked dynamic wave control by incorporating temporal modulation, thereby enabling nonlinear signal processing directly within the wireless channel 23 – 26 . This capability has spurred a diverse range of applications, including spatial frequency translation 27 – 30 , simplified RF front-ends 31 – 34 , chirp modulation for radar 35 – 39 , and nonreciprocal beam steering 40 – 43 . Notably, STCMs have been increasingly applied to wireless communications 44 – 46 , with a specific focus on multiplexing schemes such as time-division multiplexing, frequency-division multiplexing, and space-division multiplexing (SDM) 47 – 50 . Despite these promising advancements, these schemes still operate in a manner where one channel carries one data stream, thus failing to realize parallel multi-dimensional utilization of spectral resources. Consequently, the information-carrying efficiency per unit bandwidth is far below the theoretical maximum, leading to insufficient resource utilization. More recently, the introduction of pseudo-random sequences Figure 1. Conceptual illustration of the proposed hybrid CDM and SDM wireless communication scheme using a STCM. The coding matrix that control the states of the PIN diodes integrated on the metasurface unit cells, which are mapped from the encoded streams, are prestored in the FPGA. During operation, the FPGA outputs corresponding bias voltages to precisely switch the diodes, thereby encoding the phase response of the metasurface. The STCM is partitioned into regions, each assigned a data stream and designed with a phase gradient. Illuminated by a monochromatic wave at f 0 ​, each metasurface region reflects a beam that is simultaneously encoded with its data stream and directed by its phase gradient, realizing parallel multi-stream transmission. By applying orthogonal code correlation-based algorithms, receiver antenna 1 despreads both message #1 and message #2 from the composite received signal. Similarly, receiver antenna 2 simultaneously recovers message #3 and message #4. This ability to support both directional multi-user communication and parallel multi-stream delivery underscores the scheme’s flexible reception performance across various communication scenarios. characterized by excellent autocorrelation and low cross-correlation properties as temporal modulation codes of STCMs has further expanded their functionality 51 – 53 . These properties enable the sequences to support advanced functions including electromagnetic camouflaging 54 , 55 , spatial encryption 56 , and target recognition 57 . Since pseudo-random sequences with excellent autocorrelation and low cross-correlation attributes serve as a key technology in CDM 58 , 59 , STCMs with pseudo-random sequence modulation have great potential in designing cost- and energy-effective CDM wireless communication systems. This paper proposes a wireless CDM scheme using a pseudo-random-coded STCM to enable multi-stream transmission over a shared channel. In the proposed approach, each data stream is spread with a distinct orthogonal pseudo-random code. These uniquely encoded streams then modulate different spatial partitions of the metasurface. When illuminated by a monochromatic carrier wave, the STCM simultaneously upconverts and directs each encoded stream into tailored spatial coordinates. By independently engineering the phase gradients of different metasurface partitions, the system can either aggregate multiple signals into a unified beam or distribute them toward distinct angular directions in free space. At the receiver, the desired data stream is recovered by correlating the received signal with the corresponding orthogonal code, thereby decoupling the overlapping transmissions. This study investigates three scenarios to experimentally validate the CDM capabilities of the proposed communication scheme, in which multi-stream transmission is first realized to a single receiver, then single-stream delivery is extended to multiple receivers at distinct angles, and finally the scheme’s core capability of enabling reliable transmission of multiple spread data streams to multiple receivers at distinct angles is confirmed, achieving the joint operation of CDM and SDM. In contrast to conventional CDM, which relies on intricate RF chains with costly wideband components, the presented metasurface-based scheme performs spectrum spreading and beamforming directly in free space. By offloading this complexity, the system operates with a drastically simplified and low-cost RF front-end. By seamlessly integrating code-domain multiplexing with other dimensions such as space, this architecture presents a compelling pathway toward future budget-sensitive, high-capacity wireless applications. Result Concept and Operating Principles Figure 1 conceptually illustrates the proposed wireless communication scheme based on a STCM for hybrid CDM and SDM. The metasurface is composed of a two-dimensional array of programmable unit cells, each integrated with three PIN diodes to enable dynamic control of the reflection phase. In operation, multiple streams of digital data sharing the same spectrum are encoded using a set of binary orthogonal codes to spread their spectra. These encoded streams are then mapped to the coding matrix with an additional phase gradient for beam deflection, which controls the states of the PIN diodes integrated on the metasurface unit cells. The coding matrix is prestored in the field-programmable gate array (FPGA). As a result, when the metasurface is illuminated by a monochromatic incident wave, independent directional transmission of the encoded streams is achieved, allowing users at specific locations to receive the multiple streams directed toward them. The prior knowledge of the orthogonal spread-spectrum codes enables each user to separate their intended stream from the shared channel and spectrum. To better illustrate the operating principle of the proposed STCM based wireless CDM, Fig. 2 presents a schematic depicting the scenario with two messages to be sent. Figure 2a details the transmitter architecture. The messages to be sent are first transformed into binary bit streams \(\:{s}_{1}\left(t\right)\) and \(\:{s}_{2}\left(t\right)\) . A pair of 8-bit Walsh codes \(\:{c}_{1}\left(t\right)\) and \(\:{c}_{2}\left(t\right)\) serve as orthogonal codes for spectrum-spreading. To facilitate transmission and processing, all the above binary bit streams are mapped to bipolar symbols, where binary ‘1’ is mapped to ‘+1’ and binary ‘0’ to ‘ \(\:-\) 1’. The encoded stream \(\:{m}_{n}\left(t\right)\) after spreading process for the n -th data stream can be written as $$\:\begin{array}{c}{{m}_{n}\left(t\right)=s}_{n}\left(t\right){c}_{n}\left(t\right)\#\text{(}\text{1}\text{)}\end{array}$$ whose time-domain waveforms are shown in Fig. 2b in detail. Since the bit rate of the spreading codes is eight times that of the original bit streams to be transmitted, the bit rate of the encoded streams is thus eight times higher than that of the original ones. To further explore the beam shaping and SDM capability of the metasurface, the encoded streams \(\:{m}_{n}\left(t\right)\) are superimposed with a preset gradient phase for beam deflection. Therefore, the coding sequences for k -th column becomes \(\:{M}_{k}\left(t\right)={m}_{n}\left(t\right){e}^{j2\pi\:{\varphi\:}_{k}}\) , where \(\:{\varphi\:}_{k}\) is the gradient phase for k -th column. Assuming the metasurface functions in a slow-varying regime, where the modulation frequency is significantly lower than the carrier frequency of the incident wave, the time-varying reflection coefficient of the metasurface is approximately equal to its applied coding sequence, namely, \(\:{{{\Gamma\:}}_{k}\left(t\right)=M}_{k}\left(t\right)\) . Under the given assumptions, when a monochromatic harmonic wave at \(\:{f}_{0}\) impinges on the metasurface, it is scattered into a modulated wave, which can be approximated expressed as $$\:\begin{array}{c}{s}_{scatt}\left({\theta\:}_{r},t\right)\approx\:\sum\:_{k}{{\Gamma\:}}_{k}\left(t\right){e}^{jkd\text{s}\text{i}\text{n}{\theta\:}_{r}}{e}^{j{2\pi\:f}_{0}t}.\#\text{(}\text{2}\text{)}\end{array}$$ where \(\:{\theta\:}_{r}\) denotes the scattering angle of the reflected wave relative to the metasurface’s normal direction, and d represents the center-to-center spacing between adjacent columns of unit cells. This scattered wave \(\:{s}_{scatt}\left({\theta\:}_{r},t\right)\) thus contains all the multi-stream data after the spectrum-spreading process, with all streams sharing the same spectral, spatial, and temporal resources. The receiver architecture is depicted in Fig. 2c. At the receiver, a single receiving antenna is used to capture the superposition of all encoded streams, which is first acquired by an oscilloscope for signal observation and recording before being subsequently subjected to down-conversion and carrier phase synchronization. By leveraging prior knowledge of the orthogonal codes, the receiver can despread the signal one by one and recover the original transmitted message. The orthogonality of the codes ensures that each stream can be separated without interference from the others. In practice, this scheme supports two primary scenarios. First, multiple data streams can be intended for a single user, who can then receive all streams simultaneously. Alternatively, the streams can be directed to different users at various locations; in this case, each user can independently receive their designated data stream without interference from the others’ streams. Hybrid Multi-stream CDM and SDM Transmission based on STCM To elucidate the operating principle of the proposed STCM-based wireless CDM, three different scenarios are respectively studied, as illustrated in Fig. 3. Figure 3 presents the encoded streams, coding matrices, and corresponding reflection patterns for three distinct communication scenarios. The first scenario considers multi-stream transmission to a single user. As depicted in Fig. 3a, two independent data streams are encoded using orthogonal spread spectrum codes. To accommodate the two streams, the metasurface is partitioned into two independent regions, with columns 1–4 forming Region 1 and columns 5–8 forming Region 2 (Fig. 3b). Each region is independently controlled by a binary stream, which is mapped to the metasurface phase via binary phase-shift keying (BPSK). For a target receiving angle of \(\:{\theta\:}_{r}=0^\circ\:\) , no inter-column phase gradient is required within each region. Consequently, both regions generate reflection patterns directed normally, as shown in Fig. 3c. The user, equipped with a single antenna positioned at \(\:{\theta\:}_{r}=0^\circ\:\) , captures the superimposed signal and subsequently recovers the original streams via correlation despreading using the corresponding orthogonal codes. It is worth noting that supplementary note 1 proposes a simplified implementation alternative. Unlike conventional approaches requiring dedicated physical partitions for each data stream, this advanced design enables the entire metasurface to collectively encode superimposed data streams through joint amplitude-phase modulation. While this scheme reduces coding complexity, it imposes stricter requirements on the amplitude-phase regulation accuracy of individual unit cells. The second scenario addresses the case where multiple users, located at distinct spatial positions, each receive a single data stream. Using the same two-stream configuration (Fig. 3d, identical to Fig. 3a), the key distinction lies in the metasurface coding matrix design. As illustrated in Fig. 3e, a beam-steering phase \(\:{\psi\:}_{ij}\) is applied to the j-th column of the metasurface for the i-th region, where i denotes the region index and j denotes the column index within the region. The detailed calculation of this beam-steering phase is provided in Supplementary Note 2. The reflection phase of each column is obtained by summing the beam-steering phase and the BPSK-modulated phase of the corresponding data stream, thereby deflecting each region’s reflection pattern toward its target angle. Owning to the 2-bit phase modulation constraint, the steering phases for the two regions are set to \(\:{\psi\:}_{13}={\psi\:}_{12}=90^\circ\:\) , \(\:{\psi\:}_{23}={\psi\:}_{22}=90^\circ\:\) , and \(\:{\psi\:}_{11}={\psi\:}_{21}=0^\circ\:\) , with an inter-column spacing of 18.5 mm. This configuration yields a reflection pattern for Region 1 directed at \(\:{\theta\:}_{r1}=-20^\circ\:\) and for Region 2 at \(\:{\theta\:}_{r2}=20^\circ\:\) , as verified in Fig. 3f. When a receiver is positioned at the target angle, the undesired signal from the other region is suppressed to a negligible level, ensuring that only the intended signal is effectively received. Subsequent despreading then recovers the original single data stream. Supplementary Note 3 further expands this concept by introducing flexible partition designs tailored to target reflection patterns, enabling adaption to complex spatial deployment scenarios. The most comprehensive scenario involves multiple users, each located at a distinct spatial angle and requiring simultaneous reception of multiple streams. This configuration effectively combines the features of the two previous scenarios. Consider a case with four data streams, as shown in Fig. 3g. Streams 1 and 2 are allocated to target angle \(\:{\theta\:}_{r12}\) , while streams 3 and 4 are allocated to \(\:{\theta\:}_{r34}\) . The metasurface is divided into four independent regions, each modulated by one data stream (Fig. 3h). A critical design principle is that the regions serving the same receiver share an identical inter-column phase gradient. Specifically, the two regions carrying streams 1 and 2 are configured with a beam-steering phase \(\:{\psi\:}_{1}\) , while those carrying streams 3 and 4 employ \(\:{\psi\:}_{2}\) . This ensures that reflection patterns for regions targeting the same angle are perfectly aligned, while those for different angles are steered toward distinct directions. For example, when both \(\:{\psi\:}_{1}\) and \(\:{\psi\:}_{2}\) are \(\:90^\circ\:\) , Regions 1 and 2 point to \(\:{\theta\:}_{r12}=-50^\circ\:\) , and Regions 3 and 4 point to \(\:{\theta\:}_{r34}=50^\circ\:\) . Figure 3i confirms that the patterns of regions corresponding to the same receiver completely overlap. A receiver deployed at the target angle thus captures the superimposed signal of its two assigned streams and subsequently separates them via orthogonal spread spectrum code despreading. In summary, STCM-based multi-stream transmission achieves crosstalk-free communication in the code domain by leveraging both code orthogonality and spatial directivity. The introduction of beam-steering phases enables seamless progression from single-angle to multi-angle multi-stream scenarios, offering a flexible and scalable framework for advanced wireless CDM systems. Experimental Demonstration To validate the proposed concepts and methodologies, a wireless communication testbed operating at 5 GHz is established in this study. The metasurface employed is a 2-bit programmable metasurface, whose unit cell is illustrated in Fig. 4a. As shown, the unit cell consists of two substrate layers and three metal layers, with three PIN diodes integrated at the bottom to enable reflection phase control. Figure 4b presents the simulated reflection phase under different biasing states of PIN diodes, denoted as 00, 01, 10, and 11, clearly demonstrating 2-bit phase quantization characteristics. Detail information regarding the metasurface can be found in Materials and Method section, and in Supplementary note 4. Figure 4c shows the experiment configuration. The transmitter comprises a signal generator (Agilent Technologies E8257D), an FPGA, a horn antenna, and a metasurface array, where the metasurface dynamically reconfigures its properties through FPGA-controlled real-time coding sequence loading. The receiver employs a horn antenna positioned 1 m from the metasurface, with its angle relative to the metasurface adjustable as needed. The captured signals acquired by a high-speed oscilloscope (Tektronix MSO64B) and subsequently transferred via Ethernet interface to computer platform for post-processing. Experimental results are presented in Fig. 5. The multi-stream single-user scenario is experimentally demonstrated by dividing the metasurface into left and right regions, each consisting of five columns. Each region is modulated independently using distinct signals, spread by orthogonal codes \(\:{c}_{1}\) = [1,0,0,1,0,1,1,0] and \(\:{c}_{2}\) = [1,0,1,0,0,1,0,1], respectively. Figure 5a presents the constellation diagram of the composite received signal, which results from the superposition of reflections from all unit cells. The spectrum of the transmitted signal exhibits clear spread spectrum characteristics: compared with the original pre-spread signal, the bandwidth of received signal is expanded by a factor of eight, corresponding to the length of the spreading code (Fig. 5b). Figure 5c and Fig. 5d present the separated constellation diagrams and the corresponding decoded message from the two independent metasurface regions. All constellation points are clearly distinguishable, confirming the system’s reliability for high-quality image data transmission. This configuration also allows a single user to receive more than two data streams, with detailed test results provided in Supplementary note 5. For the scenario where multiple users, located at distinct spatial positions, each receive a single data stream, the metasurface is partitioned as illustrated in Fig. 3e. The two remaining columns are covered with microwave-absorbing material to eliminate unwanted reflections. Figure 5e and Fig. 5g show the constellation diagram received by users at \(\:-20^\circ\:\) and \(\:20^\circ\:\) , respectively. The observed clustering or dispersion in these constellations is attributed to the sidelobes in the reflection patterns of each region, where residual energy from undesired signals is not fully suppressed, thereby introducing interference to the intended signal. Figure 5f and Fig. 5h present the constellation diagrams and the corresponding recovered messages corresponding to each independent region of the metasurface. Although slight dispersion remains observable in the constellations, the clustering structure is still clearly distinguishable, confirming the successful seperation of the signals. For the four-stream two-user scenario where each user receives two data streams, the following orthogonal spreading codes are assigned to each stream: \(\:{c}_{1}\) = [1,0,0,1,0,1,1,0] \(\:{c}_{2}\) = [1,0,1,0,0,1,0,1] \(\:{c}_{3}\) = [1,0,0,1,1,0,0,1] \(\:{c}_{4}\) = [1,0,1,0,1,0,1,0] The metasurface is partitioned as depicted in Fig. 5h. Figure 5i and Fig. 5l present the constellation diagrams received by users located at \(\:-50^\circ\:\) and \(\:50^\circ\:\) , respectively. As the number of signals to be transmitted increases, the directivity of the radiation patterns diminishes due to the decreased number of columns in each region, resulting in increased dispersion in the received constellation diagrams. Nevertheless, this increase does not affect the correct discrimination of the signals. Figure 5j and Fig. 5k show the demodulated constellation diagram and the corresponding original transmitted image for the signal received at \(\:-50^\circ\:\) , while Fig. 5m and Fig. 5n present those for the signal received at \(\:50^\circ\:\) . In both cases, the images are accurately reconstructed. These experimental results confirm that spatially separated receivers can successfully and independently recover their intended data streams. Discussion This study presents a code-division wireless communication system based on an STCM, capable of simultaneously transmitting multi-stream messages to the same receiver while enabling space-division multiplexing. Unlike previous metasurface-enabled multiplexing systems, or CDM systems that rely on intricate RF chains, the proposed scheme achieves secure multi-user transmission with enhanced spectral efficiency with simplified, low-cost RF front-ends. To demonstrate that multi-streams received by single channel can be reliably recovered through code-domain separation, experimental validation confirms the successful transmission of single or dual images to a single user or two distinct users at a pre-specified angle. The presented work establishes a new paradigm for applications in scenarios requiring low-power, high-density access. Materials and Methods Details on the space-time coding metasurface The designed space-time coding metasurface consists of a 10×10 array of unit cells. Each unit cell has a side length of 18.5 mm, and comprises two substrates and three metal layers. Three PIN diodes are soldered on the bottom layer of the unit cell. Specifically, simultaneous switching of PIN 1 and PIN 2 introduces a 90° phase shift in reflection between their ON and OFF states, while an additional 180° phase shift is achieved through the switching of PIN 3. Detailed information regarding the unit cell design and its working principle can be found in Supplementary note 4 and also Ref. 60. To realize independent and flexible spatiotemporal modulation, each column of the metasurface is individually controlled by an output port of an FPGA (Altera DE2-115). To facilitate the desired partitioning of the metasurface in scenario 2 and scenario 3, two columns on one end of the metasurface array are shielded by absorbing materials, which serves to eliminate unwanted electromagnetic reflections. Experiment setup The experiments are conducted in a microwave anechoic chamber to minimize unwanted electromagnetic reflections and external interferences. A signal generator (Agilent Technologies E8257D) is used to generate a monotone signal at 5 GHz, with an amplitude of 25 dBm. An oscilloscope (Tektronix MSO64B) is utilized to capture the real part of the electric field reflected by the STCM. The oscilloscope is connected to a computer via an Ethernet cable to enable data transmission from the oscilloscope to the computer for post-processing. A transmit horn antenna is aligned to the normal direction of the metasurface array and positioned 0.6 m from the metasurface. This distance is greater than the far-field distance of the transmit horn to ensure the metasurface is uniformly illuminated by the incident wave. The receive horn antenna is placed 1 m from the metasurface. While constrained by the anechoic chamber’s spatial limitations, this distance still approximates the far-field requirement of the metasurface to ensure valid measurement conditions. Generation, reception and processing of data streams To generate bit streams from image data, each pixel is mapped to one bit information: colored pixels are encoded as 1, and white pixels as 0. To acquire the generated bit stream, the oscilloscope’s sampling rate is set to 1.5625 GS/s, which is equivalent to down-converting the received signal to 312.5 MHz. Further downconversion is conducted using MATLAB. During transmission, a 2000-bit frame header with a bit rate of 5 MHz is adopted, consisting of 1000 successive 0s followed by 1000 successive 1s. When processing the received data using MATLAB, the phase of the successive 1s in the frame header is taken as the reference phase, and the phase of the received signal is compared with this reference phase to achieve phase alignment. Declarations Author Contributions X. W and G.-M. Y conceived the concept, Y. C designed the experiments. Y.-Q. J supervised the work. Y. C wrote the manuscript with discussion from all authors. Competing Interests The authors declare no competing interests. Acknowledgements The authors acknowledge financial support from National Natural Science Foundation of China under Grant 62471146, State Key Laboratory of Radio Frequency Heterogeneous Integration Open Scientific Research Program No. KF2024017. Data availability The authors declare that all relevant data are available in the paper and its Supplementary Information files, or from the corresponding author on request. 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Additional Declarations There is no conflict of interest Supplementary Files SupplementaryInformationforCodeDivisionMultiplexingUsingSpaceTimeCodingMetasurfacelightv1.docx Code-Division Multiplexing Using Space-Time-Coding Metasurface Cite Share Download PDF Status: Under Review Version 1 posted Review # 5 received at journal 03 May, 2026 Review # 3 received at journal 20 Apr, 2026 Review # 4 received at journal 19 Apr, 2026 Reviewer # 5 agreed at journal 15 Apr, 2026 Review # 2 received at journal 13 Apr, 2026 Reviewer # 4 agreed at journal 08 Apr, 2026 Reviewer # 3 agreed at journal 08 Apr, 2026 Reviewer # 2 agreed at journal 07 Apr, 2026 Review # 1 received at journal 02 Apr, 2026 Reviewer # 1 agreed at journal 30 Mar, 2026 Reviewers invited by journal 29 Mar, 2026 Submission checks completed at journal 29 Mar, 2026 Editor assigned by journal 27 Mar, 2026 First submitted to journal 27 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9239883","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":614247380,"identity":"59029290-ff43-4950-a6b7-ed5c7e97b7cb","order_by":0,"name":"Guo-min Yang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/ElEQVRIiWNgGAWjYLCCBDDJfOADAxuYZUCsFrbEGcRrgQAeQ+K0yEckH93wcMdheXP+NR+becrs8hjYm7dJMNTcwanF8EZa2o3EM4cNd854u7GZ51xyMQPPsTIJhmPPcGuZkWN2I7HtMOOGG2e3P+ZtY05skMgxk2BsOExQi/2GG2ceNvO21Sc2yL/Br0VeAqIlccP5HkaglsNAW3jwazHgeQb0S1t68oYbbIaNc84dT2zjSSu2SDiGx5b25GM3f7ZZ2244f/hhw5uy6sR+9sMbb3yowWPLATDVzMAgkQARAUdNAk4NQFsawFQdAwP/ATzKRsEoGAWjYEQDAIIIX0fc2BkuAAAAAElFTkSuQmCC","orcid":"","institution":"Fudan University","correspondingAuthor":true,"prefix":"","firstName":"Guo-min","middleName":"","lastName":"Yang","suffix":""},{"id":614247381,"identity":"516a11e8-22fc-4a26-a4d5-1d6c54c78d66","order_by":1,"name":"Yuzhen Chen","email":"","orcid":"","institution":"Fudan University","correspondingAuthor":false,"prefix":"","firstName":"Yuzhen","middleName":"","lastName":"Chen","suffix":""},{"id":614247382,"identity":"68571f6c-82f7-4c8a-8cdc-538453cbc7d0","order_by":2,"name":"Xiaoyi Wang","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Xiaoyi","middleName":"","lastName":"Wang","suffix":""},{"id":614247383,"identity":"8a624dbb-d4d2-4b93-91fc-35844e51b588","order_by":3,"name":"Ya-Qiu Jin","email":"","orcid":"","institution":"Fudan University","correspondingAuthor":false,"prefix":"","firstName":"Ya-Qiu","middleName":"","lastName":"Jin","suffix":""}],"badges":[],"createdAt":"2026-03-27 04:21:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9239883/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9239883/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105888102,"identity":"64f5808f-77a4-4985-bd57-4fb81e3b0e53","added_by":"auto","created_at":"2026-04-01 07:43:11","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":328478,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eConceptual illustration of the proposed hybrid CDM and SDM wireless communication scheme using a STCM.\u003c/strong\u003e The coding matrix that control the states of the PIN diodes integrated on the metasurface unit cells, which are mapped from the encoded streams, are prestored in the FPGA. During operation, the FPGA outputs corresponding bias voltages to precisely switch the diodes, thereby encoding the phase response of the metasurface. The STCM is partitioned into regions, each assigned a data stream and designed with a phase gradient. Illuminated by a monochromatic wave at\u0026nbsp;\u003cem\u003ef\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, each metasurface region reflects a beam that is simultaneously encoded with its data stream and directed by its phase gradient, realizing parallel multi-stream transmission. By applying orthogonal code correlation-based algorithms, receiver antenna 1 despreads both message #1 and message #2 from the composite received signal. Similarly, receiver antenna 2 simultaneously recovers message #3 and message #4. This ability to support both directional multi-user communication and parallel multi-stream delivery underscores the scheme’s flexible reception performance across various communication scenarios.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-9239883/v1/d5ed642187b205255aab1d3c.jpeg"},{"id":105888109,"identity":"3dd50bd8-9061-4285-b072-67f2990c6bbc","added_by":"auto","created_at":"2026-04-01 07:43:12","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":516178,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic of the dual-stream wireless communication system based on the STCM. a Block diagram of the transmitting process. The messages to be sent are converted into bit streams, then spread using orthogonal codes. The encoded streams with gradient phases are then mapped to the coding matrix for the metasurface, which is pre-stored in a field-programmable gate array (FPGA). Based on the mapped coding matrix, the FPGA precisely controls the reflection phase of each unit cell in the metasurface by regulating the on/off states of the switching components integrated in each unit cell. When illuminated by a monochromatic wave at frequency f\u003csub\u003e0\u003c/sub\u003e, the metasurface reflects the incident wave to generate reflected signals that carry the encoded information, and the superposition of these reflected signals propagates as the final transmitted signals for communication. b Spreading process for bit streams. The bit streams to be transmitted are respectively multiplied by their corresponding orthogonal spreading codes, yielding the final encoded streams. c Block diagram of the receiving process, in which the received signal captured by a single receiving antenna is first acquired by an oscilloscope for signal recording and storage, then downconverted, undergoes pilot-aided carrier phase synchronization, and is finally despread to recover the original messages.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-9239883/v1/f01b9746b3fe384a726f602c.png"},{"id":105888108,"identity":"490b8a3f-8ef0-4fea-a2b5-87fbfc54439b","added_by":"auto","created_at":"2026-04-01 07:43:12","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":673192,"visible":true,"origin":"","legend":"\u003cp\u003eEncoded streams, coding matrices, and metasurface reflection patterns for three scenarios. a Encoded streams for scenario 1. b Coding matrix for scenario 1. The metasurface is divided into two regions, each modulated by one stream. Different colors indicate different reflection phases. c Radiation patterns of each region in scenario 1, both pointing to 0°. d Encoded streams for scenario 2. e Coding matrix for scenario 2. The metasurface is divided into two regions, each modulated by one stream with an additional beam steering phase incorporated within the region. f Radiation patterns of scenario 2, pointing to -20° and 20°, respectively. g Encoded streams for the scenario 3. h Coding matrix for scenario 3. The metasurface is divided into four regions, each modulated by one stream with an additional beam steering phase incorporated within the region. The beam steering phase distribution in regions 1 and 2 are consistent, as well as those in regions 3 and 4. i Radiation patterns of each region in scenario 3. Regions 1 and 2 point to -50°, while regions 3 and 4 point to 50°.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-9239883/v1/e628a1fc896e38be00fbea8e.png"},{"id":105888117,"identity":"d200acfe-81fb-45f6-bae8-df004b93b603","added_by":"auto","created_at":"2026-04-01 07:43:15","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":429425,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDetails of the designed metasurface and experimental configuration. a\u003c/strong\u003e Illustration of the space-time coding metasurface unit cell. \u003cstrong\u003eb\u003c/strong\u003eSimulated reflection phase response of the unit cell. \u003cstrong\u003ec\u003c/strong\u003e Experimental configuration of the wireless communication testbed, capable of simultaneously transforming muti-stream data to various users. The CDM system operates at a chip rate of 5 MHz under a carrier frequency of 5 GHz.\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-9239883/v1/77739681ed3a9b7471d90239.jpeg"},{"id":105888200,"identity":"09feeeba-9aaf-4ee0-bf40-8362cd0967e6","added_by":"auto","created_at":"2026-04-01 07:43:32","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":656040,"visible":true,"origin":"","legend":"\u003cp\u003eMeasured constellations, frequency spectrum, and recovered images in three cases. a Scenario 1: measured constellation at the receiver. b Scenario 1: measured frequency spectra of the received signal and the pre-spread signal. c Scenario 1: constellation diagram of the despread data stream 1 and its recovered image. d Scenario 1: constellation diagram of the despread data stream 2 its recovered image. e Scenario 2: measured constellation at θ\u003csub\u003er1\u003c/sub\u003e. f Scenario 2: constellation diagram of the despread data stream 1 and its recovered image. g Scenario 2: measured constellation at θ\u003csub\u003er2\u003c/sub\u003e. h Scenario: constellation diagram of the despread data stream 2 and its recovered image. i Case 3: measured constellation at θ\u003csub\u003er12\u003c/sub\u003e. j Scenario 3: constellation diagram of the despread data stream 1 and its recovered image. k Case 3: constellation diagram of the despread data stream 2 and its recovered image. l Scenario 3: measured constellation at θ\u003csub\u003er34\u003c/sub\u003e. m Scenario 3: constellation diagram of the despread data stream 3 its recovered image. n Scenario 3: constellation diagram of the despread data stream 4 and its recovered image.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-9239883/v1/670d3fd2da883db8645899db.png"},{"id":105888578,"identity":"07df0a3f-1ea7-4223-83ec-d06008807dbb","added_by":"auto","created_at":"2026-04-01 07:44:34","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3020092,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9239883/v1/d177d5c6-04a6-4993-803a-ec0b838bcfc6.pdf"},{"id":105888376,"identity":"c1bbe03d-9d5e-499d-9ba2-54579c33d8ee","added_by":"auto","created_at":"2026-04-01 07:44:04","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1846285,"visible":true,"origin":"","legend":"Code-Division Multiplexing Using Space-Time-Coding Metasurface","description":"","filename":"SupplementaryInformationforCodeDivisionMultiplexingUsingSpaceTimeCodingMetasurfacelightv1.docx","url":"https://assets-eu.researchsquare.com/files/rs-9239883/v1/b98dbbdd36aa4d93c75c2484.docx"}],"financialInterests":"There is no conflict of interest","formattedTitle":"Code-Division Multiplexing Using Space-Time-Coding Metasurface","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe rise of the Internet of things (IoT) and the advent of sixth-generation (6G) networks are intensifying the demand for wireless systems that support massive connectivity\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Code-division multiplexing (CDM) is a pivotal technique for meeting this demand, as it allows multiple users to share the same frequency band simultaneously, thereby boosting network capacity and resilience\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. However, conventional CDM relies on intricate radio-frequency (RF) chains, which comprise mixers, filters, amplifiers, and antennas, to generate and process wideband signals. This complexity translates into high power consumption, physical bulk, and elevated cost. These drawbacks become particularly prohibitive at higher frequencies, such as the millimeter-wave bands envisioned for 6G, where the high expense and energy consumption of traditional phased arrays are major impediments\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. Overcoming the hardware inefficiency of conventional CDM RF systems is therefore a critical step towards making next-generation wireless technology both economically and environmentally sustainable.\u003c/p\u003e\u003cp\u003eIn the pursuit of more efficient signal processing, metasurfaces as artificially engineered thin-film structures with tailored electromagnetic properties have emerged as a disruptive platform\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e–\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. Their inherently low-profile and cost-effective nature, combined with an exceptional ability to manipulate electromagnetic waves in real-time, positions them as a foundational technology for future wireless systems\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e–\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. Current applications already demonstrate their utility in dynamic coverage enhancement\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e–\u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e, wireless power transfer\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e, and holographic multiple-input multiple-output (MIMO) systems\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e–\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e, showcasing a paradigm shift from circuit-based to free-space-based signal processing.\u003c/p\u003e\u003cp\u003eThe recent advancement of space-time-coding metasurfaces (STCMs) has unlocked dynamic wave control by incorporating temporal modulation, thereby enabling nonlinear signal processing directly within the wireless channel\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e–\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. This capability has spurred a diverse range of applications, including spatial frequency translation\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e–\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e, simplified RF front-ends\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e–\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e, chirp modulation for radar\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e–\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e, and nonreciprocal beam steering\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e–\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e. Notably, STCMs have been increasingly applied to wireless communications\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e–\u003cspan class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e, with a specific focus on multiplexing schemes such as time-division multiplexing, frequency-division multiplexing, and space-division multiplexing (SDM) \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e–\u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e. Despite these promising advancements, these schemes still operate in a manner where one channel carries one data stream, thus failing to realize parallel multi-dimensional utilization of spectral resources. Consequently, the information-carrying efficiency per unit bandwidth is far below the theoretical maximum, leading to insufficient resource utilization. More recently, the introduction of pseudo-random sequences\u003c/p\u003e\u003cp\u003e\u003cb\u003eFigure\u0026nbsp;1. Conceptual illustration of the proposed hybrid CDM and SDM wireless communication scheme using a STCM.\u003c/b\u003e The coding matrix that control the states of the PIN diodes integrated on the metasurface unit cells, which are mapped from the encoded streams, are prestored in the FPGA. During operation, the FPGA outputs corresponding bias voltages to precisely switch the diodes, thereby encoding the phase response of the metasurface. The STCM is partitioned into regions, each assigned a data stream and designed with a phase gradient. Illuminated by a monochromatic wave at \u003cem\u003ef\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e​, each metasurface region reflects a beam that is simultaneously encoded with its data stream and directed by its phase gradient, realizing parallel multi-stream transmission. By applying orthogonal code correlation-based algorithms, receiver antenna 1 despreads both message #1 and message #2 from the composite received signal. Similarly, receiver antenna 2 simultaneously recovers message #3 and message #4. This ability to support both directional multi-user communication and parallel multi-stream delivery underscores the scheme’s flexible reception performance across various communication scenarios.\u003c/p\u003e\u003cp\u003echaracterized by excellent autocorrelation and low cross-correlation properties as temporal modulation codes of STCMs has further expanded their functionality\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e51\u003c/span\u003e–\u003cspan class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e. These properties enable the sequences to support advanced functions including electromagnetic camouflaging\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e54\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e55\u003c/span\u003e\u003c/sup\u003e, spatial encryption\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e56\u003c/span\u003e\u003c/sup\u003e, and target recognition\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/sup\u003e. Since pseudo-random sequences with excellent autocorrelation and low cross-correlation attributes serve as a key technology in CDM\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e58\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e, STCMs with pseudo-random sequence modulation have great potential in designing cost- and energy-effective CDM wireless communication systems.\u003c/p\u003e\u003cp\u003eThis paper proposes a wireless CDM scheme using a pseudo-random-coded STCM to enable multi-stream transmission over a shared channel. In the proposed approach, each data stream is spread with a distinct orthogonal pseudo-random code. These uniquely encoded streams then modulate different spatial partitions of the metasurface. When illuminated by a monochromatic carrier wave, the STCM simultaneously upconverts and directs each encoded stream into tailored spatial coordinates. By independently engineering the phase gradients of different metasurface partitions, the system can either aggregate multiple signals into a unified beam or distribute them toward distinct angular directions in free space. At the receiver, the desired data stream is recovered by correlating the received signal with the corresponding orthogonal code, thereby decoupling the overlapping transmissions. This study investigates three scenarios to experimentally validate the CDM capabilities of the proposed communication scheme, in which multi-stream transmission is first realized to a single receiver, then single-stream delivery is extended to multiple receivers at distinct angles, and finally the scheme’s core capability of enabling reliable transmission of multiple spread data streams to multiple receivers at distinct angles is confirmed, achieving the joint operation of CDM and SDM. In contrast to conventional CDM, which relies on intricate RF chains with costly wideband components, the presented metasurface-based scheme performs spectrum spreading and beamforming directly in free space. By offloading this complexity, the system operates with a drastically simplified and low-cost RF front-end. By seamlessly integrating code-domain multiplexing with other dimensions such as space, this architecture presents a compelling pathway toward future budget-sensitive, high-capacity wireless applications.\u003c/p\u003e"},{"header":"Result","content":"\u003cp\u003e\u003cb\u003eConcept and Operating Principles\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eFigure\u0026nbsp;1\u003c/b\u003e conceptually illustrates the proposed wireless communication scheme based on a STCM for hybrid CDM and SDM. The metasurface is composed of a two-dimensional array of programmable unit cells, each integrated with three PIN diodes to enable dynamic control of the reflection phase. In operation, multiple streams of digital data sharing the same spectrum are encoded using a set of binary orthogonal codes to spread their spectra. These encoded streams are then mapped to the coding matrix with an additional phase gradient for beam deflection, which controls the states of the PIN diodes integrated on the metasurface unit cells. The coding matrix is prestored in the field-programmable gate array (FPGA). As a result, when the metasurface is illuminated by a monochromatic incident wave, independent directional transmission of the encoded streams is achieved, allowing users at specific locations to receive the multiple streams directed toward them. The prior knowledge of the orthogonal spread-spectrum codes enables each user to separate their intended stream from the shared channel and spectrum.\u003c/p\u003e\u003cp\u003eTo better illustrate the operating principle of the proposed STCM based wireless CDM, \u003cb\u003eFig.\u0026nbsp;2\u003c/b\u003e presents a schematic depicting the scenario with two messages to be sent. Figure\u0026nbsp;2a details the transmitter architecture. The messages to be sent are first transformed into binary bit streams\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{s}_{1}\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{s}_{2}\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e. A pair of 8-bit Walsh codes \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{1}\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{2}\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e serve as orthogonal codes for spectrum-spreading. To facilitate transmission and processing, all the above binary bit streams are mapped to bipolar symbols, where binary ‘1’ is mapped to ‘+1’ and binary ‘0’ to ‘\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:-\\)\u003c/span\u003e\u003c/span\u003e1’. The encoded stream\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{n}\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e after spreading process for the \u003cem\u003en\u003c/em\u003e-th data stream can be written as\u003c/p\u003e\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}{{m}_{n}\\left(t\\right)=s}_{n}\\left(t\\right){c}_{n}\\left(t\\right)\\#\\text{(}\\text{1}\\text{)}\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003ewhose time-domain waveforms are shown in Fig.\u0026nbsp;2b in detail. Since the bit rate of the spreading codes is eight times that of the original bit streams to be transmitted, the bit rate of the encoded streams is thus eight times higher than that of the original ones.\u003c/p\u003e\u003cp\u003eTo further explore the beam shaping and SDM capability of the metasurface, the encoded streams \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{n}\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e are superimposed with a preset gradient phase for beam deflection. Therefore, the coding sequences for \u003cem\u003ek\u003c/em\u003e-th column becomes \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{M}_{k}\\left(t\\right)={m}_{n}\\left(t\\right){e}^{j2\\pi\\:{\\varphi\\:}_{k}}\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varphi\\:}_{k}\\)\u003c/span\u003e\u003c/span\u003e is the gradient phase for \u003cem\u003ek\u003c/em\u003e-th column. Assuming the metasurface functions in a slow-varying regime, where the modulation frequency is significantly lower than the carrier frequency of the incident wave, the time-varying reflection coefficient of the metasurface is approximately equal to its applied coding sequence, namely, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{{\\Gamma\\:}}_{k}\\left(t\\right)=M}_{k}\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e. Under the given assumptions, when a monochromatic harmonic wave at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{0}\\)\u003c/span\u003e\u003c/span\u003e impinges on the metasurface, it is scattered into a modulated wave, which can be approximated expressed as\u003c/p\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}{s}_{scatt}\\left({\\theta\\:}_{r},t\\right)\\approx\\:\\sum\\:_{k}{{\\Gamma\\:}}_{k}\\left(t\\right){e}^{jkd\\text{s}\\text{i}\\text{n}{\\theta\\:}_{r}}{e}^{j{2\\pi\\:f}_{0}t}.\\#\\text{(}\\text{2}\\text{)}\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{r}\\)\u003c/span\u003e\u003c/span\u003e denotes the scattering angle of the reflected wave relative to the metasurface’s normal direction, and \u003cem\u003ed\u003c/em\u003e represents the center-to-center spacing between adjacent columns of unit cells. This scattered wave \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{s}_{scatt}\\left({\\theta\\:}_{r},t\\right)\\)\u003c/span\u003e\u003c/span\u003e thus contains all the multi-stream data after the spectrum-spreading process, with all streams sharing the same spectral, spatial, and temporal resources.\u003c/p\u003e\u003cp\u003eThe receiver architecture is depicted in Fig.\u0026nbsp;2c. At the receiver, a single receiving antenna is used to capture the superposition of all encoded streams, which is first acquired by an oscilloscope for signal observation and recording before being subsequently subjected to down-conversion and carrier phase synchronization. By leveraging prior knowledge of the orthogonal codes, the receiver can despread the signal one by one and recover the original transmitted message. The orthogonality of the codes ensures that each stream can be separated without interference from the others. In practice, this scheme supports two primary scenarios. First, multiple data streams can be intended for a single user, who can then receive all streams simultaneously. Alternatively, the streams can be directed to different users at various locations; in this case, each user can independently receive their designated data stream without interference from the others’ streams.\u003c/p\u003e\u003cp\u003e\u003cb\u003eHybrid Multi-stream CDM and SDM Transmission based on STCM\u003c/b\u003e\u003c/p\u003e\u003cp\u003eTo elucidate the operating principle of the proposed STCM-based wireless CDM, three different scenarios are respectively studied, as illustrated in Fig.\u0026nbsp;3. Figure\u0026nbsp;3 presents the encoded streams, coding matrices, and corresponding reflection patterns for three distinct communication scenarios. The first scenario considers multi-stream transmission to a single user. As depicted in Fig.\u0026nbsp;3a, two independent data streams are encoded using orthogonal spread spectrum codes. To accommodate\u003c/p\u003e\u003cp\u003ethe two streams, the metasurface is partitioned into two independent regions, with columns 1–4 forming Region 1 and columns 5–8 forming Region 2 (Fig.\u0026nbsp;3b). Each region is independently controlled by a binary stream, which is mapped to the metasurface phase via binary phase-shift keying (BPSK). For a target receiving angle of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{r}=0^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e, no inter-column phase gradient is required within each region. Consequently, both regions generate reflection patterns directed normally, as shown in Fig.\u0026nbsp;3c. The user, equipped with a single antenna positioned at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{r}=0^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e, captures the superimposed signal and subsequently recovers the original streams via correlation despreading using the corresponding orthogonal codes. It is worth noting that supplementary note 1 proposes a simplified implementation alternative. Unlike conventional approaches requiring dedicated physical partitions for each data stream, this advanced design enables the entire metasurface to collectively encode superimposed data streams through joint amplitude-phase modulation.\u003c/p\u003e\u003cp\u003eWhile this scheme reduces coding complexity, it imposes stricter requirements on the amplitude-phase regulation accuracy of individual unit cells.\u003c/p\u003e\u003cp\u003eThe second scenario addresses the case where multiple users, located at distinct spatial positions, each receive a single data stream. Using the same two-stream configuration (Fig.\u0026nbsp;3d, identical to Fig.\u0026nbsp;3a), the key distinction lies in the metasurface coding matrix design. As illustrated in Fig.\u0026nbsp;3e, a beam-steering phase \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\psi\\:}_{ij}\\)\u003c/span\u003e\u003c/span\u003e is applied to the j-th column of the metasurface for the i-th region, where i denotes the region index and j denotes the column index within the region. The detailed calculation of this beam-steering phase is provided in Supplementary Note 2. The reflection phase of each column is obtained by summing the beam-steering phase and the BPSK-modulated phase of the corresponding data stream, thereby deflecting each region’s reflection pattern toward its target angle. Owning to the 2-bit phase modulation constraint, the steering phases for the two regions are set to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\psi\\:}_{13}={\\psi\\:}_{12}=90^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\psi\\:}_{23}={\\psi\\:}_{22}=90^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\psi\\:}_{11}={\\psi\\:}_{21}=0^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e, with an inter-column spacing of 18.5 mm. This configuration yields a reflection pattern for Region 1 directed at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{r1}=-20^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e and for Region 2 at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{r2}=20^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e, as verified in Fig.\u0026nbsp;3f. When a receiver is positioned at the target angle, the undesired signal from the other region is suppressed to a negligible level, ensuring that only the intended signal is effectively received. Subsequent despreading then recovers the original single data stream. Supplementary Note 3 further expands this concept by introducing flexible partition designs tailored to target reflection patterns, enabling adaption to complex spatial deployment scenarios.\u003c/p\u003e\u003cp\u003eThe most comprehensive scenario involves multiple users, each located at a distinct spatial angle and requiring simultaneous reception of multiple streams. This configuration effectively combines the features of the two previous scenarios. Consider a case with four data streams, as shown in Fig.\u0026nbsp;3g. Streams 1 and 2 are allocated to target angle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{r12}\\)\u003c/span\u003e\u003c/span\u003e, while streams 3 and 4 are allocated to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{r34}\\)\u003c/span\u003e\u003c/span\u003e. The metasurface is divided into four independent regions, each modulated by one data stream (Fig.\u0026nbsp;3h). A critical design principle is that the regions serving the same receiver share an identical inter-column phase gradient. Specifically, the two regions carrying streams 1 and 2 are configured with a beam-steering phase \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\psi\\:}_{1}\\)\u003c/span\u003e\u003c/span\u003e, while those carrying streams 3 and 4 employ \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\psi\\:}_{2}\\)\u003c/span\u003e\u003c/span\u003e. This ensures that reflection patterns for regions targeting the same angle are perfectly aligned, while those for different angles are steered toward distinct directions. For example, when both\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{\\psi\\:}_{1}\\)\u003c/span\u003e \u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\psi\\:}_{2}\\)\u003c/span\u003e\u003c/span\u003e are \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:90^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e, Regions 1 and 2 point to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{r12}=-50^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e, and Regions 3 and 4 point to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{r34}=50^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e. Figure\u0026nbsp;3i confirms that the patterns of regions corresponding to the same receiver completely overlap. A receiver deployed at the target angle thus captures the superimposed signal of its two assigned streams and subsequently separates them via orthogonal spread spectrum code despreading.\u003c/p\u003e\u003cp\u003eIn summary, STCM-based multi-stream transmission achieves crosstalk-free communication in the code domain by leveraging both code orthogonality and spatial directivity. The introduction of beam-steering phases enables seamless progression from single-angle to multi-angle multi-stream scenarios, offering a flexible and scalable framework for advanced wireless CDM systems.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExperimental Demonstration\u003c/b\u003e\u003c/p\u003e\u003cp\u003eTo validate the proposed concepts and methodologies, a wireless communication testbed operating at 5 GHz is established in this study. The metasurface employed is a 2-bit programmable metasurface, whose unit cell is illustrated in Fig.\u0026nbsp;4a. As shown, the unit cell consists of two substrate layers and three metal layers, with three PIN diodes integrated at the bottom to enable reflection phase control. Figure\u0026nbsp;4b presents the simulated reflection phase under different biasing states of PIN diodes, denoted as 00, 01, 10, and 11, clearly demonstrating 2-bit phase quantization characteristics. Detail information regarding the metasurface can be found in Materials and Method section, and in Supplementary note 4. Figure\u0026nbsp;4c shows the experiment configuration. The transmitter comprises a signal generator (Agilent Technologies E8257D), an FPGA, a horn antenna, and a metasurface array, where the metasurface dynamically reconfigures its properties through FPGA-controlled real-time coding sequence loading. The receiver employs a horn antenna positioned 1 m from the metasurface, with its angle relative to the metasurface adjustable as needed. The captured signals acquired by a high-speed oscilloscope (Tektronix MSO64B) and subsequently transferred via Ethernet interface to computer platform for post-processing.\u003c/p\u003e\u003cp\u003eExperimental results are presented in Fig.\u0026nbsp;5. The multi-stream single-user scenario is experimentally demonstrated by dividing the metasurface into left and right regions, each consisting of five columns. Each region is modulated independently using distinct signals, spread by orthogonal codes \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{1}\\)\u003c/span\u003e\u003c/span\u003e= [1,0,0,1,0,1,1,0] and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{2}\\)\u003c/span\u003e\u003c/span\u003e= [1,0,1,0,0,1,0,1], respectively. Figure\u0026nbsp;5a presents the constellation diagram of the composite received signal, which results from the superposition of reflections from all unit cells. The spectrum of the transmitted signal exhibits clear spread spectrum characteristics: compared with the original pre-spread signal, the bandwidth of received signal is expanded by a factor of eight, corresponding to the length of the spreading code (Fig.\u0026nbsp;5b). Figure\u0026nbsp;5c and Fig.\u0026nbsp;5d present the separated constellation diagrams and the corresponding decoded message from the two independent metasurface regions. All constellation points are clearly distinguishable, confirming the system’s reliability for high-quality image data transmission. This configuration also allows a single user to receive more than two data streams, with detailed test results provided in Supplementary note 5.\u003c/p\u003e\u003cp\u003eFor the scenario where multiple users, located at distinct spatial positions, each receive a single data stream, the metasurface is partitioned as illustrated in Fig.\u0026nbsp;3e. The two remaining columns are covered with microwave-absorbing material to eliminate unwanted reflections. Figure\u0026nbsp;5e and Fig.\u0026nbsp;5g show the constellation diagram received by users at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:-20^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:20^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e, respectively. The observed clustering or dispersion in these constellations is attributed to the sidelobes in the reflection patterns of each region, where residual energy from undesired signals is not fully suppressed, thereby introducing interference to the intended signal. Figure\u0026nbsp;5f and Fig.\u0026nbsp;5h present the constellation diagrams and the corresponding recovered messages corresponding to each independent region of the metasurface. Although slight dispersion remains observable in the constellations, the clustering structure is still clearly distinguishable, confirming the successful seperation of the signals.\u003c/p\u003e\u003cp\u003eFor the four-stream two-user scenario where each user receives two data streams, the following orthogonal spreading codes are assigned to each stream:\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{1}\\)\u003c/span\u003e \u003c/span\u003e= [1,0,0,1,0,1,1,0]\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{2}\\)\u003c/span\u003e \u003c/span\u003e= [1,0,1,0,0,1,0,1]\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{3}\\)\u003c/span\u003e \u003c/span\u003e= [1,0,0,1,1,0,0,1]\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{4}\\)\u003c/span\u003e \u003c/span\u003e= [1,0,1,0,1,0,1,0]\u003c/p\u003e\u003cp\u003eThe metasurface is partitioned as depicted in Fig.\u0026nbsp;5h. Figure\u0026nbsp;5i and Fig.\u0026nbsp;5l present the constellation diagrams received by users located at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:-50^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:50^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e, respectively. As the number of signals to be transmitted increases, the directivity of the radiation patterns diminishes due to the decreased number of columns in each region, resulting in increased dispersion in the received constellation diagrams. Nevertheless, this increase does not affect the correct discrimination of the signals. Figure\u0026nbsp;5j and Fig.\u0026nbsp;5k show the demodulated constellation diagram and the corresponding original transmitted image for the signal received at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:-50^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e, while Fig.\u0026nbsp;5m and Fig.\u0026nbsp;5n present those for the signal received at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:50^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e. In both cases, the images are accurately reconstructed. These experimental results confirm that spatially separated receivers can successfully and independently recover their intended data streams.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study presents a code-division wireless communication system based on an STCM, capable of simultaneously transmitting multi-stream messages to the same receiver while enabling space-division multiplexing. Unlike previous metasurface-enabled multiplexing systems, or CDM systems that rely on intricate RF chains, the proposed scheme achieves secure multi-user transmission with enhanced spectral efficiency with simplified, low-cost RF front-ends. To demonstrate that multi-streams received by single channel can be reliably recovered through code-domain separation, experimental validation confirms the successful transmission of single or dual images to a single user or two distinct users at a pre-specified angle. The presented work establishes a new paradigm for applications in scenarios requiring low-power, high-density access.\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cp\u003e\u003cb\u003eDetails on the space-time coding metasurface\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThe designed space-time coding metasurface consists of a 10×10 array of unit cells. Each unit cell has a side length of 18.5 mm, and comprises two substrates and three metal layers. Three PIN diodes are soldered on the bottom layer of the unit cell. Specifically, simultaneous switching of PIN 1 and PIN 2 introduces a 90° phase shift in reflection between their ON and OFF states, while an additional 180° phase shift is achieved through the switching of PIN 3. Detailed information regarding the unit cell design and its working principle can be found in Supplementary note 4 and also Ref. 60.\u003c/p\u003e\u003cp\u003eTo realize independent and flexible spatiotemporal modulation, each column of the metasurface is individually controlled by an output port of an FPGA (Altera DE2-115). To facilitate the desired partitioning of the metasurface in scenario 2 and scenario 3, two columns on one end of the metasurface array are shielded by absorbing materials, which serves to eliminate unwanted electromagnetic reflections.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExperiment setup\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThe experiments are conducted in a microwave anechoic chamber to minimize unwanted electromagnetic reflections and external interferences. A signal generator (Agilent Technologies E8257D) is used to generate a monotone signal at 5 GHz, with an amplitude of 25 dBm. An oscilloscope (Tektronix MSO64B) is utilized to capture the real part of the electric field reflected by the STCM. The oscilloscope is connected to a computer via an Ethernet cable to enable data transmission from the oscilloscope to the computer for post-processing. A transmit horn antenna is aligned to the normal direction of the metasurface array and positioned 0.6 m from the metasurface. This distance is greater than the far-field distance of the transmit horn to ensure the metasurface is uniformly illuminated by the incident wave. The receive horn antenna is placed 1 m from the metasurface. While constrained by the anechoic chamber’s spatial limitations, this distance still approximates the far-field requirement of the metasurface to ensure valid measurement conditions.\u003c/p\u003e\u003cp\u003e\u003cb\u003eGeneration, reception and processing of data streams\u003c/b\u003e\u003c/p\u003e\u003cp\u003eTo generate bit streams from image data, each pixel is mapped to one bit information: colored pixels are encoded as 1, and white pixels as 0. To acquire the generated bit stream, the oscilloscope’s sampling rate is set to 1.5625 GS/s, which is equivalent to down-converting the received signal to 312.5 MHz. Further downconversion is conducted using MATLAB. During transmission, a 2000-bit frame header with a bit rate of 5 MHz is adopted, consisting of 1000 successive 0s followed by 1000 successive 1s. When processing the received data using MATLAB, the phase of the successive 1s in the frame header is taken as the reference phase, and the phase of the received signal is compared with this reference phase to achieve phase alignment.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cb\u003eAuthor Contributions\u003c/b\u003e\u003c/p\u003e\u003cp\u003eX. W and G.-M. Y conceived the concept, Y. C designed the experiments. Y.-Q. J supervised the work. Y. C wrote the manuscript with discussion from all authors.\u003c/p\u003e \u003ch2\u003eCompeting Interests\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eThe authors acknowledge financial support from National Natural Science Foundation of China under Grant 62471146, State Key Laboratory of Radio Frequency Heterogeneous Integration Open Scientific Research Program No. KF2024017.\u003c/p\u003e\u003ch2\u003eData availability\u003c/h2\u003e \u003cp\u003eThe authors declare that all relevant data are available in the paper and its Supplementary Information files, or from the corresponding author on request.\u003c/p\u003e\u003ch2\u003eCode availability\u003c/h2\u003e \u003cp\u003eThe custom computer codes used in this study are available from the corresponding authors on request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eWang, C.-X., You, X., Gao, X., Zhu, X., et. al. 6G: On the road to 6g: Visions, requirements, key technologies, and testbeds. \u003cem\u003eIEEE Commun. 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Express\u003c/em\u003e, 33, 12890\u0026ndash;12900 (2025).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"light-science-and-applications","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"lsa","sideBox":"Learn more about [Light: Science \u0026 Applications](http://www.nature.com/lsa/)","snPcode":"41377","submissionUrl":"https://mts-lsa.nature.com/","title":"Light: Science \u0026 Applications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-9239883/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9239883/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Code-division multiplexing (CDM) is essential for supporting massive connectivity in wireless networks, but its implementation typically requires complex and costly radio-frequency (RF) chains. This work presents a simplified, low-cost wireless CDM system based on a space-time-coding metasurface (STCM). By modulating distinct spatial partitions of the metasurface with data streams pre-spread via orthogonal pseudo-random codes, the STCM functions as a distributed parallel modulator. This architecture enables the metasurface to perform simultaneous upconversion while directing modulated reflections from multiple spatial partitions toward either shared or distinct directions. Although these data-carrying waves may physically overlap in the far-field, the inherent orthogonality of the spread codes ensures that the receiver can successfully decorrelate and recover each multiplexed stream. Experimental validation demonstrates three core scenarios: multi-stream transmission to a single direction, single-stream to multiple directions, and multi-stream to multiple directions, all achieved without conventional RF chains. The proposed STCM-based CDM architecture enables simultaneous multi-user communication with a radically simplified RF front-end, paving the way for energy- and cost-efficient high-capacity wireless systems for future wireless networks.","manuscriptTitle":"Code-Division Multiplexing Using Space-Time-Coding Metasurface","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-01 07:40:50","doi":"10.21203/rs.3.rs-9239883/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"This content is not available.","date":"2026-05-04T00:37:15+00:00","index":5,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2026-04-20T12:23:30+00:00","index":3,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2026-04-19T04:17:14+00:00","index":4,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2026-04-15T13:56:17+00:00","index":5,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2026-04-13T09:45:03+00:00","index":2,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2026-04-08T14:55:19+00:00","index":4,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2026-04-08T06:05:26+00:00","index":3,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2026-04-08T02:50:41+00:00","index":2,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2026-04-02T13:19:42+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2026-03-30T04:09:06+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewersInvited","content":"","date":"2026-03-30T03:50:25+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-30T03:29:10+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-27T04:19:59+00:00","index":"","fulltext":""},{"type":"submitted","content":"Light: Science \u0026 Applications","date":"2026-03-27T04:19:58+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"light-science-and-applications","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"lsa","sideBox":"Learn more about [Light: Science \u0026 Applications](http://www.nature.com/lsa/)","snPcode":"41377","submissionUrl":"https://mts-lsa.nature.com/","title":"Light: Science \u0026 Applications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"791b1292-ad30-4375-8dee-c5ec8bef482b","owner":[],"postedDate":"April 1st, 2026","published":true,"recentEditorialEvents":[{"type":"editorInvitedReview","content":"This content is not available.","date":"2026-05-04T00:37:15+00:00","index":5,"fulltext":"This content is not available."}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":65356256,"name":"Physical sciences/Physics/Electronics, photonics and device physics"},{"id":65356257,"name":"Physical sciences/Optics and photonics/Applied optics"}],"tags":[],"updatedAt":"2026-04-01T07:40:50+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-01 07:40:50","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9239883","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9239883","identity":"rs-9239883","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}