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MIMO Transmission through Reconfigurable Intelligent Surface: System Design, Analysis, and Implementation

Wankai Tang, Jun Yan Dai, Ming Zheng Chen, Kai-Kit Wong, Xiao Li, Xinsheng Zhao, Shi Jin, Qiang Cheng, Tie Jun Cui

arXiv:1912.09955v2eess.SPcs.IT

TL;DR

Existing RIS transmitters lack analytical models that capture hardware constraints and have been demonstrated mainly for basic SISO communication. This paper develops an amplitude-and-phase-varying RIS architecture with analytical system modeling for MIMO-QAM and validates it in real time over the air, achieving 20 Mbps in a 2×2 MIMO 16-QAM prototype.

  • Problem

    Existing RIS-transmitter research lacks hardware-aware analytical formulations and has largely remained limited to basic SISO communication.

  • Method

    The paper models RIS-based MIMO-QAM transmission and uses amplitude-and-phase-varying modulation with two symbol degrees of freedom to support higher-order modulation.

  • Results

    20 Mbps was achieved in a real-time over-the-air 2×2 MIMO 16-QAM prototype with approximately 0.7 W power consumption.

  • Takeaways & Limitations

    The results support RIS-based MIMO-QAM as an attractive architecture for UM-MIMO and holographic MIMO with affordable hardware complexity.

Abstract

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Reconfigurable intelligent surface (RIS) is a new paradigm that has great potential to achieve cost-effective, energy-efficient information modulation for wireless transmission, by the ability to change the reflection coefficients of the unit cells of a programmable metasurface. Nevertheless, the electromagnetic responses of the RISs are usually only phase-adjustable, which considerably limits the achievable rate of RIS-based transmitters. In this paper, we propose an RIS architecture to achieve amplitude-and-phase-varying modulation, which facilitates the design of multiple-input multiple-output (MIMO) quadrature amplitude modulation (QAM) transmission. The hardware constraints of the RIS and their impacts on the system design are discussed and analyzed. Furthermore, the proposed approach is evaluated using our prototype which implements the RIS-based MIMO-QAM transmission over the air in real time.

I. INTRODUCTION … 1) RIS-based Modulation:

The paper motivates RIS as a lower-cost alternative for future high-dimensional wireless systems, develops a physics-aware RIS-based MIMO-QAM design, and validates it with a real-time prototype. The system model shows that tunable unit-cell reflection amplitude and phase can directly modulate an air-fed carrier for wireless transmission.

  • I. INTRODUCTION: RIS can reduce the implementation burden of terahertz, ultra-massive-MIMO, and other 6G architectures requiring costly hardware and many RF chains.RISs use programmable metasurfaces to manipulate reflected electromagnetic-wave amplitude and phase through externally controlled unit cells.
  • A. Related Work: Existing RIS transmitters demonstrated BFSK, QPSK, 8PSK, and multi-modulation transmission, but lacked analytical models capturing RIS physics and electromagnetic behavior.Prior work also developed symbol-error analysis and modulation/resource-allocation methods for RIS-based transmitters.
  • B. Main Contributions: The paper formulates physics- and electromagnetics-aware RIS-based MIMO transmission, showing that its working principle and basic expression match conventional non-RIS MIMO communication.It further introduces constant-envelope nonlinear modulation for high-order modulation and analyzes discrete phase-shift impacts on RIS-based MIMO-QAM design.
  • B. Main Contributions: A varactor-diode programmable metasurface prototype implements real-time RIS-based MIMO-QAM wireless communication, with about 0.7 W consumed by the metasurface and control board.The prototype is presented as the world’s first implementation of real-time RIS-based MIMO-QAM wireless communication.
  • C. Organization: The paper progresses from RIS-transmitter fundamentals and MIMO system modeling to MIMO-QAM design, hardware constraints, transceiver implementation, and experimental results.This organization connects the analytical system model to the subsequent design and prototype evaluation.
  • A. Fundamentals of RIS-based Transmitter: An RIS is a programmable metasurface of regularly arranged subwavelength unit cells whose tunable electromagnetic properties are controlled externally.Each unit cell typically combines a designed metal pattern, dielectric material, and tunable component.
  • 1) RIS-based Modulation:: Adjusting each unit cell’s equivalent load impedance changes its reflection amplitude and phase, enabling amplitude-and-phase modulation of an air-fed single-tone carrier.When all cells share one control signal, the RIS performs the same modulation across the surface and realizes basic SISO communication.

2) RIS-based Multi-channel Transmitter: · B. Communication Model

The RIS-based transmitter enables multi-channel communication by independently controlling unit-cell reflection coefficients, while avoiding conventional RF chains and using one narrowband power amplifier. Its MIMO model represents each received signal as the superposition of unit-cell reflections, with programmable amplitudes and phases governed by the RIS geometry, propagation channels, and receiver noise.

  • 2) RIS-based Multi-channel Transmitter:: Independent unit-cell control maps multiple baseband bitstreams to DAC-driven reflection coefficients, enabling RIS-based multi-channel transmission.The maximum number of transmitted bitstreams is determined by the available unit cells and their control paths.
  • 2) RIS-based Multi-channel Transmitter:: The architecture directly connects baseband modules to radiating unit cells, eliminating conventional RF chains and requiring only one narrowband power amplifier.This arrangement avoids the power-amplifier nonlinearity issue associated with conventional multi-channel transmitters.
  • B. Communication Model: The communication model contains an N-by-M RIS with independently DAC-controlled unit cells, characterized by reflection coefficients, dimensions, gains, and radiation patterns.The receiver has K antennas, and the model specifies the distances and angular relationships between each unit cell and receiving antenna.
  • B. Communication Model: The model assumes uniform illumination, with identical incident amplitude and phase across unit cells under normal-incidence far-field conditions without feed-path obstruction.A feed antenna placed directly in front of the RIS is given as the practical basis for this assumption.
  • B. Communication Model: In free space without noise, each receiving antenna observes the coherent superposition of signals reflected by all RIS unit cells.Each path’s amplitude depends on antenna and unit-cell gains, radiation patterns, incident energy flux, unit-cell size, wavelength, and inverse propagation distance; its phase includes propagation and reflection shifts.
  • B. Communication Model: The resulting RIS-MIMO formulation uses programmable unit-cell amplitudes A_n,m and phase shifts ϕ_n,m, with each unit cell transmitting power p = Sdxdy.This expression establishes the basic mechanism by which RIS elements control the transmitted signal.
  • B. Communication Model: For flat fading, the received vector follows the conventional MIMO form y = Hx + n, where H is the RIS-to-receiver channel matrix and n is receiver noise.The RIS system retains the conventional principle of modulating a carrier and radiating signals over wireless channels, while its chain-free and power-efficient hardware supports UM-MIMO and holographic MIMO applications.
  • B. Communication Model: RIS-based MIMO can apply established MIMO transmission schemes and algorithms while offering a chain-free, power-efficient architecture for systems constrained by conventional hardware cost and heat dissipation.The model identifies the RIS approach as functionally analogous to conventional MIMO but distinct in its transmitter implementation.

III. RIS-BASED MIMO-QAM TRANSMISSION

This section designs RIS-based QAM modulation and MIMO transmission, addressing why QAM is natural for conventional IQ transmitters but difficult for RIS-based transmitters. It then introduces constant-envelope QAM using nonlinear modulation while noting the phase-focused unit-cell assumption.

  • Design motivation: RIS-based transmitters are designed for QAM modulation and MIMO transmission, unlike conventional transmitters whose independent IQ baseband signals directly control carrier amplitude and phase.The section identifies QAM as natural in conventional RF-chain architectures but difficult to achieve with RIS-based transmitters.
  • RIS response assumption: The RIS unit-cell design assumes an approximately unchanged amplitude response, such as A_n,m = 1, while enabling a flexible phase response.This design seeks a large phase-shift range with small amplitude fluctuation.
  • Constant-envelope QAM: Under the constant-envelope constraint, the proposed QAM approach uses nonlinear modulation.The section introduces and analyzes QAM modulation under this constraint.

A. Basic Method

The method uses time-varying linear phase responses to overcome RIS unit cells’ constant-envelope limitation and realize independent amplitude-and-phase control for QAM on harmonic frequencies. This enables RIS-based MIMO-QAM transmission, including 16-QAM on the first-order harmonic.

  • A. Basic Method: The nonlinear modulation technique overcomes the constant-envelope constraint that prevents high-order modulation and limits RIS transmission rate.A unit cell’s conventional response generates constant-envelope carrier-frequency symbols, motivating harmonic-based modulation.
  • A. Basic Method: 16-QAM is demonstrated on the first-order harmonic, with symbol mapping based on selecting t0 and Δϕ for each transmitted bit pattern.The example identifies the first-order harmonic as f = f_c + 1/T_s and summarizes the mapping in Table II.
  • A. Basic Method: Linear time-varying phase responses provide two degrees of freedom, Δϕ and t0, enabling independent amplitude and phase adjustment of harmonic components.Δϕ controls harmonic amplitude, while t0 controls harmonic phase across symbol periods.
  • A. Basic Method: The resulting harmonic-domain QAM formulation enables RIS-based MIMO-QAM transmission by substituting the proposed symbol representation into the MIMO signal model.Each unit cell transmits a symbol defined by the time-varying phase construction.

B. Beamforming and Gain … 1) Phase Dependent Amplitude:

The proposed RIS transmitter supports simultaneous high-order modulation and beamforming under a constant-envelope constraint, with beamforming gain increasing with RIS aperture. Its QAM design remains robust to phase-dependent amplitude responses, including practical 16-QAM symbol generation.

  • B. Beamforming and Gain: The RIS formulation provides a general baseband expression for simultaneous high-order modulation and beamforming under a constant-envelope constraint.
  • B. Beamforming and Gain: Beamforming is analyzed for free-space propagation with receiving antennas in the RIS far field, when signals are aligned toward the kth receiving antenna.All unit cells transmit the same symbol s in this beamforming configuration.
  • B. Beamforming and Gain: Beamforming gain scales with the number of RIS unit cells NM and the square root of unit-cell area, so larger apertures provide higher gain.
  • IV. SYSTEM DESIGN AND ANALYSIS: The proposed 2×2 MIMO-QAM prototype validates the method while the design approach is stated to generalize to arbitrary MIMO sizes.The system design addresses RIS hardware constraints and specifies the transmitter and receiver.
  • 1) Phase Dependent Amplitude:: Practical RIS unit cells couple amplitude and phase responses, but the proposed RIS-based QAM method is robust to this phase-dependent amplitude constraint.Unit-cell design typically minimizes amplitude fluctuation while preserving a sufficiently broad controllable phase range [39]–[41].
  • 1) Phase Dependent Amplitude:: A phase-dependent amplitude response with 3 dB maximum fluctuation is analyzed as a concrete hardware example for QAM symbol design.
  • 1) Phase Dependent Amplitude:: 16-QAM symbols ‘0’, ‘2’, ‘8’, and ‘10’ are realized through circular time shifts, while other symbols such as ‘5’ use a solved phase difference and time-delay design.The method extends to QAM for various phase-dependent amplitude functions encountered in practice.

2) Discrete Phase Shift:

Discrete DAC-controlled phase shifts make the ideal continuous-time RIS-QAM waveform impractical, creating a tradeoff between phase resolution and symbol rate. Increasing the number of phase-shift steps reduces discretization distortion, with the first-harmonic amplitude approaching the ideal value.

  • 2) Discrete Phase Shift:: The ideal continuously varying phase response requires a high-resolution DAC, whereas practical control signals have discrete output levels.The continuous-phase assumption used to design the QAM symbol does not exist directly in practical implementation.
  • 2) Discrete Phase Shift:: 100 MSa/s with q = 1000 limits the maximal RIS-QAM symbol rate to 100kS/s, illustrating the resolution–rate tradeoff.The maximal symbol rate is constrained by the DAC sampling rate and the number q of discrete phase-shift steps.
  • 2) Discrete Phase Shift:: Larger q produces a smaller impact of discrete phase shifts on the RIS-QAM baseband symbol, and |ea1| quickly approaches the ideal |a1|.The comparison concerns the amplitude of the 1st order harmonic component with and without phase discretization.

B. Transmitter Design

The transmitter uses a 256-cell RIS but implements a 2×2 MIMO-QAM system because experimental hardware provides only two DACs. Its two RIS halves transmit separate streams, preserving the conventional 2×2 MIMO-QAM signal expression and enabling a common wireless frame structure.

  • B. Transmitter Design: Two DACs control the 256-cell RIS in the implemented system, enabling a 2×2 MIMO-QAM transmitter; dedicated DACs could independently control all 256 unit cells.The RIS dimensions are N = 32 and M = 8, giving 256 unit cells.
  • B. Transmitter Design: The RIS is divided into red and orange halves, with each half transmitting one of the two bit streams to the receiver antennas.This partition forms the basis of the RIS-based 2×2 MIMO-QAM system diagram in Fig. 8.
  • B. Transmitter Design: The four channel coefficients describe links from each RIS half to each receiving antenna, covering the red-to-Rx1, red-to-Rx2, orange-to-Rx1, and orange-to-Rx2 paths.These coefficients specify the channels used by the two RIS halves and two receiving antennas.
  • B. Transmitter Design: The RIS-based 2×2 MIMO-QAM signal expression matches conventional MIMO-QAM, so the transmitter uses a common wireless frame structure.The frame structure includes synchronization, as shown in the wireless frame diagram in Fig. 9.

C. Receiver Design · D. BER Performance

The receiver recovers RIS-based 2×2 MIMO-QAM symbols through oversampling, FFT-based harmonic extraction, synchronization, channel estimation, detection, and demodulation. Under a constant wireless channel, the RIS-based system has the same BER performance as conventional MIMO at the same SNR, with theoretical BER derived for 16-QAM over AWGN.

  • C. Receiver Design: Least-squares channel estimation and zero-forcing equalization are selected because their implementation simplicity enables rapid validation of RIS-based MIMO-QAM transmission.
  • D. BER Performance: The proposed RIS-based MIMO system has the same BER performance as conventional MIMO under the same SNR because their essential transmission principle and mathematical expression are shared.
  • D. BER Performance: The BER analysis assumes a constant 2×2 wireless channel, matching the stationary indoor prototype measurement conditions used to compare theoretical and measured BER.The people, RIS-based transmitter, and conventional receiver remain stationary during measurement, making the channel approximately changeless.
  • D. BER Performance: Zero-forcing equalization recovers the two streams, after which standard 16-QAM Gray-coded symbols are demodulated by Euclidean distance under an AWGN model.The resulting stream BERs are expressed theoretically using the complementary error function, erfc(·).
  • D. BER Performance: The theoretical BER expressions use an approximate Gray-coded 16-QAM AWGN formula that retains only the first and second terms of the exact expression.These theoretical BERs, including the prototype’s total BER, rely on the changeless-channel assumption.

V. IMPLEMENTATION AND MEASUREMENT … 9) SDR Platform:

The prototype realizes real-time over-the-air RIS-based 2×2 MIMO-QAM transmission using an integrated RIS, control, RF, PXIe, SDR, computing, and antenna platform. Its hardware implements programmable phase control, digital-to-analog waveform generation, synchronized RF operation, and two-channel baseband reception for practical measurement.

  • V. IMPLEMENTATION AND MEASUREMENT: Real-time over-the-air experiments demonstrate the feasibility of the proposed RIS-based 2×2 MIMO-QAM architecture.The prototype setup includes the RIS, control circuit board, RF signal generator, PXIe modules, SDR platform, host computer, and antennas.
  • 1) RIS:: The RIS uses 256 varactor-diode unit cells whose control voltages provide approximately 450° of continuous phase manipulation from 0 V to 21 V at 4.25 GHz.The unit cells are arranged with N = 32 and M = 8; each has a simulated gain of about 9 dBi assuming 100% efficiency.
  • 2) Control Circuit Board:: The control circuit board bridges the DACs and RIS, amplifying the two DAC outputs to control the left and right halves of the unit cells.Its fixed voltage amplification gain enables the DAC-generated control signals to drive the programmable metasurface.
  • 3) Central Controller:: The central controller develops the host and FPGA programs for two source bitstreams, digital baseband, frame structure, and peripheral control.The PXIe chassis provides the data and control interface between the central controller and peripheral modules.
  • 5) FPGA+DAC Module:: Two 16-bit, 100 MSps DACs convert the complete RIS-based 2×2 MIMO-QAM digital frame into analog voltage sequences for the control circuit board.The FPGA+DAC module supplies the two control inputs that drive the RIS modulation hardware.
  • 6) DC Power Supply:: The DC power supply provides ±12 V to the control-board voltage amplifiers, while a shared 10 MHz reference synchronizes the FPGA, DAC, and RF signal generator.Together, these modules provide power and timing coordination for the prototype platform.
  • 8) RF Signal Generator:: A 4.25 GHz single-tone RF generator illuminates the RIS through a horn antenna, with manually varied output power enabling BER measurements under different transmission-power and SNR conditions.A low-cost single-tone RF source could provide the carrier in practical applications instead of the RF signal generator.
  • 9) SDR Platform:: The SDR platform uses two receiving channels to downmix received RF signals to baseband and send digital samples to the host computer.The two receiving antennas are single-polarized dipoles with 7.4 dBi gain each.

10) Host Computer: · B. Experimental Results · VI. CONCLUSION

The prototype realizes real-time RIS-based 2×2 MIMO 16-QAM transmission over the air, achieving 20 Mbps while consuming about 0.7 W in the RIS and control board. Measured BER closely matches theoretical performance and remains robust under discrete phase-shift quantization.

  • 10) Host Computer:: The host computer performs 2×2 MIMO channel estimation, detection, QAM demodulation, constellation display, and BER calculation.These processing functions support recovery and evaluation of the received bitstreams.
  • B. Experimental Results: The indoor over-the-air experiment used approximately 1.5 m between the RIS and the two receiving antennas, with clear recovered constellations for the transmitted bitstreams.The prototype system and recovered constellation diagrams are shown in Fig. 11.
  • B. Experimental Results: The measured BER curves for both streams match the exact theoretical BER curves well across the tested SNR range.The comparison is shown in Fig. 12, using measured SNR of the receiving chain connected to Rx antenna 1 as the BER-curve abscissa.
  • B. Experimental Results: The BER curves for q = 40 and q = 10 almost coincide, validating robustness to discrete phase-shift steps at a 2.5 MSps symbol rate.The default setting is q = 40, while q = 10 represents a more discretized phase shift; the comparison is provided in Fig. 13.
  • VI. CONCLUSION: The paper formulates RIS-based MIMO-QAM transmission while analyzing RIS hardware constraints, including phase-dependent amplitude and discrete phase shifts, and their system-design impacts.It presents a basic method and transceiver design for high-order modulation and MIMO transmission through RISs, together with the implemented prototype.
  • B. Experimental Results: 20 Mbps data rate and about 0.7 W power consumption were achieved for real-time RIS-based 2×2 MIMO 16-QAM transmission over the air.The prototype realized 16-QAM and 2×2 MIMO transmission, with overhead from synchronization and pilot subframes excluded from the data-rate figure.

APPENDIX A

Appendix A proves Theorem 1 by deriving the received electric field and instantaneous signal power from the incident carrier, unit-cell reflection, propagation, and antenna reception. The derivation combines energy conservation with coherent superposition across all RIS unit cells.

  • Proof of Theorem 1: The proof starts by expressing the incident single-tone carrier power and electric field at each unit cell Un,m.The electric-field expression is referenced to.
  • Proof of Theorem 1: Energy conservation relates each unit cell’s incident power, reflection coefficient Γn,m = An,mejϕn,m, and total reflected-signal power.The reflection coefficient amplitude and phase follow the definition in (1).
  • Proof of Theorem 1: The proof derives the reflected electric field received by antenna k from unit cell Un,m using propagation, reflection phase, and the receiving-antenna aperture Ar.The propagation and reflection terms determine the phase alteration of the received component.
  • Proof of Theorem 1: The total received field at antenna k is the superposition of reflections from all unit cells, from which instantaneous received power and received signal follow.The final power expression uses the receiving-antenna aperture and the previously derived field relations.

APPENDIX B

Appendix B proves Theorem 2 by expanding the periodic signal in an exponential Fourier series and evaluating two cases based on whether Δϕ−2lπ equals zero. The proof then accounts for the circular time shift between the theorem’s baseband symbol and the signal in (51).

  • The proof begins by representing the periodic signal with its exponential Fourier series expansion.
  • The Fourier-series expression is evaluated separately when Δϕ−2lπ=0 and when Δϕ−2lπ≠0.
  • Theorem 2 follows after combining the case results and applying the Fourier-transform time-delay property to account for the circular shift t0.The baseband symbol in Theorem 2 has a circular time shift t0 relative to the signal defined in (51).
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