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A Fully Wave-Domain Wideband MU MIMO OFDM Transmitter via Stacked Intelligent Metasurfaces

Zheao Li, Jiancheng An, Chau Yuen

arXiv:2609.09727v1eess.SPcs.AR

TL;DR

Conventional wideband MU-MIMO OFDM transmitters retain digital baseband waveform generation, and existing SIM designs do not synthesize the complete transmitter chain. This paper uses cascaded SIMs to realize symbol loading and precoding, then IDFT and CP insertion, in the wave domain; its SE-oriented SIM1 slightly outperforms digital-ZF in the low-power regime.

  • Problem

    Existing SIM-based wideband systems use SIM mainly for spatial processing while retaining digital-baseband IDFT and CP insertion, leaving the complete transmitter chain unrealized in the wave domain.

    Source: §I · p. 2

  • Method

    A cascaded SIM architecture assigns channel-adaptive symbol loading and precoding to SIM1 and offline-configured wave-domain IDFT and CP materialization to SIM2.

    Source: §I · p. 2, A. Offline SIM2 Design for Wave-Domain… · p. 5

  • Results

    The proposed SE-oriented SIM1 optimization slightly outperforms the digital-ZF benchmark in the low-power regime.

    Source: E. Sum Spectral Efficiency versus… · p. 12

  • Takeaways & Limitations

    The architecture provides an alternative physical realization of the conventional MU-MIMO OFDM transmitter, with spatial precoding and temporal waveform synthesis mapped to distinct wave-domain blocks.

    Source: §VI · p. 12

Abstract

from arXiv · show

This paper proposes an advanced realization principle for wideband multiuser multiple-input multiple-output orthogonal frequency-division multiplexing (MU-MIMO OFDM) transmitters, where the conventional transmitter-side baseband chain is physically synthesized in the wave domain. For design and optimization purposes, this fully wave-domain wideband MU-MIMO OFDM transmitter implemented by a cascaded SIM structure is functionally partitioned into two cascaded SIM blocks. The first block, denoted as SIM_1, integrates symbol loading and channel-adaptive MU-MIMO precoding updated at the channel-coherence timescale, mapping the user streams to a virtual port-subcarrier representation. The second block, denoted as SIM_2, acts as an offline-configured sampling-rate modulator that materializes the inverse discrete Fourier transform (IDFT) and cyclic prefix (CP) insertion directly in the wave domain. This baseband-free architecture establishes a virtual-to-physical transition from information bits to radiated CP-extended OFDM waveforms. To account for practical nonidealities, SIM_2 is optimized to fit the ideal multi-port CP-OFDM operator, and its residual response is mapped into an effective coupling matrix. Then, SIM_1 is optimized in a communication-oriented manner by jointly adapting discrete phase shifts and stream-subcarrier power loading to maximize the sum spectral efficiency. Results demonstrate the convergence, architecture trade-off, wave-domain OFDM materialization accuracy, and competitive performance of the proposed baseband-free transmitter.

I. INTRODUCTION

Conventional wideband MU-MIMO OFDM transmitters retain a costly digital baseband waveform-generation chain, and existing SIM designs do not synthesize that complete chain. The paper proposes cascaded SIM blocks that move symbol loading, precoding, IDFT, and CP insertion into wave-domain processing.

I. INTRODUCTION

  • As antenna, user, and subcarrier counts grow, conventional transmitters face substantial baseband-computing complexity, RF-chain cost, stringent DAC requirements, and power consumption.The digital chain performs stream loading, subcarrier-wise precoding, IDFT, and CP insertion before DAC conversion.Source: §I · p. 1
  • Prior SIM designs mainly provide spatial processing, while wideband SIM systems still perform IDFT and CP insertion in digital baseband.This leaves the complete transmitter-side MU-MIMO OFDM chain unrealized in the wave domain.Source: §I · pp. 1–2
  • The proposed cascaded SIM architecture assigns channel-adaptive symbol loading and MU-MIMO precoding to SIM1, and wave-domain CP-OFDM materialization to SIM2.This shifts transmitter-side processing from digital baseband to programmable electromagnetic propagation.Source: §I · p. 2

A. Architecture Overview and Design Rationale

  • SIM1 adapts at the channel-coherence timescale, whereas channel-independent SIM2 materializes the waveform at the sampling timescale and can be optimized offline.The two blocks can be consecutive regions of one integrated multilayer metasurface device.Source: A. Architecture Overview and Design… · p. 3
  • SIM1 outputs a virtual space-frequency representation; SIM2 converts it into a temporal waveform, after which receiver-side CP removal and DFT yield physical OFDM subcarriers.The subcarrier indices before SIM2 denote logical OFDM modes, not physical frequencies.Source: A. Architecture Overview and Design… · pp. 3–4

B. SIM1-Based Symbol Loading and MU-MIMO Precoding

SIM1 combines symbol loading, stream-subcarrier power loading, and channel-adaptive MU-MIMO precoding to produce virtual space-frequency outputs. Its layered propagation and block-diagonal structure preserve separable virtual subcarrier branches.

B. SIM1-Based Symbol Loading and MU-MIMO Precoding

  • SIM1's layer 0 loads symbols onto a common carrier and applies nonnegative power-loading coefficients by user stream and virtual subcarrier.Subsequent layers perform channel-adaptive precoding, with the final layer providing an NK-dimensional virtual-port interface.Source: B. SIM1-Based Symbol Loading and… · p. 4
  • SIM1's propagation matrices connect the symbol-loading layer, hidden M1-dimensional layers, and final NK-dimensional virtual-port layer.The inter-layer matrix entries are determined by propagation geometry, including meta-atom area, spacing, and propagation distance.Source: B. SIM1-Based Symbol Loading and… · p. 4
  • A block-diagonal SIM1 constraint suppresses mappings across virtual subcarrier branches, with each precoding block P[k] assigned to one virtual subcarrier.This preserves separability of virtual OFDM modes before SIM2 materializes the waveform.Source: B. SIM1-Based Symbol Loading and… · p. 4
  • The virtual output xv is formed by applying the phase-controlled precoder P(Φ) to the power-loaded stacked stream vector.The phase shifts are layer-wise, and each P[k] column corresponds to a user-stream precoder on virtual subcarrier k.Source: B. SIM1-Based Symbol Loading and… · p. 4

C. SIM2-Based Wave-Domain OFDM Modulation

SIM2 is a high-speed spatio-temporal modulator that transforms SIM1's virtual port-subcarrier vector into radiated CP-extended OFDM waveforms. During each block, it applies a sampling-period-matched sequence of phase patterns.

C. SIM2-Based Wave-Domain OFDM Modulation

  • SIM2 materializes IDFT and CP insertion directly in the wave domain by transforming SIM1's NK-dimensional virtual port-subcarrier vector.It is reused during online transmission as a high-speed modulator.Source: C. SIM2-Based Wave-Domain OFDM… · p. 4
  • SIM2's layers connect an NK-port input through hidden M2-dimensional layers to the N physical transmit ports.The inter-module propagation matrix U1 connects SIM1's virtual output interface to SIM2's independently programmable input layer.Source: C. SIM2-Based Wave-Domain OFDM… · p. 4
  • Across one CP-extended OFDM block, SIM1's virtual excitation stays constant while SIM2 applies T phase patterns at intervals matched to sampling period Ts.The block length is T = K + N_CP.Source: C. SIM2-Based Wave-Domain OFDM… · pp. 4–5
  • Stacking SIM2's time-indexed operators yields the overall modulation operator that produces the transmitted N-dimensional waveform at each time index.The waveform spans one CP-extended OFDM block.Source: C. SIM2-Based Wave-Domain OFDM… · p. 5

D. Wideband Receiver Model

The receiver model describes a frequency-selective wideband channel from physical transmit ports to single-antenna users. Under perfect synchronization and ideal OFDM materialization, CP removal and DFT yield a nominal subcarrier-decoupled model.

D. Wideband Receiver Model

  • Each user's received signal before CP removal is the linear convolution of the transmitted waveform with D discrete-time channel taps, plus receiver AWGN.The frequency-domain channel can also be expressed using dominant paths, steering vectors, and path gains.Source: D. Wideband Receiver Model · p. 5
  • With perfect synchronization, standard CP removal and K-point DFT produce the frequency-domain channel representation for each subcarrier.Under ideal SIM2 materialization, the resulting nominal model is subcarrier-decoupled.Source: D. Wideband Receiver Model · p. 5
  • The nominal model is an ideal benchmark; the actual received signal includes residual cross-subcarrier coupling from nonideal SIM2 materialization.The model assumes a sufficiently long CP removes inter-block interference and treats frequency-domain noise as Gaussian.Source: D. Wideband Receiver Model · p. 5

III. PROBLEM FORMULATION

The architecture separates channel-adaptive SIM1 processing from offline SIM2 synthesis of the CP-OFDM modulation operator. SIM2 is fitted under practical hardware constraints, and its calibrated residual coupling is carried into online design.

III. PROBLEM FORMULATION

  • SIM1 is optimized online under the fixed residual coupling produced by offline SIM2 design.The coupling is embedded in the end-to-end system model.Source: §III · p. 5

A. Offline SIM2 Design for Wave-Domain OFDM Modulation

B. SIM2-Induced Effective OFDM-Domain Coupling

The fitted SIM2 response is converted into a fixed OFDM-domain coupling operator after receiver-side CP removal and DFT. Its off-diagonal blocks capture residual cross-subcarrier leakage that the online design must account for.

B. SIM2-Induced Effective OFDM-Domain Coupling

  • With CP length N_CP ≥ D − 1, CP stripping removes inter-block interference and leaves circular convolution over each OFDM block.The receiver then applies CP removal and the normalized K-point DFT.Source: B. SIM2-Induced Effective OFDM-Domain… · p. 6
  • The effective operator T⋆ is formed from the optimized SIM2 configuration and its calibrated response.It is represented block-wise across subcarriers.Source: B. SIM2-Induced Effective OFDM-Domain… · p. 6
  • Diagonal blocks T⋆[k,k] describe inband mapping, while off-diagonal blocks quantify residual cross-subcarrier coupling from imperfect OFDM materialization.Under ideal conditions T⋆ = I_NK; practical SIM setups must account for leakage in online design.Source: B. SIM2-Induced Effective OFDM-Domain… · p. 6
  • For a fitted SIM2 satisfying CP consistency with small residual error, the effective received-signal model is described as accurate.It captures integrated power loading, SIM1 precoding, SIM2-induced coupling, and the physical wideband channel; leakage contributes a distinct interference term.Source: B. SIM2-Induced Effective OFDM-Domain… · pp. 6–7

C. Joint SIM1 Phase and Power Optimization

The framework jointly adapts SIM1 phase shifts and symbol-loading powers to maximize sum spectral efficiency under the fixed SIM2 coupling. It also uses offline SIM2 phase refinement to produce the reusable coupling matrix.

C. Joint SIM1 Phase and Power Optimization

  • SIM1 jointly optimizes discrete phase shifts and stream-subcarrier power coefficients for sum spectral efficiency under the actual channel and fixed SIM2 coupling.The resulting non-convex design adapts physical SIM1 behavior to the end-to-end communication environment.Source: C. Joint SIM1 Phase and Power… · p. 7

IV. PROPOSED OPTIMIZATION FRAMEWORK

  • The two-stage alternating-optimization framework first synthesizes SIM2 offline, then optimizes SIM1 phase responses and power loading online under fixed T⋆.The online objective is sum spectral efficiency.Source: §IV · p. 7

A. Offline Optimization of SIM2

  • SIM2 phase design uses a continuous-phase Adam-PGD warm-up followed by quantization and exact element-wise discrete refinement.The warm-up uses projected gradient steps before the E-BCD refinement.Source: A. Offline Optimization of SIM2 · p. 7
  • Alternating updates of the scaling coefficients and SIM2 phase vectors yield the offline solution and its effective OFDM-domain coupling matrix.The phase refinement operates over a finite discrete codebook.Source: A. Offline Optimization of SIM2 · pp. 7–8

B. Online Optimization of SIM1 Under Fixed T⋆

With T⋆ fixed, SIM1 maximizes sum spectral efficiency over its phase shifts and power coefficients. Fractional programming reformulates the coupled objective so auxiliary variables, powers, and phases can be updated in alternation.

B. Online Optimization of SIM1 Under Fixed T⋆

1) FP-Based Equivalent Reformulation

  • The reformulation applies a Lagrangian dual transform and a multidimensional complex quadratic transform to decouple the fractional objective.Auxiliary variables η and y are introduced for the equivalent objective.Source: 1) FP-Based Equivalent Reformulation · p. 8
  • The equivalent problem alternately updates auxiliary blocks (η, y), power coefficients ρ, and phase shifts Φ.For fixed Φ and ρ, the optimal η variables are explicit; the quadratic-transform variable also has a closed form for fixed blocks.Source: 1) FP-Based Equivalent Reformulation · p. 8

2) Power-Loading Update

The power-loading update derives stream-subcarrier allocations using KKT conditions and a bisection-selected global power level. SIM1 phase optimization alternates continuous projected-gradient updates with discrete coordinate refinement, alongside auxiliary-variable updates under the fixed coupling matrix.

2) Power-Loading Update

  • KKT conditions yield nonnegative power-loading coefficients, with zero allocation when the corresponding linear coefficient is nonpositive.For active stream-subcarrier pairs, complementary slackness sets the nonnegativity multiplier to zero.Source: 2) Power-Loading Update · p. 8
  • A bisection search selects the global water level to satisfy the total power constraint.Source: 2) Power-Loading Update · p. 8

3) Layer-Wise Phase Optimization of SIM1

  • Each SIM1 phase layer receives an Adam-based projected-gradient warm-up, followed by discrete refinement using nearest feasible codewords.The coordinate-wise update exactly maximizes its localized subproblem; sweeping the coordinates refines the layer's discrete phases.Source: 3) Layer-Wise Phase Optimization of SIM1 · pp. 8–9
  • The online procedure alternates phase-layer updates with auxiliary-variable updates to optimize SIM1 under the fixed residual coupling matrix.Source: 3) Layer-Wise Phase Optimization of SIM1 · p. 9

V. RESULTS AND ANALYSIS

The evaluation uses a four-user, 16-subcarrier wideband MU-MIMO OFDM downlink and a two-stage optimization procedure. The specified default SIM configurations use seven SIM1 layers and nine SIM2 layers, each with hidden width 160 and six-bit phase resolution.

A. Simulation Setup

  • The simulated downlink serves four single-antenna users over 16 subcarriers using six transmit ports, four channel taps, and a cyclic prefix of length four.The carrier frequency is 28 GHz, bandwidth is 100 MHz, and total transmit power is 20 dBm.Source: A. Simulation Setup · p. 9
  • The two-stage framework first optimizes SIM2 offline and computes its fixed coupling matrix, then optimizes SIM1 online.Source: A. Simulation Setup · p. 9
  • The online stage alternates auxiliary-variable and power updates with projected-gradient warm-up and discrete phase updates until convergence.Source: A. Simulation Setup · p. 9
  • The default setup uses SIM1 with seven layers and width 160, and SIM2 with nine layers and width 160; both use six-bit phase resolution.Source: A. Simulation Setup · p. 9

B. Convergence and Phase-Resolution Analysis of SIMs

The reported studies examine solver convergence, phase resolution, SIM architecture trade-offs, and wave-domain CP-OFDM fidelity. Under the tested configurations, six-bit phase control closely tracks continuous-phase references, while increasing SIM depth and width improves performance until gains saturate.

B. Convergence and Phase-Resolution Analysis of SIMs

  • The SIM2 fitting error falls rapidly during continuous-phase warm-up, while quantization floors differ by phase resolution; six-bit performance stays close to the continuous-phase reference.One- and two-bit phase control produce severe quantization loss, while four-bit resolution significantly reduces fitting error.Source: B. Convergence and Phase-Resolution… · pp. 9–10, Figure 3 · p. 10
  • Under ideal SIM2, all SIM1 solver curves converge within a small number of outer iterations, and sum spectral efficiency rises with phase resolution.The six-bit curve nearly overlaps the continuous-phase reference and approaches digital-ZF.Source: B. Convergence and Phase-Resolution… · p. 10, Figure 4 · p. 10

C. Architecture Configuration of SIMs

  • SIM2 accuracy improves and ICI-to-desired power decreases as depth and width increase, with gains slowing beyond L2 = 9 and around M2 = 160.The study identifies these settings as a favorable balance between fitting accuracy and hardware complexity.Source: C. Architecture Configuration of SIMs · p. 10, Figure 5 · p. 10
  • At SIM1 depth L1 = 7 and width M1 = 160, performance gains have largely saturated, with normalized spectral efficiency near digital-ZF and residual MUI significantly suppressed.These settings are selected as a cost-effective configuration.Source: C. Architecture Configuration of SIMs · pp. 10–11, Figure 6 · p. 10
  • More than 99% of recovered energy remains on the desired subcarrier for selected tones, and the fitted SIM2 waveform closely overlaps the ideal CP-extended waveform.The frequency-domain responses preserve neighboring-subcarrier zerocrossings; the time-domain comparison covers both useful and CP intervals.Source: Figure 7 · p. 11, C. Architecture Configuration of SIMs · p. 11
  • The leakage map distinguishes intra-subcarrier MUI from cross-subcarrier ICI: SIM1 imperfections produce localized spatial leakage, while SIM2 imperfections produce global cross-subcarrier leakage.The displayed map suppresses the desired main-diagonal entries to expose residual interference.Source: C. Architecture Configuration of SIMs · p. 11, Figure 8 · p. 11

E. Sum Spectral Efficiency versus Transmit Power

The proposed SIM1 optimizer slightly exceeds digital ZF at low transmit power and remains competitive without digital baseband precoding; its performance reflects residual MUI and SIM2-induced ICI.

E. Sum Spectral Efficiency versus Transmit Power

  • The architecture comparison includes ideal digital-ZF and dynamic-subarray hybrid benchmarks, plus SIM cascades that isolate SIM1 and SIM2 losses.The digital-ZF and hybrid baselines share the same total-power constraint and FP/KKT stream-subcarrier power-loading routine.Source: E. Sum Spectral Efficiency versus… · pp. 11–12
  • At low transmit power, the proposed SIM1 optimizer slightly outperforms digital ZF, while residual MUI and SIM2-induced ICI drive high-power interference limitation.Scaled ZF-fitted SIM1 improves high-power behavior but uses auxiliary per-subcarrier fitting gains not adopted in the proposed design.Source: E. Sum Spectral Efficiency versus… · p. 12
  • FP/KKT power loading with PGD/E-BCD phase optimization achieves the highest sum spectral efficiency over almost the entire transmit-power range.The comparison attributes gains to interference-aware loading and discrete phase refinement; water-filling performs similarly at low power but can saturate or decline at high power.Source: E. Sum Spectral Efficiency versus… · p. 12, Figure 10 · p. 12

VI. CONCLUSION

  • The conclusion attributes the remaining performance gap to residual MUI from SIM1 and residual ICI from SIM2, and reports diminishing returns from added SIM depth or width.Simulations also validate convergence, phase-resolution behavior, architecture trade-offs, CP-OFDM materialization accuracy, and spectral-efficiency performance.Source: §VI · p. 12
  • Practical deployment remains contingent on further study of metasurface control, broadband dispersion and loss, calibration, mutual coupling, and robustness to hardware and CSI uncertainty.The paper points to prototype-driven EM co-design and robust wave-domain optimization as future research directions.Source: §VI · pp. 12–13
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