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Dynamic Metasurface Antennas for Uplink Massive MIMO Systems

Nir Shlezinger, Or Dicker, Yonina C. Eldar, Insang Yoo, Mohammadreza F. Imani, David R. Smith

arXiv:1901.01458v2cs.IT

TL;DR

Massive MIMO promises scalable throughput, but implementing its large antenna arrays is costly, power-intensive, and physically demanding. This paper models DMA-based uplink systems, characterizes their limits, and develops two alternating-optimization design algorithms. The resulting systems achieve performance comparable to ideal unconstrained antenna arrays while using DMA hardware that reduces implementation demands.

  • Problem

    Massive MIMO's theoretical gains are established, but practical large-scale antenna arrays face cost, power-consumption, and physical-size challenges.

  • Method

    The paper models DMA-constrained uplink MIMO channels, characterizes fundamental sum-rate limits, and derives two alternating optimization algorithms for practical DMA design.

  • Results

    Numerical analysis shows DMA-based massive MIMO performance is comparable to theoretical fundamental limits achievable with unconstrained antenna arrays.

  • Takeaways & Limitations

    DMAs can implement compact, low-cost, and low-power massive MIMO base stations while approaching ideal-array performance under the studied conditions.

Abstract

from arXiv · show

Massive multiple-input multiple-output (MIMO) communications are the focus of considerable interest in recent years. While the theoretical gains of massive MIMO have been established, implementing MIMO systems with large-scale antenna arrays in practice is challenging. Among the practical challenges associated with massive MIMO systems are increased cost, power consumption, and physical size. In this work we study the implementation of massive MIMO antenna arrays using dynamic metasurface antennas (DMAs), an emerging technology which inherently handles the aforementioned challenges. Specifically, DMAs realize large-scale planar antenna arrays, and can adaptively incorporate signal processing methods such as compression and analog combining in the physical antenna structure, thus reducing the cost and power consumption. We first propose a mathematical model for massive MIMO systems with DMAs and discuss their constraints compared to ideal antenna arrays. Then, we characterize the fundamental limits of uplink communications with the resulting systems, and propose two algorithms for designing practical DMAs for approaching these limits. Our numerical results indicate that the proposed approaches result in practical massive MIMO systems whose performance is comparable to that achievable with ideal antenna arrays.

I. INTRODUCTION

Massive MIMO offers scalable throughput but practical large antenna arrays face cost, power, and size constraints. The paper studies DMA-based uplink systems, modeling their physical constraints, characterizing performance limits, and designing practical configurations that approach ideal-array performance.

  • Massive MIMO can increase throughput scalably with the number of base-station antennas, but standard large-scale arrays are difficult to implement because of cost, power, and physical-size constraints.
  • Prior approaches reduce hardware demands through analog combining, low-resolution quantization, antenna selection, or efficient power amplifiers, but assume a fixed optimal antenna array.
  • DMAs combine antenna design with reconfigurable analog combining, compression, and antenna selection, enabling compact, low-cost, and spectrally efficient massive MIMO base stations.
  • The proposed DMA model incorporates element frequency response, waveguide propagation, and mutual coupling into an equivalent channel with frequency selectivity and constrained linear combining.
  • When channels are frequency flat and element frequency selectivity is identical, DMA arrays with at least as many DMAs as user terminals can approach ideal unconstrained-array sum-rate limits.
  • Alternating optimization algorithms configure practical DMAs for the analyzed scenarios, and numerical results show performance comparable to theoretical limits achieved with larger, costlier, and more power-intensive unconstrained arrays.

A. Dynamic Metasurface Antennas

A DMA uses tunable subwavelength radiators fed by microstrips, with each microstrip producing one RF-chain output through physically constrained linear combining. Its model captures filtering, propagation-induced frequency selectivity, spatial correlation, and configurable compression while reducing hardware requirements relative to standard arrays.

  • Metasurface antennas use subwavelength metamaterial radiators excited by waveguides or cavities, while DMAs electrically tune their radiators through independently addressed switchable components.
  • Each microstrip feeds one RF chain, whose digital output is a linear combination of radiation observed by its metamaterial elements.
  • Metamaterial elements typically impose bandpass filtering, which may be treated as frequency flat over relevant communication bandwidths; at 1.9 GHz, quality factor 30 corresponds to 63 MHz bandwidth.
  • Propagation along each microstrip contributes a frequency-dependent phase and is modeled as a causal finite-impulse-response filter with complex taps and finite memory.
  • The DMA model represents K microstrips with L elements each, mapping the element observations y[i] to K-dimensional outputs z[i] while allowing spatially correlated inputs.
  • Tunable coefficients follow feasible amplitude or binary-amplitude sets, while DMA structure also imposes filtering, spatial correlation, and adjustable signal compression.
  • With one RF chain and ADC per microstrip, DMAs reduce cost, memory usage, and power consumption by a factor of L relative to standard arrays with one chain and ADC per radiator.

B. System Model

The system models uplink multi-user MIMO with a DMA at the base station, where the DMA maps the received signal to a lower-dimensional decoding output under frequency-selective and structural constraints. Performance is evaluated using achievable average sum-rate, with optimal MIMO providing an unconstrained-array reference.

  • System configuration: The uplink system has a base station equipped with a DMA serving multiple user terminals.The DMA receives the wireless-channel output and produces a vector used to decode the transmitted signals.
  • System configuration: A DMA with K microstrips and L elements per microstrip uses N = K · L radiating elements and serves U ≤ N user terminals.
  • Channel and DMA model: The channel model includes frequency-selective wireless propagation, while the DMA operation adds metasurface frequency selectivity and constrained linear processing.The model explicitly differs from memoryless massive-MIMO formulations by accounting for channel memory and frequency selectivity.
  • Performance metric: The DMA output is a deterministic mapping of the wireless-channel output, so optimal MIMO cannot have a smaller achievable sum-rate than the DMA system.This comparison follows from the data processing inequality for the information-stable channel.
  • Performance metric: Achievable average sum-rate is the paper’s fundamental performance metric, defined through increasingly long multi-user codes with vanishing error requirements.

III. ACHIEVABLE AVERAGE SUM-RATES

The section characterizes achievable average sum-rates for DMA-based channels and relates them to fundamental limits obtained with optimal unconstrained antenna arrays. It also identifies the difficulty of optimizing DMA weights under integration and structural constraints.

  • Theorem 1 gives the maximal achievable average sum-rate for a fixed DMA weights matrix Q.
  • The rate characterization incorporates DMA operation into the channel and treats the resulting system as a finite-memory multiple-access channel.
  • The corresponding optimal-MIMO corollary provides the fundamental performance limits achievable with unconstrained antenna arrays.
  • DMA weight optimization is generally difficult because of the integration operation and structural constraints on Q.
  • The analysis therefore first considers identical metasurface frequency-selectivity profiles and frequency-flat wireless channels.

A. Optimal Weights for Flat Channels with Identical Frequency Selectivity

For flat channels with identical frequency selectivity, the achievable rate depends on Q through a whitened-channel subspace, enabling an unconstrained optimum based on dominant eigenvectors. With enough microstrips, this optimum reaches the fundamental MIMO limits, although additional microstrips increase system costs.

  • Rate dependence on the weights: The achievable average sum-rate depends on Q only through the first K right eigenvectors of the transformed matrix ˜Q = QC1/2_W.
  • Unconstrained optimum: When Q is unrestricted, the maximal achievable average sum-rate is obtained by selecting the dominant eigenvector subspace of ˜G.
  • Unconstrained optimum: Increasing K beyond rank(˜G) does not improve the optimal sum-rate.
  • Unconstrained optimum: When K ≥ rank(˜G), the optimized DMA sum-rate achieves the fundamental MIMO limits.
  • Interpretation of the optimal weights: Each additional microstrip requires an RF chain and ADC, increasing cost, power usage, and memory requirements.
  • Interpretation of the optimal weights: The optimal weights first whiten noise and then project onto the least noisy subspace identified by the largest singular values of the whitened channel.

B. Practical Design for Flat Channels with Identical Frequency Selectivity

The section develops an alternating-minimization design for feasible DMA weights in flat channels with identical frequency selectivity. It approximates the unconstrained optimum while accounting for structural and coefficient constraints.

  • Constrained approximation: The unconstrained optimal weight matrix ignores DMA structure constraints, so the design seeks the closest feasible matrix in Frobenius norm.The feasible set restricts both the matrix structure and its nonzero coefficients.
  • Alternating minimization: Algorithm 1 alternates optimization over the DMA weights, unitary matrix, and diagonal matrix until convergence.The alternating optimization is guaranteed to converge because the Frobenius-norm objective is differentiable.
  • Alternating minimization: The unconstrained optimum achieves the same sum-rate for any settings of the auxiliary unitary and diagonal matrices, enabling feasible approximations near the optimum.These auxiliary matrices are used as optimization variables to reduce the distance to a feasible weight matrix.
  • Extension to frequency selectivity: For arbitrary frequency selectivity, the sum-rate is approximated by a log-det expression analogous to the identical-selectivity case.The equivalent weights matrix is constrained to the form I_B ⊗ Q, and the same design principles can be reused.
  • Extension to frequency selectivity: The arbitrary-selectivity formulation therefore adapts the identical-selectivity DMA design while imposing the additional block-structured constraint on the weights.The approximation converges to the actual sum-rate as the number of frequency samples increases.

QAM2 (M)

This section extends the DMA design to arbitrary frequency-selectivity profiles and characterizes an upper bound for evaluating practical configurations. The resulting algorithm adapts the identical-selectivity design under a block-repetition constraint.

  • Algorithm 2: Algorithm 2 adapts Algorithm 1 by replacing the matrices with their block-diagonal frequency-sampled counterparts.Its alternating updates repeatedly compute Q, the unitary factor, and the diagonal factor until termination.
  • Performance bound: The optimal average sum-rate is upperbounded by a formulation that permits frequency-selective DMA weights.The bound assumes a nonsingular Γ(ω) for every frequency.
  • Performance bound: Because practical DMA weights are frequency-invariant, the system generally cannot attain this upper bound.The bound effectively permits cancellation of channel and microstrip frequency selectivity through frequency-selective weights.
  • Numerical implication: The practical DMA design achieves an average sum-rate within a reasonable gap of the upper bound, with both curves scaling similarly with SNR.This comparison is reported for the numerical evaluations using Algorithm 2.
  • Performance bound: When K is at least the rank of the relevant frequency-dependent matrix at every frequency, the upper bound coincides with the fundamental performance limits.This identifies a condition under which the bound is tight relative to the stated limits.

IV. NUMERICAL STUDY

The numerical study evaluates DMA designs in uplink multi-user MIMO channels under flat and frequency-selective conditions. It compares constrained weights with unconstrained, analog-combining, and switching baselines using Monte Carlo simulations.

  • Simulation setup: The simulated cell serves 10 user terminals uniformly in a 400 m-radius hexagonal cell, excluding a 20 m-radius region around the base station.The channel is modeled in a rich-scattering environment.
  • Channel and noise model: The channel model includes exponentially decaying multipath, subwavelength-induced spatial correlation, and shadow fading with an 8 dB standard deviation.Noise covariance accounts for coupling between DMA elements.
  • Channel and noise model: The spatial-correlation model uses Jakes’ model with element spacing of 0.2 wavelength within each microstrip.The model assumes radiating patterns share the same azimuth.
  • Compared configurations: The study evaluates unconstrained, amplitude-only, and binary-amplitude DMA weights as separate achievable average sum-rate configurations.The corresponding feasible sets are Q = C, Q = [0.001, 5], and Q = {0, 0.1}.
  • Compared configurations: For frequency-flat scenarios, the study also compares DMAs with fully connected phase-shift and switching analog-combining networks using K RF chains.The analog-combining results are averaged over 1000 Monte Carlo simulations.

A. Flat Channel with Identical Frequency Selectivity

For flat channels with identical frequency selectivity, practical DMA receivers approach unconstrained-array performance, with small gaps that vary with microstrip count and weight constraints.

  • The Lorentzian-constrained phase restriction causes negligible loss for L = 10 across SNR values and for L = 15 above 15 dB.
  • For K > 3, the optimal performance remains constant, while DMA-based performance can increase as additional microstrips improve feasible weight-matrix approximation.
  • Increasing microstrip elements can increase propagation attenuation, so practical designs must balance RF-port cost, losses, and performance.
  • Binary amplitude weights achieve roughly the same performance as continuous-valued amplitude weights.
  • Overall, DMA sum-rate is comparable to costly unconstrained arrays and is not smaller, and can be larger, than standard fully connected analog combiners.

B. Varying Frequency Selectivity

For frequency-selective channels, DMA performance scales similarly to the theoretical limit with SNR but remains separated by an approximately 10 dB SNR gap. With signal propagation inside microstrips, increasing the number of microstrips worsens performance, while binary amplitude settings perform roughly like other feasible settings.

  • Frequency-selective channels: Approximately 10 dB in SNR separates the DMA performance from the upper bound on maximal achievable performance.The gap is attributed to frequency selectivity induced by the metasurface that cannot be mitigated through the coefficient matrix Q.
  • Frequency-selective channels: The frequency-selective DMA achieves performance that scales similarly to the theoretical limit as SNR increases.The achievable performance remains comparable with the theoretical limit despite a gap.
  • Microstrip scaling: Increasing the number of microstrips worsens performance when signal propagation inside the microstrip is modeled.Additional attenuation from more elements in each microstrip impairs the base station's ability to recover messages.
  • Microstrip scaling: Binary amplitude settings achieve roughly the same performance as the other feasible settings Q.This makes binary amplitude an appealing candidate for practical implementations.
  • Future design: The results indicate that varying DMA element frequency responses could substantially improve performance in frequency-selective channels.The observed gap between the frequency-selective-weight upper bound and fixed-weight performance motivates future DMA design work.
  • Scope: The paper studies uplink massive MIMO with DMAs and proposes two algorithms for designing practical DMAs across channel conditions.The algorithms target frequency-flat channels with common element selectivity and general multipath channels with arbitrary selectivity profiles.

APPENDIX A. Proof of Theorem 1

The proof models the DMA-based system as a finite-memory Gaussian multiple-access channel. Its achievable average sum-rate then follows from the power spectral densities of the transmitted signal, effective noise, and channel response.

  • Channel representation: The DMA operation is incorporated into the massive MIMO channel to establish the theorem.The proof begins by writing the DMA operation as part of the channel model.
  • Gaussian MAC: The effective noise is a stationary proper-complex Gaussian process with finite memory, so the model becomes a finite-memory Gaussian MAC.The memory is finite because it is bounded by mh+mg.
  • Rate expression: The achievable average sum-rate is derived using the power spectral densities of the input, effective noise, and channel response.The proof identifies these quantities as Sx(ω), S_w̃(ω), and the DTFT of the channel impulse response.
  • Conclusion: The resulting expression coincides with equation (7), completing the theorem proof.The equality follows after using the stated input and noise covariance assumptions.

B. Proof of Lemma 2

The lemma's minimization separates across matrix entries and diagonal components, while the unitary component is solved through a unitary Procrustes problem. These steps yield the optimizer specified by the lemma.

  • Entry-wise optimization: Because the feasible set Q_K×N is defined entry-wise, minimizing the Frobenius norm reduces to entry-wise projection.The proof applies this property to equality (15a).
  • Diagonal optimization: The minimizing diagonal matrix in (15c)–(15d) is obtained by optimizing its diagonal components.The proof then specifies the optimal setting subject to the stated lower-bound constraint.
  • Unitary optimization: The minimizing unitary matrix in (15b) follows from the unitary Procrustes problem.This completes the proof of the lemma.

C. Proof of Proposition 1

The proposition is proved by allowing the DMA coefficient matrix to vary with frequency and reformulating it through a transformed matrix. A frequency-wise upper bound then establishes the result.

  • Frequency-dependent weights: The proposition replaces the fixed coefficient matrix Q with a frequency-dependent matrix Q(ω).This models frequency-selective DMA weights.
  • Matrix transformation: The transformed matrix Q̃(ω) is defined as Q(ω)Γ(ω), and Q(ω) can be recovered because Γ(ω) is non-singular.This change of variables supports the proposition's rate bound.
  • Upper bound: The result follows by upper-bounding the integrand separately for every frequency ω.The proof invokes Corollary 2 for the frequency-wise bound.
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