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Intelligent Surface-Aided Transmitter Architectures for Millimeter Wave Ultra Massive MIMO Systems

Vahid Jamali, Antonia M. Tulino, Georg Fischer, Ralf Müller, Robert Schober

arXiv:1902.07670v3cs.ITmath.IT

TL;DR

The paper targets the scalability and energy-efficiency limits of mmWave massive MIMO, where conventional and lens-array architectures require costly RF chains, analog networks, or increasing active-antenna counts. It proposes IRS/ITS-aided transmitters, models their constraints and losses, and designs MI- and OMP-based precoders. Simulations report improved achievable rate from proper active-antenna positioning and full scalability in the number of transmit antennas.

  • Problem

    MmWave massive-MIMO architectures face high RF-network or active-antenna costs as the number of transmit antennas grows.

    Source: §I · p. 1

  • Method

    The paper models IRS/ITS precoder constraints and imperfections, then designs mutual-information and OMP-based precoders exploiting mmWave channel sparsity.

    Source: §I · p. 3

  • Results

    IRS/ITS architectures achieve full transmit-antenna scalability, while proper active-antenna positioning considerably improves achievable rate.

    Source: §I · p. 3

  • Takeaways & Limitations

    Reconfigurable intelligent surfaces offer a practical route toward scalable and energy-efficient mmWave ultra-massive MIMO transmitters.

    Source: §I · p. 3, A. Conclusions · p. 19

Abstract

from arXiv · show

In this paper, we study two novel massive multiple-input multiple-output (MIMO) transmitter architectures for millimeter wave (mmWave) communications which comprise few active antennas, each equipped with a dedicated radio frequency (RF) chain, that illuminate a nearby large intelligent reflecting/transmitting surface (IRS/ITS). The IRS (ITS) consists of a large number of low-cost and energy-efficient passive antenna elements which are able to reflect (transmit) a phase-shifted version of the incident electromagnetic field. Similar to lens array (LA) antennas, IRS/ITS-aided antenna architectures are energy efficient due to the almost lossless over-the-air connection between the active antennas and the intelligent surface. However, unlike for LA antennas, for which the number of active antennas has to linearly grow with the number of passive elements (i.e., the lens aperture) due to the non-reconfigurablility (i.e., non-intelligence) of the lens, for IRS/ITS-aided antennas, the reconfigurablility of the IRS/ITS facilitates scaling up the number of radiating passive elements without increasing the number of costly and bulky active antennas. We show that the constraints that the precoders for IRS/ITS-aided antennas have to meet differ from those of conventional MIMO architectures. Taking these constraints into account and exploiting the sparsity of mmWave channels, we design two efficient precoders; one based on maximizing the mutual information and one based on approximating the optimal unconstrained fully digital (FD) precoder via the orthogonal matching pursuit algorithm. Furthermore, we develop a power consumption model for IRS/ITS-aided antennas that takes into account the impacts of the IRS/ITS imperfections, namely the spillover loss, taper loss, aperture loss, and phase shifter loss.

I. INTRODUCTION

The paper addresses mmWave massive-MIMO scalability and energy efficiency with few active antennas illuminating large reconfigurable intelligent surfaces. It develops models and precoders for these architectures and compares their scaling with conventional and lens-array designs.

I. INTRODUCTION

  • Conventional fully digital and hybrid MIMO architectures become costly or energy-inefficient as antenna counts grow because RF chains and analog networks consume substantial power.Partially connected hybrids reduce components but their power consumption still scales with the number of antennas.Source: §I · p. 1
  • Lens-array scalability is limited because increasing passive elements requires more active antennas to preserve beam-direction resolution, making implementations costly and bulky.The lens aperture controls beam narrowness, while active antennas determine the available beam directions.Source: §I · pp. 1–2
  • The proposed transmitter architectures use few RF-chain-equipped active antennas to illuminate large IRS or ITS surfaces containing low-cost passive elements.The intelligent surface is embedded in the transceiver, so the active-antenna-to-surface channel can be designed during manufacturing.Source: §I · p. 2
  • The study focuses on IRS/ITS-embedded transmitter architectures, whereas multi-user precoder and combiner design is left for future work.The considered transmitter structures can also serve as receivers by reciprocity, but receiver design is not developed here.Source: §I · p. 2
  • Unlike fixed lens arrays, reconfigurable IRS/ITS phase shifters directly control beam direction, so passive-element counts can increase without proportionally increasing active antennas.IRS reflects the phase-shifted field, whereas ITS transmits it forward; their over-the-air space feeding is described as inherently more energy efficient than analog RF feeding.Source: Figure 1 · p. 2, §I · p. 3
  • The paper models IRS/ITS precoder constraints and illumination strategies, then designs mutual-information and OMP precoders that exploit mmWave channel sparsity.The MI design provides a performance upper bound for the lower-complexity OMP design.Source: §I · p. 3
  • Its power model includes spillover, taper, aperture, and phase-shifter losses alongside digital-processing and amplifier consumption for fair architectural comparisons.The study also accounts for conventional architectures’ RF-feed and switching-network losses.Source: §I · pp. 3–4
  • Simulations report that active-antenna positioning improves achievable rate and that IRS/ITS architectures are fully scalable in transmit-antenna count relative to FD, FC, PC, and LA designs.The paper identifies these architectures as candidates for practical mmWave ultra-massive MIMO.Source: §I · p. 3

B. Transmit Signal Model

The signal model represents Q data streams precoded onto the intelligent surface under a normalized precoder and radiated-power constraint. The channel model uses a low-rank mmWave representation with a limited number of scattering paths and array steering vectors.

B. Transmit Signal Model

  • The transmitted intelligent-surface vector is generated by a precoder F from Q independent data streams, with E{ssH}=I_Q and ∥F∥F=1.F incorporates baseband processing, the active-antenna-to-surface channel, IRS/ITS imperfections, and the surface phase change.Source: B. Transmit Signal Model · p. 5
  • The model constrains the maximum power radiated by the intelligent surface into the channel, while the derivations also apply to active-antenna power constraints.The paper focuses on the former constraint for comparison with conventional MIMO architectures.Source: B. Transmit Signal Model · p. 5

C. Channel Model

  • The point-to-point channel follows y=Hx+z, where H is a low-rank channel matrix and z is additive white Gaussian noise.The receive vector has J antennas, and the noise is modeled as CN(0_J,σ^2I_J).Source: C. Channel Model · p. 5
  • The low-rank mmWave channel is formed from L effective paths with path coefficients and transmitter and receiver steering vectors indexed by their departure and arrival angles.The transmitter steering vector describes the intelligent-surface array response, with passive elements uniformly distributed on the surface.Source: C. Channel Model · p. 5

III. MATHEMATICAL MODELING OF THE IRS/ITS-AIDED MIMO ARCHITECTURES

The architecture imposes a structured precoder composed of a digital baseband matrix, a fixed propagation matrix, and a diagonal intelligent-surface phase-shift matrix. The fixed matrix depends on illumination geometry and efficiency, while the other components can be adapted using channel state information.

III. MATHEMATICAL MODELING OF THE IRS/ITS-AIDED MIMO ARCHITECTURES

  • The maximum number of independent streams is limited by the RF-chain count and the channel rank, typically yielding Q ≤ min{N, L} in sparse mmWave systems.The relevant rank bound is min{M, J, L}, while mmWave arrays typically satisfy M, J ≫ N, L.Source: A. Constraints on the Precoder · p. 6

A. Constraints on the Precoder

  • For the m-th element, the intelligent surface applies phase shift 2πβm before reflection/transmission, producing xm = ȳm√ρsrf exp(j2πβm), where ρsrf is a power-efficiency factor.The associated matrix is described as a diagonal phase-shift matrix controlling the intelligent surface.Source: A. Constraints on the Precoder · p. 6
  • The precoder has the form F = DTB, where B controls active-antenna signals, T is fixed, and D applies intelligent-surface phase shifts.B and D are adjustable during transmission, whereas T is determined during manufacturing and depends on surface efficiency, antenna gains, and positioning.Source: A. Constraints on the Precoder · p. 6
  • The matrix formulation follows by combining the active-antenna propagation relation with the surface phase operation and the baseband precoder.The efficiency factor is included in T when rewriting the signal model in matrix form.Source: A. Constraints on the Precoder · p. 6

B. Illumination Strategies

The paper compares illumination strategies that determine how active antennas couple to the intelligent surface, then models the resulting power consumption and losses. Separate illumination avoids inter-RF-chain interference, while the loss model accounts for propagation, aperture, phase-shifter, and circuit effects.

B. Illumination Strategies

  • The fixed matrix T captures illumination geometry, including active-antenna placement, orientation, distance, and surface efficiency.The framework considers full, partial, separate, blockage-free, and hypothetical uniform separate illumination.Source: B. Illumination Strategies · pp. 6–7
  • Separate illumination physically shields surface regions so each receives one active-antenna signal, avoiding the interference that remains under partial illumination.Partial illumination assigns neighboring passive-element subsets to active antennas but wide beams still illuminate other subsets.Source: B. Illumination Strategies · p. 7
  • Non-uniform received power creates taper loss and reduces achievable multi-stream rate, motivating hypothetical uniform separate illumination as a reference case.Uniform separate illumination assigns identical received powers to each active antenna’s responsible passive elements.Source: B. Illumination Strategies · p. 7

C. Power Consumption and Losses

  • The model separates spillover, taper, aperture, phase-shifter, power-amplifier, RF-chain, and baseband contributions to total consumption.Spillover reflects uncaptured radiated power; aperture loss includes reception, transmission, absorption, and unwanted-reflection inefficiencies.Source: C. Power Consumption and Losses · pp. 7–8
  • IRS phase shifters are traversed twice, whereas ITS phase shifters are traversed once, producing overall efficiencies ρP^2(β/2) and ρP(β), respectively.The paper assumes phase-shifter efficiency is practically constant across phase shifts and neglects control power for low-consumption technologies.Source: C. Power Consumption and Losses · p. 8
  • For an ideal well-conditioned T, the active-antenna radiated power equals the intelligent-surface radiated power, while total consumption does not explicitly scale with passive-element count M.In practice, the condition number and spillover efficiency can depend on surface size and antenna positioning; proper positioning can keep the condition number close to one.Source: C. Power Consumption and Losses · p. 9
  • Taper loss reduces achievable rate but is not itself a power loss.This distinction separates spectral-efficiency degradation from the power-loss terms in the consumption model.Source: C. Power Consumption and Losses · p. 9

D. Special Case

The special-case analysis uses a parameterized axisymmetric feed pattern to study spillover and taper efficiencies as functions of feed directivity and surface angular extent. It identifies a positioning regime where these losses do not scale with the number of passive elements.

D. Special Case

  • The adopted axisymmetric feed pattern is parameterized by κ, whose value represents active-antenna gain and must be jointly optimized with antenna placement and orientation.The example pattern is used for the analysis and simulations, while the derivations remain valid for general feed patterns.Source: D. Special Case · p. 9
  • Increasing κ decreases spillover loss but increases taper loss, exposing a direct trade-off in feed-pattern design.The taper efficiency is normalized so that uniform illumination gives ρT = 1.Source: D. Special Case · p. 9
  • For square surfaces, the efficiencies are approximated by replacing the square with an equal-area circular surface and using its elevation extent θ0.The equivalent angular extent depends on the distance between the active antenna and the intelligent surface.Source: D. Special Case · pp. 9–10
  • When the distance and surface size scale so that θ0 is independent of M, spillover and taper losses do not scale with M.This provides the special-case condition for maintaining loss behavior as the passive-element count grows.Source: D. Special Case · p. 10

IV. PRECODER DESIGN FOR IRS/ITS-AIDED MIMO ARCHITECTURES

The paper formulates precoder design as mutual-information maximization under the IRS/ITS structure and also considers approximation of the optimal unconstrained fully digital precoder. The resulting problem is nonconvex, so the proposed methods combine tractable digital updates with heuristic phase-shift selection based on sparse mmWave directions.

IV. PRECODER DESIGN FOR IRS/ITS-AIDED MIMO ARCHITECTURES

  • The mutual-information design maximizes R(F) = I(s; y) subject to the transmit-power constraint and the structured feasible precoder set.CSI is assumed available at the transmitter, and updates should follow the channel coherence time.Source: §IV · p. 10
  • The constrained precoder problem is nonconvex because the intelligent-surface phase-shift matrix has unit-modulus entries, preventing direct use of conventional-MIMO solutions.The feasible set F = {DTB} differs from conventional architectures because of the structured factorization and unit-modulus constraint.Source: §IV · p. 10
  • At each iteration, the digital baseband precoder is optimized globally for a fixed phase-shift matrix, while phase shifts are restricted to channel AoD directions as a heuristic.The phase-shift restriction exploits sparse mmWave channels but is not generally optimal.Source: §IV · p. 10
  • The proposed precoders are reported to outperform the benchmark IRS-aided scheme from in simulations.The comparison concerns the method that approximates the optimal fully digital precoder rather than maximizing mutual information.Source: §IV · p. 10

A. Rationale Behind the Proposed Precoders

The proposed precoders exploit the structure and sparsity of IRS/ITS channels by decomposing the passive surface into subspaces and selecting representative channel paths.

A. Rationale Behind the Proposed Precoders

  • For any precoder F, projecting onto the channel-response space preserves the rate while not increasing the Frobenius norm.This motivates restricting the design to F = H_tC, which includes the optimal fully digital precoder.Source: A. Rationale Behind the Proposed… · p. 10
  • The IRS/ITS precoder is partitioned into N components using mutually exclusive passive-element sets M_n and corresponding subspaces H_t^{M_n}.The partition enables comparison between the constrained precoder components and channel-response subspaces.Source: A. Rationale Behind the Proposed… · pp. 10–11
  • Because each D_{M_n} has fewer nonzero elements than H_t^{M_n}, exact reconstruction is impossible, so one representative channel-response column is reconstructed per subspace.The remaining columns are treated as interference, which approaches zero through channel hardening when M ≫ N.Source: A. Rationale Behind the Proposed… · p. 11
  • MI-based and OMP-based strategies select the best N channel-response columns, reducing phase-shift search from a continuous multidimensional set to NL candidates.When N, L ≪ M, exhaustive search over this reduced set can obtain an optimal phase-shift matrix for a given baseband precoder.Source: A. Rationale Behind the Proposed… · p. 11

B. MI-based Precoder

The MI-based design alternates between selecting phase-shift components and optimizing the corresponding baseband precoder to maximize mutual information.

B. MI-based Precoder

  • The MI-based precoder uses an outer loop over N surface components and an inner loop over L candidate channel paths.Each inner iteration optimizes the baseband precoder for a candidate phase-shift matrix, and the best candidate is retained.Source: B. MI-based Precoder · p. 11
  • For a fixed phase-shift matrix, the baseband optimization is reduced using the singular value decomposition of the effective channel.The resulting solution uses singular vectors and chooses the threshold to satisfy the total power constraint.Source: B. MI-based Precoder · p. 11
  • The optimized baseband precoder eliminates interference between data streams.This property follows from the stated solution of the baseband optimization problem.Source: B. MI-based Precoder · p. 11
  • The phase-shift optimization initializes each component to the identity and updates it by exhaustively testing the L-element candidate set.The candidate set cardinality makes exhaustive optimization feasible for each component.Source: B. MI-based Precoder · p. 11

C. OMP-based Precoder

The OMP-based precoder approximates the unconstrained fully digital solution with lower complexity, while both proposed algorithms scale linearly with the number of passive elements.

C. OMP-based Precoder

  • The OMP-based design approximates the optimal unconstrained FD precoder by minimizing their Frobenius-norm difference under IRS/ITS constraints.It iteratively selects phase-shift components and solves the corresponding baseband problems.Source: C. OMP-based Precoder · pp. 11–12
  • The OMP-based precoder is computationally less complex than the MI-based precoder and achieves similar performance in poor-scattering environments.The paper positions the MI-based method as the higher-complexity alternative and OMP as its efficient approximation.Source: C. OMP-based Precoder · p. 11
  • At each iteration, OMP projects the residual precoder onto the channel-response space and selects the direction with the maximum projected value.The selected phase-shift matrix is paired with a normalized least-squares baseband solution.Source: C. OMP-based Precoder · p. 12

D. Complexity Analysis

  • O(MN^2JL) and O(M(N^2 + J)L) are the respective complexity orders of the MI-based and OMP-based precoders when N = Q.Both complexities are linear in M, while OMP is lower for typical N, J > 1.Source: D. Complexity Analysis · p. 12

V. SIMULATION RESULTS

The simulations evaluate proposed and conventional architectures under modeled channel, geometry, blockage, and power-consumption assumptions, including FD, hybrid, and lens-array benchmarks.

V. SIMULATION RESULTS

  • The simulation study covers proposed-precoder performance, system-parameter effects, conventional-architecture comparisons, and imperfect-CSI performance.Results are averaged over 10^3 random channel realizations.Source: §V · p. 12, A. Simulation Setup · p. 12

A. Simulation Setup

  • Active antennas are positioned relative to the intelligent surface according to the considered illumination scenarios, with geometry scaled as the passive surface grows.The setup includes blockage-free IRS illumination and scenario-dependent scaling of R_r and R_d.Source: A. Simulation Setup · pp. 12–13

B. Benchmark Schemes

  • The benchmarks include FD, fully-connected hybrid, partially-connected hybrid, and lens-array architectures with corresponding precoder and power-consumption models.The conventional models account for architecture-specific RF-network or switching characteristics.Source: B. Benchmark Schemes · p. 13
  • Fully-connected hybrid benchmarks model RF-network losses using cascaded dividers, combiners, phase shifters, line connections, and gain-compensation amplifiers.The stated loss model includes divider and combiner stages and the associated amplification consumption.Source: B. Benchmark Schemes · p. 13
  • The partially-connected benchmark uses a block-diagonal analog precoder with equal antenna allocation across RF chains and applies the OMP design for fair comparison.Its power model excludes a power combiner and includes the corresponding divider network.Source: B. Benchmark Schemes · p. 13
  • Lens-array benchmarks include full-K and fixed-K cases, with full-K active antennas increasing linearly with the effective lens aperture.The lens-array model also includes the additional consumption of active switches.Source: B. Benchmark Schemes · p. 14

C. Performance of Proposed Precoders and Impact of the System Parameters

The proposed architectures and precoders improve spectral efficiency under favorable illumination and channel conditions while scaling passive antennas without proportionally increasing active hardware. Across comparisons, IRS/ITS-aided designs offer energy-efficiency and scalability advantages, with MI-based precoding strongest in rich-scattering tests.

C. Performance of Proposed Precoders and Impact of the System Parameters

  • The MI-based precoder outperforms OMP-based precoding, although its additional gain is small at larger M and increases in rich-scattering channels.The MI design maximizes achievable rate, while OMP approximates the optimal unconstrained FD precoder.Source: C. Performance of Proposed Precoders… · p. 14, D. Comparison of Different MIMO… · p. 17
  • PI outperforms FI because active-antenna placement reduces interference between passive-element subsets, whereas blockage-free PI suffers higher over-the-air loss and less uniform illumination.Uniform SI outperforms SI, but its additional gain is small.Source: C. Performance of Proposed Precoders… · pp. 14–15
  • SI maintains a near-ideal condition number across positioning ranges and yields better performance than FI and PI, while also simplifying hardware implementation.For SI, the condition number remains close to one; uniform SI is exactly one across the considered ranges.Source: C. Performance of Proposed Precoders… · p. 15

D. Comparison of Different MIMO Architectures

  • The proposed OMP-based precoder outperforms the AO-based precoder in by a large margin, attributed to exploiting mmWave channel sparsity rather than risking local optima.For the comparison, IRS/ITS architectures use OMP and SI; the precoder uses FI and has higher power consumption.Source: D. Comparison of Different MIMO… · pp. 15–17
  • IRS/ITS-aided architectures scale more favorably than conventional FD, FC, and PC systems because their total power remains nearly constant as M increases.FD, FC, and PC energy efficiency decreases with M, whereas IRS/ITS energy efficiency increases; the over-the-air active-passive connection drives this difference.Source: D. Comparison of Different MIMO… · pp. 15–17
  • IRS/ITS-aided MIMO with M = 1024 achieves 37.5 bits/s/Hz, matching FD and FC MIMO with M = 256 while using the scalable passive surface.Conventional architectures require substantially more power as M increases, whereas LA and IRS/ITS power remains almost constant.Source: D. Comparison of Different MIMO… · p. 16
  • At M = 256, the ITS-aided architecture with 4 active antennas outperforms the LA architecture with K = 132 active antennas.LA spectral efficiency improves with K but saturates for approximately K > M because the passive lens limits beam narrowness.Source: D. Comparison of Different MIMO… · p. 17
  • Across the tested scattering and antenna settings, the proposed MI-based precoder outperforms both the proposed OMP-based precoder and the AO-based precoder in.As L increases, the proposed methods first benefit from path-selection diversity and then decline because they select only N of L paths, unlike.Source: D. Comparison of Different MIMO… · p. 17, Figure 10 · p. 17

E. CSI Imperfection

CSI errors reduce spectral efficiency, with inaccurate AoAs/AoDs forming the main bottleneck. The paper concludes that IRS/ITS architectures are scalable and energy efficient, while future work must address receiver design, multi-user systems, and practical channel estimation.

E. CSI Imperfection

  • For small NMSE, precoders designed with estimated and perfect channels perform similarly; angle errors increasingly reduce spectral efficiency, while coefficient errors lead to saturation at a higher value.Source: E. CSI Imperfection · p. 18
  • At large NMSE, designs based on inaccurate angle information can underperform a random precoder because they transmit toward incorrect directions.Source: E. CSI Imperfection · p. 18
  • Imperfect AoAs/AoDs are the performance bottleneck when both angles and path coefficients are estimated, and their impact is similar for FD and IRS-aided architectures.Source: E. CSI Imperfection · p. 18

A. Conclusions

  • IRS/ITS-aided architectures are energy efficient through nearly lossless over-the-air coupling and scalable because they require only a few active antennas.Source: A. Conclusions · pp. 18–19

B. Future Work

  • The study focuses on transmitter precoding; receiver combining, multi-user precoding and combining, and robust or efficient channel-estimation methods remain future research directions.Source: B. Future Work · p. 19

APPENDIX A PROOF OF LEMMA 1

The appendices derive power expressions and bounds for the proposed architecture, accounting for how active-antenna radiation couples to the intelligent surface. They also establish properties used in the achievable-rate analysis.

APPENDIX A PROOF OF LEMMA 1

  • The power radiated by active antennas is derived using the precoder normalization and matrix-trace identities, yielding bounds for the consumed power.Source: Appendix A · p. 19
  • The fraction of power collected by the surface is linked to spillover and passive-antenna aperture losses, with identical active-antenna conditions producing a common expression.Source: Appendix A · p. 19

APPENDIX B PROOF OF LEMMA 2

  • The achievable rate depends only on the channel-relevant component of the precoder, while its orthogonal component does not affect the rate under the stated trace relation.Source: Appendix B · p. 20

APPENDIX C PROOF OF LEMMA 3

The appendix transforms the constrained optimization into mutual-information maximization for an equivalent channel. Under a nonsingularity assumption, the resulting baseband precoder is obtained by waterfilling.

APPENDIX C PROOF OF LEMMA 3

  • The constraint is rewritten using trace cyclicity and the equivalent channel definition, assuming C_H1 C_1 is nonsingular.Source: Appendix C · p. 20
  • The transformed problem has the form of fully digital mutual-information maximization, so waterfilling gives the optimal equivalent-channel baseband precoder.Source: Appendix C · p. 20
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