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Reconfigurable Intelligent Surface-Based Index Modulation: A New Beyond MIMO Paradigm for 6G

Ertugrul Basar

arXiv:1904.06704v3cs.ITeess.SP

TL;DR

Future wireless systems need physical-layer paradigms that address demanding 6G requirements, while RIS and index modulation offer complementary opportunities to control propagation and convey information through indices. The paper proposes RIS-SSK and RIS-SM with greedy and ML detectors and a unified error analysis. Simulations and theoretical results show high spectral efficiency at extremely low SNR values, with performance depending on indexing load, RIS size, and detector choice.

  • Problem

    The paper addresses how RIS-assisted transmission can be combined with index modulation to improve reliability and spectral efficiency for beyond-MIMO wireless systems.

  • Method

    The paper proposes RIS-SSK and RIS-SM using receive-antenna indices, formulates greedy and ML detectors, and derives a unified framework for theoretical error performance.

  • Results

    Theoretical and simulation results show accurate error-performance predictions, improved BER with larger RIS size, and detector- and configuration-dependent performance trade-offs.

  • Takeaways & Limitations

    RIS-assisted index modulation has potential to provide high spectral efficiency at extremely low SNR values through smart indexing of available receive antennas.

Abstract

from arXiv · show

Transmission through reconfigurable intelligent surfaces (RISs), which control the reflection/scattering characteristics of incident waves in a deliberate manner to enhance the signal quality at the receiver, appears as a promising candidate for future wireless communication systems. In this paper, we bring the concept of RIS-assisted communications to the realm of index modulation (IM) by proposing RIS-space shift keying (RIS-SSK) and RIS-spatial modulation (RIS-SM) schemes. These two schemes are realized through not only intelligent reflection of the incoming signals to improve the reception but also utilization of the IM principle for the indices of multiple receive antennas in a clever way to improve the spectral efficiency. Maximum energy-based suboptimal (greedy) and exhaustive search-based optimal (maximum likelihood) detectors of the proposed RIS-SSK/SM schemes are formulated and a unified framework is presented for the derivation of their theoretical average bit error probability. Extensive computer simulation results are provided to assess the potential of RIS-assisted IM schemes as well as to verify our theoretical derivations. Our findings also reveal that RIS-based IM, which enables high data rates with remarkably low error rates, can become a potential candidate for future wireless communication systems in the context of beyond multiple-input multiple-output (MIMO) solutions.

I. INTRODUCTION

The paper motivates RIS-based index modulation as a beyond-MIMO approach for future wireless systems, combining programmable wave reflection with information-bearing antenna indices. It focuses on receive-antenna indexing and develops RIS-SSK/RIS-SM schemes, detectors, error analysis, and simulations.

  • The proposed approach is positioned as a potential beyond-MIMO physical-layer paradigm for challenging future 6G communication requirements.
  • RISs use software-controlled phase shifts on passive elements to deliberately alter electromagnetic-wave propagation without dedicated RF processing, decoding, encoding, or retransmission.
  • The paper considers indexing source transmit antennas, RIS reflector regions, or destination receive antennas, then focuses on receive-antenna indexing.Source indexing requires an additional source-to-RIS signaling link, while reflector-region indexing reduces effective received signal power.
  • RIS-SSK and RIS-SM combine RIS-assisted transmission with receive-antenna index modulation to target high reliability and high spectral efficiency.
  • The proposed schemes use the RIS to boost signal quality in hostile fading channels while selecting a receive-antenna index from information bits.
  • The paper formulates greedy and maximum-likelihood detectors, derives a unified theoretical error-performance framework, and evaluates the schemes through computer simulations.

A. RIS-Assisted Space Shift Keying

RIS-SSK encodes information in the index of a receive antenna by configuring RIS phases to maximize that antenna’s received SNR. The paper compares non-coherent greedy energy detection with CSI-based ML detection and analyzes their error performance and complexity.

  • The received signal consists of the RIS-reflected carrier plus AWGN, with N reflecting elements and noise distributed as CN(0, N0).
  • Incoming log2 nR bits select receive antenna m, and the RIS sets φi = ψm,i to maximize the selected antenna’s instantaneous received SNR.
  • The greedy detector selects the receive antenna with the highest instantaneous energy and does not require channel estimation at the receiver.
  • The selected RIS phases maximize the mean of the desired signal term while giving the competing term zero mean, supporting the phase choice for error performance.
  • The ML detector uses the received signals at all destination antennas and requires CSI for exhaustive detection.
  • The ML detector requires approximately NnR^2 real multiplications, whereas greedy detection requires approximately nR real multiplications.

B. RIS-Assisted Spatial Modulation

RIS-SM combines receive-antenna index modulation with conventional amplitude/phase modulation, while offering greedy and ML detection options with different CSI and complexity requirements.

  • Scheme design: RIS-SM partitions log2 nR + log2 M bits between the selected receive-antenna index and an M-ary modulated symbol.The RIS phases encode the antenna index, while the RF source transmits the amplitude/phase-modulated symbol.
  • Detection: The greedy detector sequentially detects the receive-antenna index by energy and then demodulates the transmitted symbol.It uses the same antenna-index rule as RIS-SSK before searching for the constellation point.
  • Detection: The ML detector jointly searches over the antenna index and transmitted symbol using all received signals.This joint decision contrasts with the greedy detector’s disjoint detection of the two quantities.
  • Complexity and CSI: The RIS-SM ML detector requires full CSI and approximately (N + M)nR^2 RMs, whereas the greedy detector requires approximately (nR + M) RMs.The complexity gap follows from joint versus sequential detection.
  • Complexity and CSI: For large N and nR, the greedy detector is presented as more practical because it avoids dedicated channel estimation at D.Its practical advantage is tied to the operating regime and its reduced CSI requirement.

III. GREEDY DETECTION: PERFORMANCE ANALYSIS

This section analyzes the theoretical bit error probability of RIS-SSK and RIS-SM under greedy detection, including their asymptotic behavior.

  • Scope: The analysis derives theoretical BEP expressions for the proposed RIS-SSK and RIS-SM schemes with greedy detection.It also examines asymptotic behavior to provide additional performance insight.

A. Performance of RIS-SSK

The RIS-SSK greedy-detector analysis derives exact and approximate pairwise error probabilities, then relates them to BEP and antenna-count behavior.

  • PEP derivation: For N ≫ 1, the interfering channel sum is approximated with the central limit theorem as a complex Gaussian variable.The approximation uses independent uniformly distributed RIS phase differences and yields ˆB ∼ CN(0, N).
  • PEP derivation: The pairwise error event is expressed as P(m → m̂) = P(Y1 + Y2 − Y3 < 0).The terms are formed from non-central and central chi-square random variables associated with the selected and erroneously detected antennas.
  • Exact analysis: The exact PEP is obtained as the CDF value FY(0), with the characteristic function of the sum formed by multiplying independent-variable characteristic functions.Gil-Pelaez inversion is then evaluated numerically at y = 0.
  • Asymptotic analysis: For large N, the PEP is upper-bounded using E[Y1] ≫ E[Y2], yielding an asymptotic expression for RIS-SSK performance.This approximation targets the regime where the RIS contribution dominates the secondary term.
  • Asymptotic analysis: Increasing N suggests superior RIS-SSK index detection probability, including considerably low BEP values at relatively small SNR.The stated SNR condition is Es/N0 ≪ 10.
  • BEP calculation: For nR = 2, the PEP equals the exact BEP; for nR > 2, a union bound is used with uniform pairwise error probability.The general-case BEP accounts for Hamming distances between binary antenna-index representations.
  • BEP calculation: Under greedy detection, the PEP is independent of nR, while doubling nR doubles Pb at high SNR.This distinction separates pairwise detection behavior from the resulting bit error probability.

B. Performance of RIS-SM

The RIS-SM analysis derives error probabilities for greedy detection by combining index-detection errors with symbol errors, including constellation-dependent pairwise error behavior.

  • B. Performance of RIS-SM: RIS-SM bit-error analysis combines erroneous index detection with symbol errors conditioned on correct index detection.The formulation uses correct detection probability, symbol error probability, and erroneous index detection probability, with a conservative 50% bit-error assumption after index errors.
  • B. Performance of RIS-SM: For QPSK, the pairwise error probability is independent of the transmitted symbol.For M-QAM with M > 4, the conditional pairwise error probability depends on the transmitted constellation point, requiring averaging over symbols.
  • B. Performance of RIS-SM: The average symbol error probability is computed under correct index detection using the instantaneous received SNR and its moment-generating function.The resulting expressions support BPSK and square M-QAM constellations.
  • B. Performance of RIS-SM: At high SNR, Pb is dominated by erroneous index detection, which deteriorates with increasing nR.The analysis states Pc(m)Ps ≪ Pe(m) in this regime, so Pb ∝ Pe(m).

IV. MAXIMUM LIKELIHOOD DETECTION: PERFORMANCE ANALYSIS

The maximum-likelihood performance analysis treats RIS-SM jointly and obtains RIS-SSK by specializing the transmitted symbol to an unmodulated carrier.

  • IV. MAXIMUM LIKELIHOOD DETECTION: PERFORMANCE ANALYSIS: The ML analysis first derives RIS-SM performance and then extends the result to RIS-SSK by setting x = x̂ = √Es.This provides a common analytical treatment for both schemes.

A. Performance of RIS-SM

For ML detection of RIS-SM, the paper derives pairwise error probabilities for joint receive-antenna-index and symbol detection, handling distinct correct- and incorrect-index cases through Gaussian quadratic-form statistics.

  • A. Performance of RIS-SM: The ML detector analyzes the joint error event for receive antenna index m and transmitted symbol x.The conditional pairwise error probability is averaged over channel coefficients to obtain the unconditional result.
  • A. Performance of RIS-SM: For large N, the analysis uses complex Gaussian approximations and moment-generating functions of quadratic Gaussian forms to evaluate the PEP.The remaining term can be represented as a sum of nR − 2 independent central χ2 random variables with two degrees of freedom.
  • A. Performance of RIS-SM: The resulting unconditional PEP is independent of the particular transmitted and detected antenna indices.Numerical integration of the derived expression yields the desired PEP.
  • A. Performance of RIS-SM: The unconditional PEP depends on whether the detected receive antenna index is incorrect or correct.These cases produce different distributions and correlations among the channel-dependent terms.
  • A. Performance of RIS-SM: The BEP is obtained from a union bound that weights each pairwise event by its number of erroneous bits.The analysis is stated to apply generally to all constellations, while simplified BPSK and QPSK expressions are left for future derivation.

B. Performance of RIS-SSK

The RIS-SSK analysis specializes the ML framework to an unmodulated carrier and compares theoretical BEP behavior across increasing receive-antenna counts.

  • B. Performance of RIS-SSK: RIS-SSK conditional PEP is obtained by substituting x = x̂ = √Es, corresponding to an unmodulated baseband carrier.The unconditional PEP and BEP upper bound follow from the corresponding ML analysis with suitable modifications.
  • B. Performance of RIS-SSK: Figure 3 presents theoretical BEP performance for RIS-SSK and RIS-SM as nR increases.The comparison is made with respect to Es/N0.
  • B. Performance of RIS-SSK: For ML detection, increasing nR improves RIS-SSK and RIS-SM BER while also increasing data rate.The paper identifies a trade-off among complexity, performance, and data rate.

V. SIMULATION RESULTS

The simulations validate the theoretical BER results for RIS-SSK and RIS-SM under greedy and ML detection, while showing how system parameters and detector choice affect performance. RIS-based schemes also compare favorably with reference approaches and remain sensitive to phase-estimation accuracy.

  • Greedy detection: Theoretical BER results closely match computer simulations for RIS-SSK and RIS-SM with greedy detection.The comparison is made using the theoretical results in (23) and (24).
  • Greedy detection: Increasing bpcu, or equivalently nR, degrades the BER performance of RIS-SSK and RIS-SM with greedy detection.
  • ML detection: With ML detection, increasing nR causes little BER degradation for RIS-SSK, whereas increasing M has a more evident effect on RIS-SM; ML performance also improves with N.
  • Detector comparison: The ML detector provides approximately 2 dB improvement in required SNR for RIS-SSK in the considered setups, while the greedy–ML gap is smaller for RIS-SM at N = 128.The RIS-SSK setups are N = 64, nR = 2 and N = 128, nR = 8.
  • Reference comparisons: At 3, 4, and 6 bpcu, RIS-SSK has better BER than RIS-SM, RIS-AP cannot compete with the proposed schemes, and conventional RSSK-MIMO requires more than 15 dB higher SNR.The comparison uses ML detection; RIS-SM trades some BER performance for fewer receive antennas at the same bpcu.
  • Imperfect phase estimates: Phase-estimation accuracy affects BER: degradation is not significant for κ = 10 but becomes noticeable for κ = 5 in both proposed schemes.The phase error is modeled with a von Mises distribution.

VI. CONCLUSIONS

The paper presents RIS-assisted index modulation as a potential beyond-MIMO paradigm through RIS-SSK and RIS-SM. It supports this concept with theoretical derivations and computer simulations, while identifying receiver design, system imperfections, and richer channel models as open problems.

  • RIS-assisted IM is proposed as a potential beyond-massive-MIMO paradigm for next-generation wireless networks.
  • The proposed RIS-SSK and RIS-SM schemes are evaluated through comprehensive theoretical derivations and computer simulations.
  • Low-complexity receiver architectures and analyses involving system imperfections or more sophisticated channel and correlation models remain open research problems.
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