PaperlayerView exact revision on arXiv

Source-linked AI summary

Pinching-Antenna Differential Spatial Modulation with RSSI-Assisted Selection and Low-Complexity Detection: Methods and Performance Analysis

Yusuf Akar, Mahmoud Raeisi, Henk Wymeersch, Mikko Valkama, Ertugrul Basar

arXiv:2609.37305v1eess.SP

TL;DR

Existing PA-assisted IM/SM commonly requires instantaneous CSI, while PA-DSM also faces PA-subset selection and a joint permutation-symbol search. The paper combines differential signaling, RSSI-assisted selection, and a PSK-specialized LC-ML detector. The detector matches exhaustive detection, and the analysis shows that prior-state alignment can affect the LoS contribution without changing pairwise rank or eigenvalues.

Abstract

from arXiv · show

Pinching antenna (PA) systems provide macroscopic spatial reconfigurability by enabling signal radiation from favorable locations along a dielectric waveguide. Exploiting this flexibility, however, typically requires channel knowledge for PA configuration, which can introduce substantial overhead in dynamic propagation environments. This paper proposes PA-assisted differential spatial modulation (PA-DSM), enabling data transfer with spatial index selection and non-coherent data detection without instantaneous channel state information (CSI) at the receiver. To exploit PA reconfigurability while preserving this CSI-efficient operation, we introduce a slow-timescale received signal strength indicator (RSSI)-assisted selection strategy that identifies a favorable subset of PAs from scalar power measurements. We further specialize a two-stage low-complexity maximum-likelihood (LC-ML) detector to phase shift keying (PSK) signaling, obtaining closed-form symbol decisions that remove the joint modulation-combination search while preserving the minimizer of exhaustive differential detection. Furthermore, a moment generating function (MGF)-based pairwise error analysis and the corresponding bit error probability (BEP) bound are developed under normalized common-K Rician fading, revealing how the difference rank and spectrum, number of receive antennas, and previous-state-dependent line-of-sight (LoS) alignment affect the error performance. Numerical results across representative indoor-office, indoor-factory, and street-canyon sixth-generation (6G) Frequency Range 3 (FR3) scenarios validate the analytical trends and quantify when PA-DSM outperforms coherent benchmark schemes whose channel estimates age between pilot transmissions.

I. INTRODUCTION

PA reconfigurability offers a way to exploit spatial degrees of freedom, but PA-assisted index modulation commonly relies on coherent detection and instantaneous CSI. The paper proposes PA-DSM with RSSI-based PA selection and a PSK-specialized low-complexity detector, alongside an architecture that reuses its selected PA subset over multiple blocks.

I. INTRODUCTION

  • PA systems radiate from selected locations along a dielectric waveguide, a capability the paper identifies as attractive for FR3 deployments affected by propagation loss, blockage, and channel variation.The paper situates this approach among techniques that make the effective wireless channel more controllable.Source: §I · p. 1

A. Related Works

  • Most existing PA-assisted IM/SM frameworks use coherent detection and require instantaneous CSI, while single-waveguide PA-DSM must also select PAs and manage a joint permutation-symbol search.Differential SM offers non-coherent detection without explicit instantaneous CSI acquisition.Source: A. Related Works · pp. 1–2

B. Motivation and Contributions

  • PA-DSM combines differential encoding with scalar-RSSI subset selection and a PSK-specialized LC-ML detector that preserves the exhaustive minimizer while removing the modulation-combination search.The detector uses phase quantization for symbol decisions before evaluating admissible permutations.Source: B. Motivation and Contributions · p. 2

A. System Model

  • A single-RF-chain BS selects Nt PAs from Nall candidates using an uplink beacon, then activates the selected PAs sequentially for data transmission.The RSSI-selected subset is reused across multiple blocks and updated when large-scale propagation conditions change appreciably.Source: A. System Model · pp. 2–3
  • Selection costs NallLp beacon samples and a reference block per subset update; the relative overhead is 0.51% in the street-canyon case and 0.085% indoors.The comparison is against coherent pilot overhead under the parameters referenced in the supplied passage.Source: A. System Model · p. 3

B. Channel Model

The channel model combines deterministic in-waveguide propagation with wireless fading, while the signal model encodes information in both PA activation order and PSK symbols. Each block activates every selected PA once, with one PA radiating per time slot.

B. Channel Model

  • The PA-assisted channel combines large-scale fading, in-waveguide phase shift, and wireless Rician fading, with blocked LoS links represented by K=0.The model also includes a distance-dependent LoS phasor and a normalized scattered component.Source: B. Channel Model · p. 3

1) Signal Construction and Spectral Efficiency:

  • Each information block combines a permutation matrix for the PA activation sequence with a diagonal matrix of M-PSK symbols.Spatial-index bits select a permutation, while modulation bits determine the symbols on the diagonal.Source: 1) Signal Construction and Spectral… · pp. 3–4
  • The Nt selected PAs each activate once per block, with one PA radiating in each time slot, avoiding the non-uniform radiated-power distribution associated with simultaneous radiation.For Nt=3, two spatial-index bits select one of four activation patterns from six possible permutations.Source: 1) Signal Construction and Spectral… · p. 4, Table I · p. 4

2) Differential Encoding and Detection:

Differential encoding supports non-coherent detection from consecutive received blocks, while the PSK-specialized LC-ML detector preserves the exhaustive-search minimizer with less search.

2) Differential Encoding and Detection:

  • The recursive differential state preserves a monomial unitary structure, so only one PA radiates in each time slot.The known initialization is S0 = INt.Source: 2) Differential Encoding and Detection · p. 4
  • The differential detector compares received blocks Yk and Yk−1 against candidate information matrices, avoiding decision-feedback error propagation.Adjacent blocks share noise, which is addressed in the performance analysis.Source: 2) Differential Encoding and Detection · p. 4

III. LOW-COMPLEXITY MAXIMUM-LIKELIHOOD DECODING FOR PA-DSM

  • PSK phase quantization followed by evaluation of the Q admissible permutations returns the exhaustive detector’s minimizer without searching M Nt modulation-symbol combinations.The procedure separates symbol decisions from spatial-permutation evaluation.Source: §III · p. 4

A. Phase 1: Symbol Metric Pre-Computation

The analysis develops a high-SNR conditional pairwise-error approximation and an efficient PSK detector procedure, then characterizes how normalized channel power and shared noise enter the error analysis.

A. Phase 1: Symbol Metric Pre-Computation

  • Phase 1 finds the nearest-phase PSK symbol for each pairing and reuses the resulting symbols and costs across admissible permutations.The supplied passages describe this reuse but do not provide a complete Phase 1 cost expression.Source: A. Phase 1: Symbol Metric… · p. 5

B. Phase 2: Spatial Hypothesis Evaluation and Decision

  • Phase 2 evaluates each admissible permutation using Phase 1 costs and recovers the symbols paired with the selected permutation.Evaluating all Q permutations preserves the minimizer of exhaustive joint search.Source: B. Phase 2: Spatial Hypothesis… · p. 5

A. Conditional Pairwise Error Probability

  • The conditional PEP analysis adopts a high-SNR approximation because equivalent noise and the previous received block share a noise realization, and assumes unit average channel-coefficient power.The normalization is E[|h_i,j|^2] = 1.Source: §IV · p. 5, A. Conditional Pairwise Error… · p. 5

IV. THEORETICAL PERFORMANCE ANALYSIS

  • The conditional PEP forms the basis for channel averaging and asymptotic analysis of the differential detector.The equivalent noise is characterized before deriving the conditional error probability.Source: A. Conditional Pairwise Error… · p. 5

B. Channel- and State-Averaged PEP and BEP Analysis

The analysis averages conditional error probabilities using an MGF under a normalized common-K Rician model, identifying pairwise difference structure and LoS alignment as performance factors.

B. Channel- and State-Averaged PEP and BEP Analysis

  • Craig’s Q-function representation and the conditional MGF are used to average the conditional PEP over the Rician channel and then over previous differential states.The MGF is defined for ξ conditioned on the previous state.Source: B. Channel- and State-Averaged PEP and… · pp. 5–6

1) Conditional MGF Under Normalized Rician Fading:

  • The normalized i.i.d. Rician model uses unit average link power and a shared K factor, with a deterministic LoS mean and independently scattered NLoS entries.The homogeneous LoS mean supports tractable evaluation.Source: 1) Conditional MGF Under Normalized… · p. 6
  • Pairwise error probability depends on difference-matrix eigenvalues, receive-antenna count, scattered-channel variance, and LoS energy along each error direction.The previous state affects the conditional MGF through LoS-dependent alignment; without LoS, that dependence disappears.Source: 1) Conditional MGF Under Normalized… · p. 6

2) State-Averaged PEP and BEP:

State-conditioned pairwise error probabilities are averaged over previous states, with homogeneous LoS enabling a permutation reduction; the resulting BEP expression weights pairwise events by bit distance.

2) State-Averaged PEP and BEP:

  • The state-conditioned PEP is invariant to the accumulated permutation under the homogeneous LoS model, but this relies on H̄P_k−1 = H̄ and need not hold for geometry-dependent LoS.The state average can consequently be reduced to accumulated phase matrices.Source: 2) State-Averaged PEP and BEP · p. 6
  • The state-averaged PEP averages over possible accumulated phase matrices after homogeneous-LoS invariance removes the explicit permutation dimension.The state-conditioned PEP still depends on the previous differential state.Source: 2) State-Averaged PEP and BEP · p. 6
  • The BEP expression weights pairwise detection events by dH, the number of bit errors from detecting one information matrix instead of another.The expression is formed over transmitted and erroneously detected information matrices.Source: 2) State-Averaged PEP and BEP · p. 7
  • The derived expressions apply to normalized i.i.d. common-K Rician fading and omit link-dependent path loss, blockage, Rician factors, waveguide attenuation, and geometry-dependent LoS structure.The phase-state reduction also relies on a homogeneous LoS mean.Source: 2) State-Averaged PEP and BEP · p. 7

C. Asymptotic Pairwise Error and Codebook Analysis

The analysis derives a high-SNR pairwise error bound and identifies how difference rank controls its polynomial SNR exponent. It also distinguishes phase-independent pairwise coding terms from LoS contributions that depend on previous-state alignment.

C. Asymptotic Pairwise Error and Codebook Analysis

  • The asymptotic pairwise error bound has polynomial SNR exponent Gd = rNr and a phase-dependent LoS contribution.The phase-state average preserves Gd and the coding coefficient Gc while averaging the LoS-dependent factor.Source: C. Asymptotic Pairwise Error and… · p. 7
  • Within the analytical BEP union bound, lower-rank pairwise terms decay more slowly, so the minimum difference rank determines its slowest-decaying terms.The polynomial SNR exponent for a pairwise term is Gd = rNr.Source: C. Asymptotic Pairwise Error and… · p. 7
  • The employed codebook has minimum difference rank one for both complete-codebook and reference-codeword errors, giving minimum exponent Nr.Every transmitted matrix has a one-symbol alternative, and nonsingularity of Aq makes that difference rank one.Source: C. Asymptotic Pairwise Error and… · p. 7
  • Reference-codeword curves share the complete bound’s minimum SNR exponent, but need not match its finite-SNR values or asymptotic coefficients.The differences can reflect bit counts, pairwise eigenvalues, and deterministic LoS energy across transmitted matrices.Source: C. Asymptotic Pairwise Error and… · p. 7
  • The previous phase state leaves the pairwise coding coefficient unchanged but can alter the LoS contribution through alignment with pairwise error directions.The nonzero eigenvalues of ∆∆H are unchanged by the unitary previous phase state.Source: C. Asymptotic Pairwise Error and… · p. 7
  • A larger K reduces the scattered-channel coding coefficient but strengthens the LoS contribution, whose effect depends on phase-state alignment.The overall effect of K cannot be inferred from scattered-channel variance alone.Source: C. Asymptotic Pairwise Error and… · p. 8

V. NUMERICAL RESULTS AND COMPLEXITY ASSESSMENT

The section evaluates PA-DSM in representative FR3 environments using geometry-dependent Monte Carlo simulations and compares those results with a reference-codeword MGF characterization. The simulation setup specifies the PA and receiver layouts, channel assumptions, and differential-block conditions.

V. NUMERICAL RESULTS AND COMPLEXITY ASSESSMENT

  • The evaluation uses geometry-dependent Monte Carlo simulations in indoor-office, indoor-factory, and street-canyon FR3 deployments, then compares them with the reference-codeword MGF characterization.The deployments are evaluated at 16.95 GHz.Source: §V · p. 8

A. Simulation Environments and Parameters

  • Candidate PAs are uniformly placed along an x-directed waveguide, and the UE uses a half-wavelength-spaced x-directed ULA centered at height 1.5 m.For each UE location, Nt PAs are selected once and held fixed during the PA-DSM trials.Source: A. Simulation Environments and… · p. 8
  • Channel realizations remain unchanged across the two consecutive blocks used for differential detection, while link-level LoS states, shadowing, and scattered coefficients are generated independently.This follows the stated quasi-static assumption for differential detection.Source: A. Simulation Environments and… · p. 8
  • The link model combines free-space reference loss, environment-dependent distance loss, waveguide attenuation, and shadow fading; its small-scale fading is Rician in LoS and has K = 0 in NLoS.The LoS K-factor is distance-dependent.Source: A. Simulation Environments and… · pp. 8–9

V. NUMERICAL RESULTS AND COMPLEXITY ASSESSMENT

  • Fig. 3 reports the bit-error-rate (BER) performance of PA-DSM in indoor-office, indoor-factory, and street-canyon environments, evaluated at η = 4 bps/Hz with Nt = 4.Source: Figure 3 · p. 9

B. Performance Evaluation Across Diverse FR3 Environments

Across the evaluated FR3 settings, PA-DSM’s relative BER depends on environment and transmit power. RSSI-based PA selection adapts effectively, while benchmark results show a trade-off between coherent gain and avoiding channel-estimation aging.

B. Performance Evaluation Across Diverse FR3 Environments

  • As transmit power rises, the lowest-BER environment changes from indoor-office at low power to indoor-factory at higher power, with street-canyon generally between the indoor cases.The paper attributes this crossover to differences in pairwise hypothesis distances, which depend on PA locations and several propagation factors; it does not isolate spatial correlation or angular spread.Source: B. Performance Evaluation Across… · p. 9

C. RSSI-Assisted PA Selection Performance

  • Both adaptive PA subsets keep BER in the 10^-5 range across 200 m, while the fixed subset remains above 7 × 10^-2; RSSI selection further beats nearest-PA selection by a factor of 2 to 3 in BER.RSSI selection incurs 0.09 dB mean link-gain loss versus genie selection, compared with 2.79 dB for nearest-PA and 13.41 dB for fixed selection, without UE-location knowledge.Source: C. RSSI-Assisted PA Selection… · p. 9

D. Robustness Comparison Against Benchmarks

  • The PSK-specialized LC-ML and exhaustive-ML BER curves coincide over the evaluated transmit-power range, confirming that LC-ML returns the exhaustive differential metric’s minimizer.The coherent benchmark comparison uses MMSE estimates based on Nt pilots reused over Tp = 0.5 ms at 1 m/s.Source: D. Robustness Comparison Against… · pp. 9–10
  • With channel estimates reused across pilot intervals, aging caps coherent-link quality at 24.0 dB, while PA-DSM BER continues decreasing; PA-DSM becomes preferable when pilot intervals cannot be short relative to coherence time.PA-DSM avoids explicit instantaneous channel estimates for data detection but remains sensitive to variation between adjacent blocks.Source: D. Robustness Comparison Against… · p. 10
  • Under equal feed power with αe = 0.5, PA-DSM has lower BER than same-waveguide DSTBC; under perfect CSI, coherent SM needs approximately 3 dB less transmit power than PA-DSM at the indicated BER.Source: D. Robustness Comparison Against… · pp. 9–10

E. Impact of Antenna Scaling Under Rician Fading

Under common-K Rician fading, increasing receive antennas reduces BER and steepens its high-SNR slope; increasing active PAs costs about 1 dB at Nr = 1 but has little effect for Nr ≥2. The PSK-specialized detector also sharply reduces search complexity while preserving the exhaustive minimizer.

E. Impact of Antenna Scaling Under Rician Fading

  • Increasing Nr from one to three reduces BER and steepens the high-SNR slope; rank-one pairwise events set the codebook-level polynomial SNR exponent Gd,min = Nr.The analytical curves use a reference codeword and high-SNR equivalent-noise approximation, so they characterize slope variation rather than complete finite-SNR BER.Source: E. Impact of Antenna Scaling Under… · pp. 10–11
  • At Nr = 1, Nt = 4 costs approximately 1 dB versus Nt = 3; for Nr ≥2, the configurations perform within 0.1 dB, despite Nt = 4 conveying 9% more information per channel use.The comparison uses equal M = 8 rather than equal spectral efficiency: η is 3.67 bps/Hz for Nt = 3 and 4 bps/Hz for Nt = 4.Source: E. Impact of Antenna Scaling Under… · p. 11
  • The analytical and Monte Carlo curves differ in absolute BER because the analysis uses a high-SNR equivalent-noise approximation; their Nr-dependent slope trends remain consistent.The approximation is less accurate outside the high-SNR range.Source: E. Impact of Antenna Scaling Under… · p. 11

F. Complexity Analysis

  • For Nt = 4, Nr = 2, M = 8, and Q = 16, the proposed detector uses approximately 224 real multiplications and 64 metric accumulations, versus 262 144 accumulations for exhaustive search.The detector removes the M^Nt joint modulation-combination search while returning the same minimizer of the exhaustive differential metric.Source: F. Complexity Analysis · p. 11

VI. CONCLUSION

  • The paper combines differential spatial modulation with RSSI-assisted PA selection and develops MGF-based error analysis separating scattered and deterministic LoS contributions.The previous differential state preserves pairwise rank and eigenvalues but can change the LoS contribution through spatial alignment.Source: §VI · p. 11

APPENDIX A PROOF OF LEMMA 1

The appendix derives a conditional MGF for pairwise error by decomposing the channel-dependent distance into independent eigenmode contributions. It then establishes that the previous state’s permutation component does not affect the conditional pairwise error probability under the stated homogeneous LoS model.

APPENDIX A PROOF OF LEMMA 1

  • The channel-dependent squared distance is expressed through an eigendecomposition, and projected vectors from distinct eigenmodes are independent when conditioned on the previous differential state.The proof uses orthogonality of eigenvectors and the jointly complex Gaussian projected vectors.Source: Appendix A · p. 12
  • Each nonzero eigenmode contribution has a scaled noncentral chi-square form, enabling its MGF to be combined into the conditional MGF of the distance.The proof identifies the noncentrality parameter with the deterministic LoS component and multiplies the individual eigenmode MGFs.Source: Appendix A · p. 12

APPENDIX B PROOF OF LEMMA 2

  • Under the homogeneous LoS model, the conditional PEP is invariant to the permutation component of the previous differential state.The proof reduces the state dependence to LoS-related terms; the pairwise difference eigenvalues and other channel parameters remain unchanged.Source: Appendix B · p. 12

APPENDIX C PROOF OF THEOREM 1

The proof bounds the pairwise-error integral using a representative previous phase state, then evaluates the resulting MGF bound at high SNR to obtain the theorem.

APPENDIX C PROOF OF THEOREM 1

  • Because the PEP is independent of the previous state’s permutation component, the proof evaluates it using a representative phase state without changing the pairwise eigenvalues.The representative state is Sk−1 = Φk−1.Source: Appendix C · p. 12
  • Because ξ ≥ 0 by (22), the conditional MGF is nondecreasing in its real argument; the proof then applies the pointwise bound to the integral in (25).Source: Appendix C · p. 12
  • The high-SNR limits of the scattered-channel and deterministic LoS MGF factors yield the theorem’s asymptotic expression.The proof substitutes these limits into the integral bound and applies the definitions of Gd, Gc, and ΓPA.Source: Appendix C · pp. 12–13
Loading 2609.37305v1…