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On the Performance of Uplink Pinching Antenna Systems (PASS)

Tianwei Hou, Yuanwei Liu, Arumugam Nallanathan

arXiv:2502.12365v1cs.ITmath.IT

TL;DR

The paper examines uplink PASS deployment choices in light of a waveguide that only delays signals. It analyzes three PA configurations and reports that PASS and optimized PA placement improve rate performance.

Abstract

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Pinching antenna (PA) is a flexible antenna composed of a waveguide and multiple dielectric particles, which is capable of reconfiguring wireless channels intelligently in line-of-sight links. By leveraging the unique features of PAs, we exploit the uplink (UL) transmission in pinching antenna systems (PASS). To comprehensively evaluate the performance gains of PASS in UL transmissions, three scenarios, multiple PAs for a single user (MPSU), a single PA for a single user (SPSU), and a single PA for multiple users (SPMU) are considered. The positions of PAs are optimized to obtain the maximal channel gains in the considered scenarios. For the MPSU and SPSU scenarios, by applying the optimized position of PAs, closed-form expressions for analytical, asymptotic and approximated ergodic rate are derived. As the further advance, closed-form expressions of approximated ergodic rate is derived when a single PA is fixed in the SPMU scenario. Our results demonstrate the following key insights: i) The proposed PASS significantly outperforms conventional Multiple-input Single-output networks by exploiting the flexibility of PAs; ii) The PA distribution follows an asymmetric non-uniform distribution in the MPSU scenario; iii) Optimizing PA positions significantly enhances the ergodic sum rate performance.

I. INTRODUCTION

The introduction motivates uplink PASS for indoor line-of-sight links and identifies limited comprehensive analysis of uplink performance. It previews three user/antenna configurations, PA-position optimization, and ergodic-rate analysis.

I. INTRODUCTION

  • The introduction points to indoor limitations of existing antenna approaches and a gap in comprehensive uplink PASS performance analysis.It notes that fixed arrays require many antennas and that fluid-antenna advantages diminish in LoS settings; prior PASS studies primarily addressed downlink.Source: §I · pp. 1–2, A. Motivation and Contribution · p. 2

A. Motivation and Contribution

  • In MPSU, optimized PA locations are asymmetric and non-uniform in the near zone, but approach symmetric uniformity in the far zone.The far-zone condition is defined using the reference distance relative to Nλ.Source: A. Motivation and Contribution · p. 2
  • The study analyzes MPSU, SPSU, and SPMU; it derives ergodic-rate results for SPSU and examines fixed and optimized PA positions for SPMU.For SPSU, the analysis includes closed-form ergodic rates and analytical, asymptotic, and approximated high-SNR results; multiple PAs enhance individual-user ergodic rates.Source: A. Motivation and Contribution · p. 2
  • The MPSU ergodic sum rate exceeds SPSU and SPMU, and optimizing PA positions significantly enhances ergodic sum rate.The proposed PASS also outperforms conventional networks by mitigating large-scale fading.Source: A. Motivation and Contribution · pp. 2–3

B. Organization and Notations

  • The article organizes its model, analytical results, numerical results, and conclusion across Sections II–V, and defines E(·) as expectation.Source: B. Organization and Notations · p. 3

A. Antenna and Channel Model

  • The model places an AP and ceiling-edge waveguide in an indoor room, assumes an ideal waveguide and LoS large-scale channels, and distributes users uniformly across the floor.The small-scale channel is normalized and retains phase shift from propagation distance.Source: A. Antenna and Channel Model · p. 3

B. Signal Model

The uplink signal model uses exclusive time slots for users and accounts for phase changes through the waveguide. The performance analysis considers three PA deployment scenarios; in MPSU, optimized placement yields different near- and far-zone distributions and high-SNR rate insights.

B. Signal Model

  • Uplink users receive exclusive TDMA slots, and waveguide propagation phase remains part of the signal model despite negligible path loss.Source: B. Signal Model · p. 3

III. PERFORMANCE ANALYSIS

  • The analysis treats MPSU, SPSU, and SPMU, with PA placement optimized for channel gain or ergodic sum rate according to the scenario.Source: §III · p. 3

A. Using Multiple PAs for a Single User (MPSU)

B. Using A Single PA for A Single User (SPSU)

The SPSU scenario uses one PA per user as a more practical subset of MPSU, given the impracticality of deploying massive numbers of PAs indoors. The section derives ergodic-rate results and compares SPSU with MPSU.

B. Using A Single PA for A Single User (SPSU)

C. Using A Single PA for Multiple Users (SPMU)

In SPMU, one PA at the waveguide center serves multiple users across all time slots. The section derives ergodic-rate results for this arrangement and contrasts its implementation simplicity with SPSU.

C. Using A Single PA for Multiple Users (SPMU)

1) Optimized PA position for SPMU Scenario:

For two floor users sharing one PA in LoS, the optimized PA position depends on the users’ distance ratio. When their y-coordinates match, the optimum is the midpoint of their x-coordinates.

1) Optimized PA position for SPMU Scenario:

IV. NUMERICAL RESULTS

The numerical-results section uses Monte Carlo simulations to verify the analytical results. The stated setup includes a 2.4 GHz carrier, 1 MHz bandwidth, and two users.

IV. NUMERICAL RESULTS

  • Monte Carlo simulations are used to verify the accuracy of the analytical results.Source: §IV · p. 8
  • Figure 3 depicts MPSU PA spacing with N = 10.Source: Figure 3 · p. 8
  • The carrier frequency is 2.4 GHz, the transmission bandwidth is 1 MHz, and the user count is two.Source: §IV · p. 8

1) Spacing of PAs in the MPSU scenario with different distances:

Across MPSU and single-PA settings, optimized PA placements shape rate and spacing: MPSU PAs are asymmetric in NZ and nearly symmetric-uniform in FZ. In SPMU, optimized placement beats fixed placement and conventional SISO in ergodic sum rate.

1) Spacing of PAs in the MPSU scenario with different distances:

  • In NZ, PA spacing increases with PA count in the NA and decreases in the FA, producing an asymmetric non-uniform distribution; FZ spacing is nearly constant and symmetric-uniform.At high PA counts, FA spacing approaches the wavelength threshold while NA spacing increases.Source: 1) Spacing of PAs in the MPSU scenario… · p. 8

2) Ergodic rate in the MPSU scenario with different number of PAs:

  • As PA count rises, MPSU ergodic rate improves and the analytical–asymptotic gap diminishes, although analytical results diverge more from simulation at N = 4.The figure evaluates N = 4, 10, and 20; the large-N analytical approximation neglects the signal from the nearest PA.Source: 2) Ergodic rate in the MPSU scenario… · pp. 8–9, Figure 4 · p. 9

3) Ergodic rate in the MPSU scenario impacted by NZ and FZ cases:

  • For N = 10, NZ analytical results approach simulation as minimum distance exceeds 5 meters, while the approximation gap narrows at high SNR and approaches 0.2 bits/s/Hz.The FZ approximation is applicable when user-to-PA distance is much greater than Nλ.Source: 3) Ergodic rate in the MPSU scenario… · p. 9, Figure 5 · p. 9

4) Ergodic Rate comparison between MPSU and SPSU scenarios:

  • MPSU consistently outperforms SPSU; the ergodic-rate gaps are about 2.6 bits/s/Hz between MPSU N = 10 and N = 5, and 2.2 bits/s/Hz between MPSU and SPSU at N = 5.Smaller rooms and waveguide heights also yield higher MPSU rates in the reported comparison.Source: 4) Ergodic Rate comparison between… · p. 9, Figure 6 · p. 9

B. SPSU Scenario; 5) Ergodic Rate in the SPSU Scenario:

6) Ergodic rate in the SPSU scenario:

8) Ergodic sum rate comparison between optimized PASS and fixed PASS:

7) Ergodic rate difference in SPSU and SPMU Scenarios; V. CONCLUSIONS

  • The multiple-PA scenario outperforms the single-PA scenario, with larger rooms and lower waveguides associated with a more pronounced ergodic-rate gap.The rate gain comes with increased hardware complexity; future work includes dynamic placement when PAs are fewer than users and systems with multiple waveguides.Source: 7) Ergodic rate difference in SPSU and… · p. 10, §V · p. 11

APPENDIX A: PROOF OF LEMMA 1

Appendix A derives coherence conditions for PAs on either side of the reference position. Appendix B derives the user’s rate expression and closed-form ergodic rate using equal TDMA allocation and a random user-to-nearest-PA distance.

APPENDIX A: PROOF OF LEMMA 1

  • For the FA with n > 0, coherent reception requires xn + dn = d0 + nλ, making transmission-distance phase shifts integer multiples of λ.Here, dn is the distance from the i-th user to the n-th PA.Source: Appendix A · p. 11
  • For the NA with n < 0, coherence requires a corresponding relation, derived under the condition d0 > |n| λ.Source: Appendix A · p. 11

APPENDIX B: PROOF OF THEOREM 1

  • With equal TDMA resource allocation, the i-th user’s rate is expressed first, then its ergodic-rate expectation is reformulated for a randomly distributed nearest-PA distance and yields the results in (27).Source: Appendix B · p. 11

APPENDIX C: PROOF OF COROLLARY 2

Appendix C uses a Maclaurin expansion of an inverse trigonometric function to obtain an approximated achievable rate. Appendix D derives the expressions in (36) using high-SNR and geometric approximations.

APPENDIX C: PROOF OF COROLLARY 2

  • Appendix C expands the inverse trigonometric function using its Maclaurin series as a step toward an approximated achievable rate.Source: Appendix C · pp. 11–12
  • The resulting derivation gives an approximated achievable rate for the i-th user.Source: Appendix C · p. 12

APPENDIX D: PROOF OF COROLLARY 4

  • Appendix D derives the expressions in (36) from L3 and L4, applying arctan x → x in the high-SNR regime and an approximation when h ≫ D.Source: Appendix D · p. 12

APPENDIX E: PROOF OF PROPOSITION 7

Appendix E reformulates the ergodic-rate difference between the multiple-PA and single-PA scenarios. It examines the expression at D = 0 as part of the comparison.

APPENDIX E: PROOF OF PROPOSITION 7

  • The proof reformulates the ergodic-rate difference between the MPSU and SPSU scenarios for comparison.Source: Appendix E · p. 12
  • The proof uses the inequality D^2 + h^2 ≤ 2D^2 + h^2, which it states always holds.Source: Appendix E · p. 12
  • In the D = 0 case, the comparison expression approaches 0.Source: Appendix E · p. 12

APPENDIX F: PROOF OF THEOREM 4

Appendix F formulates an optimization for the ergodic rate of two randomly deployed users. It derives the optimized PA position under the indoor high-SNR setting.

APPENDIX F: PROOF OF THEOREM 4

  • For two randomly deployed users, the optimal PA position x lies between xu1 and xu2.Source: Appendix F · pp. 12–13
  • The indoor scenario is analyzed using the high-SNR approach.Source: Appendix F · p. 13
  • The proof obtains the optimized PA position by differentiating with respect to x and setting the derivative to zero.Source: Appendix F · p. 13

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