Flexible-Antenna Systems: A Pinching-Antenna Perspective

Motivation

• Flexible-antenna systems reconfigure effective wireless channel gains, but existing RIS/IRS, fluid, and movable antennas have limited ability to combat large-scale path loss.RIS/IRS systems can suffer double attenuation, while fluid and movable antennas remain limited in addressing large-scale path loss.Source: §I · p. 1

Pinching-Antenna Concept

• Pinching antennas are activated by applying small dielectric particles to a dielectric waveguide, and their locations can be flexibly adjusted over a large scale.This flexibility can place an antenna close to a target receiver to create or strengthen a line-of-sight link.Source: §I · p. 1
• Additional pinches can resize the antenna system, and multiple pinching antennas can be applied to one or multiple waveguides in a flexible, low-cost manner.This capability provides a possible route toward MIMO implementation.Source: §I · p. 1

Single-Antenna Analysis

• For a single pinching antenna and waveguide, the paper derives closed-form ergodic sum-rate expressions and shows strong LoS links can mitigate large-scale path loss.The performance gain over conventional antennas is affected by the area in which users are deployed.Source: §I · p. 2

Multiple Antennas

• With multiple antennas on one waveguide, transmit power per antenna decreases, yet TDMA analysis shows users’ data rates increase monotonically with antenna count.Multiple antennas are therefore analytically beneficial in the considered TDMA-assisted system.Source: §I · p. 2

Multiuser Transmission

• Because antennas on one waveguide share the same signal, user signals must be superimposed, motivating NOMA for simultaneous multiuser transmission.The multi-waveguide case is treated as a MISO interference channel, where channel reconfiguration can make the performance upper bound achievable under identified conditions.Source: §I · p. 2

Scope and Assumptions

• The analysis assumes LoS links and omits waveguide propagation loss, so reported performance can be an upper bound and NLoS performance remains outside scope.The omitted propagation loss is much smaller than free-space path loss in the cited 28-GHz example.Source: A. Conventional Antenna Systems · p. 3, B. Pinching-Antenna Systems · p. 3

Performance Comparison

• The pinching-antenna sum rate is always larger than that of a conventional antenna, and the high-SNR sum-rate difference increases monotonically with D/d.The comparison is based on the stated analytical result for the considered systems.Source: B. Pinching-Antenna Systems · p. 4

• Because antennas on one waveguide receive phase-shifted versions of the same signal, conventional independent-signal MISO strategies do not directly apply.Source: §III · p. 4
• The model assumes equal sharing of total transmit power among the activated pinching antennas.The waveguide wavelength is related to the free-space wavelength through the effective refractive index.Source: §III · p. 4
• Multiple pinching antennas provide additional reconfigurable degrees of freedom through their positions, affecting large-scale path loss and phase shifts.Source: §III · p. 5
• Pinching antennas can be added to one or multiple waveguides flexibly and at low cost, enabling changes in antenna-system size.Source: §III · p. 5

• Under OMA, users are served individually, and multiple pinching antennas can improve each user’s data rate by positioning antennas near the closest waveguide point.Source: A. OMA-Assisted Pinching-Antenna Systems · p. 5
• If antenna locations can satisfy the required phase-alignment condition, an upper bound on the user data rate becomes attainable.The condition requires the relevant phase terms to sum to an integer multiple of 2π.Source: A. OMA-Assisted Pinching-Antenna Systems · p. 5
• The illustrated deployment uses one waveguide and two pinching antennas, with weak and strong users uniformly distributed in separate equal-sized squares.Source: Figure 3 · p. 5
• A sequential location-search algorithm places the first antenna and then successive antennas along the waveguide while enforcing a guard distance to avoid coupling.Source: A. OMA-Assisted Pinching-Antenna Systems · p. 5
• Unlike conventional antennas and other flexible antennas, pinching antennas can realize this upper bound through large-scale repositioning and require only one RF chain.Source: A. OMA-Assisted Pinching-Antenna Systems · p. 5

• NOMA superimposes multiple users’ signals when multiple pinching antennas on a single waveguide serve users simultaneously.Source: B. NOMA Assisted Pinching-Antenna… · p. 5
• Each pinching antenna is placed closest to its assigned user, while users are ordered by ascending channel strength for successive interference decoding.Source: B. NOMA Assisted Pinching-Antenna… · p. 5
• Scheduling users far apart makes the antenna nearest each user dominant in its effective channel, reducing the need for fine-tuned placement.Source: 1) User Scheduling: η · p. 6

The Case of M = N = 2

• For large D1, the two users’ separated square deployments permit simplified channel-gain expressions and preserve the assumed weak-to-strong channel ordering.Source: 2) The Case of M = N = 2 · p. 6
• The users’ ergodic data rates are evaluated from their uniform spatial distributions and then approximated in the high-SNR regime.Source: 2) The Case of M = N = 2 · p. 6
• A closed-form approximation for the NOMA-assisted ergodic sum rate is obtained for large D1 and high SNR.Source: 2) The Case of M = N = 2 · p. 6
• Under the stated large-D1 condition, the difference between the NOMA and OMA sum rates is guaranteed to be positive.Source: 2) The Case of M = N = 2 · pp. 6–7
• For a fair comparison, the analysis assumes MP = Pm, matching total transmit power across NOMA and OMA.Source: 2) The Case of M = N = 2 · p. 7

• Multiple waveguides can be fed with different signals, unlike multiple antennas on one waveguide.This allows the received signal at each user to combine independently transmitted waveguide signals.Source: §IV · p. 7
• The channel between user U_m and waveguide k depends on the corresponding pinching-antenna configuration.Source: §IV · p. 7
• Beamforming coefficients p_m,k allocate user m’s signal across waveguides under an overall transmit-power constraint.Source: §IV · p. 7
• The received signal and SINR expressions account for propagation phase shifts along waveguides and from antennas to users.Source: §IV · p. 7
• The resulting system resembles a conventional multiuser MISO interference channel, with the special case M = K = 2 analyzed in detail.Source: §IV · p. 7

• Optimizing two users’ SINRs is inherently coupled because improving one user can degrade the other user’s performance.Source: A. Existing Results for Two-User… · p. 7
• MRC maximizes intended-user signal strength but leaves interference uncontrolled, whereas ZF suppresses cochannel interference without maximizing intended signal strength.Source: , SINRMRC · p. 7, 1) Practical Approaches · p. 7
• The interference-channel SINR upper bound corresponds to each user occupying the whole bandwidth without the other user’s interference.Source: 2) An Upper Bound · p. 7, A. Existing Results for Two-User… · p. 7

Upper-bound conditions

• Phase matching aligns each user’s beamforming coefficient with its intended channel, maximizing the desired-signal numerator.Source: B. Approaching the Upper Bound · p. 7
• Orthogonality removes inter-user interference from each SINR denominator.Source: B. Approaching the Upper Bound · p. 8
• Because antenna locations configure the channels, moving pinching antennas can make the upper bound achievable when both conditions hold on a micrometer scale.The bound changes with antenna locations but remains nearly unchanged for micrometer-scale movements.Source: B. Approaching the Upper Bound · p. 8, 1) Feasibility Analysis · p. 8

• When users lie on the x-axis and waveguides are placed as specified, antenna locations can be selected to satisfy the orthogonality constraint.Source: 2) A Special Case Which Guarantees… · p. 8
• The relevant function is monotonic, so adjusting a pinching-antenna coordinate can realize every value within its stated range.Source: 2) A Special Case Which Guarantees… · p. 8
• For sufficiently separated users, the achievable range becomes much larger than the wavelength, supporting feasible constraint satisfaction.Source: 2) A Special Case Which Guarantees… · p. 8

Search-based design

• Algorithm 1 enumerates candidate antenna locations and selects the pair maximizing the minimum two-user SINR after obtaining ZF beamforming vectors.Source: 2) A Special Case Which Guarantees… · p. 9

• Multiple feasible integer choices exist even when users are not located on a line parallel to the waveguides.Source: 2) A Special Case Which Guarantees… · p. 9

Search-based algorithm

• The search-based algorithm enumerates candidate antenna locations to find configurations that approach the interference-channel upper bound using ZF or MRC.Source: 3) A Search-Based Algorithm to… · p. 9, B. The Multiple-Pinching-Antenna… · p. 10

Simulation results

• In the single-antenna case, pinching antennas achieve higher ergodic sum rates than conventional antennas by reducing users’ path losses.Source: A. The Single-Pinching-Antenna… · p. 9, Figure 5 · p. 9
• The pinching-antenna gain over conventional antennas increases as the deployment area or rectangle’s long side grows.With fixed rectangle width, users’ path losses through pinching antennas remain unchanged as the long side increases.Source: A. The Single-Pinching-Antenna… · p. 9
• Increasing the number of pinching antennas significantly increases performance gain over conventional antennas, and the search algorithm achieves the upper bound in (16).Source: B. The Multiple-Pinching-Antenna… · pp. 9–10, Figure 6 · p. 10

NOMA results

• NOMA increases sum rate relative to benchmark schemes and can outperform OMA, especially when users’ channel conditions differ more.Source: B. The Multiple-Pinching-Antenna… · p. 10, Figure 8 · p. 10
• NOMA’s sum-rate gain favors the strong user, while the weak user’s data rate decreases, particularly at high SNR.The weak user treats the partner’s signal as noise, causing its high-SNR rate to approach a constant.Source: B. The Multiple-Pinching-Antenna… · p. 10

System model

• The considered case activates two pinching antennas on two waveguides to serve two users, forming a two-user MISO interference-channel setting.The system uses N = K = M = 2.Source: C. The Multi-Pinching-Antenna… · p. 10

Performance

• Exhaustive antenna-location search shows that pinching antennas outperform conventional-antenna benchmarks in the considered deployment.The benchmarks include MRC, ZF, and an upper bound based on conventional-antenna locations.Source: C. The Multi-Pinching-Antenna… · p. 11

Low-complexity design

• A search restricted to locations near associated users achieves the same performance as the upper bound for the deployment considered in Fig. 10.The restricted search focuses on locations close to ψPin_m.Source: C. The Multi-Pinching-Antenna… · p. 11
• The two antenna-location searches in Fig. 10 achieve the same performance, indicating that optimal pinching-antenna locations are very close to ψPin_m.This observation motivates placing antennas next to associated users before applying ZF or MRC.Source: C. The Multi-Pinching-Antenna… · p. 11

Achievability conditions

• Upper-bound achievability depends on user/waveguide deployment: it is always achieved in the separated-rectangle case but not in every same-square realization.For users uniformly distributed within the same square, one random realization achieves the bound and another does not.Source: C. The Multi-Pinching-Antenna… · p. 11, Table I · p. 12

Conclusion

• The paper concludes that reconfigurable pinching antennas can achieve the interference-channel performance upper bound, while the general MISO case remains future work.The studied MISO setting is the special case M = N = K = 2.Source: §VI · p. 12

Proof strategy

• The proof begins from the conventional-antenna ergodic sum-rate expression and develops an upper bound for analytically comparing systems.The upper bound is motivated by the difficulty of obtaining the exact sum rate.Source: Appendix A · p. 12
• A high-SNR approximation is used to obtain insight into the performance difference between conventional and pinching-antenna systems.The approximation relies on the high-SNR assumption.Source: Appendix A · p. 12

Analytical reduction

• The performance difference between pinching and conventional antennas is expressed analytically using auxiliary functions such as g3(x).The proof reduces the desired inequality to properties of these functions.Source: Appendix A · p. 12

Monotonicity argument

• Showing that g3(x) is monotonically increasing and satisfies g3(0) = 0 establishes g3(x) ≥ 0 for x ≥ 0.The proof uses derivative calculations and limits to establish monotonicity.Source: Appendix A · p. 13

Conclusion

• The nonnegative auxiliary-function result completes the proof that the pinching-antenna performance gain over the conventional system is always positive.This conclusion follows from the two limits and the monotonicity of g3(x).Source: Appendix A · p. 13