Pinching Antenna and Relay Assisted Joint Indoor Outdoor NOMA Communications with SWIPT

I. INTRODUCTION

• Severe building-penetration loss makes direct outdoor-BS links to indoor users less reliable, motivating relaying; AF is described as attractive for its low processing complexity and latency.Conventional relays require an external power supply, while SWIPT can provide harvested RF energy for self-powered AF relaying.Source: §I · p. 1
• The two-stage method uses AO to select an energy-feasible indoor operating point, then SQP to allocate residual BS power among outdoor NOMA users according to channels and priority weights.The AO stage jointly determines the indoor-power fraction, power-splitting ratio, and PA position; the proposed procedure is reported to converge stably.Source: §I · pp. 1–2
• The unified architecture combines a SWIPT-enabled AF relay, movable waveguide-mounted PA, ZF beamforming, and outdoor NOMA to support energy-sustainable indoor connectivity and spatially separate transmission streams.The AF relay harvests RF energy for forwarding, addressing the external-power burden of conventional relays.Source: §I · pp. 1–2
• The joint formulation maximizes outdoor WSR under indoor and outdoor QoS constraints, coupling the BS indoor-power fraction, SWIPT power-splitting ratio, PA position, and NOMA power coefficients.The BS power fraction affects both harvested relay energy and power available to outdoor users, while NOMA coefficients are coupled through SIC and QoS constraints.Source: §I · pp. 1–2
• 3.1953 bps/Hz is reached in outdoor WSR at 110 dB SNR; increasing the BS array from M = 8 to M = 16 raises indoor QoS satisfaction to 100% for target rates up to 1.0 bps/Hz.Equal user weighting is generally suboptimal for outdoor WSR.Source: §I · p. 2

II. SYSTEM MODEL

• The rooftop BS uses ZF beamforming to separate indoor and outdoor links, assigning fraction ρP to the indoor link and (1 − ρ)P to the outdoor link.The indoor AP relays using harvested energy, and its movable PA adjusts the radiation point along a dielectric waveguide.Source: §II · p. 2, Figure 1 · p. 2
• The indoor stream passes through a self-powered SWIPT-enabled AF AP, which forwards without decoding; outdoor users are served directly by the BS using power-domain NOMA and SIC.The PA is movable along a dielectric waveguide to optimize its radiation point.Source: §II · p. 2
• Outdoor NOMA symbols are formed from user symbols weighted by coefficients b_k, which sum to one and are ordered b_1 ≥ b_2 ≥ ··· ≥ b_Kout.The indoor and outdoor beamforming vectors are w_in and w_out, and the normalized NOMA symbols have unit expected power.Source: §II · p. 2

A. Channel Model

• Channels are assumed constant within each transmission block.Source: A. Channel Model · p. 2

1) BS-to-Relay Channel:

• The BS-to-relay channel h_BR is modeled using large-scale path-loss attenuation β_BR and small-scale fading g_BR, with path loss depending on the BS-relay distance and path-loss exponent.The fading vector is complex circularly symmetric Gaussian with covariance I_M; the path-loss expression also uses reference loss C0.Source: 1) BS-to-Relay Channel · p. 2

2) Relay-to-Indoor User Pinching Channel:

• The relay-to-indoor-user channel depends on the movable PA position q, waveguide attenuation, and the physical propagation distance to the user.The term exp(−αq) scales signal loss from the corner-fed feed point to radiation point q.Source: 2) Relay-to-Indoor User Pinching Channel · pp. 2–3

3) Outdoor BS-to-User Channel:

• The BS directly serves outdoor users whose path loss depends on distance and whose channels follow a Rician fading model.The model includes a line-of-sight steering-vector component and a non-line-of-sight Rayleigh component.Source: 3) Outdoor BS-to-User Channel · p. 3

III. PROBLEM FORMULATION AND PROPOSED SOLUTION

• ZF beamforming is used to eliminate mutual interference, isolating the signal received at the AP from outdoor interference.The beamforming condition is stated using the aggregate outdoor channel matrix.Source: §III · p. 3
• The relay noise is modeled as additive white Gaussian noise.Source: §III · p. 3

• The AP allocates fraction ρR of received power to information processing and the remaining fraction to energy harvesting.Source: A. SWIPT-Based Energy Harvesting at… · p. 3
• The harvested relay power is scaled by the RF-to-DC conversion efficiency ξ.The passage defines ξ as an efficiency in (0, 1].Source: A. SWIPT-Based Energy Harvesting at… · p. 3
• All harvested energy is assumed to be used immediately for relay transmission.Source: A. SWIPT-Based Energy Harvesting at… · p. 3

• The relay retransmits the indoor signal using AF without decoding, subject to a transmit-power constraint set by harvested power.Source: B. AF Relay and Data Rates · p. 3
• The algorithm updates the BS indoor-power fraction, SWIPT ratio, and antenna position to meet indoor QoS, then uses SQP to allocate remaining power among outdoor NOMA users.It stops if the indoor target cannot be sustained and returns the optimized parameters and user rates otherwise.Source: B. AF Relay and Data Rates · p. 3
• The indoor achievable rate is obtained from the received indoor SINR.Source: B. AF Relay and Data Rates · p. 3

• The BS serves K outdoor users through power-domain NOMA and SIC decoding ordered by channel quality.Source: C. Outdoor Data Rate · p. 3
• The received SINR is formulated for outdoor user k under the NOMA and SIC model.Source: C. Outdoor Data Rate · p. 3
• Each outdoor user’s achievable data rate is given in terms of its received SINR.Source: C. Outdoor Data Rate · p. 3

D. Problem Formulation

• The objective maximizes outdoor WSR subject to minimum-rate requirements for the indoor user and each outdoor NOMA user.The design variables include the indoor power fraction, SWIPT power-splitting ratio, pinching-antenna position, and outdoor NOMA power coefficients.Source: D. Problem Formulation · pp. 3–4
• The constraints bound power fractions and antenna position physically, while distributing outdoor power among users with normalized NOMA coefficients.C3 requires full distribution of outdoor-subsystem power; C4 constrains each NOMA coefficient to its valid normalized range.Source: D. Problem Formulation · p. 4
• The coupled nonconvex problem is split by first minimizing the indoor power fraction to maximize power available to outdoor users.The first subproblem is subject to indoor QoS and the feasible power-fraction and antenna-position bounds.Source: D. Problem Formulation · p. 4
• Alternating optimization updates the indoor power fraction, splitting ratio, and antenna position; SQP then solves the outdoor NOMA allocation.The final solution is summarized by the optimized indoor variables and NOMA allocation vector.Source: D. Problem Formulation · p. 4

E. Convergence of P(1.1)

• For M = 16, the indoor SNR is approximately −25 dB while meeting the 0.5 bps/Hz indoor QoS target, with outdoor NOMA WSR of 1.6281 bps/Hz.The reported convergence results cover target rates of 0.5 and 1 bps/Hz.Source: E. Convergence of P(1.1) · p. 4
• Fig. 2 tracks convergence of P(1.1) when the indoor and outdoor minimum-rate targets are equal.The figure caption denotes the shared target as Rmin.Source: Figure 2 · p. 4
• The optimized antenna position is q⋆ = 1.69 and offsets from the user's coordinate x = 2 because of waveguide attenuation.Source: E. Convergence of P(1.1) · p. 4

IV. SIMULATION RESULTS

• 3.1953 bps/Hz is the outdoor WSR at 110 dB, rising from 1.7150 bps/Hz over the 100–110 dB SNR range.With unequal weights, User 2's rate rises from 3.3398 to 6.9690 bps/Hz; the equal-weight baseline assigns the highest rate to the nearest user, User 1.Source: §IV · p. 5
• As User 1's weight rises from 0.1 to 0.9, its rate increases while User 2's falls for both array sizes; WSR rises beyond its minimum at weight 0.5.At weight 0.9, WSR is 4.5807 bps/Hz for M = 8 and 4.7930 bps/Hz for M = 16; the WSR is consistently higher with M = 16.Source: §IV · p. 5, Figure 4 · p. 5
• For M = 16 with weights [0.1, 0.4, 0.3, 0.2], indoor QoS satisfaction remains 100% through a 1 bps/Hz target, while outdoor user rates remain stable across thresholds.The simulation results are averaged over independent channel realizations.Source: §IV · p. 5

V. CONCLUSION

• The framework integrates AF relaying, SWIPT, pinching-antenna positioning, ZF beamforming, and outdoor NOMA.The joint optimization targets weighted sum rate under indoor and outdoor QoS constraints.Source: §V · pp. 5–6
• The relay forwards indoors using harvested RF energy, while pinching-antenna positioning adds a degree of freedom for improving indoor coverage.Source: §V · p. 5
• Higher indoor rate requirements reduce outdoor performance, while additional BS antennas improve QoS satisfaction.The results describe a balance between indoor QoS and outdoor weighted sum rate.Source: §V · p. 6
• The nonconvex problem is decomposed into indoor operating-point optimization and outdoor NOMA power allocation, solved using AO and SQP, respectively.Source: §V · p. 6