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Millimeter-Wave Full-Duplex UAV Relay: Joint Positioning, Beamforming, and Power Control
Lipeng Zhu, Jun Zhang, Zhenyu Xiao, Xianbin Cao, Xiang-Gen Xia, Robert Schober
TL;DR
Blocked direct links and high path loss complicate mmWave communication between ground nodes. This paper jointly optimizes FD-UAV relay positioning, analog beamforming, and power control, using a conditional position solution and an alternating interference suppression algorithm. Simulations show the method outperforms three benchmark schemes and closely approaches a performance upper bound.
Problem
The paper addresses how to maximize the achievable rate between ground nodes when mmWave path loss and blockage motivate an FD-UAV relay, while relay position, beamforming, and power control are coupled.
Source: §I · p. 2Method
It derives a conditional relay position under LoS and ideal beamforming assumptions, then uses AIS to jointly design beamforming vectors and power control.
Source: §I · p. 2Results
The proposed joint method outperforms three benchmark schemes and closely approaches a performance upper bound for mmWave FD-UAV relay systems.
Source: §I · p. 3, §V · p. 13Takeaways & Limitations
The results support the proposed positioning, beamforming, and power-control solution as a near-upper-bound approach for the considered mmWave FD-UAV relay system.
Source: §V · p. 13Position optimization assumes LoS links and ideal beamforming, and uses approximate upper bounds because NLoS paths are not known across candidate UAV positions.
Source: A. Positioning Under Ideal Beamforming · p. 6
Abstract
from arXiv · showhide
In this paper, a full-duplex unmanned aerial vehicle (FD-UAV) relay is employed to increase the communication capacity of millimeter-wave (mmWave) networks. Large antenna arrays are equipped at the source node (SN), destination node (DN), and FD-UAV relay to overcome the high path loss of mmWave channels and to help mitigate the self-interference at the FD-UAV relay. Specifically, we formulate a problem for maximization of the achievable rate from the SN to the DN, where the UAV position, analog beamforming, and power control are jointly optimized. Since the problem is highly non-convex and involves high-dimensional, highly coupled variable vectors, we first obtain the conditional optimal position of the FD-UAV relay for maximization of an approximate upper bound on the achievable rate in closed form, under the assumption of a line-of-sight (LoS) environment and ideal beamforming. Then, the UAV is deployed to the position which is closest to the conditional optimal position and yields LoS paths for both air-to-ground links. Subsequently, we propose an alternating interference suppression (AIS) algorithm for the joint design of the beamforming vectors and the power control variables. In each iteration, the beamforming vectors are optimized for maximization of the beamforming gains of the target signals and the successive reduction of the interference, where the optimal power control variables are obtained in closed form. Our simulation results confirm the superiority of the proposed positioning, beamforming, and power control method compared to three benchmark schemes. Furthermore, our results show that the proposed solution closely approaches a performance upper bound for mmWave FD-UAV systems.
I. INTRODUCTION
The paper addresses blocked mmWave links using an FD-UAV relay and jointly designs relay placement, analog beamforming, and transmit power. Its model uses simultaneous source-to-relay and relay-to-destination transmissions, with the end-to-end rate limited by the weaker hop.
I. INTRODUCTION
- mmWave’s high propagation loss requires beamforming, yet ground obstacles can block LoS links and severely attenuate received power.UAVs offer flexible deployment and often have a high probability of LoS to ground users; large arrays support directional gains and interference suppression.Source: §I · pp. 1–2
- The paper places an FD-UAV relay between the source node (SN) and destination node (DN) to establish an LoS route when buildings block the direct mmWave link.The relay uses large antenna arrays and directional beams; unavoidable sidelobes can still create self-interference (SI).Source: §I · p. 2, Figure 1 · p. 3
- Prior mmWave relay studies did not consider 3-D UAV positioning, while cited UAV studies did not account for mmWave channels and 3-D analog beamforming.The paper therefore jointly considers relay position, beamforming, and power control.Source: §I · p. 2
- The paper formulates achievable-rate maximization and proposes a conditional closed-form relay position plus an alternating interference suppression (AIS) algorithm for beamforming and power control.AIS alternates target-signal beam-gain maximization with successive interference reduction and updates the optimal powers in closed form.Source: §I · p. 2
A. Signal Model
- The SN transmits to the UAV while the UAV concurrently transmits to the DN, making the relay full duplex and exposing its receiver to SI.Analog beamforming is chosen for energy efficiency and to support analog-domain SI cancellation before digital sampling.Source: A. Signal Model · p. 3
- The end-to-end achievable rate is the minimum of the SN-to-UAV and UAV-to-DN link rates, while the blocked direct SN-to-DN signal is treated as interference at the DN.The link-rate expressions assume coherent detection.Source: A. Signal Model · p. 4
B. Channel Model
The channel model represents the air-to-ground and direct links as sparse far-field multipath channels, while modeling relay self-interference in the near field. It makes channel conditions and link geometry dependent on the UAV’s position.
B. Channel Model
- The S2V, V2D, and S2D channels are modeled as superpositions of multipath components with distinct departure and arrival angles, reflecting mmWave channel sparsity and directionality.The direct SN-to-DN LoS path is assumed blocked, motivating the relay.Source: B. Channel Model · p. 4
- The relay’s LoS self-interference channel uses a near-field model because the far-field range condition generally does not hold between its transmit and receive arrays.Although NLoS SI paths may exist, the model focuses on the more powerful LoS component; the relay is assumed to obtain slowly varying SI-channel state information.Source: B. Channel Model · p. 4
- For the far-field links, NLoS path angles are uniformly distributed and fading coefficients are modeled as circularly symmetric complex Gaussian variables, corresponding to Rayleigh fading.LoS existence for the air-to-ground links is modeled as a logistic function of elevation angle, with parameters that depend on the propagation environment.Source: B. Channel Model · pp. 4–5
- The S2V and V2D channel geometry depends on the UAV’s three-dimensional coordinates, with the SN and DN at zero altitude and the UAV at altitude hV.The model specifies link distances and LoS departure and arrival angles from this coordinate system.Source: B. Channel Model · pp. 4–5
- The channel matrices, path loss, spatial angles, and LoS probabilities vary with UAV position, but instantaneous CSI is assumed available only after deployment at a fixed position and channel estimation.The UAV can acquire CSI only for its current position.Source: B. Channel Model · pp. 4–5
C. Problem Formulation
The paper formulates joint optimization of UAV position, analog beamforming, and transmit powers, then develops a suboptimal solution because these variables are highly coupled. Positioning uses an LoS, ideal-beamforming approximation followed by a search for a nearby position with LoS on both hops.
C. Problem Formulation
- The optimization jointly selects the UAV position, beamforming vectors, and SN and relay transmit powers to maximize the SN-to-DN achievable rate.The relay must lie between the nodes, satisfy altitude bounds, obey power limits, and use constant-modulus analog beamforming vectors.Source: C. Problem Formulation · p. 5
- The coupled, high-dimensional, non-convex variables make direct solution difficult, so the paper develops a suboptimal staged solution.It first optimizes position, then jointly optimizes beamforming and power for the selected position and its CSI.Source: C. Problem Formulation · p. 5, §III · p. 5
A. Positioning Under Ideal Beamforming
- The position stage neglects NLoS paths and assumes LoS on both air-to-ground links with ideal beamforming, which gives full array gains and eliminates SI and direct-link interference in the beamforming domain.Under these assumptions, the upper-bound rates depend on link distances and transmit powers.Source: A. Positioning Under Ideal Beamforming · pp. 5–6
- The approximate upper bounds use pure-LoS rates, whereas the strict upper bounds also account for NLoS paths.The paper evaluates the gap between these bounds in simulation.Source: A. Positioning Under Ideal Beamforming · p. 6
- Theorem 1 gives a closed-form conditional optimal relay position for the LoS, ideal-beamforming setting.The position maximizes an approximate upper bound; NLoS paths are not known in advance for different candidate positions, so the approximate rather than strict upper bounds guide placement.Source: A. Positioning Under Ideal Beamforming · p. 6
- If the conditional optimal position lacks LoS on both hops, the UAV searches progressively larger neighborhoods and selects a nearest candidate that provides LoS for both links.The search is over the feasible position region; when multiple candidates tie for nearest, one is selected at random.Source: A. Positioning Under Ideal Beamforming · pp. 6–7
- Maximal transmit powers during positioning can waste power or worsen the rate when one hop is already the bottleneck or residual SI increases with relay power.The paper therefore designs beamforming before optimizing power control.Source: A. Positioning Under Ideal Beamforming · p. 7
B. Beamforming Design
The AIS algorithm alternates beamformer design to increase desired-link gains while progressively suppressing self-interference and direct-link interference. Its relaxed beamformer updates have limited rate impact after normalization, while stricter interference suppression trades off against target-signal gain.
B. Beamforming Design
- AIS alternates SN, DN, and UAV transmit/receive beamformer updates, maximizing desired-link power while suppressing S2D interference or relay self-interference.The beamformer design assumes full CSI and accounts for LoS and NLoS components on the S2V and V2D links.Source: B. Beamforming Design · p. 7
- At convergence, the self-interference and S2D interference powers are bounded by the suppression-factor limit.The paper states that the suppression factor converges to its lower bound η.Source: B. Beamforming Design · p. 8
- Smaller suppression-factor limits reduce interference, but overly strict limits also reduce target-signal gains.The paper describes a tradeoff between interference power and target-signal power.Source: B. Beamforming Design · p. 8
- The relaxed beamformer solution can violate the constant-modulus constraint in at most one element, limiting normalization's impact when arrays are large.The paper states that a single element's normalization has a small effective-channel-gain impact for large antenna counts.Source: B. Beamforming Design · p. 8
C. Power Control
For fixed UAV position and beamformers, the paper derives an optimal transmit-power allocation for the source and relay. The allocation targets balanced hop rates while limiting total transmit power.
C. Power Control
- The optimal power allocation is derived for a given UAV position and set of beamformers.The objective is to maximize the minimum of the S2V and V2D rates while minimizing total transmit power.Source: C. Power Control · p. 8
- At least one of the source or relay transmit powers takes its maximum allowed value at the optimum.Source: C. Power Control · p. 8
- The power-control derivation balances the S2V and V2D achievable rates by adjusting source and relay transmit powers.The passages describe changing one node's power to trade rate between the two hops.Source: C. Power Control · pp. 8–9
D. Overall Solution
The overall procedure first selects an FD-UAV position under idealized assumptions, then keeps that position fixed while alternating beamformer and power updates. It stops when the achievable-rate improvement falls below a threshold.
D. Overall Solution
- The procedure first finds a conditional optimal UAV position assuming LoS and ideal beamforming, then searches its neighborhood for a deployment position.Source: D. Overall Solution · p. 9
- With the position fixed, the algorithm alternates interference-reducing beamformer subproblems and incorporates closed-form optimal power allocation at each iteration.Source: D. Overall Solution · p. 9
- The algorithm terminates when the rate improvement between iterations falls below εr, and does not update the UAV position during the iterative phase.The paper says the fixed-position solution achieves near-optimal performance when beamforming approaches ideal beamforming.Source: D. Overall Solution · p. 9
IV. PERFORMANCE EVALUATION
The performance-evaluation section assesses the proposed joint scheme through simulations and compares it with three benchmark designs. The setup averages results over node distributions and channel realizations.
IV. PERFORMANCE EVALUATION
- The simulations evaluate the proposed joint positioning, beamforming, and power-control scheme for mmWave FD-UAV relay systems.Source: §IV · p. 9
A. Simulation Setup and Benchmark Schemes
- Each simulation point averages 103 node distributions and channel realizations, with the destination randomly placed within a 500 m-radius disk centered on the source.The setup uses half-wavelength-spaced UPAs, with the relay's transmit and receive arrays separated by 10λ (approximately 8 cm).Source: A. Simulation Setup and Benchmark… · p. 9
- The comparisons include random-position AIS, designed-position steering, and designed-position OMP beamforming, all using the theorem-based optimal transmit powers.The study also considers approximate and strict achievable-rate upper bounds with the relay at its designed position.Source: A. Simulation Setup and Benchmark… · p. 10
B. Simulation Results
The proposed joint design outperforms the benchmark schemes while achieving rates close to the performance upper bound. Simulations also examine convergence and rate sensitivity to power, distance, array size, and beam misalignment.
B. Simulation Results
- With 4×4 and 8×8 relay arrays, AIS converges to within 0.3 and 0.1 bps/Hz of the upper bound, respectively; larger κ speeds convergence.The approximate upper bound is reported as very close to the strict upper bound.Source: Figure 2 · p. 10, B. Simulation Results · p. 10
- For all tested maximum relay transmit powers, AIS reaches steady state after four iterations, with higher relay power requiring more iterations as it increases self-interference.Source: Figure 3 · p. 10, B. Simulation Results · p. 11
- During AIS, the self-interference channel gain falls rapidly while the S2V and V2D gains remain nearly unchanged; relay power rises after SI suppression.Initially, the relay uses very low power because the S2V link experiences high SI; after SI falls, it can increase power to improve the V2D rate.Source: Figure 4 · p. 11, B. Simulation Results · p. 11
- The proposed joint positioning, beamforming, and power-control method stays close to the performance upper bound and outperforms all benchmark schemes as SN transmit power varies.The results are shown for achievable rate versus SN transmit power.Source: Figure 5 · p. 11, B. Simulation Results · p. 11
- As relay power increases, the proposed method's rate improves more slowly because the UAV shifts toward the SN and the S2V link eventually limits performance.The “DesPos & steer” scheme remains low-rate as relay power rises because steering-vector beamforming leaves high SI at the relay.Source: Figure 6 · p. 11, B. Simulation Results · p. 12
- As SN power increases, the conditional UAV position shifts toward the DN, eventually leaving the V2D link as the rate-limiting link.At sufficiently large SN power, the conditional position is directly above the DN and the V2D rate cannot increase further.Source: B. Simulation Results · p. 11
- All five schemes lose achievable rate as SN-DN distance grows, while “RandPos & AIS” declines rapidly because random UAV placements can stray farther from the conditional optimum.Source: Figure 7 · p. 12, B. Simulation Results · p. 12
- Larger arrays increase the proposed method's rate through higher array gains and more SI-suppression degrees of freedom; rates remain close to the upper bound for misalignment deviations up to 10°.The authors report that larger arrays have narrower beams and are more sensitive to misalignment.Source: Figure 8 · p. 12, B. Simulation Results · p. 12
V. CONCLUSION
The paper jointly optimizes FD-UAV positioning, analog beamforming, and power control for a mmWave relay, using a conditional position result and an iterative design. Simulations show the method approaches an achievable-rate upper bound and outperforms three benchmarks.
V. CONCLUSION
- The conditional optimal relay position maximizes an approximate achievable-rate upper bound under LoS and ideal beamforming assumptions.The deployed UAV is placed closest to that conditional position while yielding LoS paths on both air-to-ground links.Source: §V · pp. 12–13
- The proposed joint positioning, beamforming, and power-control method closely approaches an achievable-rate upper bound and significantly outperforms three benchmark schemes.The relay-positioning step uses an approximate upper bound under LoS and ideal-beamforming assumptions; the iterative step updates beamforming vectors and power control.Source: §V · p. 13
- The iterative algorithm jointly optimizes beamforming vectors and power-control variables, reducing interference while maximizing target-signal beam gains.Optimal power-control variables are updated in closed form in each iteration.Source: §V · p. 13
APPENDIX A PROOF OF THEOREM 1
The proof places the relay on the SN–DN segment at minimum altitude and selects its position to maximize the minimum of the two hop rates. The optimum is an endpoint when one link rate dominates throughout; otherwise, it equalizes the link rates.
APPENDIX A PROOF OF THEOREM 1
- The relay lies on the SN–DN line segment at minimum altitude, since moving off it increases both hop distances and propagation loss.Its coordinates are parameterized as (ρxD, ρyD, hmin), with 0 ≤ ρ ≤ 1.Source: Appendix A · p. 13
- When the S2V rate is the limiting rate throughout, the minimum rate is maximized by placing the relay at the SN; when the V2D rate limits throughout, it is placed at the DN.These endpoint cases correspond to ρ⋆ = 0 and ρ⋆ = 1, respectively.Source: Appendix A · p. 13
- When neither hop rate dominates throughout, the minimum rate is maximized where the S2V and V2D rates are equal.The resulting equation for ρ has a unique solution in [0, 1].Source: Appendix A · p. 13
APPENDIX B PROOF OF THEOREM 2
The proof establishes that an optimal beamforming vector can always be chosen with at most one element violating the CM constraint. It uses a constant-ratio property and pairwise element adjustments that preserve optimality.
APPENDIX B PROOF OF THEOREM 2
- With other BFV elements fixed, the proof adjusts a pair of elements while preserving an optimal solution.In one case, phase adjustments yield an optimal solution with all elements satisfying the CM constraint; in another, an optimal solution can be formed with only one of the pair violating it.Source: Appendix B · pp. 13, 15
- The constant-ratio property states that the relevant ratio for two BFV elements remains the same regardless of their values.This property supports constructing another optimal solution in which at least one of the two elements satisfies the CM constraint.Source: Appendix B · p. 14
- An optimal beamforming vector always exists with at most one element that does not satisfy the CM constraint.The proof reduces multiple violating elements through repeated pairwise construction.Source: Appendix B · p. 15