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Cellular UAV-to-X Communications: Design and Optimization for Multi-UAV Networks

Shuhang Zhang, Hongliang Zhang, Boya Di, Lingyang Song

arXiv:1801.05000v2eess.SP

TL;DR

The paper addresses uplink data collection in multi-UAV cellular networks where weak direct UAV-to-BS links require U2U relaying. It proposes a cooperative protocol and an iterative optimization algorithm for channel allocation and UAV speeds, achieving about 10% more uplink sum-rate than a greedy algorithm.

  • Problem

    Low-SNR UAVs may have weak direct links to the BS, motivating a communication design that supports timely data upload through U2I and U2U modes.

  • Method

    The paper proposes a cooperative UAV sense-and-send protocol and iteratively solves decomposed U2I/CU allocation, U2U allocation, and UAV speed optimization sub-problems.

  • Results

    10% more uplink sum-rate is achieved by ISASOA than by the greedy algorithm.

  • Takeaways & Limitations

    The proposed UAV-to-X design combines direct U2I uploads with U2U relaying for multi-UAV data collection and uplink optimization.

Abstract

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In this paper, we consider a single-cell cellular network with a number of cellular users (CUs) and unmanned aerial vehicles (UAVs), in which multiple UAVs upload their collected data to the base station (BS). Two transmission modes are considered to support the multi-UAV communications, i.e., UAV-to-infrastructure (U2I) and UAV-to-UAV (U2U) communications. Specifically, the UAV with a high signal to noise ratio (SNR) for the U2I link uploads its collected data directly to the BS through U2I communication, while the UAV with a low SNR for the U2I link can transmit data to a nearby UAV through underlaying U2U communication for the sake of quality of service. We first propose a cooperative UAV sense-and-send protocol to enable the UAV-to-X communications, and then formulate the subchannel allocation and UAV speed optimization problem to maximize the uplink sum-rate. To solve this NP-hard problem efficiently, we decouple it into three sub-problems: U2I and cellular user (CU) subchannel allocation, U2U subchannel allocation, and UAV speed optimization. An iterative subchannel allocation and speed optimization algorithm (ISASOA) is proposed to solve these sub-problems jointly. Simulation results show that the proposed ISASOA can upload 10\% more data than the greedy algorithm.

I. INTRODUCTION

The paper develops cellular UAV-to-X communications for UAVs that collect data along trajectories and upload it to a BS, including low-SNR UAV relaying through U2U links. It jointly addresses spectrum allocation and UAV speed optimization, proposing ISASOA, which achieves about 10% higher uplink sum-rate than a greedy algorithm.

  • UAVs collect sensory data along predetermined trajectories and upload it to a cellular base station.
  • Low-SNR UAVs relay collected data through U2U links to nearby high-SNR UAVs, which cache and later upload it to the BS.
  • U2U transmissions underlay U2I and CU links, creating mutual interference that requires efficient spectrum allocation.
  • The paper proposes a cooperative UAV sense-and-send protocol and formulates joint subchannel allocation and UAV speed optimization for uplink sum-rate maximization.
  • The NP-hard optimization is decomposed into U2I/CU allocation, U2U allocation, and UAV speed optimization, solved iteratively by ISASOA.
  • 10% higher uplink sum-rate is achieved by ISASOA than by the greedy algorithm in simulations.

II. SYSTEM MODEL

The system model defines a single-cell network with a BS, CUs, and mobile UAVs that collect and transmit data over U2I or U2U links. U2U links reuse U2I and CU spectrum under allocation, rate, and mobility constraints.

  • A. Scenario Description: The network contains one BS, multiple fixed cellular users, and UAVs moving along predetermined trajectories to collect data.
  • A. Scenario Description: UAV position evolves with its per-slot velocity and trajectory direction, while speed is bounded by the rotary-wing UAV maximum velocity.
  • B. Data Transmission: High-SNR UAVs use direct U2I transmission, whereas low-SNR UAVs send data to high-SNR UAVs through U2U relaying.
  • B. Data Transmission: U2U transmissions operate as an underlay and share spectrum with U2I and CU transmissions, while sensing and transmission occur simultaneously.
  • B. Data Transmission: Each subchannel serves at most one U2I or CU link but may serve multiple U2U links, subject to per-link subchannel limits.
  • B. Data Transmission: Binary matrices Φ(t) and Ψ(t) represent U2I/CU and U2U subchannel assignments, while ξ_i,j(t) indicates U2U pairing.

C. Channel Model

The channel model distinguishes U2I, CU, and U2U transmissions according to their propagation characteristics. For U2I links, air-to-ground path loss, line-of-sight probability, interference, noise, and received power determine SINR and rate.

  • U2I, CU, and U2U links use different channel models because their line-of-sight probabilities and elevation angles differ.
  • 1) U2I Channel Model: The U2I model uses air-to-ground propagation with free-space path loss and additional LoS and NLoS attenuation factors.
  • 1) U2I Channel Model: LoS probability is modeled from elevation angle using environment-dependent constants a and b.
  • 1) U2I Channel Model: The BS SINR combines received signal power, U2U interference, and AWGN, and determines the received U2I data rate.
  • 1) U2I Channel Model: Because each subchannel has at most one U2I or CU link, U2I interference comes from U2U transmissions sharing that subchannel.

2) CU Channel Model:

The paper models CU and U2U channels and uses a five-step cooperative sense-and-send protocol to coordinate UAV data transmission through the BS.

  • 2) CU Channel Model:: The macrocell pathloss model is used for CU-to-BS links, while free-space channels are used for U2U communication.
  • 2) CU Channel Model:: CU and UAV transmissions share subchannels, so received signals account for interference and additive white Gaussian noise.The text defines received powers, interference terms, and AWGN for the relevant links.
  • 3) U2U Channel Model:: U2U data rate is expressed as Rk_i,j(t) = log2(1 + γk_i,j(t)).The U2U SINR γk_i,j(t) incorporates the received signal, interference, and noise over subchannel k.
  • III. COOPERATIVE UAV SENSE-AND-SEND PROTOCOL: The protocol divides each time slot into UAV sensing, UAV report, BS decision, link access, and data transmission.UAVs cache sensed data, report IDs and locations, receive BS decisions, establish links, and transmit during the slot.
  • III. COOPERATIVE UAV SENSE-AND-SEND PROTOCOL: The BS categorizes UAVs by received SNR, assigning high-SNR UAVs to U2I transmission and low-SNR UAVs to U2U transmission.Low-SNR UAVs are paired with their closest UAVs performing U2I transmission.
  • III. COOPERATIVE UAV SENSE-AND-SEND PROTOCOL: After optimization results are delivered, UAVs move at the optimized speed and transmit over allocated U2I or U2U subchannels.U2U UAVs establish links with corresponding UAV relays before data transmission begins.

IV. PROBLEM FORMULATION

The paper formulates uplink sum-rate maximization with subchannel allocation and UAV speed variables, then decomposes the NP-hard problem into three iteratively solved sub-problems.

  • IV. PROBLEM FORMULATION: The joint subchannel allocation and UAV speed optimization problem maximizes uplink sum-rate over allocation and UAV speed variables.The optimized variables include Φ(t), ω(t), and UAV speed norms ∥vi(t)∥.
  • A. Joint Subchannel Allocation and UAV Speed Optimization Problem Formulation: The formulation includes minimum U2U rate, maximum UAV speed, task completion time, subchannel exclusivity, and χmax allocation constraints.Each subchannel serves at most one U2I UAV or CU, while each UAV and CU can use at most χmax subchannels.
  • B. Problem Decomposition: The NP-hard problem is decoupled into U2I/CU subchannel allocation, U2U subchannel allocation, and UAV speed optimization.In each sub-problem, the other relevant pairing matrices or speed variables are held fixed.
  • V. JOINT SUBCHANNEL ALLOCATION AND UAV SPEED OPTIMIZATION: ISASOA obtains a sub-optimal solution by solving the three sub-problems iteratively.The iterations continue until the objective function converges to a constant.
  • A. U2I and CU Subchannel Allocation Algorithm: The U2I and CU allocation sub-problem is relaxed to a standard linear program solvable with existing convex techniques such as CVX.The objective and constraints of the relaxed problem are linear in Φ(t).
  • V. JOINT SUBCHANNEL ALLOCATION AND UAV SPEED OPTIMIZATION: The non-convex U2U allocation sub-problem is solved using branch-and-bound, while the speed sub-problem is converted into a convex problem.The speed problem is solved with existing convex techniques after its feasible region is analyzed.
  • A. U2I and CU Subchannel Allocation Algorithm: Theorem 2 shows that the relaxed U2I/CU allocation solution has binary Φ(t) variables and is equivalent to the original sub-problem.Thus, relaxing φi,k(t) does not affect the solution of sub-problem (25).

B. U2U Subchannel Allocation Algorithm

The U2U subchannel allocation problem is NP-hard and remains non-convex under relaxation because of inter-link interference. The paper therefore uses branch-and-bound with an LFSS-generated feasible starting solution.

  • Problem (26) is a 0-1 programming problem that is NP-hard.
  • Interference among U2U links leaves the relaxed problem non-convex in Ψ(t), preventing direct use of existing convex techniques.
  • The branch-and-bound method searches the binary solution tree while pruning infeasible branches to approach the optimal U2U pairing efficiently.
  • LFSS constructs an initial feasible solution by assigning preferred subchannels until every U2U transmitter meets its minimum rate threshold.
  • Each U2U transmitter ranks subchannels by achievable rate while initially accounting for U2I and CU interference.

2) Bound Calculation:

The bound-calculation procedure evaluates objective and constraint upper bounds, prunes nodes that cannot improve the current feasible solution, and fixes variables when only one value remains feasible.

  • The initial feasible U2U pairing solution is used as the lower bound before searching the binary tree.
  • Objective-bound calculation fathoms a node when its upper bound falls below the current solution lower bound.
  • Constraint-bound calculation fathoms a node when some UAV cannot reach its minimum U2U rate threshold under the node’s most favorable assignments.
  • Variable fixation sets an unfixed ψ_i,k(t) to 0 or 1 when the alternative branch violates objective or constraint bounds.
  • The search terminates when all variables are fixed, yielding the final U2U subchannel allocation solution.

C. UAV Speed Optimization Algorithm

UAV speed optimization is separated for non-U2U UAVs and U2U-participating UAV pairs. The resulting subproblems are approximated or reformulated as convex problems under trajectory and propagation assumptions.

  • Speed optimization separates non-U2U-participating UAVs from U2U-participating transmitting and receiving UAVs.
  • Trajectory constraints limit future movement to the remaining time slots multiplied by the maximum UAV speed.
  • For non-U2U UAVs, the LoS/NLoS pathloss is assumed unchanged within a time slot because movement is much shorter than trajectory length.
  • The non-U2U speed problem is approximated as convex and solved using existing convex optimization methods.

2) U2U Participated UAV Speed Optimization:

For U2U-participating UAV pairs, the paper converts the U2U rate constraint into a distance constraint and derives feasible speed ranges before solving convex speed subproblems. ISASOA iteratively updates allocations and speeds until convergence.

  • 2) U2U Participated UAV Speed Optimization:: A U2U-transmitting UAV sends collected data to its paired receiving UAV, which simultaneously performs U2I transmission.
  • 2) U2U Participated UAV Speed Optimization:: The U2U rate constraint is transformed into a distance constraint given the U2I and U2U subchannel pairing matrices.
  • 2) U2U Participated UAV Speed Optimization:: Because U2U transmission distance greatly exceeds one-slot movement, interference is approximated as constant.
  • 2) U2U Participated UAV Speed Optimization:: The paired UAV speeds are restricted to feasible ranges derived from trajectory limits and maximum pairwise distance.
  • ISASOA alternates U2I/CU allocation, U2U allocation, and speed optimization until successive objective values differ by less than ε.
  • ISASOA is convergent, with complexity O((N_h(t) + M) × 2^N_l(t)).

VI. SIMULATION RESULTS

Simulations evaluate ISASOA under varying transmission ratios, task deadlines, UAV heights, and speed limits. ISASOA generally improves uplink performance over the greedy algorithm, while network conditions create trade-offs between U2I and U2U throughput.

  • Overall comparison: 10% higher uplink sum-rate is achieved by ISASOA than by the greedy algorithm on average.The reported improvement is attributed to efficient U2I and U2U subchannel allocation.
  • U2I/U2U allocation trade-off: Increasing the U2U-UAV/UAV ratio decreases uplink sum-rate because fewer UAVs perform U2I transmission and more UAVs receive U2U data.The total U2U transmission rate increases with the ratio, but its increment decreases as the ratio grows.
  • Network capacity: More U2I UAVs increase U2I and CU transmission sum-rate, but growth slows as N increases because network capacity saturates.U2U transmission rates can be constrained by interference and by U2U rate requirements.
  • Task completion time and height: A larger minimum task completion time T increases uplink sum-rate, while the 200 m height scenario outperforms the 100 m scenario.The height difference is attributed to a higher probability of LoS U2I transmission at 200 m, and the gap decreases as T grows.
  • UAV speed: Uplink sum-rate increases significantly with maximum UAV speed when vmax ≤20 m/time slot and becomes stable when vmax >30 m/time slot.Higher speed provides more freedom for speed optimization, but speed is no longer the main restriction once sufficiently large.

VII. CONCLUSION

The paper studies data delivery from multiple UAVs to a BS through U2I and U2U transmissions. It proposes a cooperative protocol, decomposes the NP-hard optimization, and reports about 10% higher uplink sum-rate than a greedy algorithm.

  • The study considers a single-cell multi-UAV network in which UAVs upload collected data to the BS through U2I and U2U transmissions.
  • A cooperative UAV sense-and-send protocol and a joint subchannel allocation and UAV speed optimization problem are proposed.
  • The NP-hard optimization is decomposed into U2I/CU allocation, U2U allocation, and UAV speed optimization sub-problems.
  • ISASOA uses optimization methods to obtain a convergent solution to the decomposed problem.
  • The studied single-cell network can be extended to multiple cells with BS association and inter-cell interference consideration.
  • About 10% more uplink sum-rate is achieved by ISASOA than by the greedy algorithm.

APPENDIX A PROOF OF THEOREM 1

The appendix proves that the joint optimization problem is NP-hard by reducing a constructed instance to three-dimensional matching. It also establishes that optimal allocation variables are binary.

  • NP-hardness proof: The proof constructs an instance with U2I/CU UAVs, U2U UAVs, and subchannels represented as ordered triples.
  • NP-hardness proof: A subset of triples satisfying distinctness and cardinality conditions forms a three-dimensional matching.
  • NP-hardness proof: Because three-dimensional matching is NP-complete, the constructed instance and the original optimization problem are NP-hard.
  • Binary allocation: Any solution containing a fractional allocation variable can be improved by reallocating assignment weight among variables.
  • Binary allocation: All variables in Φ(t) are either 0 or 1 at the optimum.
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