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Achievable Rate Region Characterization of Rotatable Antenna-assisted Interference Channel
Junran Pei, Guangji Chen, Qingqing Wu, Qiaoyan Peng, Wei Cai
TL;DR
Fixed-position antennas may not fully exploit available spatial degrees of freedom, while joint beamforming and rotation optimization is challenging. The paper characterizes the achievable rate region using rotation and beamforming designs, and reports that RA-optimized strategies can approach the interference-free bound while simple MRT can yield comparable performance with simpler transceiver design.
Problem
Fixed-position antennas may not fully unlock spatial degrees of freedom, while rotation makes joint beamforming optimization challenging.
Source: §I · p. 1, §II · p. 2Method
The paper derives closed-form rotation and beamforming solutions for two receivers and extends their insights to a general multi-receiver optimization approach.
Source: §I · p. 1Results
RA-optimized MRT and ZF achieve performance nearly identical to the interference-free upper bound in both low- and high-SNR regimes.
Source: A. Two-receiver Scenario · p. 5Takeaways & Limitations
Under favorable channel conditions created by RAs, simple MRT approaches the interference-free upper bound with negligible performance loss, simplifying transceiver design.
Source: §I · p. 2
Abstract
from arXiv · showhide
This paper characterizes the achievable rate region of a rotatable antenna (RA)-assisted multiple-input single-output (MISO) interference channel. We exploit the additional spatial degrees of freedom (DoFs) offered by the dynamic orientation of RAs to simultaneously enhance the desired signal and suppress interference, thereby significantly enlarging the achievable rate region of the interference network. To this end, we invoke the rate-profile technique to formulate a sum-rate maximization problem for jointly optimizing the transmit beamforming and the array rotation, subject to the practical mechanical constraints of the RAs. For the special case of a two-receiver scenario, we introduce the concept of subspace correlation coefficient to derive closed-form solutions for the optimal RA rotation angles and transmit beamforming vectors. Inspired by the insights obtained in the two-receiver special case, we propose an efficient two-step optimization framework to obtain a high-quality solution for the general multi-receiver case. In particular, the array rotation angle of each transmitter is optimized to minimize the leakage interference to non-associated receivers. With the optimized array rotation angles, the optimal transmit beamforming is obtained by invoking the second order cone programming based approach. Numerical results demonstrate that the proposed solution achieves near-optimal performance and that integrating RAs effectively simplifies transceiver designs by enabling simple maximum ratio transmission (MRT) beamforming with negligible performance loss.
I. INTRODUCTION
The paper addresses the largely unknown achievable rate region of an RA-assisted MISO interference channel, where antenna rotation adds a design dimension but makes joint optimization challenging. It models LoS links and uses rate profiles to characterize the region under power and rotation constraints.
I. INTRODUCTION
- The achievable rate region of an RA-assisted MISO interference channel remains largely unknown, motivating its characterization.Co-channel interference is a critical challenge in networks with dense nodes and universal frequency reuse.Source: §I · p. 1
- The paper derives closed-form rotation and beamforming solutions for two receivers, then proposes a low-complexity two-stage algorithm for general multi-receiver scenarios.The general method minimizes leakage to non-associated receivers before applying SOCP beamforming.Source: §I · p. 1
II. SYSTEM MODEL
- The system has K transmitter–receiver pairs, each transmitter using a uniform linear RA array and serving an associated single-antenna receiver over LoS-dominated channels.The model defines the channel using transmitter–receiver geometry and the array rotation angle.Source: §II · p. 2
- The rate-profile technique characterizes Pareto-boundary rate tuples by maximizing sum rate for target rate ratios, subject to per-transmitter power limits and rotation angles in [0, π).The complete boundary is obtained by solving for all possible rate-profile weights.Source: §II · p. 2
- Jointly optimizing beamforming and rotation is challenging because rotation affects channel vectors nonlinearly, and no standard method solves the formulation optimally.Rotation adds a design dimension for shaping the spatial interference subspace.Source: §II · p. 2
III. PROPOSED SOLUTION
The solution strategy uses a closed-form two-receiver case to inform a high-quality algorithm for general multi-receiver scenarios.
III. PROPOSED SOLUTION
- The two-receiver case has a closed-form optimal solution that provides insights for an efficient, high-quality solution in the general multi-receiver case.The passage presents the special case as the basis for the general algorithm.Source: §III · p. 2
A. Special Case of Two-receiver Setup
For two receivers, the paper relates the interference-free rate upper bound to spatial orthogonality and derives closed-form antenna rotations and beamforming solutions.
A. Special Case of Two-receiver Setup
- Achieving the rate upper bound requires complete spatial orthogonality between the desired and interference channels, which the subspace correlation coefficient measures.The paper introduces the coefficient to quantify this orthogonality condition.Source: A. Special Case of Two-receiver Setup · p. 3
- A minimum spatial-angle separation condition permits perfect desired–interference channel orthogonality and is described as readily satisfied when each receiver is near its associated transmitter.The condition is derived for the optimal rotation angles.Source: A. Special Case of Two-receiver Setup · p. 3
- With the optimal rotation, each transmitter’s optimal beamforming reduces to maximum ratio transmission, which can cancel interference without losing desired-signal power.Under ideal spatial orthogonality, Gaussian signaling with MRT becomes information-theoretically optimal.Source: A. Special Case of Two-receiver Setup · p. 3
B. General Multi-receiver Scenario
For general multi-receiver scenarios, the approach first analyzes the gap to the interference-free bound, then optimizes rotation and beamforming.
B. General Multi-receiver Scenario
- The general method minimizes interference leakage by optimizing antenna rotations, then obtains optimal transmit beamforming under those rotations.The rotation optimization is motivated by an upper-bound analysis of the performance gap to the interference-free bound.Source: B. General Multi-receiver Scenario · p. 3
1) Rate Gap Analysis:
This section bounds the rate gap between arbitrary antenna rotations and the interference-free rate upper bound. It uses an MRT-based lower bound on achievable rate to establish the gap bound.
1) Rate Gap Analysis:
- The rate-gap analysis compares rates under arbitrary rotations with an ideal interference-free upper bound.The interference-free rate upper bound is defined for each receiver.Source: 1) Rate Gap Analysis · pp. 3–4
- The analysis defines each receiver’s rate gap as the interference-free rate upper bound minus its achievable rate under arbitrary rotations.Theorem 2 provides an upper bound on this gap for any receiver.Source: 1) Rate Gap Analysis · p. 3
- For arbitrary rotation angles, MRT beamforming yields a lower bound on each receiver’s achievable rate.The bound is obtained by expressing the interference leaked from each transmitter under MRT and its total across interfering transmitters.Source: 1) Rate Gap Analysis · p. 4
2) Optimization of Rotation Angle:
The rotation-angle design criterion is to reduce residual interference leakage to approach the rate upper bound. The resulting angle optimization separates into independent one-dimensional searches at each transmitter.
2) Optimization of Rotation Angle:
- Each transmitter’s rotation angle should minimize the total residual interference leakage it causes to non-associated receivers.Theorem 2 identifies this criterion for closely approaching the information-theoretic rate upper bound.Source: 2) Optimization of Rotation Angle · p. 4
- The rotation-angle optimization decouples into K independent single-variable subproblems.Each transmitter can construct its objective locally and use a low-complexity one-dimensional grid search in parallel.Source: 2) Optimization of Rotation Angle · p. 4
3) Optimization of transmit beamforming:
With the rotation angles fixed, the problem reduces to conventional MISO interference-channel beamforming. The method uses a second-order cone feasibility formulation and bisection to find the maximum sum rate.
3) Optimization of transmit beamforming:
- Fixing the optimized array orientations reduces the joint problem to conventional MISO interference-channel beamforming with fixed channels.The method then formulates beamforming feasibility for a given sum-rate target and rate-profile weights.Source: 3) Optimization of transmit beamforming · p. 4
- A common phase shift makes each desired-channel beamforming product real, allowing the rate constraints to be recast as second-order cone constraints.The resulting feasibility problem is a standard convex SOCP.Source: 3) Optimization of transmit beamforming · p. 4
- Bisection over the sum-rate target combined with the SOCP solver yields the maximum sum rate and optimal beamforming vectors.The overall complexity is O(KG+IK^3.5N^3.5), where G is the number of search grids and I the number of bisection iterations.Source: 3) Optimization of transmit beamforming · p. 4
IV. NUMERICAL RESULTS
The numerical section compares rotatable-antenna and fixed-position-antenna schemes under low- and high-SNR settings. The supplied passages specify the simulation parameters and rate-boundary figures but do not report numerical outcomes.
IV. NUMERICAL RESULTS
- The evaluation uses fc = 10 GHz, N = 4, β0 = 10−4, and receiver noise power σ2_k = −70 dBm.The comparison includes MRT, ZF, and SOCP-based optimal beamforming with and without antenna rotation, plus an interference-free bound.Source: §IV · p. 4
- The listed baselines distinguish fixed-position antennas without rotation from rotatable antennas with optimized rotation, across MRT, ZF, and optimal beamforming.The comparison also includes an interference-free achievable-rate upper bound.Source: §IV · p. 4
- The rate-boundary figures cover low-SNR operation at Pmax = 10 dBm and high-SNR operation at Pmax = 20 dBm.The captions identify the respective operating regimes.Source: Figure 2 · p. 5, Figure 3 · p. 5
A. Two-receiver Scenario
In the two-receiver scenario, optimizing RA rotations significantly enlarges the achievable rate region, bringing both MRT and ZF close to the interference-free upper bound at low and high SNR.
A. Two-receiver Scenario
- At Pmax = 10 dBm and 20 dBm, RA-optimized MRT and ZF achieve performance nearly identical to the interference-free upper bound.The two settings represent the low- and high-SNR regimes, respectively.Source: A. Two-receiver Scenario · p. 5
- Optimizing the RA rotation angles significantly enlarges the achievable rate region in both SNR regimes.The comparison is with conventional FPA systems using ϕ1 = ϕ2 = 0.Source: A. Two-receiver Scenario · p. 5
- For conventional FPA systems, MRT performs slightly better at low SNR, whereas ZF yields a larger rate region at high SNR.The compared regimes use Pmax = 10 dBm and Pmax = 20 dBm, respectively.Source: A. Two-receiver Scenario · p. 5
B. Multi-receiver Scenario
For K = 4, the optimized RA design closely approaches the interference-free upper bound despite high spatial correlation, and MRT performs comparably to optimal beamforming. The conclusion reports that RA-assisted optimization enlarges the rate region and outperforms conventional FPA networks.
B. Multi-receiver Scenario
- The multi-receiver evaluation uses K = 4 transmitters and receivers arranged in the specified two clusters.Transmitters are at (0, 0), (0, 100), (0, −1200), and (0, −1300) m; receivers are at (60, 200), (−60, 200), (60, −1200), and (−60, −1300) m.Source: B. Multi-receiver Scenario · p. 5
- With K = 4, optimized RA plus MRT closely approaches the interference-free upper bound and performs comparably to RA with optimal beamforming, substantially outperforming conventional FPA.The comparison is for minimum achievable rate versus maximum transmit power; the topology has high spatial correlation among channel vectors.Source: B. Multi-receiver Scenario · p. 5, Figure 4 · p. 5
V. CONCLUSION
- The conclusion states that jointly optimizing RA rotation angles and transmit beamforming enlarges the achievable rate region, and numerical results show significant gains over conventional FPA.The paper also identifies simpler transceiver design as a benefit of integrating RAs.Source: §V · p. 5