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Achievable Rate maximization by Passive Intelligent Mirrors
Chongwen Huang, Alessio Zappone, Mérouane Debbah, Chau Yuen
TL;DR
The paper addresses sum-rate maximization in a multi-user MISO downlink using a Passive Intelligent Mirror while satisfying user QoS requirements. It jointly designs transmit powers and mirror phases, combining alternating optimization with majorization-minimization to handle the non-convex problem. Numerically, the proposed scheme achieves near-optimal performance and improves sum rate by more than 40% over systems without PIM.
Problem
The paper studies how to maximize multi-user MISO downlink sum rate with PIM reflection design and individual user QoS guarantees despite a non-convex formulation.
Method
The proposed approach jointly designs transmit powers and PIM phases using alternating optimization combined with the majorization-minimization method.
Results
More than 40% higher sum rate than traditional systems without PIM is achieved, with near-optimal performance reported for the proposed scheme.
Takeaways & Limitations
PIM can improve system throughput without additional energy consumption, while the proposed algorithm retains low complexity and near-optimal performance.
Takeaways & Limitations
The phase-shift optimization has a non-differentiable objective and a non-convex constraint, complicating solution of the PIM design subproblem.
Abstract
from arXiv · showhide
This paper investigates the use of a Passive Intelligent Mirrors (PIM) to operate a multi-user MISO downlink communication. The transmit powers and the mirror reflection coefficients are designed for sum-rate maximization subject to individual QoS guarantees to the mobile users. The resulting problem is non-convex, and is tackled by combining alternating maximization with the majorization-minimization method. Numerical results show the merits of the proposed approach, and in particular that the use of PIM increases the system throughput by at least $40\%$, without requiring any additional energy consumption.
1. INTRODUCTION
The paper positions Passive Intelligent Mirrors as an energy-saving technology for wireless networks and develops an outdoor MISO downlink design that optimizes transmit powers and phase shifts for sum-rate maximization. Numerical results report more than 40% higher system sum-rate without additional energy consumption.
- Future cellular networks must deliver 1000× higher data rates while halving energy consumption, creating demand for green wireless solutions.
- Passive Intelligent Mirrors are metasurfaces made of many small reflectors with low-cost sensors and a cognitive engine.
- By designing reflector phase shifts, a PIM constructively combines reflected signals and acts as an amplify-and-forward relay without a dedicated energy source.
- Earlier PIM research focused mainly on indoor scenarios and did not provide a system design method.
- The work studies an outdoor MISO downlink, jointly optimizes transmit powers and PIM phase shifts, and addresses the resulting non-convex problem with alternating optimization and majorization-minimization.
- More than 40% higher system sum-rate is achieved with PIM without additional energy consumption.
2. SYSTEM MODEL
The system uses a multi-antenna base station and a reflecting PIM relay to serve single-antenna users over cascaded channels. The design optimizes transmit powers and PIM phases for sum-rate maximization under power, QoS, and phase constraints, but the formulation is non-convex.
- A base station with M antennas serves K single-antenna users through a PIM containing N reflecting units that acts as a relay.
- The direct BS-to-user path is neglected because line-of-sight communication is assumed absent.
- The received signal combines the BS transmission, cascaded BS–PIM and PIM–user channels, PIM phase shifts, and thermal noise.
- The BS transmit signal uses user-specific transmit powers, information symbols, and beamforming vectors.
- The objective is to optimize transmit powers and the PIM phase matrix for system sum-rate maximization using zero-forcing transmission.
- The formulation imposes bounded PIM phases and is non-convex, making optimization with respect to the phase matrix challenging.
3. PROPOSED APPROACH
The approach alternates transmit-power and PIM phase-shift optimization, using MM to handle the non-convex phase-shift subproblem and yielding a convergent algorithm.
- Alternating optimization: Transmit powers P and PIM phase shifts Θ are optimized separately and iteratively to tackle the sum-rate problem.This alternating optimization separates the two design variables.
- Majorization-minimization: For fixed P, the phase-shift update uses an MM subproblem whose unit-modulus solution is x = e^-jarg(y).The update follows Proposition 1 and is repeated until convergence.
- Optimization with respect to Θ: The phase-shift problem uses φ_k = e^jθ_k with unit-modulus constraints, but remains challenging because its objective is non-differentiable and non-convex.The phase range is 0 ≤ θ_i ≤ 2π, while |φ_i| = 1 encodes the phase-shift constraint.
- Majorization-minimization: Majorization-minimization replaces the phase-shift objective with a differentiable upper bound that coincides at the previous iterate and monotonically improves the true objective.The objective is lower-bounded over the feasible set, supporting convergence in objective value.
- Optimization with respect to P: The power-allocation subproblem is convex and can be solved using standard convex optimization techniques and KKT-based closed-form expressions.The power constraints include each user’s QoS requirement, and the algorithm updates powers after obtaining Φ.
- Overall algorithm: Algorithm 1 nests MM phase-shift updates inside alternating maximization and converges in objective value because the objective is continuous over a compact feasible set.The algorithm checks feasibility and declares unfeasibility when the power requirement exceeds Pmax.
4. NUMERICAL RESULTS
The numerical results compare the proposed MM-based algorithm with global optimization and a no-PIM baseline across SNR, PIM-unit count, and convergence. The proposed method achieves near-global performance while retaining limited complexity.
- The simulations average results over 500 independent channel and user-position realizations for the considered system scenarios.The scenarios include K = 16, M = 32, N = 32 and K = 8, M = 8, N = 8.
- The proposed algorithm increases achievable sum rate by more than 40% compared with resource allocation without PIM.The no-PIM scheme serves as the baseline, while global optimization provides a higher-complexity benchmark.
- The proposed Algorithm 1 has a limited performance gap relative to the global optimization method despite its much lower complexity.
- The proposed Algorithm 1 matches global optimization in sum spectral efficiency as the number of PIM units varies.The comparison uses SNR = 20 dB, K = 16, M = 8, and Rmin,k = 2 bps/Hz.
- Increasing the number of PIM units raises sum spectral efficiency, although the improvement saturates as the number of units grows.
- The MM-based algorithm reaches acceptable MSE values within a few dozen iterations, with more iterations required for larger N.Larger N increases the number of optimization variables, while each iteration uses simple closed-form computations, confirming limited complexity.
5. CONCLUSION
The paper develops a sum-rate maximization scheme for PIM-based multi-user MIMO under a non-convex resource-allocation formulation. Combining MM with alternating optimization yields a provably convergent, low-complexity method with near-optimal performance and more than 40% higher sum rate than systems without PIM.
- The proposed scheme combines majorization-minimization and alternating optimization to solve the non-convex radio resource allocation problem.
- The resulting algorithm is provably convergent and low-complexity.
- More than 40% higher sum rate is achieved compared with traditional systems without PIM.