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Beyond Cell-free MIMO: Energy Efficient Reconfigurable Intelligent Surface Aided Cell-free MIMO Communications
Yutong Zhang, Boya Di, Hongliang Zhang, Jinlong Lin, Yonghui Li, Lingyang Song
TL;DR
The paper addresses the hardware and power costs of cell-free MIMO by studying a multi-RIS-assisted system for energy-efficient cooperative communication. It combines BS digital beamforming with RIS analog beamforming and solves the resulting optimization iteratively. Analysis and simulations show that energy efficiency depends on RIS deployment and size and exceeds that of conventional systems.
Problem
Cell-free MIMO reduces inter-cell interference through cooperative BS service but suffers high hardware and power costs from large-scale BS deployment.
Method
The paper proposes an RIS-aided cell-free MIMO system with hybrid beamforming and an iterative EEM algorithm for jointly optimizing BS beamforming and RIS phase shifts.
Results
The RIS-aided system achieves better energy efficiency than conventional systems, with optimal performance depending on the number and size of RISs.
Takeaways & Limitations
RIS deployment provides a low-cost way to improve cell-free energy efficiency, but RIS count and size must be selected for the desired operating trade-offs.
Abstract
from arXiv · showhide
Cell-free systems can effectively eliminate the inter-cell interference by enabling multiple base stations (BSs) to cooperatively serve users without cell boundaries at the expense of high costs of hardware and power sources due to the large-scale deployment of BSs. To tackle this issue, the low-cost reconfigurable intelligent surface (RIS) can serve as a promising technique to improve the energy efficiency of cell-free systems. In this paper, we consider an RIS aided cell-free MIMO system where multiple RISs are deployed around BSs and users to create favorable propagation conditions via reconfigurable reflections in a low-cost way, thereby enhancing cell-free MIMO communications. To maximize the energy efficiency, a hybrid beamforming (HBF) scheme consisting of the digital beamforming at BSs and the RIS-based analog beamforming is proposed. The energy efficiency maximization problem is formulated and an iterative algorithm is designed to solve this problem. The impact of the transmit power, the number of RIS, and the RIS size on energy efficiency are investigated. Both theoretical analysis and simulation results reveal that the optimal energy efficiency depends on the numbers of RISs and the RIS size. Numerical evaluations also show that the proposed system can achieve a higher energy efficiency than conventional ones.
I. INTRODUCTION
The paper targets the energy-efficiency costs of cell-free MIMO by coordinating multiple RISs with BSs and users. It proposes hybrid beamforming and an iterative optimization framework, then analyzes RIS deployment factors and compares energy efficiency with conventional systems.
- Cell-free MIMO avoids cell boundaries through cooperative BS service but incurs high hardware and power costs from large-scale BS deployment.
- RISs use programmable elements to reflect signals and form directional beams without the extra hardware and processing power required by conventional phased-array implementations.
- Prior work considered RIS-assisted cell-free sum-rate optimization and energy efficiency mainly for single-RIS or single-cell settings, leaving coordinated multi-RIS energy efficiency insufficiently explored.
- The proposed system coordinates multiple BSs and RISs to serve users through direct and reflected paths, using BS digital beamforming and RIS analog beamforming.
- An energy-efficiency maximization problem is decomposed into digital and RIS-based analog beamforming subproblems and solved iteratively by an EEM algorithm.
- Simulations report better energy efficiency than DAS, conventional cell-free, and no-RIS systems, while examining transmit power, RIS count, RIS size, and phase-shift quantization.
II. SYSTEM MODEL
The system model considers multi-antenna BSs and multiple RISs jointly serving single-antenna users. RISs passively reflect BS signals toward users, creating direct and reflected transmission paths with programmable phase responses.
- The downlink system contains N BSs with N_a antennas each, M RISs deployed around them, and K single-antenna users served cooperatively.
- RISs act as distant antenna arrays that can improve capacity and coverage while supporting low-cost transmission through direct and reflected links.
- A central processing unit controls network planning and transmission scheduling using the locations of BSs, RISs, and users.
- The model assumes that the CPU perfectly knows direct and multi-RIS reflected channel state information.
- Users receive signals directly from BSs and through multiple RIS reflections operating synchronously at the same frequency.
- Each RIS is modeled as a programmable surface whose elements manipulate electromagnetic responses through controllable PIN diodes and phase shifts.
C. Channel Model
The system combines direct BS–user links with RIS-reflected links, using RIS phase shifts for analog beamforming and BSs for digital processing. Its energy-efficiency model accounts for data rate, transmit power, and hardware power consumption.
- Each user receives signals directly from N BSs and through M RISs, each containing L reflecting elements.
- The channel comprises a direct component and reflected links represented through an ML × ML diagonal phase-shift matrix Q.
- The HBF scheme assigns digital beamforming to BSs and analog beamforming to RISs through their element phase shifts.
- BSs encode K user streams with a digital beamformer, allocate transmit powers, and transmit through their distributed antennas.
- RIS elements passively reflect signals by controlling phase shifts, so RIS power consumption depends on hardware cost and quantization bits rather than transmit power.
- Energy efficiency is formed from the aggregate user data rate divided by total power, including BS transmit and hardware-static consumption.
C. Problem Decomposition
The energy-efficiency problem is difficult because interference couples the variables and RIS beamforming contains many discrete phase shifts. The paper decomposes it into digital and RIS-based analog beamforming subproblems and solves them iteratively.
- The joint optimization is difficult because of complicated interference terms and the large number of discrete RIS phase-shift variables.
- With fixed RIS beamforming, the digital beamforming subproblem is optimized separately.
- The digital beamformer uses zero-forcing with power allocation to manage inter-user interference and approach optimal MIMO performance.
- Assuming equal BS power-amplifier efficiency, the digital subproblem reduces to power allocation and is transformed into a convex optimization problem.
- Algorithm 1 initializes a feasible power allocation, alternates auxiliary-variable and convex updates, and derives the digital beamformer from the optimized allocation.
B. RIS-based Analog Beamforming Design
The RIS analog-beamforming subproblem is reformulated as power minimization and solved by sequentially updating RIS elements. Continuous phase solutions are quantized to the available discrete phase-shift set.
- With digital beamforming fixed, the RIS analog-beamforming objective depends on Q through the power constraint and is reformulated as power minimization.
- The large-scale Q matrix is simplified by separating one diagonal phase variable from the remaining fixed elements.
- The elementwise objective is simplified using the Sherman–Morrison formula, yielding a phase-dependent expression whose minimizer can be derived.
- Each continuous phase solution is quantized to the nearest feasible phase because RIS elements provide only a limited number of discrete phase shifts.
- Starting from a random RIS beamformer, Algorithm 2 sequentially updates each element until convergence to a local minimum.
C. Overall Algorithm Description
The EEM algorithm alternates digital and RIS-based analog beamforming updates to optimize energy efficiency. Its objective is non-decreasing across iterations, guaranteeing convergence, while RIS updates have linear per-iteration complexity in the number of elements.
- Overall EEM procedure: The EEM procedure first designs digital beamforming with fixed RIS beamforming, then optimizes RIS analog beamforming using the updated digital solution.
- Convergence: The algorithm stops when the objective-value difference between adjacent iterations is at most a predefined threshold ε.
- Convergence: The objective value is non-decreasing after each iteration, so the proposed EEM algorithm is guaranteed to converge.
- Computational complexity: Digital beamforming requires solving a convex problem with polynomial complexity in the number of users K.
- Computational complexity: RIS analog beamforming updates each element sequentially, requiring O(ML) complexity per iteration independent of the phase-quantization bits b.
B. Performance Analysis of RIS Aided Cell-free System
The analysis characterizes how transmit power and RIS deployment affect energy efficiency in RIS-aided cell-free systems. Energy efficiency rises rapidly at low transmit power, then flattens; with many total RIS elements, adding RISs can reduce energy efficiency.
- 1) Impact of the transmit power:: The transmit-power derivative is positive below the optimal total power and negative above it, identifying an interior energy-efficiency optimum.The derivative changes sign around the power allocation that maximizes energy efficiency.
- 1) Impact of the transmit power:: Energy efficiency grows rapidly at low transmit power and gradually flattens as the transmit-power budget becomes large.This behavior is stated in Proposition 1 and its supporting analysis.
- 2) Impact of the number of RISs:: RISs are analyzed as a way to create favorable propagation conditions and enhance cell-free communication through reconfigurable reflections.The analysis fixes the total number of BSs and RISs when studying the number of RISs.
- 2) Impact of the number of RISs:: When M × L →∞, energy efficiency decreases as the number of RISs grows.This is the stated conclusion of Proposition 2 for a large total number of RIS elements.
3) Impact of the size of each RIS:
The RIS-size analysis finds a non-monotonic energy-efficiency trend: efficiency initially increases with RIS size but tends to zero as the size becomes unbounded. Simulations evaluate this behavior alongside transmit power, RIS count, quantization, and benchmark schemes.
- 3) Impact of the size of each RIS:: Energy efficiency initially increases with RIS size L and then gradually drops to zero as L grows.Proposition 3 states this trend, while the lemma gives the limiting behavior as L →∞.
- 1) Impact of the transmit power:: With M = 3, L = 64, and b = 3, energy efficiency grows rapidly at low transmit power and gradually flattens as power increases.The observed trend agrees with Proposition 1.
- VI. SIMULATION RESULTS: The simulations examine energy efficiency versus transmit power, RIS count, RIS size, and discrete-phase-shift quantization bits.The evaluation compares these factors using several benchmark communication schemes.
- A. Comparison with Benchmarks: RIS deployment improves energy efficiency relative to the no-RIS case, while the proposed system improves on the conventional DAS.The proposed system benefits from signals traveling through a larger number of independent paths.
B. Impact of Number of RISs
The RIS count and size jointly shape energy efficiency: adding RISs helps initially, but hardware power creates an optimum, while larger RISs eventually reduce efficiency.
- RIS count: Energy efficiency increases with RIS count for small-scale deployments, but its slope decreases as RIS quantization bits increase.Higher-resolution phase shifts increase each RIS's hardware static power consumption.
- RIS count: As M × L →∞, energy efficiency decreases because RIS hardware static power consumption becomes increasingly significant.The analysis proves this limiting decline and identifies hardware power as the governing cost.
- RIS count: The optimal number of deployed RISs occurs at a smaller M when RIS phase shifts use higher quantization resolution, especially continuous phase shifts.Higher quantization bits increase RIS energy consumption.
- RIS size: Energy efficiency first increases and then decreases as RIS size L grows because each RIS's hardware static power rises with its element count.The observed unimodal behavior verifies the theoretical analysis in Proposition 3.
- RIS size: The optimal RIS size L is smaller when more RISs are deployed, while the energy-efficiency curves' size gap shrinks as RIS count grows.The corresponding sum-rate behavior gradually converges as RIS size increases.
- Convergence: The iterative algorithm converges within 12 iterations for most cases, although convergence slows as RIS size grows because more variables require optimization.The reported convergence behavior supports an acceptable computational complexity.
- Design implications: Energy efficiency rises rapidly with transmit power and gradually flattens at sufficiently large power, and an optimal RIS count exists.The conclusions also identify a trade-off between energy efficiency and sum rate determined by RIS size.
APPENDIX A
Appendix A analyzes the derivative of high-SNR energy efficiency with respect to RIS count, showing that the relevant numerator is negative under the stated assumptions.
- High-SNR analysis: At high SNR, energy efficiency is rewritten in terms of the RIS count M and total deployment N0 = N + M before differentiation.The appendix defines the total number of BSs and RISs as N0.
- Derivative analysis: The derivative with respect to M is expanded into terms involving c1 through c5, whose signs determine the monotonicity result.The denominator is rewritten separately, and the proof focuses on the derivative numerator.
- Sign analysis: The proof establishes that term 3 is non-positive and that term 1 is negative because c1 < c2 under Jensen's inequality.The argument invokes the high-SNR setting and the stated comparison between c1 and c2.
B. Proof of 2⃝< 0
Appendix B proves the second derivative-related term is negative under the large-deployment assumption, supporting the decline of energy efficiency with RIS count.
- Proof of term 2: Under the assumption M × L →∞, the proof establishes c5 < M^2c3 and, after multiplication and comparison, c1c5 < M^2c2c3.These inequalities determine the sign of term 2 in the derivative numerator.
- RIS-size behavior: For small RIS size L, the proof defines a condition under which g(L) > 0, using the stated SNR and power relationship.The derivation considers the limit L → 1 and compares the resulting expressions.
- RIS-size behavior: Based on Lemma 2, energy efficiency increases when RIS size is small and gradually drops to zero as the relevant size or power regime grows.This completes the stated proof of the RIS-size behavior.