Source-linked AI summary
Energy-Efficient Design of IRS-NOMA Networks
Fang Fang, Yanqing Xu, Quoc-Viet Pham, Zhiguo Ding
TL;DR
The paper addresses energy-efficient transmission in IRS-assisted NOMA networks by seeking a tradeoff between sum-rate maximization and total power minimization. It alternately optimizes BS beamforming and IRS phase shifts using approximation-based subproblem solvers, and reports higher energy efficiency than OMA and random-phase schemes.
Problem
The paper seeks an energy-efficient design for a downlink MISO IRS-NOMA network that balances sum-rate maximization with total power minimization.
Method
An alternating optimization algorithm uses SCA for beamforming and lower-bound approximation with SDR for IRS phase shifts.
Results
The proposed scheme achieves higher energy efficiency than IRS-OMA and IRS-NOMA with random phases.
Takeaways & Limitations
Jointly optimizing transmit beamforming and IRS phase shifts provides the paper’s reported energy-efficiency improvement over the compared schemes.
Abstract
from arXiv · showhide
Combining intelligent reflecting surface (IRS) and non-orthogonal multiple access (NOMA) is an effective solution to enhance communication coverage and energy efficiency. In this paper, we focus on an IRS-assisted NOMA network and propose an energy-efficient algorithm to yield a good tradeoff between the sum-rate maximization and total power consumption minimization. We aim to maximize the system energy efficiency by jointly optimizing the transmit beamforming at the BS and the reflecting beamforming at the IRS. Specifically, the transmit beamforming and the phases of the low-cost passive elements on the IRS are alternatively optimized until the convergence. Simulation results demonstrate that the proposed algorithm in IRS-NOMA can yield superior performance compared with the conventional OMA-IRS and NOMA with a random phase IRS.
I. INTRODUCTION
The paper combines IRS and NOMA in a downlink MISO network to improve coverage and pursue an energy-efficiency tradeoff between data transmission and power consumption.
- IRS passively reflects signals while adjusting element phases to modify propagation and improve coverage, throughput, and energy efficiency.
- NOMA offers high spectral and energy efficiency, motivating its combination with IRS for B5G wireless networks.
- The paper targets energy efficiency by balancing sum-rate maximization against power minimization in a downlink MISO IRS-NOMA network.
A. IRS Assisted NOMA
The considered system uses an IRS to serve two dead-zone single-antenna users from a multi-antenna BS, with NOMA decoding ordered by effective channel gain.
- An IRS with N reflecting elements assists an M-antenna BS in serving two dead-zone single-antenna users without direct BS-user links.The model assumes perfect channel state information and fixed unit amplitude reflection coefficients.
- The IRS reflection matrix is Θ = diag(β1e^jθ1, · · ·, βNe^jθN), with βn = 1 and θn representing element phase shifts.
- The BS transmits the superposed signal w1s1+w2s2, where beamforming vectors serve the two users.
- Each user’s SINR is defined as the minimum SINR across the receivers that decode that user’s message, determining the achievable rates.
B. Problem formulation
The optimization maximizes system energy efficiency, defined from sum rate and total power, subject to user QoS and transmit-power constraints.
- Energy efficiency is formulated as the ratio of system sum rate to total power consumption, including BS amplifier and circuit power.The circuit power is Pc = MPd + P0, with Pd dynamic and P0 static power consumption.
- The formulation imposes individual minimum-rate requirements and a total transmit-power budget Pmax.
- The minimum rate is Rk,min = log2(1 + Γk,min), with Γk,min = 2^Rk,min − 1 serving as the required SINR.
- Joint optimization over Θ and w is non-convex because R is not jointly concave in the reflection matrix and beamforming vectors.Consequently, obtaining a globally optimal solution is challenging.
III. ALTERNATING OPTIMIZATION SOLUTION
The proposed solution alternates between beamforming and phase-shift optimization, using convex approximations tailored to each subproblem.
- III. ALTERNATING OPTIMIZATION SOLUTION: The algorithm decouples the problem into beamforming and phase-shift subproblems and solves them alternately.
- III. ALTERNATING OPTIMIZATION SOLUTION: Sequential convex approximation and successive convex approximation optimize beamforming, while lower-bound approximation and semidefinite relaxation optimize IRS phases.
A. Beamforming Optimization
The beamforming subproblem is convexified through slack-variable reformulations and successive convex approximation, then solved iteratively with feasible initialization until convergence.
- A. Beamforming Optimization: For fixed phase shifts, slack variables reformulate the beamforming problem before convex approximation.The reformulation introduces t and ρ, while additional variables γ, δ, and β express rate and interference constraints.
- A. Beamforming Optimization: Second-order cone representations handle the convex constraints involving transmit power, QoS, and interference terms.The reformulated QoS and power-related inequalities are expressed as SOC constraints.
- A. Beamforming Optimization: SCA replaces the remaining non-convex constraints with first-order Taylor approximations evaluated at the previous iteration.The approximations produce a convex problem that is solved repeatedly for updated beamforming variables.
- A. Beamforming Optimization: The resulting convex problem is iteratively solved, and the authors report better performance for SCA than for a Dinkelbach-based alternative.The SCA-based beamforming procedure is used in steps 3–8 of Algorithm 1.
- A. Beamforming Optimization: The SCA beamforming method requires feasible initial variables because convergence is sensitive to the starting point.Initialization uses a feasibility problem satisfying the user-rate and transmit-power constraints, with tolerance ϵ = 0.001 for termination.
B. Phase shift optimization
With beamforming fixed, phase optimization is converted from energy-efficiency maximization to sum-rate maximization and handled through convex lower bounds and semidefinite relaxation.
- B. Phase shift optimization: Given transmit beamforming vectors, phase optimization reduces the energy-efficiency problem to maximizing the system sum rate.The unit-modulus IRS phase constraints remain non-convex in this formulation.
- B. Phase shift optimization: The max-min rate objective is transformed using a slack variable, while the IRS phase vector is represented through quadratic forms.The vector v encodes the IRS phases, and V = vv^H enables trace-based reformulation.
- B. Phase shift optimization: A convex lower bound approximates the non-convex rate constraint, producing a transformed problem whose solution remains feasible for the original phase problem.Proposition 1 establishes feasibility of the transformed solution relative to the original formulation.
- B. Phase shift optimization: Semidefinite relaxation removes the non-convex rank-one constraint from the lifted phase optimization problem.The relaxed problem is an SDP and can be solved by standard solvers such as CVX.
- B. Phase shift optimization: The recovered IRS phase vector is obtained by SVD when the relaxed solution is rank one, or by Gaussian randomization otherwise.The simulations reportedly always produced a rank-one solution for the relaxed problem.
C. Algorithm Design
Algorithm 1 alternates beamforming optimization and phase-shift optimization, with energy efficiency evaluated after each outer iteration; the procedure is guaranteed to converge.
- C. Algorithm Design: The alternating procedure terminates when the energy-efficiency improvement falls below ϵ or the phase optimization becomes infeasible.The algorithm evaluates EE after each outer iteration.
- C. Algorithm Design: Energy efficiency is nondecreasing across alternating updates, so Algorithm 1 is guaranteed to converge.Beamforming optimizes the current phase-shift subproblem, while phase optimization increases the sum-rate numerator.
IV. SIMULATION RESULTS
Simulations evaluate IRS-NOMA under Rician fading and compare the proposed optimization with IRS-OMA and random-phase IRS-NOMA baselines across reflecting-element and circuit-power settings.
- IV. SIMULATION RESULTS: The simulations use Rician fading channels and compare the proposed algorithm with optimized IRS-OMA and random-phase IRS-NOMA.The benchmark IRS-OMA scheme also uses SCA and SDR optimization.
- IV. SIMULATION RESULTS: Increasing the number of IRS reflecting elements increases energy efficiency for both proposed and random-phase IRS-NOMA schemes.The proposed scheme consistently achieves higher energy efficiency than the random-phase scheme.
- IV. SIMULATION RESULTS: The energy-efficiency improvement becomes smaller as the number of transmit antennas M increases under fixed Pmax.The passage attributes this behavior to a narrower feasible channel domain between antennas.
- IV. SIMULATION RESULTS: Increasing BS circuit power Pc decreases energy efficiency, although the decline becomes less steep at larger Pc.The proposed MISO IRS-NOMA scheme remains above the random-phase scheme across the considered transmit-power budgets.
V. CONCLUSION
The proposed IRS-NOMA approach improves energy efficiency by alternately optimizing beamforming and phase shifts, achieving higher energy efficiency than OMA and random-phase schemes.
- Beamforming and phase shifts are alternately optimized to maximize system energy efficiency.Beamforming uses auxiliary variables and SCA, while phase shifts use a lower bound and SDR.
- The proposed algorithm achieves higher energy efficiency than the OMA system and random phase scheme.
- The proposed scheme can extend to the multi-user case with a different phase optimization scheme.