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Joint Beamforming Design and Power Splitting Optimization in IRS-Assisted SWIPT NOMA Networks
Zhendong Li, Wen Chen, Qingqing Wu, Kunlun Wang, Jun Li
TL;DR
The paper addresses transmit-power minimization in IRS-assisted SWIPT NOMA networks with changing decoding-order challenges. It proposes a two-stage joint optimization framework and reports reduced BS transmit power compared with baseline algorithms, while highlighting IRS's practical auxiliary role.
Problem
Changing wireless channels complicate users’ SIC decoding order, motivating transmit-power minimization in IRS-assisted SWIPT NOMA networks.
Method
A two-stage algorithm jointly optimizes SIC decoding order, BS beamforming, PS ratio, and IRS phase shift using SDR, Gaussian randomization, and SCA.
Results
The proposed algorithm significantly reduces BS transmit power compared with other baseline algorithms.
Takeaways & Limitations
IRS provides an important auxiliary role that can greatly relieve BS pressure at low practical cost.
Abstract
from arXiv · showhide
This paper proposes a novel network framework of intelligent reflecting surface (IRS)-assisted simultaneous wireless information and power transfer (SWIPT) non-orthogonal multiple access (NOMA) networks, where IRS is used to enhance the NOMA performance and the wireless power transfer (WPT) efficiency of SWIPT. We formulate a problem of minimizing base station (BS) transmit power by jointly optimizing successive interference cancellation (SIC) decoding order, BS transmit beamforming vector, power splitting (PS) ratio and IRS phase shift while taking into account the quality-of-service (QoS) requirement and energy harvested threshold of each user. The formulated problem is non-convex optimization problem, which is difficult to solve it directly. Hence, a two-stage algorithm is proposed to solve the above-mentioned problem by applying semidefinite relaxation (SDR), Gaussian randomization and successive convex approximation (SCA). Specifically, after determining SIC decoding order by designing IRS phase shift in the first stage, we alternately optimize BS transmit beamforming vector, PS ratio, and IRS phase shift to minimize the BS transmit power. Numerical results validate the effectiveness of our proposed optimization algorithm in reducing BS transmit power compared to other baseline algorithms. Meanwhile, compared with non-IRS-assisted network, the IRS-assisted SWIPT NOMA network can decrease BS transmit power by 51.13\%.
I. INTRODUCTION
The paper motivates combining IRS, SWIPT, and NOMA to address variable user channels, energy-constrained devices, and distance-limited wireless power transfer. It formulates joint optimization of decoding order, beamforming, power splitting, and IRS phases to reduce BS transmit power.
- Proposed framework: The paper proposes an IRS-assisted SWIPT NOMA framework in which users share resource blocks while receiving information and energy.The BS transmit-power minimization jointly optimizes SIC decoding order, beamforming, PS ratio, and IRS phase shift under QoS and harvested-energy constraints.
- Motivation: NOMA performance can suffer when users’ channel conditions are similar because practical wireless channels are random and difficult to control.IRS is introduced to adjust channels and increase channel-condition differences among users.
- Motivation: SWIPT lets users receive information and energy simultaneously, while power splitting divides received power between information decoding and energy harvesting.This supports large-scale, low-power, energy-constrained IoT devices.
- Motivation: Conventional SWIPT suffers sharply reduced WPT efficiency as distance increases because of severe propagation loss.Strengthening channel conditions can improve WPT efficiency and coverage.
- IRS-assisted networking: IRS uses passive reflecting elements to adjust wireless channels, improving NOMA performance, SWIPT WPT efficiency, and network coverage.Its passive operation avoids additional noise and requires lower hardware cost and power consumption than MIMO.
- Results: The proposed algorithm reduces BS transmit power relative to baseline algorithms, while more IRS reflecting elements further reduce the required power.The numerical results also report good convergence.
A. System Model
The system is an IRS-assisted SWIPT NOMA downlink with one BS, one IRS, and multiple users, combining beamforming, SIC, and power splitting. Channels include direct and IRS-reflected links, while users divide received power between information decoding and energy harvesting.
- The network comprises one BS, one IRS with M reflecting elements, and K single-antenna users served by an N-antenna ULA BS.
- The IRS reflection uses amplitude coefficients β_m ∈ [0,1] and phase shifts θ_m ∈ [0,2π], with β_m typically set to 1 to maximize reflected signal power.
- The wireless channel consists of BS–IRS, IRS–user, and direct BS–user links, modeled with Rician fading for links involving the IRS and Rayleigh fading for direct links.
- Each user receives a dedicated information beam through linear transmit precoding, with independently distributed CSCG data symbols.
- Each user applies power splitting, directing a ρ_k portion of received power to information decoding and the remaining 1 − ρ_k to energy harvesting.
- IRS phase shifts alter combined channel gains, making SIC decoding order dependent on the IRS-assisted channel conditions rather than only direct BS–user gains.
B. Problem Formulation for the IRS-assisted SWIPT NOMA Networks
The paper formulates BS transmit-power minimization by jointly designing SIC order, beamforming, power splitting, and IRS phases under QoS and harvested-energy constraints. Coupling among these variables and the IRS-dependent decoding order makes the problem non-convex and difficult to solve directly.
- The objective is to minimize BS transmit power by jointly optimizing SIC decoding order, transmit beamforming, received power-splitting ratios, and IRS phase shifts.
- QoS constraints enforce each user’s SINR threshold γ_k, while energy constraints require harvested power to reach threshold e_k.
- SIC constraints ensure that users decoding another user’s information achieve the required comparative SINR conditions.
- The formulation is non-convex because beamforming, PS ratios, and IRS phases are coupled, while phase shifts and IRS-dependent SIC orders introduce additional nonlinearity.
III. THE PROPOSED TWO-STAGE OPTIMIZATION ALGORITHM FOR THE IRS-ASSISTED SWIPT NOMA NETWORKS
A two-stage algorithm first determines SIC decoding order through IRS phase design, then alternately optimizes beamforming, PS ratios, and IRS phases using SDR, Gaussian randomization, and SCA. The SDR-randomization procedure provides a π/4 approximation for the first-stage objective, while the overall method yields a sub-optimal solution.
- Two-stage optimization: The algorithm decouples the problem into SIC decoding-order determination followed by alternating optimization of beamforming, PS ratios, and IRS phases.
- Two-stage optimization: The second stage applies SDR, SCA, and Gaussian randomization to optimize the coupled design variables for a fixed SIC order.
- SIC decoding order determination: The first stage maximizes the sum of users’ combined channel gains because IRS phase shifts affect all users’ gains and therefore their SIC order.
- SDR and randomization: SDR converts the relaxed first-stage problem into a semidefinite program, but the solution is generally high-rank and supplies an upper bound rather than an exact rank-one solution.
- SDR and randomization: Gaussian randomization reconstructs rank-one candidate reflection solutions from the relaxed result and selects the candidate maximizing the combined channel gain.
- Performance guarantee: π/4 approximation is guaranteed for the optimal objective value of the first-stage problem, while the complete JDBPR algorithm obtains a sub-optimal solution to problem (P1).
B. BS Beamforming Vector Optimization
The BS beamforming subproblem is transformed into an SDP using SDR and SCA to handle its rank-one and non-convex constraints. The SDR is proved tight, yielding a rank-one optimal solution.
- Given the SIC decoding order, PS ratio, and IRS phase shift, the problem is transformed into a BS beamforming feasibility-check problem.
- SDR relaxes the rank-one constraint, while SCA converts the remaining non-convex constraint into a tractable form.
- The relaxed problem is a standard SDP that can be solved using CVX.
- The optimal relaxed solution satisfies Rank(W*_k) = 1, so the SDR for the BS beamforming problem is tight.
C. PS Ratio Optimization
The PS-ratio subproblem fixes the BS beamforming vector and IRS phase shift, then applies SCA to convert its non-convex constraint into a convex optimization problem solvable by CVX.
- With the BS beamforming vector and IRS phase shift fixed, the original problem becomes a PS-ratio feasibility-check problem.
- SCA transforms the non-convex PS-ratio constraint into a tractable approximation.
- The resulting PS-ratio problem is a standard convex optimization problem solved using the CVX toolbox.
E. Two-stage Overall Optimization Algorithm
The JDBPR algorithm first determines SIC decoding order and then alternately optimizes beamforming, PS ratios, and IRS phase shifts. Its objective is non-increasing across iterations and therefore converges to a sub-optimal solution.
- Stage 1: SIC decoding order determination: Stage 1 optimizes IRS phase shifts to maximize combined channel gain, then determines SIC decoding order from users’ combined channel gains.
- Stage 2: Joint optimization: Stage 2 alternately optimizes the BS beamforming vector, PS ratio, and IRS phase shift using SDR, SCA, and Gaussian randomization.
- Convergence: Gaussian randomization achieves an approximate value of at least π/4 for the first-stage optimal objective, while the overall JDBPR solution is sub-optimal.
- Stage 2: Joint optimization: The algorithm updates beamforming, PS ratio, and IRS phase shift in sequence until the fractional objective decrease falls below ε.
- Convergence: The objective function is non-increasing after each second-stage iteration, and finite lower bounds guarantee convergence.
IV. NUMERICAL RESULTS
Numerical results show that JDBPR converges quickly and reduces required BS transmit power as IRS resources increase. It performs similarly to exhaustive-order search while outperforming the other baselines.
- Convergence: The JDBPR algorithm converges by the 8-th iteration, with BS transmit power gradually decreasing as iterations increase.
- QoS and harvested-energy thresholds: BS transmit power increases with users’ QoS threshold under energy harvested thresholds e = 0dBm and e = −10dBm.
- Baseline comparisons: TS-JDBPR-opt has transmit-power performance similar to EX-JBPR-opt but substantially lower complexity than exhaustive search.
- Baseline comparisons: TS-JDBPR-opt outperforms the other baselines because it uses global optimization, optimized beamforming, and optimized IRS phase shifts.
- QoS and harvested-energy thresholds: BS transmit power increases as the users’ energy harvested threshold rises, and higher QoS thresholds require more power at the same harvested threshold.
- IRS resources: Increasing the number of IRS reflecting elements lowers BS transmit power and enlarges the performance gap over non-IRS-assisted networks.
- BS antennas: Increasing the number of BS antennas decreases BS transmit power, while TS-JDBPR-opt retains a performance advantage over the comparison algorithms.
V. CONCLUSION
The paper formulates IRS-assisted SWIPT NOMA transmit-power minimization with joint design variables and proposes a two-stage optimization algorithm. Numerical results show reduced BS transmit power and highlight the auxiliary role of IRS.
- The paper investigates BS transmit-power minimization in IRS-assisted SWIPT NOMA networks under users’ QoS and energy-harvesting constraints.
- SIC decoding order, BS beamforming, PS ratio, and IRS phase shift are jointly optimized.
- A two-stage algorithm determines SIC decoding order first, then alternately optimizes beamforming, PS ratio, and IRS phase shift using SDR, SCA, and Gaussian randomization.
- The proposed JDBPR algorithm is analyzed for computational complexity and convergence.
- Numerical results show that the proposed algorithm significantly reduces BS transmit power compared with baseline algorithms.
- IRS assistance can greatly relieve pressure on the BS with low practical cost.
APPENDIX A PROOF OF EQ. (27)
The appendix transforms a logarithmic constraint using successive convex approximation and establishes properties of the beamforming subproblem through convex duality and KKT analysis.
- The proof takes the logarithm of the relevant constraint before reformulating it.
- SCA provides upper bounds for concave terms, yielding the transformed constraint in Eq. (27).
- The beamforming subproblem is convex, so Slater’s condition holds and the duality gap is zero.
- The proof formulates the Lagrangian and dual problem, then uses KKT conditions to investigate the optimal solution structure.
- The analysis investigates whether the optimal beamforming matrix W*_k is rank-one using the structure of the dual solution.
APPENDIX C PROOF OF EQ. (30)
The appendix applies logarithmic reformulation and successive convex approximation to transform constraint (29c) into Eq. (30).
- Constraint (29c) is rewritten into an equivalent expression before approximation.
- SCA obtains an upper bound for the concave fourth term on the left-hand side.
- The proof takes logarithms of both sides of the constraint before deriving the transformed form.
- SCA upper bounds the first and fourth left-hand-side terms, producing the transformed constraint in Eq. (30).