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Optimized Energy and Information Relaying in Self-Sustainable IRS-Empowered WPCN

Bin Lyu, Parisa Ramezani, Dinh Thai Hoang, Shimin Gong, Zhen Yang, Abbas Jamalipour

arXiv:2004.03108v2eess.SPcs.IT

TL;DR

This paper addresses how to improve energy transfer and information transmission in WPCNs while accounting for the IRS’s operational energy needs. It proposes self-sustainable TS and PS IRS schemes, optimizes their phase shifts and resources with two-step algorithms, and reports significant sum-rate gains over a baseline WPCN without IRS.

  • Problem

    Integrating IRS technology with WPCNs remains insufficiently investigated, particularly when the IRS’s non-negligible power consumption must be supported.

  • Method

    The paper proposes self-sustainable TS and PS schemes that harvest HAP RF energy for IRS operation, jointly optimizes phase shifts and network resources, and develops two-step algorithms for near-optimal solutions.

  • Results

    The proposed schemes achieve significant system sum-rate gains compared with the baseline WPCN protocol without IRS.

  • Takeaways & Limitations

    Self-sustainable IRS hybrid relaying can support both downlink energy transfer and uplink information transmission in WPCNs through TS or PS operation.

Abstract

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This paper proposes a hybrid-relaying scheme empowered by a self-sustainable intelligent reflecting surface (IRS) in a wireless powered communication network (WPCN), to simultaneously improve the performance of downlink energy transfer (ET) from a hybrid access point (HAP) to multiple users and uplink information transmission (IT) from users to the HAP. We propose time-switching (TS) and power-splitting (PS) schemes for the IRS, where the IRS can harvest energy from the HAP's signals by switching between energy harvesting and signal reflection in the TS scheme or adjusting its reflection amplitude in the PS scheme. For both the TS and PS schemes, we formulate the sum-rate maximization problems by jointly optimizing the IRS's phase shifts for both ET and IT and network resource allocation. To address each problem's non-convexity, we propose a two-step algorithm to obtain the near-optimal solution with high accuracy. To show the structure of resource allocation, we also investigate the optimal solutions for the schemes with random phase shifts. Through numerical results, we show that our proposed schemes can achieve significant system sum-rate gain compared to the baseline scheme without IRS.

I. INTRODUCTION

The paper motivates a self-sustainable IRS-empowered WPCN to address energy-transfer and information-transmission limitations, while accounting for IRS power consumption. It proposes TS and PS hybrid-relaying schemes, jointly optimized resource allocation, and numerical evaluation against a baseline.

  • Motivation: WPCNs rely on harvested downlink energy for uplink transmission, while distance causes severe RF attenuation that limits performance.
  • Related approaches: Active relays consume substantial harvested energy, reduce information-transmission time, and may require complex self-interference cancellation in full-duplex operation.
  • IRS rationale: IRS uses low-cost reflecting elements to improve energy and information transmission without energy-hungry RF chains or active signal generation.
  • Motivation: IRS power consumption cannot be neglected because large numbers of reflecting elements can make circuit consumption comparable to the power supply.The cited example gives 1.5 mW and 6 mW per element for 3- and 5-bit phase shifting, respectively.
  • Contributions: The paper proposes a self-sustainable IRS with TS and PS energy-harvesting schemes, using a piece-wise linear model to capture practical saturation.TS separates IRS harvesting and reflection within the ET phase, whereas PS adjusts amplitude reflection while harvesting.
  • Contributions: The study jointly optimizes phase shifts and network resources, develops two-step near-optimal algorithms, and evaluates system sum-rate gains against a baseline WPCN protocol.

A. Energy Transfer Phase

The time-switching scheme divides energy transfer into IRS self-harvesting and user-assistance sub-slots, while users harvest throughout the phase. A two-piece linear model captures increasing harvested power and saturation.

  • Time-switching operation: The IRS uses the first sub-slot for self-energy harvesting and the second to enhance users’ downlink energy harvesting.Users harvest energy over the entire energy-transfer phase.
  • Model assumptions: The analysis assumes accurately obtained channel state information, while channel-estimation errors are reserved for future investigation.The transmission block uses normalized duration T = 1 second.
  • Time-switching operation: During the first sub-slot, incident HAP signals are directed to the IRS energy harvester, while users receive direct HAP energy signals.The received powers are modeled as Ph||hr||2 at the IRS and Ph|hh,i|2 at user Ui.
  • Time-switching operation: During the second sub-slot, the IRS reflects HAP signals using phase shifts to improve the users’ harvested energy.The TS scheme sets all energy-transfer amplitude reflection coefficients to one during this sub-slot.
  • Energy-harvesting model: The two-piece linear harvesting model increases with received power before reaching saturation, limiting further harvested-power growth.Harvested energy is computed by applying the minimum of ηPr and the relevant saturation power over the harvesting duration.

2) Power-splitting scheme:

The power-splitting scheme avoids dedicated IRS harvesting time by dividing incident HAP signals between IRS energy harvesting and reflection toward users. It then models uplink user transmission using harvested energy and IRS-assisted reception at the HAP.

  • Power-splitting operation: The PS scheme removes dedicated IRS energy-harvesting time by adjusting reflection amplitudes to split HAP signals between harvesting and user assistance.The reflected portion enhances users’ harvested energy during the energy-transfer phase.
  • Energy-harvesting model: The PS model uses a two-piece linear energy-harvesting approximation that is tractable and sufficiently accurate for practical harvesting circuits.The model captures nonlinear behavior and saturation while using a constant linear-regime efficiency η.
  • Power-splitting operation: All IRS energy-transfer amplitude reflection coefficients are constrained to a common value, βe,k = βe, to simplify the circuit design.Amplitude control can be implemented with devices including PIN diodes, FETs, MEMS switches, and variable resistor loads.
  • Information transmission phase: In the uplink, users transmit through time division multiple access using energy harvested during the energy-transfer phase.User transmit power accounts for circuit power consumption, while IRS circuit consumption is modeled through phase-shifting operations.
  • Information transmission phase: The IRS uses unit-amplitude phase shifts for uplink reflection, and the HAP evaluates each user’s received signal and signal-to-noise ratio.The phase-shift matrix is parameterized by θd,i,k with unit-modulus coefficients.

III. SUM-RATE MAXIMIZATION FOR THE TS SCHEME

The TS scheme jointly optimizes IRS phase shifts, time allocation, and user power to maximize WPCN sum-rate. Because the problem is non-convex, a two-step procedure combines closed-form IT phase shifts with search, relaxation, and randomization methods.

  • The TS sum-rate problem jointly optimizes IRS phase shifts for ET and IT, network scheduling, and users’ power allocation.
  • The problem is non-convex because variables are coupled in both the objective function and constraints.
  • Optimal phase shift design for IT: The optimal IT phase shifts are obtained in closed form, and they can enhance the received HAP SNR by up to (1 + δ)^2 over no IRS.
  • Optimizing phase shift design for ET, time scheduling, and power allocation: The ET optimization uses one-dimensional search, semidefinite relaxation, SVD, and Gaussian randomization to construct a near-optimal rank-one solution.
  • The algorithm sequentially updates the ET duration and relaxed phase-shift solution, selecting the randomization outcome with the maximum objective value.
  • Multi-antenna HAP extension: For a multi-antenna HAP, alternating optimization additionally updates transmit beamforming and other variables, but the resulting implementation cost is much higher.

B. Random phase shifts with optimized resource allocation for the TS scheme

With random IRS phase shifts, the paper simplifies the TS problem to time and energy allocation and derives a convex formulation with optimal scheduling conditions.

  • The random-phase-shift case focuses on time and power allocation to reduce computational complexity and expose resource-allocation structure.
  • The resulting sum-rate maximization problem is reformulated using each user’s consumed uplink energy e_u,i = P_u,i t_i.
  • The reformulated problem is convex and can be solved using standard convex optimization methods such as Lagrange duality.
  • The optimal TS time scheduling is characterized by a common dual-variable condition, ln(2)(1 + z_i) = ξ*.

where z∗

The section completes the random-phase-shift TS solution by obtaining users’ optimal energy allocation from the scheduling result.

  • The proof for the scheduling proposition is referred to Appendix C.
  • Using the random-phase-shift rate expression and optimal scheduling, the energy allocated to each user can be obtained.
  • The allocation step follows the optimal time-scheduling result rather than introducing a separate phase-shift optimization.

IV. SUM-RATE MAXIMIZATION FOR THE PS SCHEME

The PS scheme is formulated as a sum-rate maximization problem for the IRS-assisted WPCN.

  • The PS section investigates the optimal solution to the sum-rate maximization problem for the PS scheme.
  • The PS formulation addresses resource optimization in the IRS-assisted WPCN setting.
  • This section introduces the PS optimization problem after the TS analysis.

A. Near-optimal solution to P4

P4 is solved through a sequence of reformulations, one-dimensional search, relaxation, and Gaussian randomization. The resulting Algorithm 2 provides a near-optimal solution for the PS scheme, while PS feasibility depends on IRS and network conditions.

  • PS feasibility: PS operation requires a condition ensuring that the IRS can assist both downlink ET and uplink IT.If the condition is violated, the IRS cannot improve WPCN performance under the PS scheme.
  • PS feasibility: PS applicability is restricted by the IRS element count, circuit power consumption, saturation power, HAP transmit power, and HAP–IRS channel gain.When Pirs,sat > ηPh∥hr∥2, increasing HAP transmit power or reducing the HAP–IRS distance can enable PS.
  • PS feasibility: Compared with PS, TS is free from the stated feasibility limitation and can be applied more widely.The PS scheme is analyzed under the condition required for IRS-assisted ET and IT.
  • Optimization procedure: The solution fixes t0, optimizes the remaining variables, and then obtains the optimal t0 through one-dimensional search.For fixed t0, βe is obtained from Proposition 4 before solving the remaining optimization problem.
  • Optimization procedure: After relaxing the rank-one constraint, the resulting problem follows the solution procedure used for P2.2.The paper omits repeated details and applies Gaussian randomization to recover a feasible phase-shift solution.
  • Algorithm 2: Algorithm 2 has complexity O(Ḿ max(K, N)^4 K^0.5 log(1/ε) + ḾDN) and can obtain a near-optimal solution with suitable updates and randomizations.Here Ḿ is the number of iterations used to update t0.

B. Random phase shifts with optimized resource allocation for the PS scheme

For the PS scheme with random phase shifts, the paper optimizes network resource allocation after fixing the random IRS phases. The procedure fixes t0 and allocates IT time and energy before searching for the optimal t0.

  • Problem formulation: Random phase shifts reduce the PS scheme to a resource-allocation problem after setting eu,i = Pu,i ti for every user.The phase shifts are randomly generated before resource allocation is optimized.
  • Optimization procedure: The algorithm first fixes t0 and optimizes IT time and energy allocation, then finds the optimal t0 by one-dimensional search.Afterward, optimal energy allocation follows from the equality constraint and Proposition 5.
  • Resource allocation: The optimal solution must satisfy C20 with equality.This equality is then used in the subsequent convex resource-allocation analysis.
  • Resource allocation: With fixed t0 and βe, Proposition 5 gives the optimal IT-phase time allocation through the unique solution of a dual-variable equation.The optimal dual variable is denoted by ζ∗.

V. PERFORMANCE EVALUATION

The evaluation shows that optimized IRS-assisted TS and PS schemes improve sum-rate across HAP power, IRS size, user count, and geometry, while gains are shaped by energy-harvesting time, circuit consumption, and saturation limits.

  • HAP transmit power: Higher HAP transmit power improves average sum-rate, while the PS scheme provides no IRS gain at P ≤30 dBm and becomes stable when P ≥40 dBm.Higher power reduces TS energy-harvesting time and increases PS reflection amplitude; saturation limits eventually bound harvested power.
  • IRS reflecting elements: Increasing IRS elements first raises and then reduces sum-rate because added transmission links compete with higher circuit power consumption and reduced user IT time.An appropriate IRS size is therefore important; without IRS, direct-link energy transfer yields the smallest sum-rate.
  • Number of users: Average sum-rate increases with more users but converges to an upper bound beyond a high user count as added-user gains are neutralized by shortened ET time.In TS, more users reduce ET duration; in PS, the IRS lowers its energy reflection amplitude to compensate.
  • HAP–user distance: Increasing the HAP–user distance reduces sum-rate because users receive weaker ET signals and the HAP receives weaker uplink IT signals.The optimized IRS-assisted schemes still significantly outperform the benchmark schemes.
  • HAP–IRS distance: Increasing the HAP–IRS distance reduces sum-rate because the IRS needs more harvesting time, with PS more location-sensitive than TS.PS additionally reduces the IRS amplitude reflection coefficient as distance increases, shortening effective IT support.
  • Overall comparison: Simulations show that the proposed schemes achieve remarkable sum-rate gains over WPCN without IRS, while PS can outperform TS when HAP power is sufficiently high or the HAP–IRS channel is strong.The study evaluates self-sustainable IRS operation through TS and PS energy harvesting and optimized resource allocation.

APPENDIX A PROOF OF PROPOSITION 1

The proof characterizes optimal IRS phase shifts by maximizing each element’s effective channel magnitude, then invokes the resulting optimization conditions and KKT-based solution structure.

  • Phase-shift optimization: For fixed feasible t and P_u, maximizing P1 over each IRS phase shift reduces to maximizing the corresponding effective channel magnitude.The relevant objective depends on the phase-shift variable for each IRS element.
  • Phase-shift optimization: The optimal phase shift is obtained by setting the phase-alignment offset α to zero, which maximizes the effective channel magnitude.This follows from the maximization of |g_H Θ_d,i g_u,i + g_h,i|^2.
  • Phase-shift optimization: The resulting optimal phase shift is expressed using the channel phases of the IRS-assisted and direct links.The proof introduces the phase-related vectors and channel expressions before stating the optimal elementwise phase shift.
  • Resource-allocation conditions: The objective is increasing in t_i and e_u,i, so the associated energy and time constraints must be active at the optimum.Otherwise, adjusting the time allocation could increase harvested energy and users’ transmit energies.
  • Resource-allocation conditions: The KKT conditions characterize the solution of P3.1, with each z_i determined uniquely and ξ* obtained through bisection.The uniqueness follows from strict monotonicity of the left-hand side of (34), while (35) determines ξ*.

APPENDIX D PROOF OF LEMMA 1

The lemma establishes feasibility conditions for a self-sustainable IRS assisting downlink energy transfer and uplink information transmission, and identifies the optimal reflection amplitude boundary.

  • Feasibility condition: The IRS must harvest sufficient power to operate its circuit while assisting downlink ET and uplink IT.If the required circuit power exceeds the maximum harvestable or saturation-limited power, self-sustained operation is impossible.
  • Saturation constraint: At optimality, the IRS harvester’s received power cannot exceed its saturation power.Excess received power would permit increasing the reflected power through the amplitude reflection coefficient without changing harvested power.
  • Feasibility condition: Energy causality combines the IRS harvesting expression with its circuit-power requirement to bound the feasible operating condition.The proof derives a bound involving ηP_h, the channel norm, and P_irs,sat.
  • Feasibility condition: The resulting condition is Kμ < min{ηP_h||h_r||^2, P_irs,sat}.This bound is obtained using the time-fraction constraint t_0* < 1 and the preceding feasibility relations.
  • Reflection-amplitude choice: At the optimum, the amplitude reflection coefficient is set to its upper bound to maximize the IRS reflected power.The proof connects this boundary choice to the preceding feasibility and power relations.
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