Source-linked AI summary
Wireless Information and Power Transfer in Multiuser OFDM Systems
Xun Zhou, Rui Zhang, Chin Keong Ho
TL;DR
The paper addresses resource allocation for multiuser OFDM SWIPT under practical receiver constraints, using TDMA with TS and OFDMA with PS. It derives a TS solution framework and an iterative PS algorithm, showing that peak-power constraints and user count shape their rate-energy comparison.
Problem
The paper studies how to optimize multiuser OFDM SWIPT when harvesting circuits cannot directly decode carried information, under harvested-energy and transmit-power constraints.
Method
It uses TDMA with receiver TS, OFDMA with receiver PS, convex reformulation and Lagrange duality for TS, and iterative power, subcarrier, and splitting optimization for PS.
Results
TS outperforms PS when Ppeak →∞, whereas PS outperforms TS for sufficiently small Ppeak, such as Ppeak = 4P/N.
Takeaways & Limitations
The peak power constraint and the number of users are key determinants of the schemes’ rate-energy performance comparison.
Abstract
from arXiv · showhide
In this paper, we study the optimal design for simultaneous wireless information and power transfer (SWIPT) in downlink multiuser orthogonal frequency division multiplexing (OFDM) systems. For information transmission, we consider two types of multiple access schemes, namely, time division multiple access (TDMA) and orthogonal frequency division multiple access (OFDMA). At the receiver side, due to the practical limitation that circuits for harvesting energy from radio signals are not yet able to decode the carried information directly, each user applies either time switching (TS) or power splitting (PS) to coordinate the energy harvesting (EH) and information decoding (ID) processes. For the TDMA-based information transmission, we employ TS at the receivers; for the OFDMA-based information transmission, we employ PS at the receivers. Under the above two scenarios, we address the problem of maximizing the weighted sum-rate over all users by varying the time/frequency power allocation and either TS or PS ratio, subject to a minimum harvested energy constraint on each user as well as a peak and/or total transmission power constraint. For the TS scheme, by an appropriate variable transformation the problem is reformulated as a convex problem, for which the optimal power allocation and TS ratio are obtained by the Lagrange duality method. For the PS scheme, we propose an iterative algorithm to optimize the power allocation, subcarrier (SC) allocation and the PS ratio for each user. The performances of the two schemes are compared numerically as well as analytically for the special case of single-user setup. It is revealed that the peak power constraint imposed on each OFDM SC as well as the number of users in the system play a key role in the rate-energy performance comparison by the two proposed schemes.
I. INTRODUCTION
The paper extends SWIPT to multiuser OFDM systems, addressing practical receiver limitations through TDMA with TS and OFDMA with PS while optimizing weighted sum-rate under energy and power constraints.
- SWIPT jointly transfers information and energy, but practical harvesting circuits cannot directly decode information from received radio signals.
- The study is motivated by OFDM systems whose device performance may be limited by available energy despite OFDM’s established high-rate communication role.
- The paper studies a multiuser OFDM downlink with one fixed-power AP and distributed users equipped with additional energy receivers.
- TDMA assigns users nonoverlapping information slots with TS at receivers, whereas OFDMA allocates subcarriers to users with PS at receivers.
- The optimization maximizes weighted sum-rate by varying time/frequency power allocation and switching or splitting ratios, subject to per-user harvested-energy and transmission-power constraints.
A. TDMA with Time Switching
The TDMA-based scheme uses K+1 time slots with receiver time switching: each user decodes during its assigned slot and harvests during the others, including an optional power slot.
- TDMA information transmission with TS assigns slot k to user k for information decoding and reserves slot K+1 as a possible EH-only power slot.
- The slot powers satisfy per-subcarrier peak constraints 0 ≤ p_k,n ≤ Ppeak.
- Each user decodes information in its assigned slot and harvests energy during all other slots.
- The scheme jointly varies time- and frequency-domain transmit power with TS ratios to maximize weighted sum-rate under EH and power constraints.
- Problem (P-TS) is non-convex in its original formulation, although feasibility can be checked through a linear program.
B. OFDMA with Power Splitting
The OFDMA-based scheme allocates each subcarrier to at most one user and applies receiver power splitting, jointly optimizing transmit power, subcarrier allocation, and splitting ratios under energy and power constraints.
- OFDMA assigns each subcarrier to at most one user through a subcarrier allocation function Π(n).
- Each receiver splits ratio ρ_k of received power to energy harvesting and ratio 1−ρ_k to information decoding.
- All subcarriers at a user share the same splitting ratio, and power sent to other users’ information decoding can be partly harvested but the remainder is unused.
- The optimization jointly varies frequency-domain power, subcarrier allocation, and receiver splitting ratios subject to EH and transmission-power constraints.
- Problem (P-PS) is non-convex in its current form, while its feasibility conditions match those of the TS problem.
C. Performance Upper Bound
An upper-bound problem assumes receivers can decode information and harvest energy simultaneously without implementation loss, providing a benchmark for the practical TS and PS schemes.
- The upper bound assumes simultaneous information decoding and energy harvesting from the same received signal without implementation loss.
- The upper-bound, TS, and PS problems share the same feasibility conditions.
- The analysis assumes all three optimization problems are feasible so that optimal solutions exist.
III. RESOURCE ALLOCATION IN A SINGLE-USER SYSTEM
The single-user analysis compares TS and PS under two extreme per-subcarrier peak-power regimes. Without a peak-power constraint, TS is no worse; with Ppeak = P/N, PS is no worse.
- Extreme peak-power regimes: For K = 1, the analysis examines the extreme cases Ppeak →∞ and Ppeak = P/N to compare TS and PS.These correspond respectively to no per-subcarrier peak constraint and a binding per-subcarrier-only constraint.
- No peak-power constraint: With Ppeak →∞ and E > 0, TS achieves its maximum rate as α1 →1 and α2 →0.The EH slot shrinks asymptotically while still satisfying the positive harvested-energy requirement.
- No peak-power constraint: With Ppeak →∞, PS achieves no larger maximum rate than TS: RPS(P, ∞) ≤ RTS(P, ∞).The comparison follows from the single-user EH constraint and the TS optimum.
- Only per-subcarrier peak constraint: With Ppeak = P/N, TS achieves no larger maximum rate than PS: RTS(P, P/N) ≤ RPS(P, P/N).At this peak-power level, the total-power constraint is redundant for both schemes.
1. RPS(P, P/N) is thus given
The paper compares TS and PS through analytical extreme cases and numerical rate-versus-energy curves. The comparison depends on peak power, harvested-energy requirements, and whether the system is OFDM or single-carrier.
- Single-carrier comparison: For N = 1, TS and PS achieve the same rate when Ppeak →∞, while TS is no better than PS for finite P/N ≤ Ppeak < ∞.This is the single-carrier specialization of the analytical comparison.
- Numerical comparison: For single-user OFDM, the achievable rate decreases as the minimum required harvested energy E increases for both TS and PS.The paper attributes this to less available energy for information decoding.
- Numerical comparison: With N = 64, finite peak power Ppeak = 4P/N creates a significant TS rate gap relative to Ppeak →∞, and the gap grows with E.Under an unbounded peak constraint, all transmission time can be used for information decoding; finite peak power requires a nonzero EH interval.
- Numerical comparison: For N = 64, TS outperforms PS when Ppeak →∞, whereas PS outperforms TS for sufficiently small Ppeak, such as Ppeak = 4P/N.Thus, neither scheme is uniformly better across peak-power settings.
IV. RESOURCE ALLOCATION IN A MULTIUSER SYSTEM
The multiuser section considers an OFDM-based SWIPT system and derives optimal transmission strategies for the proposed TS and PS schemes before comparing their performances.
- IV. RESOURCE ALLOCATION IN A MULTIUSER SYSTEM: For the general multiuser OFDM-based SWIPT system, the paper derives optimal transmission strategies for the two proposed schemes and compares their performances.The section extends the resource-allocation analysis from the single-user setting to multiple users.
A. Time Switching
The time-switching problem is transformed into a convex formulation by scaling power with time allocation, enabling optimal resource allocation through Lagrange duality. In the no-per-subcarrier peak-power case, multiuser systems may achieve maximum rate without a dedicated power slot.
- Problem reformulation: The transformation qk,n = αkpk,n converts the time-switching formulation into an equivalent problem with affine constraints.The transformed variables satisfy 0 ≤ qk,n ≤ αkPpeak and 0 ≤ αk ≤ 1.
- Rate implications: When the peak-power constraint is finite, zero time allocation implies zero transformed and allocated power for that slot.For Ppeak < ∞, qk,n = 0 when αk = 0, and the corresponding scheduled transmission power is zero.
- Problem reformulation: The transformed objective is jointly concave in {αk} and {qk,n}, making the reformulated problem convex and solvable optimally by Lagrange duality.The method introduces a Lagrangian and minimizes its dual function over nonnegative dual variables.
- Resource allocation: For each information-transmission user, power variables and time allocation are optimized alternately using block-coordinate descent and numerical bisection.With fixed αk, qk,n is obtained from the stationarity condition; with fixed {qk,n}, αk is found by bisection over 0 ≤ αk ≤ 1.
- Resource allocation: The time-switching algorithm has time complexity O(K^2N), excluding the continuation of the complexity expression beyond the supplied passage.The cited complexity accounts for the listed algorithmic steps and the ellipsoid-method iteration structure.
- Rate implications: With K ≥ 2 and Ppeak →∞, the maximum time-switching rate is achieved with αK+1 = 0 or αK+1 → 0.In this case, no additional power slot may be scheduled; users can harvest energy during slots assigned to other users’ information transmission.
B. Power Splitting
The power-splitting problem is non-convex because of integer subcarrier allocation, so the paper uses an iterative optimization procedure. It alternates power and subcarrier optimization with power-splitting-ratio updates and converges to a local optimum under tight harvested-energy constraints.
- Problem structure: The power-splitting problem is non-convex because subcarrier allocation is integer-valued, making an optimal solution computationally difficult to obtain.The formulation is addressed using Lagrange duality under an assumed zero duality gap for the relevant large-subcarrier setting.
- Alternating optimization: For fixed power-splitting ratios, power allocation and subcarrier allocation are obtained through per-subcarrier maximization and user search.The power allocation is given by (29), while the optimal allocation for each subcarrier is found by exhaustive search over users.
- Alternating optimization: For fixed power and subcarrier allocation, the optimal power-splitting ratios are updated, and the procedure iterates until the weighted sum-rate cannot further improve.At each iteration, ratios are decreased to make all harvested-energy constraints tight, preserving feasibility when the initialization is feasible.
- Convergence: The iterative algorithm is guaranteed to converge to a local optimum when all harvested-energy constraints are tight.The resulting local optimum depends on the initial power-splitting ratios.
- Convergence: To improve robustness, the method uses M feasible random initializations and retains the solution with the maximum weighted sum-rate.Each initialization produces a local optimum through the iterative procedure before final selection.
- Computational cost: The computation is dominated by the ellipsoid method, whose stated complexity is O(K^4 + K^3N) before accounting for the number of initializations M.The supplied passage gives the complexity for the ellipsoid component and indicates that additional initialization steps further affect total runtime.
C. Performance Comparison
The rate-energy comparison between TS and PS depends on the required harvested energy, per-subcarrier peak power, and number of users. With finite peak power and moderate energy requirements, TS can retain a rate advantage, while multiuser diversity affects both schemes.
- With Ppeak →∞, both TS and PS achievable rates decrease as the minimum required harvested energy increases, remaining below the upper bound for positive requirements.
- For sufficiently small requirements, E ≤80µW, PS achieves a larger rate than TS by exploiting frequency diversity through subcarrier allocation.
- For sufficiently large required energy under finite peak power, TS performance degrades because a nonzero EH slot reduces total information transmission time.
- For both schemes, achievable rate increases with the number of users and eventually saturates because system bandwidth and transmission power are fixed.
- For K ≥2, TS outperforms PS because power splitting discards an increasingly large portion of energy at each user's information receiver.
V. CONCLUSION
The paper optimizes resource allocation for multiuser OFDM-based downlink SWIPT using TDMA with TS and OFDMA with PS. It shows that TS can match conventional TDMA rates while harvesting energy, but high energy requirements and implementation considerations can favor PS or TS respectively.
- The study maximizes weighted sum-rate subject to per-user harvested-energy constraints and peak and/or total transmission-power constraints.
- The two investigated schemes combine TDMA-based information transmission with receiver TS and OFDMA-based information transmission with receiver PS.
- TS can achieve the same rate as conventional TDMA while allowing each user to harvest a reasonable amount of energy.
- When users require sufficiently large harvested energy, TS may need a nonzero EH slot, significantly degrading its rate so that PS may outperform it.
- TS is easier to implement at the receiver because it switches between energy harvesting and information decoding.
APPENDIX A PROOF OF LEMMA 4.1
This appendix proves concavity of the relevant function in the transformed variables by checking all cases for the time-allocation variable. It then connects the resulting inequality to the lemma's proof.
- The proof establishes joint concavity of f(q_k,n, α_k) for q_k,n ≥0 and α_k ≥0 using convex combinations of two feasible points.
- When both time variables are positive, concavity of log2 supports the required inequality for f.
- The mixed cases with one zero time variable and the case with both zero are handled separately, completing the concavity proof.
- The appendix also states that the choice of d in (21) is a subgradient of g({λ_i}, µ, ν).