Mixed-Timescale Beamforming and Power Splitting for Massive MIMO Aided SWIPT IoT Network

An Liu; Hei Victor Cheng; Kaiming Shen; Min-Jian Zhao; Xihan Chen

REVIEW 3 major objections 4 minor 16 references

Mixed-Timescale Beamforming and Power Splitting for Massive MIMO Aided SWIPT IoT Network

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper proposes a mixed-timescale joint beamforming and power splitting scheme for massive MIMO SWIPT IoT networks, solved by an online stochastic successive convex approximation algorithm that provably reaches stationary solutions…

desk verdict A useful mixed-timescale SWIPT design whose general convergence claim rests on an unproven (and likely false) equivalence between a rate bound and the true ergodic rate. read the letter →

arxiv 1908.07408 v1 pith:DVAUE63V submitted 2019-08-20 cs.IT eess.SPmath.ITmath.OC

Xihan Chen , Hei Victor Cheng , An Liu , Kaiming Shen , Min-Jian Zhao This is my paper · ORCID

classification cs.ITeess.SPmath.ITmath.OC MSC 90C2690C1594A05

keywords SWIPTmassiveMIMOpowersplittingmixed-timescaleoptimizationbeamformingstochasticsuccessiveconvexapproximationergodicrateboundsnonlinearenergyharvesting

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Simultaneous wireless information and power transfer (SWIPT) in massive MIMO systems usually assumes perfect channel state information, which is unrealistic when the base station has many antennas. This paper proposes a mixed-timescale joint beamforming and power splitting (MJBP) scheme: digital beamformers adapt to the fast, imperfect channel estimates, while the power splitters at the IoT devices change only on the slow timescale of channel statistics, to respect hardware limits and signaling overhead. The resulting network utility maximization is nonconvex and stochastic, and the paper solves it with a mixed-timescale online stochastic successive convex approximation (MO-SSCA) algorithm. The authors prove that the algorithm converges to stationary solutions of the problem, and simulations show larger average utility than fixed MRT and ZF beamforming baselines across SNR, user count, and antenna count. The takeaway is that joint optimization across two timescales is a practical and beneficial route for massive MIMO SWIPT under imperfect CSI.

What carries the argument

The carrying mechanism is the two-timescale decomposition together with a chain of convex surrogates. At each short-term slot, a fractional programming block coordinate descent (FP-BCD) algorithm uses a Lagrangian dual transform and complex quadratic transformation to turn the rate expressions into a tractable form, and majorization-minimization with a first-order Taylor expansion handles the nonconvex nonlinear energy-harvesting constraint; a sample average approximation with $N$ channel-error samples makes the expectations finite. On the long-term timescale, a concave surrogate function with proximal regularization and a recursively updated weight vector $v^t$ drive a projected closed-form update of each power splitter $\rho_k$. Theorem 2 supplies an exponential convergence guarantee for the short-term solver, and Theorem 3 chains that to the almost-sure stationarity of the mixed-timescale iterates.

What would settle it

On a small instance where the ergodic rate and its bounds can be evaluated exactly, numerically maximize the true ergodic rate and each bound separately over a coarse grid of power splitter values. If the maximizing power splitter differs, the bound-optimizer equivalence fails. Alternatively, run MO-SSCA on a synthetic channel distribution and compare its limiting utility with a brute-force search over $\rho$ on the true objective; a gap would refute the claim that the algorithm maximizes the intended utility.

Watch

Extended reading notes

Core claim

The central claim is that the mixed-timescale problem—choosing beamformers per imperfect channel realization and power splitters per channel statistics—can be solved to stationarity by the proposed MO-SSCA algorithm. Theorem 3 states that every limit point of the iterates satisfies the first-order stationary conditions for the utility maximization problem, up to an error that vanishes exponentially as the number of channel-error samples grows. The paper also claims that the MJBP scheme meaningfully outperforms MRT and ZF baselines in average sum utility, and that the gains widen as the number of users grows and remain consistent as the number of antennas grows.

Load-bearing premise

The load-bearing premise is that the lower and upper bounds on the ergodic rate derived in Proposition 1 have the same optimal power-splitting and beamforming solution as the true ergodic rate; the paper asserts this without proof, so the objective being optimized may be a surrogate that differs from the intended network utility.

Editorial extensions

If this is right

If the convergence result holds, MO-SSCA gives a principled way to optimize general utility functions in massive MIMO SWIPT without perfect CSI, using only slow updates of power splitters.
The joint design should let operators reduce feedback overhead: power splitter settings are broadcast once per channel-statistics coherence interval rather than per channel block.
The performance gains over MRT and ZF imply that optimizing the beamformer and the splitter together matters more as inter-user interference grows with the number of users.
Because the short-term subproblem is convex after transformation, each online step can be solved with standard convex solvers, making the scheme implementable.
The exponential convergence in sample size suggests that a modest number of channel-error samples suffices, limiting computational cost.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same two-timescale template could be applied to other slow variables in massive MIMO, such as user scheduling, hybrid precoding phases, or resource allocation, where fast beamformers track instantaneous CSI.
If the equivalence between optimizing the ergodic-rate bounds and the true ergodic rate fails, one could replace the surrogate by an unbiased stochastic gradient of the true rate and retrain the long-term update; this is a direct testable modification.
The simulation setup, with a small number of paths and 64 antennas, suggests the scheme could be prototyped on a testbed; a useful experiment would measure how the gain over ZF changes under measured, non-Laplacian angular spreads.
The convergence proof omits details by citing an existing approach, so a re-derivation in a journal version would be needed before relying on the guarantee in a system design.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The paper proposes a mixed-timescale joint beamforming and power splitting scheme for massive MIMO SWIPT IoT networks, claiming to maximize a general concave utility under imperfect CSI. The setting is genuinely new—nobody has mixed timescales this way in SWIPT—and the MO-SSCA design, with short-term FP-BCD and long-term stochastic SCA, is a plausible way to tackle it. The simulations show consistent gains over MRT and ZF baselines, and the paper is clearly written.

The load-bearing problem is the surrogate. Proposition 1 gives bounds \hat r ≤ r ≤ \hat r + C, where C is constant w.r.t. F and ρ. The authors then say optimizing the lower and upper bound gives the same optimal solution and proceed to optimize \hat r. That is only true for the upper bound \hat r + C, which is constant-shifted. But the actual objective in P is r, and r is not \hat r + C; the gap r − \hat r is itself a sum over beamformers and power splitters (from the variance terms in equation (1)), so it is not constant. For linear utility like sum rate, optimizing \hat r might be a reasonable surrogate, but for the claimed general concave utilities it is not equivalent. The pointwise tightness of the bounds in Fig. 2 does not fix this. So Theorem 3's stationarity result applies to the surrogate, not to P as stated.

Two smaller issues: Theorem 3's proof is deferred to a self-cited reference ([7]), and the finite-N approximation error at N=200 is not quantified. The simulations also lack error bars and no code is released, so it is hard to tell how robust the 'significant gain' is.

None of this makes the algorithm worthless. As an engineering design with a linear utility, the surrogate may be fine, and the mixed-timescale formulation is a useful addition to the SWIPT literature. But as it stands, the general convergence claim overreaches. A referee should ask the authors to either prove the equivalence under additional conditions, or reframe the problem as optimizing the lower bound and state the guarantees for that objective.

I would send this to review, but I would flag the surrogate issue as the main revision point. The paper is worth engaging with for anyone working on stochastic optimization for SWIPT or massive MIMO, but cite it for the formulation, not for the convergence guarantee.

Referee Report

3 major / 4 minor

Summary. The paper considers a downlink massive MIMO SWIPT IoT network where the transmit beamformer adapts to imperfect CSI while receive power splitters adapt only to long-term channel statistics. It formulates a mixed-timescale network utility maximization problem, proposes an online stochastic successive convex approximation algorithm (MO-SSCA) with a short-term fractional-programming block-coordinate-descent inner loop and a long-term surrogate update, and claims the algorithm converges to stationary solutions. The simulation study reports gains over MRT and ZF baselines across SNR, number of users, and number of antennas.

Significance. If the theoretical claims were fully supported, the paper would provide a practical mixed-timescale design for massive MIMO SWIPT under imperfect CSI and a useful template for two-timescale stochastic optimization. The system model and algorithmic architecture are clearly described, the short-term steps build on standard tools (SAA, fractional programming, MM), and the simulations cover several operating regimes. However, the central substitution of the true ergodic rate by an upper bound is not an equivalent reformulation for general utilities, and the main convergence theorem is not proved in the paper. These gaps currently prevent the main claims from being accepted as stated.

major comments (3)

[Section II, Proposition 1 and Eq. (2)] The assertion 'From Proposition 1, optimizing the lower and upper bound provide the same optimal solution' is not established and is false for the stated utility class. The lower bound r_k - C_k and the upper bound r_k differ by the constant C_k, so for linear utilities their maximizers coincide, but for a general concave nondecreasing g, sum_k g(r_k - C_k + gamma_k e_k) and sum_k g(r_k + gamma_k e_k) can have different argmaxes. More importantly, the true ergodic rate is not equal to either bound; the actual gap between r_k and the true rate depends on F and rho through terms of the form (1/T) sum_m log_2(1 + T Var(h_k^H f_m)/(rho_k sigma_k^2 + delta_k^2)), so replacing the true rate with r_k changes the objective by a variable-dependent term. Figure 2 only demonstrates pointwise tightness of the bounds at a simulated operating point, not optimizer equivalence. Consequently, problem P is a surrogate problem, and Theorem 3, even if valid, establishes stationarity for the surrogate rather than for the original ergodic-rate utility.
[Section III-C, Theorem 3] The main convergence theorem is stated without proof. The sentence 'Theorem 3 can be proven by a similar approach in [7]' is not an adequate proof because [7] addresses a different system (hybrid compression for C-RAN) and does not include the nonlinear energy-harvesting model or the SAA short-term subproblem used here. Since Theorem 3 is the basis for the claim that Algorithm 1 converges to stationary solutions of P, a full proof, or a precise identification of a theorem in [7] from which it follows with stated modifications, is required.
[Section III-A, Eq. (4) and problem (8)] As printed, the objective in Eq. (4) contains a positive term (w^n_k)^H w^n_k (rho_k(Gamma^n_k + sigma^2_k) + delta^2_k). With q and w fixed, Gamma^n_k is convex quadratic in F, so this term is convex in F; maximizing it over the convex set Lambda is not a convex problem. The text then states that problem (8) is convex and can be solved by CVX, which contradicts the displayed equations. Please verify the sign of the quadratic penalty in Eq. (4) and either correct it or provide a convexity argument for (8). If the sign is a typographical error, the correction is straightforward, but as written the short-term convergence of Algorithm 2 is not justified.

minor comments (4)

[Section II, Eq. (1)] Equation (1) is malformed as printed: the penalty term 'log_2(1 + T rho_k sigma^2_k + delta_k Var(h_k^H f_m))' lacks a fraction bar and correct parentheses; please re-typeset the expression.
[Section III-A, Lemma 1] In Lemma 1, the phrase 'solves the problem in (1)' should refer to problem P3 or Eq. (3), since Eq. (1) is a rate expression, not an optimization problem.
[Section IV] The relation between the coherence interval T = 400 and the stated 'coherence time of 2 ms and a coherence bandwidth of 200 kHz' should be specified explicitly, as the product of time and bandwidth does not by itself determine T.
[Throughout] There are several typographical errors, including 'postive' after Eq. (9) and 'an second-order cone programming' in the introduction; please proofread the manuscript.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the algorithm and simulations are not fitted to their claimed outputs; cited prior theorems are independent, so remaining gaps are correctness risks rather than circularity.

full rationale

The paper's derivation chain is self-contained in the required sense. Problem P is explicitly defined using the bounded ergodic rate r_k from Proposition 1, and the algorithm's convergence (Theorem 3) is delegated to a similar proof in [7]; neither step makes the conclusion its own premise. The Proposition 1 assertion that optimizing the lower and upper bounds 'provide the same optimal solution' is an unproven equivalence for general concave utilities—the bounds differ by a constant independent of F and rho, which preserves argmaxes only for linear g—but this is a technical gap between the true ergodic-rate problem and the surrogate P, not a circular reduction. Similarly, Theorem 2's proof invokes the MM convergence result of [11] and [14], and Theorem 3's proof is delegated to [7]; these are citations to independently stated and proved theorems, not to the present paper's conclusions or fitted parameters. The simulation comparison against fixed-MRT and fixed-ZF baselines is an external numerical experiment in which no parameter is fitted to produce the claimed gain. Thus no circular step is exhibited; the identified issues are completeness/correctness concerns, not self-definitional reasoning.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The paper's derivations rely on standard communication assumptions (known channel statistics, Gaussian error model, concave utility) and on two paper-specific unproved steps: the equivalence between optimizing the rate bound and the true rate, and the import of convergence proofs from prior work. No new physical entities are introduced.

free parameters (4)

Proximal regularization constant tau
Introduced in equation (9) to construct the concave surrogate; only constrained to be positive, no value or schedule is specified, which affects reproducibility.
Step-size sequences alpha_t and beta_t
The convergence theorem in Section III-C imposes conditions on alpha_t and beta_t, but the paper provides no explicit sequences; these are hand-chosen hyperparameters.
SAA sample count N = 200
Simulations fix N=200; the convergence bound decays exponentially in N but no bound is given for N=200, so the approximation error is not quantified.
Utility weight gamma_k = 10 for all users
Balances ergodic rate and harvested power in eta_k; set by hand in simulations and not part of the optimization input from a physical model.

assumptions (6)

domain assumption The BS knows the channel statistics and the error variance omega_k^2 for each device.
The SAA samples phi_k from CN(0,omega_k^2 I) and the long-term updates use these statistics; without this knowledge the scheme cannot be implemented.
domain assumption Channel error phi_k is independent of the estimate h_hat_k and Gaussian with covariance omega_k^2 I.
This is the standard imperfect CSI model used in the rate bound and SAA; if errors are non-Gaussian or correlated, Proposition 1 and the algorithm change.
ad hoc to paper Optimizing the upper and lower bounds of the ergodic rate yields the same optimal solution as optimizing the true ergodic rate.
Asserted after Proposition 1 without proof; the paper then replaces the true rate by the bound in the optimization objective, so this equivalence is load-bearing.
domain assumption The objective function g is concave, non-decreasing, and has Lipschitz continuous derivative.
Required for the surrogate construction and convergence conditions in Section III.
domain assumption The short-term FP-BCD algorithm satisfies the MM framework assumptions of [11, Theorem 4.4] and the SAA uniform convergence assumptions of [14, Theorem 3.1].
Theorem 2's proof is delegated to these references; the paper does not verify all technical conditions.
ad hoc to paper Theorem 3 can be proven by the same approach as in [7].
The convergence of the full MO-SSCA algorithm is asserted via a self-cited prior proof, with no details in this paper.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Mixed-Timescale Beamforming and Power Splitting for Massive MIMO Aided SWIPT IoT Network." pith.science (2026). https://pith.science/paper/DVAUE63V

@misc{pith2026190807408,
  author       = {Pith},
  title        = {Pith review of: Mixed-Timescale Beamforming and Power Splitting for Massive MIMO Aided SWIPT IoT Network},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DVAUE63V}},
  note         = {Machine review of arXiv:1908.07408}
}

read the original abstract

Traditional simultaneous wireless information and power transfer (SWIPT) with power splitting assumes perfect channel state information (CSI), which is difficult to obtain especially in the massive multiple-input-multiple-output (MIMO) regime. In this letter, we consider a mixed-timescale joint beamforming and power splitting (MJBP) scheme to maximize general utility functions under a power constraint in the downlink of a massive MIMO SWIPT IoT network. In this scheme, the transmit digital beamformer is adapted to the imperfect CSI, while the receive power splitters are adapted to the long-term channel statistics only due to the consideration of hardware limit and signaling overhead. The formulated optimization problem is solved using a mixed-timescale online stochastic successive convex approximation (MO-SSCA) algorithm. Simulation results reveal significant gain over the baselines.

Figures

Figures reproduced from arXiv: 1908.07408 by the authors.

**Figure 2.** Cumulative distribution function (CDF) of the lower [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** (a) Utility performance versus SNR. (b) Tradeoff [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: (a) Utility performance versus the number of devices [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages

[7]

Two-timescale hybrid compression and forward for massive MIMO aided C-RAN,

A. Liu, X. Chen, W. Y u, V . Lau, and M. Zhao, “Two-timescale hybrid compression and forward for massive MIMO aided C-RAN,” IEEE Trans. Signal Process. , vol. 67, no. 9, pp. 2484–2498, Mar 2019

work page 2019
[1]

Sensor mania! the Internet of things, wearable computing, objective metrics, and the quantiﬁed self 2.0,

M. Swan, “Sensor mania! the Internet of things, wearable computing, objective metrics, and the quantiﬁed self 2.0,” J. Sens. Actuator Netw , vol. 1, no. 3, pp. 217–253, 2012

work page 2012
[2]

MIMO broadcasting for simultaneou s wire- less information and power transfer,

R. Zhang and C. K. HO, “MIMO broadcasting for simultaneou s wire- less information and power transfer,” IEEE Trans. Wireless Commun. , vol. 12, no. 5, pp. 1989–2001, May 2013

work page 1989
[3]

Joint transmit beamfo rming and receive power splitting for MISO SWIPT systems,

Q. Shi, L. Liu, W. Xu, and R. Zhang, “Joint transmit beamfo rming and receive power splitting for MISO SWIPT systems,” IEEE Trans. Wireless Commun., vol. 13, no. 6, pp. 3269–3280, Apr 2014

work page 2014
[4]

Joint beamfo rming and power splitting for MISO interference channel with SWIPT: A n SOCP relaxation and decentralized algorithm,

Q. Shi, W. Xu, T. Chang, Y . Wang, and E. Song, “Joint beamfo rming and power splitting for MISO interference channel with SWIPT: A n SOCP relaxation and decentralized algorithm,” IEEE Trans. Signal Process. , vol. 62, no. 23, pp. 6194–6208, Dec 2014

work page 2014
[5]

Optimal downlink transmi ssion in Massive MIMO enabled SWIPT systems with zero-forcing preco ding,

G. Dong, H. Zhang, and D. Y uan, “Optimal downlink transmi ssion in Massive MIMO enabled SWIPT systems with zero-forcing preco ding,” IEEE Global Commun. Conf. , Dec 2014

work page 2014
[6]

On the ergodic rate lower bounds with applicat ions to masssive MIMO,

G. Caire, “On the ergodic rate lower bounds with applicat ions to masssive MIMO,” IEEE Trans. Wireless Commun. , vol. 17, no. 5, pp. 3258–3268, May 2018

work page 2018
[8]

Pract ical non- linear energy harvesting model and resource allocation for SWIPT systems,

E. Boshkovska, D. Ng, N. Zlatanov, and R. Schober, “Pract ical non- linear energy harvesting model and resource allocation for SWIPT systems,” IEEE Commun. Lett. , vol. 19, no. 12, pp. 2082–2085, Dec. 2015

work page 2015

Show all 16 references

[9]

Shapiro, D

A. Shapiro, D. Dentcheva, and A. Ruszczynski, Lecture on stochastic programming: modeling and theory . SIAM, 2009

2009
[10]

Fractional programming for communic ation systems – Part II: Uplink scheduling via matching,

K. Shen and W. Y u, “Fractional programming for communic ation systems – Part II: Uplink scheduling via matching,” IEEE Trans. Signal Process., vol. 66, no. 10, pp. 2631–2644, Mar 2018

2018
[11]

An expanded theoretic al treatment of iteration-dependent majorize-minimize algorithms,

M. W. Jacobson and J. A. Fessler, “An expanded theoretic al treatment of iteration-dependent majorize-minimize algorithms,” IEEE Transactions on Image Processing , vol. 16, no. 10, pp. 2411–2422, Oct 2007

2007
[12]

CVX Research, Inc. CVX: Matlab software for disciplin ed convex programming, version 2.0 beta

“CVX Research, Inc. CVX: Matlab software for disciplin ed convex programming, version 2.0 beta.” Sep, 2012. [Online]. Avail able: http:// cvxr.com/cvx

2012
[13]

Optimal of MIM O device- to-device networks via matrix fractional programming: A mi norization- maximization approach,

K. Shen, W. Y u, L. Zhao, and D. P . Palomar, “Optimal of MIM O device- to-device networks via matrix fractional programming: A mi norization- maximization approach,” arXiv.org:1808.05678, 2019

2019 arXiv
[14]

A note on uniform exponential converge nce of sample average approximation of random functions,

H. Sun and H. Xu, “A note on uniform exponential converge nce of sample average approximation of random functions,” J. Math. Anal. Appl, pp. 698–708, 2012

2012
[15]

[Online]

Technical Speciﬁcation Group Radio Access Network; Furthe r Advancements for E-UTRA Physical Layer Aspects , 3GPP TR 36.814. [Online]. Available: http://www.3gpp.org
[16]

Marzetta, E

T. Marzetta, E. G. Larsson, H. Y ang, and H. Ngo, Fundamentals of Massive MIMO . Cambridge, U.K.: Cambridge University Press, 2016

2016

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [7]

Two-timescale hybrid compression and forward for massive MIMO aided C-RAN,

A. Liu, X. Chen, W. Y u, V . Lau, and M. Zhao, “Two-timescale hybrid compression and forward for massive MIMO aided C-RAN,” IEEE Trans. Signal Process. , vol. 67, no. 9, pp. 2484–2498, Mar 2019

work page 2019

[2] [1]

Sensor mania! the Internet of things, wearable computing, objective metrics, and the quantiﬁed self 2.0,

M. Swan, “Sensor mania! the Internet of things, wearable computing, objective metrics, and the quantiﬁed self 2.0,” J. Sens. Actuator Netw , vol. 1, no. 3, pp. 217–253, 2012

work page 2012

[3] [2]

MIMO broadcasting for simultaneou s wire- less information and power transfer,

R. Zhang and C. K. HO, “MIMO broadcasting for simultaneou s wire- less information and power transfer,” IEEE Trans. Wireless Commun. , vol. 12, no. 5, pp. 1989–2001, May 2013

work page 1989

[4] [3]

Joint transmit beamfo rming and receive power splitting for MISO SWIPT systems,

Q. Shi, L. Liu, W. Xu, and R. Zhang, “Joint transmit beamfo rming and receive power splitting for MISO SWIPT systems,” IEEE Trans. Wireless Commun., vol. 13, no. 6, pp. 3269–3280, Apr 2014

work page 2014

[5] [4]

Joint beamfo rming and power splitting for MISO interference channel with SWIPT: A n SOCP relaxation and decentralized algorithm,

Q. Shi, W. Xu, T. Chang, Y . Wang, and E. Song, “Joint beamfo rming and power splitting for MISO interference channel with SWIPT: A n SOCP relaxation and decentralized algorithm,” IEEE Trans. Signal Process. , vol. 62, no. 23, pp. 6194–6208, Dec 2014

work page 2014

[6] [5]

Optimal downlink transmi ssion in Massive MIMO enabled SWIPT systems with zero-forcing preco ding,

G. Dong, H. Zhang, and D. Y uan, “Optimal downlink transmi ssion in Massive MIMO enabled SWIPT systems with zero-forcing preco ding,” IEEE Global Commun. Conf. , Dec 2014

work page 2014

[7] [6]

On the ergodic rate lower bounds with applicat ions to masssive MIMO,

G. Caire, “On the ergodic rate lower bounds with applicat ions to masssive MIMO,” IEEE Trans. Wireless Commun. , vol. 17, no. 5, pp. 3258–3268, May 2018

work page 2018

[8] [8]

Pract ical non- linear energy harvesting model and resource allocation for SWIPT systems,

E. Boshkovska, D. Ng, N. Zlatanov, and R. Schober, “Pract ical non- linear energy harvesting model and resource allocation for SWIPT systems,” IEEE Commun. Lett. , vol. 19, no. 12, pp. 2082–2085, Dec. 2015

work page 2015