On the Performance of Wireless-Energy- Transfer ... - IEEE Xplore

Received August 29, 2015, accepted September 16, 2015, date of publication October 26, 2015, date of current version October 30, 2015. Digital Object Identifier 10.1109/ACCESS.2015.2492780

On the Performance of Wireless-EnergyTransfer-Enabled Massive MIMO Systems With Superimposed Pilot-Aided Channel Estimation JIAMING LI1 , (Student Member, IEEE), HAN ZHANG1,2 , (Member, IEEE), DONG LI3 , (Member, IEEE), AND HONGBIN CHEN2 , (Member, IEEE)

1 School

of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China Key Laboratory of Wireless Wideband Communication and Signal Processing, Guilin University of Electronic Technology, Guilin 541004, China of Information Technology, Macau University of Science and Technology, Macau 999078, China

2 Guangxi 3 Faculty

Corresponding author: H. Zhang ([email protected]) This work was supported in part by the National Natural Sciences Foundation of China under Grant 61471176, Grant 61162008 and Grant 61002012, in part by the Natural Science Foundation of Guangdong under Grant S2013010016297, in part by the Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing under Grant GXKL0614204, and in part by the Scientific Research Foundation, Graduate School, South China Normal University, Guangzhou, China, under Grant 2015lkxm35.

ABSTRACT This paper concerns with a wireless-energy-transfer (WET)-enabled massive multipleinput-multiple-output (MIMO) system with superimposed pilot (SP)-aided channel estimation. Unlike the conventional WET-enabled frame transmission schemes, with the aid of SP, both the uplink (UL) channel estimation and wireless information transmission (WIT) that powered by the downlink (DL) WET can be operated simultaneously, and thus provide the potential for improving the UL achievable throughput. The impact that the SP has on the performance of such a WET-enabled massive MIMO system is mathematically characterized, and the optimal solution, including the SP power-allocation and the ratio of time-allocation between the duration of UL WIT and DL WET, is derived with regard to maximize the UL achievable throughput. Numerical results demonstrate the proposed SP-aided WET technique yields a superior performance than the conventional pilot-only-based schemes. INDEX TERMS Energy harvesting, massive MIMO, wireless information and power transfer, channel estimation, throughput maximization.

I. INTRODUCTION

Wireless energy transfer (WET) has been proposed as a promising technology to charge their users’ terminals through radiative electromagnetic waves for green communication [1], [2]. By using this technique, a power transmitter form a power source can deliver energy to a receiver who needs to harvest energy to charge its device through electromagnetic propagation, such as a terminal. Thus, WET attracts researchers’ attentions from academics to industry [3]–[5]. As regards the WET techniques, simultaneous wireless information and power transfer (SWIPT) has been firstly proposed in [3], and then, extensively studied in literature, since it offers great convenience to mobile users with concurrent data and energy supplies. Specifically, the authors in [6] studied the performance limits of a single-input single-output

2014

SWIPT system, where the optimal transmission strategy to achieve different tradeoffs for maximal information rate versus energy transfer are characterized. Researches on SWIPT have also been provided for various practical scenarios, i.e., fading channel [7], orthogonal frequency division multiplexing (OFDM) systems [8], [9], multiuser relay channel [10], and other interference and multiinput multi-output (MIMO) broadcasting channels [11]–[14]. Moreover, [15] studied the secure relay beamforming scheme for SWIPT in a nonregenerative multi-antenna relay network by employing a constrained concave convex procedure-based iterative process, while [16] presented the concept of an energy pattern-aided SWIPT system, which is capable of operating both in an integrated receiver mode and in a powersplit mode.

2169-3536 2015 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

VOLUME 3, 2015

J. Li et al.: On the Performance of WET-Enabled Massive MIMO Systems

Another emerging trend, referred to as WET-enabled techniques, focuses on the study of using wireless power to support wireless communications. To be specific, in a WET-enabled communication system, a base station (BS) with multiple antennas first broadcasts energy to multiple single-antenna user terminals via downlink (DL) beamforming, then the users use the harvested energy to perform uplink (UL) wireless information transmission (WIT) to the BS [17]. The total time duration is divided into the DL WET and the UL WIT. Assuming perfect channel state information (CSI), WET-enabled systems in a single-user scenario has been studied in [18], and then extended to the multiuser and multicarrier transmission [19]. Also assuming perfect CSI, [20] maximized the throughput by balancing the time duration between the WET phase and the WIT phase, while satisfying the energy causality constraint, the time duration constraint, as well as the quality-of-service constraint. Explicitly, WET is similar to wireless information transmission, which also suffers from the path loss, shadowing and fast fading. Thus, the knowledge of CSI is essential for DL energy beamforming and UL information decoding in a WET enabled system, since more accurate CSI contributes to higher efficiency of energy transfer and higher UL throughput. In practice, however, perfect CSI at the transmitter is unavailable due to the channel estimation (CE) error. In WET-enabled systems, the problem of CE and training design has been studied in [21] and [22]. Typically, a longer training phase can improve the accurate of CSI available at the transmitter, while simultaneously reduces both the duration of WET and WIT, and thus may lead to less harvested energy and lower throughput. Taking the effect of CSI error into consideration, [23] proposed to optimize the efficiency of WET systems based on the design of energy beamforming, and the authors in [24] proposed to maximize the efficiency of WET in multi-antenna systems with a dynamic resource (including time and power) allocation. Recently, lage-scale MIMO (a.k.a. massive MIMO) technology has been proposed to enormously improve the transmission capacity of wireless communication networks by exploiting its large array gain at the BSs [25], [26]. Large antenna arrays can significantly increase the effective signal-to-noise ratio (SNR), and in turn, potentially improve the power efficiency through precoding and coherent combining, respectively [27]. In particular, consider perfect CSI, [28] studied the problem of energy efficiency in a WET-enabled massive MIMO system, while [32] investigated the WET-enabled massive MIMO system, where by taking CSI error into consideration, the variables including the time allocation for UL CE and DL WET, as well as the fraction of energy used for CE, are optimized w.r.t. maximize the UL rate. In order to improve the transmission rate, superimposed pilot (SP) based approaches have been proposed in [29]–[31], where the wireless training transmission (WTT) phase is arithmetically merged to the WIT phase prior to transmission, and thus can provide the potential of increasing the spectral efficiency [31]. Similarly, SP can also be VOLUME 3, 2015

used to effectively enhance the transmission efficiency in a WET-enabled system, which motivates our work. In this paper, we consider a WET-enabled massive MIMO system with SP-aided UL channel estimation. In contrast to the existing schemes, the additional WTT phase is no longer required since SP is arithmetically added at a low power to the wireless information sequence. To the best of authors’ knowledge, this paper is the first in the literature to consider the WET-enabled massive MIMO systems without wireless training phase. Specifically, this paper makes the following contributions and observations: • We present to use SP to aid UL channel estimation for a WET-enabled massive MIMO system. We show that even using the simple linear detection, the proposed scheme yields a superior performance (UL achievable rate) than that of the pilot based methods [28], [32]. We also provide the asymptotic analysis when the number of BS antennas grows to infinity, i.e., M → ∞. It is shown that, the more the power allocated to SP, the higher the achievable rate can be achieved. This fact holds true even for using the most common (practical) linear combiners, and differs significantly from the conventional SP-aided schemes [31]. • We theoretically characterize the impact that SP has on a WET-enabled massive MIMO system by deriving the closed-form lower bounds on the receiver signal-to-interference plus noise ratio (SINR), which are numerically shown to be tight. We show that there are two terms remain bounded away from zero even when the number of BS antennas M → ∞. The first type, referred to as ‘‘self-contamination’’, is due to the dependency between channel estimation and estimation error. The second type, referred to as ‘‘inter-user-interference’’, results from the correlation between the SP the data signals of UTs. Both the above contamination effects are unique for the SP-aided scheme, but can be significantly reduced by an iterative process. • In order to maximize the UL achievable throughput, the optimal solutions for both the power-allocation to SP and the time-allocation between WIT and WET are derived in large-M regime, showing interesting properties of such a WET-enabled massive MIMO system that can explain the trends observed in simulations. The remainder of this paper is organized as follows: in Section II, we firstly introduce the SP-aided system model, and then mathematically analyze the harvested energy and the achievable throughput in Section III. The optimal powerallocation to SP and the time-allocation factor between WET and WIT are jointly optimized in Section IV, in order to maximize the UL throughput. Finally, we present numerical results in Section V and conclude this paper in Section VI. Notations: In this paper, scalars are denoted by italic letters. Boldface lower-and upper-case letters denote vectors and matrices, respectively. E[·] represents the expectation operation, and CN (a, b) represents circular symmetric complex 2015


Gaussian distribution with mean a and covariance b. We use (·)∗ , (·)T and (·)H to denote complex conjugate, transpose and conjugate transpose of a matrix, respectively. k · k represents the 2-norm of a vector, and → represents convergence in probability. II. SYSTEM MODEL

We consider a WET-enabled TDD massive MIMO system consisting of a central M -antenna BS and K (K ≤ M ) single-antenna user terminals (UTs) that share the same bandwidth. We consider frame-based transmission. The transmission structure is shown in Fig. 1. Clearly, unlike the pilot-only methods [25]–[28], [32], the proposed SP-aided scheme requires no additional UL WTT phase since the specific SP is superimposed onto the data sequence prior to transmission. Therefore, the time slot of one frame (coherent interval) transmission is divided into only two phases: the DL WET phase and the UL WIT phase, respectively. Specifically, suppose the length of one frame is fixed, given by T normalized symbol periods. In the first UL WIT phase of a transmission symbol periods αT (0 < α < 1), UT sends both SP and data sequences to the BS. The BS estimates the UL channel by using SP and then obtains the DL CSI by exploiting channel reciprocity. In the second DL WET phase of the remaining (1 − α)T symbol periods, the BS delivers energy in DL transmission via beamforming, and the UT harvests energy from the received RF signals (which is used for UL WIT in the forthcoming frame transmission).

where sk = [sk (1), sk (2), · · · , sk (αT )]T and pk = [pk (1), pk (2), · · · , pk (αT )]T are the data and SP vectors, respectively. Without loss of generality, we assume that αT ≥ K , and thus we can adopt mutually orthogonal SP sequences among K UTs. This implies that pH k1 pk2 = 0 if k1 6 = k2 , ∀k1 , k2 . We also assume as in [29] and [31] that {sk (t)}, ∀k and {pk (t)}, ∀k are mutually independent, and the power of data and SP, respectively, are ρs = ksk k2 = (1 − λk )ξk ,

(2)

ρp = kpk k = λk ξk ,

(3)

2

where ξk is the total transmission power harvested from the BS, and λk (0 < λk < 1) is the ratio of power allocated to SP over the total transmission power (normalized to 1). The received signal matrix at the BS, denoted by Y ∈ CM ×αT , reads, Y = GX + W K K X X = gk xTk + W = (gk pTk + gk sTk ) + W, k=1

(4)

k=1

where G = [g1 , g2 , · · · , gK ] is the M ×K UL channel matrix between the BS and the K UTs, X = [x1 , x2 , · · · , xK ]T , and W is the M × αT additive white Gaussian noise with independent and identically distributed (i.i.d.) elements and a 2 I. covariance matrix CW = σW 1) SP-AIDED CHANNEL ESTIMATION

Using the property of SP, we can perform UL channel estimation over the WIT phase of length αT symbols. When αT ≥ K , the noisy observation on gk is given by gˆ k = gk +

K 1 1 X gk (sTk p∗k ) + Wp∗k , 2 kpk k kpk k2 k=1 {z } |

(5)

1gk

FIGURE 1. Frame structure.

Without loss of generality, we model the channel √ coefficient between the BS and the kth UT as gk = βk hk , where hk is the M × 1 matrix of independent Rayleigh fading coefficients, i.e., [hk ]m,1 = hk ∼ CN (0, 1), and βk accounts for the large-scale fading factor (long-term path loss) of the channel between the BS and the kth UT. Typically, {βk } are assumed to be constant over frames and taken to be known a priori at both the BS and the specific UT [25]–[28], [32]. A. UL DATA AND SP TRANSMISSION PHASE

As in the existing pilot-only schemes [25]–[28], [32], we assume that all UTs simultaneously transmit information (composed of both data and SP) sequence in the UL WIT phase of length αT symbols, in order to get some analytical insight. Since the complex data and SP are mixed in time, the UL frame transmitted by the kth UT has the form xk = [xk (1), xk (2), · · · , xk (αT )]T = sk + pk , 2016

(1)

where the variance of estimation error, denoted by 2 ), is given by 1gk ∼ CN (0, σ1g 2 σ1g

=E

1gH k 1gk

=

X K k=1

2 σW (1 − λk )βk + IM . (6) λk αT λk ξk

It is noted that, SP requires no additional training phase when performing CE, and thereby can potentially improve the transmission efficiency in such a WET-enabled massive MIMO system. In the above, we can see that the performance of channel estimation depends on the power-allocation to SP, λk . In a typical set-up of limited transmission power, increasing λk can improve the estimation quality, but simultaneously decreases the effective data power, thus leading to performance degradation. Interesting, however, we will show in Section III-B that, the effective SINR based on the SP-aided channel estimates in (6) is directly proportional to λk when M → ∞. VOLUME 3, 2015


2) DATA DETECTION

In the UL WIT phase, all UTs simultaneously transmit to the BS. The BS adopts a linear detector A = [a1 , a2 , · · · , ak ] to detect the information for all UTs. Specifically, either a ZF or MRC detector is adopted to maintain low complexity while preserving detection performance, ( ˆ G, for MRC A= (7) ˆ G ˆ HG ˆ −1 , for ZF G ˆ = [ˆg1 , gˆ 2 , · · · , gˆ K ] is the UL M × K channel where G matrix between the BS and the K UTs. Firstly, we remove the SP interference to detection, and then perform data detection using the detector A. Specifically, at each point of time, the receive signal vector, denoted by yk = [yk,1 , yk,2 , · · · , yk,αT ]T , is given by K X

yk (t) =

k=1 K X

=

gk pk (t) + gk sk (t) + w(t),

(8)

k=1

where w(t) is the t-th column of W . The resulting signal by using the detector A is obtained as uk (t) = AH yk (t) − gˆ k pk (t) . (9) In particular, the detected signal associated with kth UT, denoted by uk (t), is written as uk (t) =

|

{z

+

}

desired signal: S(t)

+

X k 0 6 =k

aH k gk 0 |

aH k 1gk

|

T

sk (t) + pk (t) {z }

self-interference: I(t) T sk 0 (t) + pk 0 (t) + aH k w(t)

{z

inter-user-interference: Ik 0 (t)

}

. (10)

| {z }

noise: N(t)

In the above, the first term on right-hand-side of (10) is the desired signal, while the rest three terms are attributed to interference. It is noted that, we treat (aH k 1gk )(sk (t) + pk (t))T as interference although it contains part of the desired signals. Therefore, we refer to I(t) as ‘‘self-interference’’. T 0 6 = k is By analogy, since (aH k gk 0 )(sk 0 (t) + pk 0 (t)) , ∀k raised by the correlations between the SP and UTs within the cell, we thus refer to I0k (t) as ‘‘inter-user-interference’’. This is quite different from the conventional pilot-only based schemes [25]–[28], [32]. From (10), we can obtain the achievable throughput of UL transmission from kth UT as Rk = αE log2 (1 + γ ) , (11)

ξk =

VOLUME 3, 2015

(1 − α)T η M βk +

P

k 0 6 =k

(12) Compared with the pilot-only methods, the SP-aided scheme requires no additional WTT phase, and thus, can potentially improve the UL rate. Next, we will derive the exact expression for the throughput Rk in Section III-B by using the harvested energy ξk . B. DOWNLINK ENERGY TRANSFER PHASE

Using the law of energy conservation, the harvested energy at the kth UT from the BS can be expressed as [23] 2 (13) g k ) , Qk = ηP gH k f (ˆ

gk xk (t) + w(t)

ˆ k sk (t) aH k g

where γ is the effective SINR given by h 2 i E S(t) h γk = h i 2 i 2 i P h 2 E I(t) + E I k 0 (t) + E N(t) k 0 6 =k h 2 i ˆ g (1 − λk )E aH k k = h 2 i P h H 2 i αT σ 2 h H 2 i . + 1g E a H E ak gk 0 + ξk W E ak k k

k 0 6 =k

βk 0 −

2 σW βk λk

+

where P is the transmit power of BS, and η is the efficiency ratio at UT for converting the harvested energy to the electrical energy, which depends on the efficiency of power converter. The beamformer f (ˆgk ) is designed depending on the channel estimates gˆ k in (6) with unit norm, i.e., K X gˆ k f (ˆgk ) = . kˆgk k

(14)

k=1

In the following of this paper, we set P = 1 for notational convenience. Since WET and WIT are operated in different time slot, the total harvested energy at UT during the energy duration of a period (1 − α)T can be written as 2 ξk = (1 − α)T η gH gk ) . (15) k f (ˆ With the harvested energy ξk , UT transmits the mixed data and SP in the WIT phase in the forthcoming frame. The exact expression of ξk will be derived in Section III-A. III. ANALYSIS OF UPLINK ACHIEVABLE RATE

Before deriving the UL achievable throughput in Section III, we firstly evaluate the harvested energy ξk . A. HARVESTED ENERGY

Using the beamformer in (14), the harvested energy ξk in (15) can be given in the following lemma. Lemma 1: With the beamformer in (14), and when both M and T are large, the total harvested energy by kth UT is given by (16) (shown at the bottom of this page). Proof: See Appendix A.

r

(1 − α)T η M βk + 2

P

k 0 6 =k

βk 0 −

2 σW βk λk

2

+

2 4(1−λ)T ησW λk

(16)

2017


γkMRC ≈

(1 − λk )βk2 1 X X 1 1 − λk 2 1 − λk αT 2 βk + βk20 + βk βk 0 + βk σW αT λk λk M 0 M ξk k 0 6 =k k 6 =k {z } | {z } | contamination

interference

P βk 0 When M is sufficiently large, i.e. M k 0 6=k βk , the M -dependent term is dominant over other terms, and the asymptotic value of ξk approaches to lim ξk → M βk · (1 − α)T η.

M →∞

(17)

B. ACHIEVABLE THROUGHPUT WITH SP-AIDED CE

Firstly, we evaluate the output SINR for using both MRC and ZF detections. For MRC detection in (7), we have ˆ The corresponding output SINR can be obtained in A = G. the following lemma. Lemma 2: For MRC detection, using the so derived harvested energy ξk in (17), when both M and T are large, the effective SINR in (12) can be given by (18) (shown at the top of this page). Proof: See Appendix B. ˆ G ˆ HG ˆ −1 , and the For ZF detection, we have A = G corresponding output SINR can be given in the following lemma. Lemma 3: Using the so derived harvested energy ξk in (17), the effective SINR in (12) can be obtained as γkZF ≈

(1 − λk ) . 1 αT 2 1 1 − λk KM 2 + σ αT λk (M − K )2 M − K βk ξk W | {z } | {z } contamination

(19)

interference

Proof: See Appendix C. From the above, we have the following observations: • For small values of M , ZF detection achieves a superior performance in comparison with the MRC detectionPsince the latter suffers from the interference term M1 k 0 6=k βk βk 0 which can significantly be suppressed by the former detector. • For both ZF and MRC detection, the interference terms vanishes when M → ∞, whereas the contamination terms (including ‘‘self-contamination’’ and ‘‘inter-usercontamination’’) are bounded away from zero even when M → ∞ and attenuated by a factor of αT .     αlog2 1 +      Rk =     αlog2 1 +   

2018

1 αT

1 αT

(18)

This fact differs significantly from the conventional pilot-only methods [25]–[28], [32], [33]. • In large-M regime, i.e., when M → ∞ and T is fixed, the output SINR of both ZF and MRC detectors are bounded. The limiting values of γk are  αT λk   , for MRC,   P βk20  1+ β2 lim γk → (20) k 0 6 =k k  M →∞   αT λ k   , for ZF. K Interestingly, we note that ZF detection can be viewed as a special case of MRC detection in large-M regime when β1 = β2 = · · · , βK . Besides, the effective SINRs for both ZF and MRC detections grow directly proportional to the SP-size αT and the power of SP λk . The result is expected since more accurate estimation quality typically yields better detection performance. For the SP-aided scheme, the quality of channel estimation on gˆ k is directly proportional to αT . Besides, for a massive MIMO system with M → ∞, the additive noise almost vanishes thanks to the significant array gains achieved by a very large number of M . In such a ‘‘noisefree’’ scenario, increasing λk can always improve the estimation quality without reducing SNR. This leads to an increased SINR directly proportional to λk . Note that this observation is different from the conventional SP-aided schemes [29], [31]. • When both M and T go to infinity, γk can be unbounded. Accordingly, when M is sufficiently large such that (17) is satisfied, the UL achievable rate can be given by (21) (shown at the bottom of this page). From (21), we also note that Rk depends on both the time-allocation factor between WET and WIT α and the power-ratio of SP λk . In the following, we will mathematically characterize the impacts that α and λk have on the UL achievable rate. IV. ASYMPTOTICALLY OPTIMAL SOLUTION

Following the theoretical analysis in Section III, in this section, we derive the asymptotically optimal solutions for

(1 − λk )βk2 P 1−λk 2 1−λk 2 1 P k 0 6 =k β k β k 0 + k 0 6 =k λ k β k 0 + M λk βk +  (1 − λk ) , 1−λk KM 2 1 α 2 2 σW λk (M −K )2 + (M −K )

! α 2 M (1−α)η σW

, for MRC (21) for ZF

(1−α)ηβk

VOLUME 3, 2015


both the SP power allocation and the time-allocation ratio between WET and WIT w.r.t. maximize the UL throughput of all users, i.e., (P1) : max

K X

Rk (α, λk ),

of (24) as

k=1

s.t. 0 < α ≤ 1, 0 < λk ≤ 1,

∀k = 1, 2, · · · , K .

(22)

For different UTs, we note that the time ratio between WET and WIT of k-th UT, denoted by αk , ∀k = 1, 2, · · · , is unique, i.e. α1 = α2 = · · · , αK = α, but the power ratios of various UTs’ λk , ∀k = 1, 2, · · · , K are distinct. To ease our analysis, we can solve the above optimization problem with a global objective by maximizing the UL rate of each specific UT. A. ASYMPTOTICALLY OPTIMAL SP POWER ALLOCATION

Since the SINR in both (18) and (19) are functions of λk , we can derive the optimal λk w.r.t. maximize the UL rate Rk . Lemma 4: The optimal ratios of SP power allocation λ, for ZF and MRC detection, are respectively given by (23) (shown at the bottom of this page). Proof: See Appendix D. As can be observed that, when M is not sufficiently large, an increase in the power-allocation of SP does not necessarily improve the system performance since a larger λk simultaneously leads to a lower SNR. However, when M → ∞, opt we find λk → 1, which indicates that the achievable rate can always benefit from the power allocated to SP. The result is consistent with the qualitative analysis detailed in Section III-B, and differs significantly from the conventional SP-aided scheme. B. ASYMPTOTICALLY OPTIMAL TIME ALLOCATION BETWEEN WET AND WIT

From (21), for a fixed value of λk , we can derive the optimal ratio of time allocation between WIT and WET duration α w.r.t. maximize the UL achievable rate Rk . Lemma 5: In the asymptotic regime M → ∞, the optimal ratios of time allocation between WET and WIT, for both ZF and MRC detection, are lim α opt → 1. M →∞

Proof: We derive the optimal solution of α by taking the first derivative (21) with respect of α, given by (24) (shown at the bottom of this page), where we assume M is large. When M → ∞, we neglect the lower order terms O M1 and O M12 , and obtain the following asymptotic approximations  1 αT λk   + , for MRC log2 1 + PK   ln2 ∂Rk k 0 =1 βk ≈ (25)  ∂α  1 αT λ k  log2 1 + + , for ZF K ln2 It can be easily shown that, Rk is a convex function and when M → ∞, and the above derivative is positive. Therefore, we can maximize Rk when α → 1. To be specific, when M grows without a bound, a larger α yields a higher UL rate. The result is reasonable and can be explained as follows: When M is sufficiently large, SNR → ∞ due to the significant array gain. In such a nearly ‘‘noise-free’’ scenario, the longer the WIT duration, the higher the UL achievable rate is obtained. C. ASYMPTOTICALLY JOINT OPTIMIZATION OF POWER AND TIME ALLOCATION

From (21), it is easily seen that the UL achievable rate is a function of both α and λk . We thus propose to derive a joint power and time allocation scheme to maximize Rk , which is described as the following optimization problem: (P2) : max Rk , s.t. 0 < α ≤ 1, 0 < λk ≤ 1,

∀k = 1, 2, · · · , K .

(26)

The objective function (26) in a fractional program is a ratio of two functions of the optimization variables α and λk , resulting in (P2) is a fractional programming problem, which is in general nonconvex. Alternatively, we define Fk = α1 Rk , and inspired by [35], the objective function is opt equivalent to F(λk , α) − α1 Rmax k , where Rk is the maximal UL achievable rate when λk and α are equal to the optimal opt values λk and α opt of (P1) respectively, which is defined as

s  P 2 −1  α 2 T σW 1 k 0 6=k αT βk 0   + PK , for MRC PK   1+ M 0 =1 βk 0 0 =1 βk 0 M βk (1 − α)η opt k k s (23) λk =  2 −1  T (M − K )σ 1 α  W  , for ZF  1+ M βk KM (1 − α)η PK 1−λk 2  1 2 − 0 =1 αT λ βk + O M (1 − λ )β  1 k k k k log 1 +  − , for MRC PK 1−λk 2  2 2 PK 1−λk 2  ασW ln2 1 P  β + O M1 + O M12 0 0 k =1 αT λk k ∂Rk k 0 =1 αT λk βk + M ( k 0 6=k βk βk + M (1−α)η ) = 2  −(1 − α) + O M12 ∂α (1 − λ )β 1 k  k  log 1 + − for ZF ,  2  ασW  2 ln2 (1 − α) + O 12 K (1−λk ) M 2 2+ β M αT λk (M −K )2 k (M −K )M (1−α)η (24) VOLUME 3, 2015

2019


opt

opt

opt

Rk = α opt Fk (λk , α opt ) (note that αFk (λk , α) − Rk ≤ 0 opt only when α = α opt and λk = λk ). Thus, the optimization problem (P2) is equivalent to (P3) : max Fk (λk , α) − s.t. 0 < α ≤ 1, 0 < λk ≤ 1,

1 opt R , α k ∀k = 1, 2, · · · , K .

(27)

Lemma 6: The Hessian matrix of function D(λk , α) = opt F(λk , α) − α1 Rk is a negative-semidefinite matrix and 2 ∂ 2 Fk < 0 and ∂∂ 2Fαk < 0. ∂ 2 λk Proof: See Appendix E. From Lemma 6, we observe that (P3) is a convex optimization problem, which can be solved by the Lagrange multiplier method. The Lagrangian of (27) is given as follows: opt

L(µ, ν, λk , α) = Fk (λk , α) −

Rk − µ(λk −1) − ν(α−1), α (28)

where µ ≥ 0 and ν ≥ 0 are the Lagrange multipliers corresponding to the constraints 0 < λk ≤ 1 and 0 < α ≤ 1. Using (28), the dual problem of (P3) can be written as min max L µ, ν, λk , α , (29) µ,ν

λk ,α

Given µ and ν, and applying the Karush-Kuhn-Tucker (KKT) conditions to the inner maximization problem in (26), the opt optimal SP power allocation λk and time allocation α opt can be derived as ∂L(µ, ν, λk , α) ∂Fk (λk , α) = − µ = 0, ∂λk ∂λk

(30)

and ∂L(µ, ν, λk , α) ∂Fk (λk , α) = + ∂α ∂α

opt Rk α2

opt

opt

R

opt

4) If Fk (λk , α opt ) − αk > , then set Rk = α opt Fk opt opt (λk , α opt ), and go to 2). Otherwise, λk is the optiopt mal SP power allocation and α is the optimal time allocation.

Problem (P2) in (26) is thus given by  T β2   log2 1 + 2 P k , βk + k 0 6=k βk20 lim Rk →  M →∞ T   , log2 1 + K

for MRC for ZF. (34)

It is seen that the asymptotically maximum throughput is independent of M , but directly proportional to the frame-size T . The result is expected since the output SINR for both ZF and MRC detections suffer from the effect of both ‘‘self-contamination’’ and ‘‘inter-user-contamination’’, which are bounded away from zero even when M → ∞, while both the above detectors get benefits from the frame-size T since the estimation quality with SP is directly proportional to the WIT frame-size. This fact differs significantly from the conventional pilot-based scheme [25]–[28], [32]. E. PERFORMANCE ENHANCEMENT: DATA-AIDED SOLUTION

− ν = 0,

(31)

where µ and ν can be updated by the gradient method, which is given by: µ(n + 1) = µ(n) − 1µ ,

(32)

ν(n + 1) = ν(n) − 1ν ,

(33)

where n is the iteration index, 1µ and 1ν are the positive iteration steps. We thus propose to derive a joint power and time allocation scheme to maximize Rk , which is described as the following optimization problem Algorithm 1: Although the closed-form expression of the above optimization problem is untractable, it is seen in numerical results opt that both α opt → 1 and λk → 1 hold in the large-M regime. D. ASYMPTOTICALLY MAXIMUM THROUGHPUT opt

With the above optimal solutions of α opt and λk , the asymptotically maximum UL achievable throughput for the 2020

Algorithm 1 Joint Optimization of SP-Power and Time Allocation 1) Initialization: Given K , βk , η, T , SNR, 1µ , 1ν . Let opt µ = 0, ν = 0, and Rk = αFk (λk , α). is a sufficiently small positive real number. 2) Update µ, and ν according to (32), and (33), respectively. opt 3) Computing the optimal λk and α opt by (30) and (31).

In order to reduce the effect of ‘‘contamination’’ and further improve the UL achievable rate, an iterative data-aided solution [36] can be adopted to reduce the contamination effects (18) and (19), and in turn, further improve the performance of the SP-aided scheme. Specifically, the iterative procedure can be summarized as follows: In the first step of iteration, the BS detects the data symbols of specific UT. The detected data is used to aid channel estimation by using the data-aided scheme [36]. With the enhanced channel estimates, data detection is re-performed with either the ZF or the MRC criteria (7). Then, the detected data is employed to refine the channel estimates, which in turn improves the quality of data detection in the forthcoming step. Under the block fading assumption, the overall computations induced by the data-aided solution is linear to the frame-size T, and thus is acceptable for many practical scenarios. V. NUMERICAL RESULTS

Consider a simple WET-enabled massive MIMO system with a centralized BS and K randomly distributed UTs. As in [28], VOLUME 3, 2015


FIGURE 2. Power of self-interference for different α and λ when SNR = 10dB.

FIGURE 3. Power of inter-user-interference for different α and λ when SNR = 10dB.

we set η = 0.5, βk = 1, ∀k, K = 2 and P = 1 Watt. We set the signaling frame-size Tf = 1µs, which is normalized in simulations (equivalent to T = 100 symbols). The carrier frequency is 5 GHz, and the bandwidth is 100 MHz, and the channel coefficient is assumed to be quasi-static during the whole signaling frame-size T . For convenience, we drop the subscript k and let λk = λ in the following. Firstly, we conduct an experiment to validate the tightness of our theoretical analysis described in Section III, where the average power of self-interference and inter-user-interference against different SP power-allocation factor λ are plotted in Fig. 2 and Fig. 3. The number of BS antennas is fixed to M = 128. The solid line is obtained by averaging the results in (10) using Monte Carlo simulations. For reference, we also simulate the approximations derived in (56) and (58). It is seen from these figures that the so derived approximations become more reliable as either α or λ increases. In addition, both the power of self-interference and inter-user-interference reduce approximately by a factor of α. VOLUME 3, 2015

FIGURE 4. The UL achievable throughput for different values of she SP power-allocation factor λ when M are both finite (M = 32, 128) and infinite (M → ∞), α = 0.5 and SNR = 10dB.

In Fig. 4, we examine the impact that both the SP power-allocation factor λ and the time-allocation factor between WIT and WET α have on the UL achievable throughput. The plot suggests that there exists an optimal operating value of λ for maximizing the UL achievable rate. It is expected since a larger λ yields a better estimation quality but reduces the effective SNR simultaneously. In the asymptotic regime M → ∞ (we set M = 105 in simulations), the UL achievable rate becomes a monotonically increasing function of λ. These results can be well explained with the mathematically analysis in Section III-B that an infinite value of M yields an approximately ‘‘noise-free’’ transmission environment, and hence an increased SP power ratio improves the estimation quality without reducing effective SNR, and thus yields a higher UL achievable rate. We also note that, the performance of both the above two detectors turn out to be identical when M → ∞. Furthermore, as we increase the values of λ, the theoretical expression in (21) exactly matches the achievable rate obtained through simulation, which indicating our analysis in (10) are accurate approximations. Next, we plot the UL achievable rate for different values of the time-allocation factor between WET and WIT α. It can be seen from Fig. 5 that, for a fixed α, a larger value of M yields a higher UL achievable rate. The result is expected since the output SINR increases as M grows from a small value, and hence the UL achievable rate increases as M grows. The plot also suggests an optimal operating point α for which the UL transmission rate is maximized. For example, for ZF detector, when M = 128, α ≈ 0.87 gives a maximum UL achievable rate of approximately 7bits/Hz. As M grows larger, the optimal α tends to 1. The result is agreeable with our theoretical analysis in (24) that a higher ratio of WIT over the total transmission frame increases the UL achievable rate in large-M regime. In Fig. 6, we examine the optimal solutions of both α and λ for maximizing the UL achievable rate. For fairness of comparison, we also simulate the pilot-only based scheme 2021


FIGURE 5. The UL achievable throughput for different time-allocation factor α and M when λ = 0.3 and SNR = 10 dB.

FIGURE 7. Comparison of the UL achievable throughput between the SP-aided scheme and the pilot-only one for different signaling frame-size T when M = 200.

information (5) and the detected data information (9) with 2 times of iterations. Clearly, when T is large, there is significant performance gain in terms of UL throughput, especially for the SP-aided scheme with data-aided solution. Besides, as T grows larger, the performance of the pilot-only based scheme saturates quickly, while the SP-aided method can always benefit from the increase of T . Such numerical result is consistent with our theoretical analysis in (34), and further indicates the advantage of our SP-aided scheme. VI. CONCLUSION

FIGURE 6. The UL achievable throughput versus the number of BS antennas M for different schemes, and SNR = 20 dB.

(where an individual training phase is required for CE prior to the WIT phase) [32] as the latter serves as a benchmark in related works. Clearly, the graph reveals that the performance of the SP-aided scheme is less dependent on M in comparison with that in [32], which serves as a further confirmation to our theoretical analysis in Section III. Meanwhile, for a practical value of M , i.e., M ≤ 128, it can be observed that the SP-aided scheme (with jointly optimization of α and λ) performs the best among all these schemes. It is also found that the proposed optimization scheme converges after no more than 20 times iterative computation in simulations. In order to further gain an insight into the SP-aided scheme, the comparison between the SP-aided scheme and the pilot-only based one is done in Fig. 7 for different coherent signaling frame-size T (where the maximal UT’s mobility of v ≤ 43km/h is considered following the block-fading assumption [37]). To further enhance the UL rate achieved by our SP-aided scheme, we also provide the performance of the SP-aided scheme with data-aided solution [36], where the curve (labeled ‘‘SP: iter 2nd ) is obtained by removing the data interference using the estimated channel 2022

In this paper, we analyzed the performance of a WET-enabled massive MIMO system with SP-aided channel estimation. We mathematically characterize the impact that SP has on the output SINR. Through an analysis of the relative importance, we show in the large-M regime that the UL achievable rate is independent of the number of BS antennas M , but depends crucially on the ratio of power-allocation to SP λ, the time-allocation factor between WET and WIT α, and the frames-size T . Moreover, the optimal solutions of both α and λ are derived w.r.t. maximize the UL achievable rate, showing interesting properties of the SP-aided scheme that can explain the trends observed in simulations. Both theoretical analysis and numerical results confirm the effectiveness of the proposed scheme. APPENDIX A PROOF OF LEMMA 1

From (15), the harvested energy ξk can be rewritten as ξk = (1 − α)T η

K X gH g0k |2 k |ˆ . kˆg0k k2 0

(35)

k =1

From (5), it is noted that the estimation on gˆ k is composed of gk , and thus, these two terms are mutually dependent. To circumvent this problem, we decompose (5) as VOLUME 3, 2015


two independent terms as gˆ k = φk gk + e gk ,

(36)

where φk and e g are respectively given by 1 (sT p∗ ), ξk λk k k X 1 e gk = sTk0 p∗k gk 0 + Wp∗k . ξk λk 0 φk = 1 +

(37) (38)

By analogy, the denominator of (35) can be derived as P T ∗ ∗ 2

k 0 6=k (sk 0 pk )gk 0 + Wpk 2

E kˆgk k = E φk gk +

ξk λk 1 T ∗ 2 1 = M βk E 1 + sk 0 pk + ξ k λk (ξk λk )2 X h i h 2

2 i T ∗ ∗

× M βk 0 E sk 0 pk + E Wpk . k 0 6 =k

k 6 =k

Using the fact that E WsTk → 0, it can be easily checked that φk gk and e gk are mutually independent. By (36), we can thus evaluate the numerator of (35) as h 2 i ˆk E g H k g 2 X 1 H T ∗ H ∗ 0 g × s p g +g Wp = E φk gH g + 0 k k k k k k k k ξk λk k 0 6 =k h i h i 1 2 4 = 1+ E sTk p∗k E gk (ξk λk )2 2 h i M βk σW M βk X T ∗ 2 0 β E s p + + . (39) k k k ξk λk (ξk λk )2 0 k 6 =k

For a large values of T and M , and by using the law of large numbers, we have the following asymptotic results: ξ 2 λk (1 − λk ) E |sTk p∗k |2 → k , αT 2 E kWpk k2 → M ξk λk σW .

(40) (41)

On the other hand, since gk ∼ (0, βk IM ), ∀k, it yields that kgk k2 ∼ 12 βk χ(2M ), where χ(2M ) denotes the chi-square distribution with 2M degree of freedom. Then, we have E kgk k4 = (M 2 + M )βk2 . (42) Substituting (40), (41) and (42) into (39), straightforward computation yields 1 − λk 2 ˆ k |2 = 1 + E |gH (M + M )βk2 k g αT λk 2 X (1 − λk )βk 0 M βk σW + . (43) + M βk αT λk ξk λk 0 k 6 =k h i sT p∗ gH gˆ k 0 2 = E 1 + k 0 k 0 gH gk 0 k ξk 0 λk 0 k 2 1 H X T ∗ ∗ H 0 + g sk pk 0 gk + gk Wpk 0 ξ 0λ 0 k k

k

k 0 6 =k

2 X sT0 p∗0 M βk βk 0 + 0 = E 1 + k k gH g k k ξk 0 λk 0 (ξk 0 λk 0 )2 k 0 6 =k 2 2 1 H ∗ × E sTk p∗k 0 + Wp gk k0 (ξk 0 λk 0 )2 K X σ2 1 − λk 0 M βk 0 + W M . = βk M βk 0 + αT λk 0 ξk 0 λk 0 0

(45) By (40) and (41), we easily obtain K 2 X M σW (1 − λk )βk 2 E kˆgk k = βk + . M+ αT λk ξk λk

(46)

k=1

k) When T is sufficiently large, i.e. T K (1−λ αλk , the above formula can be further simplified as 2 σW 2 E kˆgk k ≈ βk + M. (47) ξ k λk

Substituting (43), (44) and (47) into (35), when T is large, (35) can be written as X ξk = βk 0 + (1 − α)T η k 0 6 =k

×

M 2β 2 + M β P k

k

k 0 6 =k

(βk +

(1−λk )βk 0 αT λk

+

2 M βk σW ξk λk

2 σW ξk λk )M

.

(48)

So we obtain the following equation as 2 X (1 − λk )βk 0 σW 2 ξk + − (1 − α)T η M βk + βk λ k αT λk k 0 6 =k 2 X (1 − λk )T ησW = 0. (49) + βk 0 ξk − λk 0 k 6 =k

Solving ξk and discarding the negative solution, we obtain the harvested energy for kth UT in (16). APPENDIX B PROOF OF LEMMA 2

With MRC, we have ak = gˆ k . The corresponding SINR of UT k can be given by E |S(t)|2 MRC γk = P E |I(t)|2 + E |I k 0 (t)|2 + E |N(t)|2 k 0 6 =k

h i 4 (1−λk )E gˆ k = h 2 i P h H 2i αT σ 2 h H 2i . + E gˆ H 1g E gˆ k gk 0 + ξk W E gˆ k k k k 0 6 =k

(50)

k =1

(44) VOLUME 3, 2015

Next, we evaluate the terms of (50) as below. 2023


1) SIGNAL AND NOISE POWER

We firstly valuate the term E kˆgk k4 contained in the numerator of (50). From (5), we have gˆ k ∼ (0, σgˆ2 I). Using the results in (17), (45) and (47), and when T is large, straightforward computation yields

3) POWER OF INTER-USER-INTERFERENCE

(1 − λk )(M 2 + M )ξk βk2 . E |S(t)|2 ≈ αT 2 E |N(t)|2 ≈ M σW βk .

(51) (52)

2) POWER OF SELF-INTERFERENCE

Form (50), it is noted that 1gk contains part of the desired signal gk . Thus 1gk and gˆ k are mutually dependent. To tackle this problem, by (36), we rewrite (5) as X 1 sTk0 p∗k gk 0 + Wp∗k 1gk = (φk − 1)gk + ξk λk 0 k 6 =k X 1 T ∗ T ∗ ∗ sk 0 pk gk 0 + Wpk . (53) sk pk gk + = ξk λk 0 k 6 =k

By (17), (36), (37) and (53), we easily obtain h 2 i 1g E gˆ H k k H X T ∗ 1 ∗ T ∗ s p gk + 0 p g +Wp s = E k k0 k k (ξk λk )2 k k k 0 6 =k 2 X sTk0 p∗k gk 0 +Wp∗k × sTk p∗k gk + =

k 0 6 =k 2 h 2 T ∗ 2 i M βk s 0 p + M βk E k k (ξk λk )2 (ξk λk )2

X

By analogy, we evaluate the inter-user interference E[|I k 0 (t)|2 ] (i.e., the second term in the numerator of (50)) as h 2 i E |Ik 0 (t)|2 = E gˆ H k gk 0 K X s∗k 0 pTk gH gk 0 = E 1+ ξk 0 λk 0 k 0 k =1 2 1 ∗ T sk 0 pk M βk 0 + pTk WH gk 0 + ξk 0 λk 0 2 K X M 2 βk20 s∗k 0 pTk 0 gH g + = E 1 + k ξk 0 λk 0 k (ξk 0 λk 0 )2 0 k =1 1 ∗ T 2 T H 2 × E sk 0 p k + pk W gk 0 (ξk 0 λk 0 )2 X K 1 − λk 0 = 1+ M βk βk 0 αT λk 0 0 k =1

σ2 1 − λk 0 2 2 M βk 0 + W M βk . + αT λk 0 ξk 0 λk 0 When T is large, i.e. T large for M , we have

h 2 i βk 0 E sT0 p∗ k

Essentially, such dependency leads to self-contamination. This effect does not exist in a conventional pilot-only schemes [25]–[28], [32], where data and pilot are timedivision-multiplexed.

k

PK

k=1

(1−λk ) αλk

(57)

and using the law of

k 0 6 =k

K h h X 2 i

2 i 2 1 T ∗ ∗

+ M βk 0 E sk 0 pk +E Wpk . (ξk λk )2 0

k =1

X

E[|Ik 0 (t)|2 ] ≈

k 0 6 =k

X 1 − λk 0 X M 2 βk20 + M βk βk 0 . αT λk 0 0 0

k 6 =k

k 6 =k

(54)

(58)

By (40) and (41), we easily obtain 2 2 h 2 i M M M (1 − λk )βk2 H +O +O . E gˆ k 1gk = T αλk T T2 (55)

In the above, it is noted that the first component of (58) do not vanish even when M → ∞ since the power of E[|I k 0 (t)|2 ] grows with M in the same order as that of desired signal in (51). We thus refer to I k (t) as ‘‘inter-user-contamination’’. Anyway, such contamination effect reduces directly proportional to the SP-size αT as well as the power allocated to SP λk . Substituting (51), (52), (56) and (57) into (50), we obtain the output SINR as in (18).

where we assumed that M is large in (55). Since when both 2 M M and T are large, either O M and O are in a lower T T2 2

(1−λ )β 2

order (in terms of T and M , respectively) than MT · αλkk k , we thus omit the two terms in (55) and obtain the following approximation h 2 i (1 − λk )M 2 βk2 ≈ E |I(t)|2 = E gˆ H . (56) k 1gk αT λk From (51) and (56), both the power of self-interference E[|I(t)|2 ] and that of data signal E[|S(t)|2 ] grow with M in an order of O(M 2 ). Thus, E[|I(t)|2 ] becomes a limiting interference component when M → ∞. In the following discussion, we thereby refer to I(t) as ‘‘self-contamination’’. As discussed above, gˆ k and gk − gˆ k are not independent. 2024

APPENDIX C PROOF OF LEMMA 3

ˆ G ˆ HG ˆ −1 . Recall (10), the output With ZF, we have A = G SINR of the kth UT can be expressed as (59) (shown at the ˆ HG ˆ is a K × K central comtop of the next page). Note that G plex Wishart matrix with M (M > K ) degrees of freedom. From [34], it can be easily shown that E

h

ˆ HG ˆ G

−1 i kk

=

1 . 2 ) (M − K )(βk − σ1g

(60)

VOLUME 3, 2015


(1 − λk ) h i h i 2 −1 αT σW 2 ˆ H ˆ −1 2 H H ˆ ˆ 0 E gˆ k 1gk E G G G G + ξk E kk kk k 0 =1  2 PK ασW 1 P βk 0 βk 0    , + + 0 0  k =1 αT λ β k 6 =k 1 M βk (1 − λk ) M βk2 (1 − α)η(1 − λ) k k µ(λk ) = = 2 ασW  KM 2 γk   + ,  αT λk (M − K )2 (M − K )(1 − α)M βk2 η(1 − λk ) γkZF =

From (6), when T is large, it can be well approximated that 2 ≈ β , and thus, we obtain βk − σ1g k h i 1 H ˆ −1 ˆ . (61) E G G ≈ kk (M − K )βk Since pH k1 pk2 = 0 for k1 6 = k2 , ∀k1 , k2 , from (5), (17), (36) and (55), we easily obtain 2 2 h 2 i M (1 − λk )βk2 M M H E gˆ k 1gk 0 = +O +O T αλk T T2 2 2 (1 − λk )M βk ≈ . (62) αT λk The result in (19) can be directly obtained by substituting the results (54), (60) and (62) into (59). APPENDIX D PROOF OF LEMMA 4

For MRC and ZF detections, we have (63) (shown at the top of this page). Setting the first derivative of (63) with respect to λk , it can be easily checked that µ(λk ) is a convex function. Therefore, the global minimum of µ(λk ) can be

k) obtained by setting ∂µ(λ ∂λk to zero, and then, we arrive at the following second-order polynomials of λk for both MRC and ZF detector, which can be given respectively by P 2 α 2 T σW 1 k 0 6=k αT βk 0 1− + PK PK M k 0 =1 βk 0 k 0 =1 βk 0 M βk (1 − α)η

× λ2k − 2λk + 1 = 0, for MRC 2 α 2 T (M − K )σW 1− λ2k − 2λk + 1 = 0, KM 3 βk2 (1 − α)η

(64) for ZF

(65)

Solving the above formula and discarding the negative solution, we obtain the optimal λk that maximizes Rk in (21). APPENDIX E PROOF OF LEMMA 6

Define H(D(λk , α)) as the Hessian matrix of function D(λk , α). Then, H(D(λk , α)) can be given by   ∂ 2H ∂ 2H   ∂λ2 ∂λ∂α  H(D(λk , α)) =  (66)  ∂ 2 H ∂ 2 H . ∂λαλ ∂α 2 VOLUME 3, 2015

(59)

K P

for MRC (63) for ZF

When M is sufficiently large, i.e. M entries of H(D(λk , α)) can be given by

2T α 2 λσW , (1−α)(1−λ)K ηβk2

∂ 2H α2T 2 = − , ∂λ2 (K + αλT )2 opt 2Rk ∂ 2H λ2 T 2 = − − , ∂α 2 (K + αλT )2 α3 ∂ 2H ∂ 2H TK . = = ∂λ∂α ∂λαλ (K + αλT )2 From the above, we can easily obtain that ∂2H ∂α 2

< 0. Besides, we have

∂2H ∂λ2

the

(67) (68) (69) < 0 and

∂ 2H ∂ 2H α 2 λ2 T 2 (T 2 − K 2 ) ∂ 2H ∂ 2H · − · = 2 2 ∂λ∂α ∂λαλ ∂λ ∂α (K + αλT )4 opt 2Rk T 2 + . (70) α(K + αλT )2 For T K , the above formula is positive. Hence, H(D(λk , α)) is a negative-semidefinite matrix. ACKNOWLEDGMENT

The authors would like to thank the editor and the anonymous reviewers for their constructive comments that significantly improve the quality of this paper. REFERENCES [1] P. Grover and A. Sahai, ‘‘Shannon meets Tesla: Wireless information and power transfer,’’ in Proc. IEEE Int. Symp. Inf. Theory, Austin, TX, USA, Jun. 2010, pp. 2363–2367. [2] V. Sharma, U. Mukherji, V. Joseph, and S. Gupta, ‘‘Optimal energy management policies for energy harvesting sensor nodes,’’ IEEE Trans. Wireless Commun., vol. 9, no. 4, pp. 1326–1336, Apr. 2010. [3] L. R. Varshney, ‘‘Transporting information and energy simultaneously,’’ in Proc. IEEE Int. Symp. Inf. Theory, Toronto, ON, Canada, Jul. 2008, pp. 1612–1616. [4] M. K. Watfa, H. Al-Hassanieh, and S. Selman, ‘‘Multi-hop wireless energy transfer in WSNs,’’ IEEE Commun. Lett., vol. 15, no. 12, pp. 1275–1277, Dec. 2011. [5] J. Gozalvez, ‘‘WiTricity-the wireless power transfer [mobile radio],’’ IEEE Veh. Technol. Mag., vol. 2, no. 2, pp. 38–44, Jun. 2007. [6] X. Zhou, R. Zhang, and C. K. Ho, ‘‘Wireless information and power transfer: Architecture design and rate-energy tradeoff,’’ IEEE Trans. Commun., vol. 61, no. 11, pp. 4754–4767, Nov. 2013. [7] L. Liu, R. Zhang, and K.-C. Chua, ‘‘Wireless information transfer with opportunistic energy harvesting,’’ IEEE Trans. Wireless Commun., vol. 12, no. 1, pp. 288–300, Jan. 2013. [8] K. Huang and E. Larsson, ‘‘Simultaneous information and power transfer for broadband wireless systems,’’ IEEE Trans. Signal Process., vol. 61, no. 23, pp. 5972–5986, Dec. 2013. 2025


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JIAMING LI received the B.Eng. degree from the School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou, China, in 2014, where he is currently pursuing the M.Sc. degree. His current research interests include massive MIMO technology, channel estimation, and OFDM system.

HAN ZHANG received the M.E. degree in electronics and communication engineering from the University of Liverpool, U.K., in 2005, and the Ph.D. degree from the School of Information Science Technology, Sun Yat-sen University, China, in 2009. From 2012 to 2013, he was a Senior Research Associate with the Department of Electrical Engineering, City University of Hong Kong, Hong Kong. Since 2009, he has been with the Faculty of Physics and Telecommunication Engineering, South China Normal University, China, where he is currently an Associate Professor. His research interests include channel estimation, synchronization, MIMO technology, and cognitive radio.

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DONG LI received the B.E. degree in communication engineering from Yunnan University, Kunming, China, in 2004, and the M.E. and Ph.D. degrees in electronics and communication engineering from Sun Yat-sen University, Guangzhou, China, in 2006 and 2010, respectively. Since 2010, he has been with the Faculty of Information Technology, Macau University of Science and Technology (MUST), Macau, China, where he is currently an Assistant Professor. He has also held a visiting position with the Institute for Infocomm Research, Singapore. His research interests include design, analysis, and optimization of wireless communications systems with a current focus on cognitive radio and cloud radio access networks. He received the Bank of China Excellent Research Award from MUST in 2011. He served as a Technical Program Committee Vice Chair of the IEEE International Conference on Communications Systems in 2014.

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HONGBIN CHEN was born in Hunan, China, in 1981. He received the B.Eng. degree in electronic and information engineering from the Nanjing University of Posts and Telecommunications, China, in 2004, and the Ph.D. degree in circuits and systems from the South China University of Technology, China, in 2009. From 2006 to 2008, he was a Research Assistant with the Department of Electronic and Information Engineering, Hong Kong Polytechnic University. In 2014, he was a Research Associate with the Department of Electronic and Information Engineering. He is currently a Professor with the School of Information and Communication, Guilin University of Electronic Technology, China. He has authored over 30 papers in renowned international journals, including the IEEE TRANSACTIONS. His research interests lie in energy-efficient wireless communications. He serves as an Editor of IET Wireless Sensor Systems.

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