Interactive communication with clustering collaboration for wireless powered communication networks

Abstract

In this article, we propose a novel wireless powered communication network, which is composed of two multiple antennas hybrid access points and a series of distributed wireless devices. The two hybrid access points transmit downlink wireless energy to the wireless devices and receive uplink wireless messages from the wireless devices; meanwhile, the information of wireless devices nearer to their corresponding hybrid access point should be transmitted to the faraway hybrid access point. To improve the throughput performance of some wireless devices away from their corresponding hybrid access point, we propose a clustering-collaboration interactive communication protocol with multiple antennas by Time Division Multiple Access, where two of the distributed wireless devices are selected as cluster heads to help relay information of other cluster members, which can efficiently improve some faraway wireless devices’ throughput performance. However, its performance is also constrained by cluster heads’ high-energy consumption. To solve this energy imbalance problem, multi-antenna energy beamforming technology is exploited for the hybrid access points, which distributes more transmission power to the cluster heads to balance all the wireless devices’ energy consumption. In particular, we obtain the proposed system’s throughput performance through the multi-antenna cluster-based collaboration, and verify through simulations that this scheme can effectively enhance user unfairness and improve the throughput performance.

Introduction

The finite battery life cycle of wireless devices (WDs) powered by battery is the bottleneck of modern wireless communication network (WCN) performance. ¹ When its energy is exhausted, a WD requires to replace/recharge the battery manually, which can lead to interruption of normal operation of WDs and serious degradation of communication performance. Moreover, the state-of-the-art development of wireless energy transmission/wireless power transmission (WET/WPT) technology makes a new network paradigm possible, called wireless powered communication network (WPCN),^2–4 in which WDs’ information transfer, such as sensors, is powered by dedicated WET to supply sustainable and continuous microwave energy through the air. The utility of WET can effectively lower the cost of batteries replaced or recharged, reduce power interruption, and improve the quality of communication. Because WET has the potential to address the key energy confinement, WET is expected to be a significant component of the future WCNs.

WPCN has drawn much attention from domestic and foreign scholars,^5–7 and has been widely applied in various fields to prolong network life cycle effectively or enhance network’s data rate, especially in the application of lower power consumption, for instance, radio frequency identification (RFID) networks, ⁸ unmanned aerial vehicle (UAV), ⁹ Mobile Edge Computing (MEC), ¹⁰ Big Data, ¹¹ 5G Communication, ¹² , ¹³ Blockchain, ¹⁴ and wireless sensor networks (WSNs).^15–17 At present, there are a large number of literatures regarding WPCN. For example, Ju and Zhang ¹⁸ studied a WPCN’s throughput performance with multi-user and one single-antenna hybrid access point (HAP), which first put forward a classical harvest-then-transmit (HTT) protocol, where in the downlink (DL) the HAP broadcasts radio frequency (RF) energy to all users, and in the uplink (UL) all users use the energy harvested DL to transfer their respective information to the HAP via Time Division Multiple Access (TDMA). However, there is a phenomenon that these users far away from their associated HAP harvest less energy but require more energy to transmit their information, and vice versa, which is so-called “doubly-near-far” unfairness problem in WPCN due to the distance-dependent power loss. This will result in lower throughput of users far away from the associated HAP, which makes user unfairness exist in the networks, and thus affects the performance of the whole networks. Therefore, Che et al. ¹⁹ also revealed that this design would lead to great unfairness in the throughput among users, especially that the data rate of these users was two orders of magnitude smaller than that of other users, and this unfairness problem was more obvious, which directly reduced the sensing accuracy of WPCN.

Subsequently, many researchers proposed different methods of user cooperation to improve user fairness of WPCN, that is, users close to the associated HAP forwarded the information of users far away from the associated HAP.^20–28 For example, Zhong et al. ²⁰ presented those two users interact with each other’s information to form a distributed system of antennas that jointly transfer their messages Chen et al. ²¹ thought of a simple reference module for three nodes in a WPCN, where a harvest-then-cooperate (HTC) protocol was first put forward, and then extended it to common multi-user collaboration scenarios. Ju and Zhang ²² proposed a two-user collaboration method, in which the closer user acted as a relay to assist in transmitting the farther user’s message to HAP. Zhong et al. ²³ further considered a general multi-user scenario: multiple users are used to assist users far from the associated HAP to transmit their formation. Besides, Yuan et al.^29–31 proposed a multi-antenna cluster-based cooperation protocol, in which a WD acted as a cluster head (CH) and relayed the other cluster members’ (CMs) messages to the HAP. While considering interactive transmission between multi-HAP and multi-user, the clustering collaboration’s throughput performance is unknown.

This article focuses on a novel WPCN system consisting of two HAPs (HAP₁ and HAP₂) and N WDs, as shown in Figure 1, where HAP₁ and HAP₂ first broadcast wireless energy to the N WDs, and the N WDs then use the collected energy from HAP₁ and HAP₂ to transmit their independent messages to the corresponding HAP. The distance between each WD and the two HAPs is compared, and the one nearer to $\mathrm{HA}{\mathrm{P}}_i$ belonged to the user of $\mathrm{HA}{\mathrm{P}}_i$ , $i=1,2$ . Assume that there is (k+1) and (N–k–1) WDs nearer to HAP₂ and HAP₁, respectively. However, our purpose is to make the (k+1) and (N – k – 1) WDs’ information transmitted to HAP₁ and HAP₂, separately. Because direct transmission leads to user unfairness, this article adopts the cluster-based cooperation protocol in Yuan et al.,^29–31 in which one of the (k+1) WDs is designated as CH to help relaying the other CMs’ information transmission as shown in Figure 2(a), and so it is the (N–k–1) WDs as shown in Figure 2(b). Some farther WDs’ throughput performance can be significantly enhanced due to the reduction of transmission power consumption. However, the shortcoming is that the two CHs can be affected by high-energy consumption, ultimately limiting the network performance. In order to address the problem of energy imbalance, this article adopts the technology of multi-antenna energy beamforming (EB) at the two HAPs to enable HAPs to transfer more energy to the two CHs to achieve a balance of the energy expenditure of all the WDs.

Figure 1.

A novel WPCN system.

Figure 2.

WIT UL: (a) WIT UL of HAP1 and (b) WIT UL of HAP2.

The main contributions of this article are shown as follows:

• A novel WPCN system model is proposed for interactive information between two HAPs and a clustering-collaboration interactive communication with multiple antennas by TDMA to improve its data rate.

• To deal with the issue of the two CHs’ high-energy consumption, multi-antenna EB technique at the HAPs is exploited, where more transmission power is concentrated into the two CHs to achieve a balance of energy consumption for all WDs. The application of multi-antenna EB technique at HAPs not only improves the efficiency of WET DL but also enhances the spectral efficiency of wireless information transmission (WIT) UL.

• We develop the issue of maximizing the minimum power received among the WDs and demonstrate through simulations that this scheme can efficiently enhance the proposed system’s throughput unfairness performance.

Modeling system

Channel model

As shown in Figure 1, a novel WPCN system model is proposed constituting two HAPs (i.e. HAP₁ and HAP₂) and N WDs, where HAP₁ and HAP₂ include (N – k – 1) and (k + 1) WDs, respectively. Specially, the two HAPs perform WET DL and receive WIT UL. The two HAPs have steady power requirement to coordinate WET and WIT from the N WDs. Each WD is furnished with an internal battery for reserving wireless energy collected from its closer HAP. All the WDs and the two HAPs run on the same frequency band, and apply a time-division-duplexing circuit ²⁵ for separating energy and message transmissions. In particular, both the two HAPs and each WD are fitted with M > 1 antennas and single antenna, respectively. Our purpose is to make their respective messages transmit to each other’s HAP. In other words, the messages of (k + 1) WDs within HAP₁ should be transmitted to HAP₂, while the messages of (N – k – 1) WDs within HAP₂ should be transmitted to HAP₁.

In this article, two of the WDs are selected to act as the CHs that assist in relaying the other CMs’ WIT UL. The means of choosing the CHs will be covered in the “Numerical results” section. In general, the two CHs are labeled as $W_0$ (i.e. CH₁) and $W_{k+1}$ (i.e. CH₂), respectively. The CMs associated with the $W_0$ are indexed as $W_1,\dots ,W_k$ , and the CMs associated with the $W_{k+1}$ are denoted as $W_{k+2},\dots ,W_{N-1}$ . It is assumed that all the channels are independent and reciprocity, and go by quasi-static flat-fading, so that all the channel coefficients stay the same within transmission time per block, expressed as $T$ , but it can change between blocks. The channel coefficient vectors between the $\mathrm{HA}{P}_j(j=1,2)$ and $W_i$ are, respectively, denoted by ${\mathbf{a}}_i\in {\mathcal{C}}^{M\times 1}$ and ${\mathbf{b}}_i\in {\mathcal{C}}^{M\times 1},$ where ${\mathbf{a}}_i~\mathcal{C}\mathcal{N}(0,{\sigma }_i^2\mathbf{I})$ and ${\mathbf{b}}_i~\mathcal{C}\mathcal{N}(0,{\sigma }_i^2\mathbf{I}),i=0,\dots ,N-1$ . In addition, the channel coefficient from the jth CM to its corresponding CH is represented as $c_j~\mathcal{C}\mathcal{N}(0,{\delta }_j^2),j=1,\dots ,N-1$ . The corresponding channel gains are denoted by ${\mathbf{a}}_i@={\mathbf{b}}_i,h_i@=|{\mathbf{a}}_i{|}^2$ and $g_i@=|c_i{|}^2$ .

At the start of a transport block, there is over a fixed time period of $t_0$ for performing channel estimation (CE). During the stage of the CE, the WDs take turns broadcasting their pilot signals, such that the two HAPs have the knowledge of ${\mathbf{a}}_i,i=0,\dots ,N-1$ , CH₁ knows $c_i,i=1,\dots ,k$ , and CH₂ also knows $c_i,i=k+2,\dots ,N-1$ , respectively. Then, CH₁ and CH₂ send their estimation of $c_i$ ’s to their corresponding HAP, so that channel state information in the WPCN is fully understood the knowledge by the two HAPs.

Clustering-cooperation Interactive communication protocol

As seen in Figure 3 after the CE phase, the multi-antenna clustering-cooperation interactive WPCN runs in three stages in each duration block $T$ by TDMA. During the first phase with time duration $\tau$ , the two HAPs separately broadcast wireless radio energy DL with a fixed transmitted power $P_1$ and $P_2$ .

Figure 3.

The clustering-cooperation interactive communication protocol.

During the second phase with $(N-2)\delta$ amount of time, the k and (N – k – 2) CMs transfer their independent information to CH₁ and CH₂ in turn, using the energy they each harvested during the first stage. In particular, assume that each CM transfers its individual information to the corresponding CH in a certain amount of time $\delta$ . During the third phase with $(N\alpha -2)\delta$ amount of time, CH₁ first transfers its own message to HAP₁ for $(1+\alpha )\delta$ amount of time, and then takes turns to relay the k CMs’ messages to HAP₁ that it spends $k\alpha \delta$ amount of time on transmitting each CM’s message. So, it is the process of CH₂’s transmitting information. Clearly, we have the following time allocation equation

$$T=t_0+\tau +N(1+\alpha )\delta$$

(1)

where $\alpha$ is a system parameter, and $\delta$ can be only confirmed by the above equation through fixing $\tau$ . To ensure generality, we assume T = 1 for the entire text. We assume that the two HAPs calculate the optimal ${\alpha }^{*}$ by knowing global channel state information, which results in maximum throughput performance, and then broadcast the value of ${\alpha }^{*}$ to all the WDs, so that the time-switching circuits of all the WDs can be synchronized in the transmission of energy and information. ²⁹ Note that, in addition to the third stage of the transmission, each CM’s information can also be overheard by the two HAPs that do not dedicate them in the second stage, which can be utilized to achieve higher overall transfer rate than that of decoding the information in the third stage alone. ²⁹ The difference with the Yuan et al. ²⁹ is that although HAP₂ and HAP₁ can, respectively, overhear their own k and (N – k – 2) WDs’ messages in the second stage, we assume that HAP₂ and HAP₁ can successfully cancel their overheated information in the third phase. The next section will derive the clustering-cooperation interactive communication protocol’s throughput performance.

Analyzing throughput performance

Stage I: design energy transfer

Note that CH₁ and CH₂ need to, respectively, transmit (k + 1) and (N – k – 1) messages in total, whose consumed energy would be considerably more than that of the other CMs. Therefore, the energy received by the two CHs is a bottleneck in network performance. In order to balance energy consumption and reception, this article considers the technology of EB^32,33to concentrate the transferred energy into the two CHs.

Within time $\tau$ , HAP₁ and HAP₂ separately transmit ${\mathbf{w}}_1(t)\in C^{M\times 1}$ and ${\mathbf{w}}_2(t)\in C^{M\times 1}$ random energy signals on the M antennas for their corresponding CHs and CMs. Specifically, the transmission power of the two HAPs is

$$\begin{array}{c}\multicolumn{1}{c}{E[|{\mathbf{w}}_i\left(t\right){|}^2]=\mathrm{tr}\left(E\{{\mathbf{w}}_i(t){\mathbf{w}}_i{(t)}^H\}\right)}\\ \multicolumn{1}{c}{@=\mathrm{tr}\left({\mathbf{Q}}_i\right)\le P_i,i=1,2}\end{array}$$

(2)

where $\mathrm{tr}(·)$ and $(·{)}^H$ express trace of a matrix and complex conjugate operator, respectively. Then, the received energy signal by the ith WD within HAP₁ is

$$y_i^{(11)}\left(t\right)={\mathbf{a}}_i^T{\mathbf{w}}_1\left(t\right)+n_i^{(1)}\left(t\right),t\in [t_0,t_0+\tau ],i=0,\dots ,k$$

(3)

where $n_i^{(1)}(t)$ represents noise power of the receiver in the first stage. Similarly, the received energy signal by the ith WD within HAP₂ is

$$\begin{array}{c}{y}_i^{(12)}\left(t\right)={\mathbf{b}}_i^T{\mathbf{w}}_2\left(t\right)+n_i^{(1)}\left(t\right),t\in [t_0,t_0+\tau ]\hfill \\ i=k+1,\dots ,N-1\hfill \end{array}$$

(4)

In particular, all WDs can harvest the energy broadcast by HAP₁ and HAP₂ within $\tau$ time duration owing to the broadcast nature of wireless energy.

Ignoring noise power, we can represent the amount of energy collected by the WDs as ²⁸

$$\begin{array}{c}\multicolumn{1}{c}{E_i=\eta \tau \{E[|y_i^{(11)}\left(t\right){|}^2]+E[|y_i^{(12)}\left(t\right){|}^2]\}}\\ \multicolumn{1}{c}{=\eta \tau [\mathrm{tr}\left({\mathbf{A}}_i{\mathbf{Q}}_1\right)+\mathrm{tr}\left({\mathbf{B}}_i{\mathbf{Q}}_2\right)],i=0,\dots ,N-1}\end{array}$$

(5)

Here, ${\mathbf{A}}_i@={\mathbf{a}}_i{\mathbf{a}}_i^H$ , ${\mathbf{B}}_i@={\mathbf{b}}_i{\mathbf{b}}_i^H$ , and $0<\eta <1$ express the efficiency of energy collection, which assumes that all the WDs are the same.

This article designs the EB matrix ${\mathbf{Q}}_1$ and ${\mathbf{Q}}_2$ in equation (2) through addressing the following optimization problem

$$\begin{array}{c}(P1):\hfill \\ \underset{{\mathbf{Q}}_1,{\mathbf{Q}}_2\succcurlyeq 0}{max}{\lambda }_1+{\lambda }_2\hfill \\ \mathrm{s}.\mathrm{t}.\mathrm{tr}\left({\mathbf{Q}}_1{\mathbf{A}}_i\right)\le P_1,i=0,\dots ,N-1\hfill \\ \mathrm{tr}\left({\mathbf{Q}}_1{\mathbf{A}}_0\right)\ge [\alpha (k+1)+1]{\lambda }_1\hfill \\ \mathrm{tr}\left({\mathbf{Q}}_2{\mathbf{B}}_i\right)\le P_2,i=0,\dots ,N-1\hfill \\ \mathrm{tr}\left({\mathbf{Q}}_2{\mathbf{B}}_{k+1}\right)\ge [\alpha (N-k-1)+1]{\lambda }_2\hfill \end{array}$$

(6)

The objective is to maximize the minimum received power among the N WDs. More specifically, ${\mathbf{Q}}_1,{\mathbf{Q}}_2\succcurlyeq 0$ makes clear that both ${\mathbf{Q}}_1$ and ${\mathbf{Q}}_2$ are positive semi-definite matrices. ${\lambda }_1$ and ${\lambda }_2$ in equation (6) express the minimum received power among the k CMs and (N – k – 2) CMs, respectively. The first and second constraints in equation (6) demonstrate that CH₁’s received power is at least $[\alpha (k+1)+1]$ times of the minimum received power among the k CMs. This is consistent with our intuition: the transmission time of CH₁ is $[\alpha (k+1)+1]$ times of a CM associated with CH₁. The third and fourth constraints in equation (6) show that CH₂’s received power is at least $[\alpha (N-k-1)+1]$ times of the minimum received power among the (N – k – 2) CMs. This is consistent with our intuition: the transmission time of CH₂ is $[\alpha (N-k-1)+1]$ times of a CM associated with CH₂.

Stage II: intra-cluster transfer

Let ${\mathbf{Q}}_1^{*}$ and ${\mathbf{Q}}_2^{*}$ express the problem’s (P1) optimal solution, and subsequently the received energy by the ith WD can be written as $E_i=\eta \tau \delta [\mathrm{tr}({\mathbf{A}}_i{\mathbf{Q}}_1^{*})+\mathrm{tr}({\mathbf{B}}_i{\mathbf{Q}}_2^{*})],i=1,\dots ,k,k+2,\dots ,N-1$ . During the second stage, the CMs transfer their information to their corresponding CHs in turn, where every CM’s transmission occupies $\delta$ amount of time. Assume that the CMs deplete the collected energy, and the transmitted power of each CM is constant in the second phase. Then, the ith CM’s transmission power is $P_i=E_i/\delta =\eta \tau [\mathrm{tr}({\mathbf{A}}_i{\mathbf{Q}}_1^{*})+\mathrm{tr}({\mathbf{B}}_i{\mathbf{Q}}_2^{*})],i=1,\dots ,k,k+2,\dots ,N-1$ . Make $s_i^{(2)}(t)$ represent the baseband signal transmitted by the ith WD during the second stage with $E[|s_i^{(2)}(t){|}^2]=1$ ; CH₁’s and CH₂’s received signals are then expressed as

$$\begin{array}{c}{y}_{0,i}^{(2)}\left(t\right)=c_i\sqrt{P_i}{s}_i^{(2)}\left(t\right)+n_i^{(2)}\left(t\right)\hfill \\ t\in [t_0+(\tau +i-1),t_0+(\tau +i)],i=1,\dots ,k\hfill \end{array}$$

(7)

$$\begin{array}{c}{y}_{k+1,i}^{(2)}\left(t\right)=c_i\sqrt{P_i}{s}_i^{(2)}\left(t\right)+n_i^{(2)}\left(t\right)\hfill \\ t\in [t_0+(\tau +i-k-1),t_0+(\tau +i-k-1)]\hfill \\ i=k+2,\dots ,N-1\hfill \end{array}$$

(8)

where $E[|n_i^{(2)}(t){|}^2]=N_0$ denotes noise power of the two CHs and $n_i^{(2)}(t)$ expresses the receiver noise, respectively. Then, the two CHs can decode their corresponding CMs’ messages at rates given by

$$\begin{array}{c}\multicolumn{1}{c}{R_i^{(2)}=\delta {\log }_2(1+\eta \tau \frac{g_i[\mathrm{tr}\left({\mathbf{A}}_i{\mathbf{Q}}_1^{*}\right)+\mathrm{tr}\left({\mathbf{B}}_i{\mathbf{Q}}_2^{*}\right)]}{N_0})}\\ \multicolumn{1}{c}{i=1,\dots ,k,k+2,\dots ,N-1}\end{array}$$

(9)

Meanwhile, the CMs’ transmission can also be overheard by HAP₁ and HAP₂, such that HAP₁ and HAP₂ can, respectively, receive

$$\begin{array}{c}{\mathbf{y}}_{C{H}_1,i}^{(2)}\left(t\right)={\mathbf{b}}_i\sqrt{P_i}{s}_i^{(2)}\left(t\right)+{\mathbf{n}}_{C{H}_1,i}^{(2)}\left(t\right)\hfill \\ t\in [t_0+(\tau +i-1),t_0+(\tau +i)]\hfill \\ i=1,\dots ,k\hfill \end{array}$$

(10)

and

$$\begin{array}{c}{\mathbf{y}}_{C{H}_2,i}^{(2)}\left(t\right)={\mathbf{a}}_i\sqrt{P_i}{s}_i^{(2)}\left(t\right)+{\mathbf{n}}_{C{H}_2,i}^{(2)}\left(t\right)\hfill \\ t\in [t_0+(\tau +i-k-2),t_0+(\tau +i-k-1)]\hfill \\ i=k+2,\dots ,N-1\hfill \end{array}$$

(11)

where ${\mathbf{n}}_{C{H}_1,i}^{(2)}(t),{\mathbf{n}}_{C{H}_2,i}^{(2)}(t)~\mathcal{C}\mathcal{N}(0,N_0\mathbf{I})$ .

Stage III: cluster-to-HAP transfer

After decoding their corresponding CMs’ information, the two CHs successively send their corresponding CMs’ information along with their own information to their relevant HAP, where each information takes $\alpha \delta$ amount of time to transfer. CH₁’s and CH₂’s transmission power, respectively, are

$$P_0=\frac{E_0}{[(k+1)\alpha +1]\delta }=\eta \tau ·\frac{\mathrm{tr}\left({\mathbf{A}}_0{\mathbf{Q}}_1^{*}\right)+\mathrm{tr}\left({\mathbf{B}}_0{\mathbf{Q}}_2^{*}\right)}{(k+1)\alpha +1}$$

(12)

and

$$\begin{array}{c}\multicolumn{1}{c}{P_{k+1}=\frac{E_{k+1}}{[(N-k-1)\alpha +1]\delta }}\\ \multicolumn{1}{c}{=\eta \tau ·\frac{\mathrm{tr}\left({\mathbf{A}}_{k+1}{\mathbf{Q}}_1^{*}\right)+\mathrm{tr}\left({\mathbf{B}}_{k+1}{\mathbf{Q}}_2^{*}\right)}{(N-k-1)\alpha +1}}\end{array}$$

(13)

Let $s_i^{(3)}(t)$ expresses the baseband signal transmitted by the ith WD during the third stage. Then, the ith WD’s information received by HAP₂ and HAP₁, respectively, is

$${\mathbf{y}}_i^{(31)}\left(t\right)={\mathbf{a}}_i\sqrt{P_0}{s}_i^{(3)}\left(t\right)+{\mathbf{n}}_i^{(31)}\left(t\right),i=0,\dots ,k$$

(14)

and

$$\begin{array}{c}\multicolumn{1}{c}{{\mathbf{y}}_i^{(32)}\left(t\right)={\mathbf{b}}_i\sqrt{P_{k+1}}{s}_i^{(3)}\left(t\right)+{\mathbf{n}}_i^{(32)}\left(t\right)}\\ \multicolumn{1}{c}{i=k+2,\dots ,N-1}\end{array}$$

(15)

More specifically, Figure 3 shows the CHs first take $(1+\alpha )\delta$ amount of time to transmit their own messages, and then relay each corresponding WD’s message within $\alpha \delta$ amount of time.

To maximize the received signal to noise power ratio (SNR), HAP₂ and HAP₁ adopt the method of maximal ratio combining (MRC), in which their combined output SNR are

$$\begin{array}{c}\multicolumn{1}{c}{{\gamma }^{(31)}=\frac{|{\mathbf{a}}_0{|}^2{P}_0}{N_0}}\\ \multicolumn{1}{c}{=\frac{\eta \tau h_0[\mathrm{tr}\left({\mathbf{A}}_0{\mathbf{Q}}_1^{*}\right)+\mathrm{tr}\left({\mathbf{B}}_0{\mathbf{Q}}_2^{*}\right)]}{[(k+1)\alpha +1]N_0}}\\ \multicolumn{1}{c}{i=0,\dots ,k}\end{array}$$

(16)

and

$$\begin{array}{c}\multicolumn{1}{c}{{\gamma }^{(32)}=\frac{|{\mathbf{a}}_{k+1}{|}^2{P}_{k+1}}{N_0}}\\ \multicolumn{1}{c}{=\frac{\eta \tau h_{k+1}[\mathrm{tr}\left({\mathbf{A}}_{k+1}{\mathbf{Q}}_1^{*}\right)+\mathrm{tr}\left({\mathbf{B}}_{k+1}{\mathbf{Q}}_2^{*}\right)]}{[(N-k-1)\alpha +1]N_0}}\\ \multicolumn{1}{c}{i=k+1,\dots ,N-1}\end{array}$$

(17)

Then, the data rates of CH₁ at HAP₂ and CH₂ at HAP₁, respectively, are

$$R_0=(1+\alpha )\delta {\log }_2(1+{\gamma }^{(31)})$$

(18)

and

$$R_{k+1}=(1+\alpha )\delta {\log }_2(1+{\gamma }^{(32)})$$

(19)

However, HAP₂ and HAP₁ receive each CM’s information in both the second and third stages, in which of the situation, the message for each CM can be co-decoded by HAP₂ and HAP₁ across two stages at a rate, respectively, given by

$$\begin{array}{c}\multicolumn{1}{c}{R_i^{C{H}_1}=min\{R_i^{(2)},V_i^{(21)}+\alpha \delta {\log }_2(1+{\gamma }^{(31)})\}}\\ \multicolumn{1}{c}{i=1,\dots ,k}\end{array}$$

(20)

and

$$\begin{array}{c}\multicolumn{1}{c}{R_i^{C{H}_2}=min\{R_i^{(2)},V_i^{(22)}+\alpha \delta {\log }_2(1+{\gamma }^{(32)})\}}\\ \multicolumn{1}{c}{i=k+2,\dots ,N-1}\end{array}$$

(21)

where $R_i^{(2)}$ is given in equation (9), and $V_i^{(21)}$ and $V_i^{(22)}$ denote the messages separately extracted by HAP₂ and HAP₁ from their received signals in equations (7) and (8) (during the second stage) employing a best and optimal MRC receiver, which are, respectively, shown as

$$\begin{array}{c}\multicolumn{1}{c}{V_i^{(21)}=\delta {\log }_2(1+\frac{\eta \tau h_i(\mathrm{tr}({\mathbf{A}}_i{\mathbf{Q}}_1^{*})+\mathrm{tr}\left({\mathbf{B}}_i{\mathbf{Q}}_2^{*}\right))}{N_0}),}\\ \multicolumn{1}{c}{i=1,\dots ,k}\end{array}$$

(22)

and

$$\begin{array}{c}\multicolumn{1}{c}{V_i^{(22)}=\delta {\log }_2(1+\frac{\eta \tau h_i(\mathrm{tr}\left({\mathbf{A}}_i{\mathbf{Q}}_1^{*}\right)+\mathrm{tr}\left({\mathbf{B}}_i{\mathbf{Q}}_2^{*}\right))}{N_0}),}\\ \multicolumn{1}{c}{i=k+2,\dots ,N-1}\end{array}$$

(23)

According to the data rates of WDs given in equations (20), (21), (22), and (23), both the spectral efficiency and fairness of our proposed protocol can be evaluated. More specifically, sum throughput performance can reflect spectral efficiency, that is

$$R_{\mathrm{sum}}=R_0+\sum _{i=1}^k{R}_i^{C{H}_1}+R_{k+1}+\sum _{i=k+2}^{N-1}{R}_i^{C{H}_2}$$

(24)

Furthermore, considering the minimum data rate among the WDs can reflect the fairness of our proposed protocol, ⁸ that is

$$R_{\min }=min\{R_0,R_1^{C{H}_1},\dots ,R_k^{C{H}_1},R_{k+1},R_{k+2}^{C{H}_2},\dots ,R_{N-1}^{C{H}_2}\}$$

(25)

It can be seen that the time allocation parameters $\tau$ and $\alpha$ determine the throughput performance. Consequently, the optimal performance in equation (24) or (25) can be more easily accessible by simply searching the feasible values of $\tau$ and $\alpha$ in two dimensions. ³⁴

Benchmark method

The classical benchmark method Independent Transmission (IT)—with two multi-antenna HAPs adopting EB (IT with two HAPs)—has been compared in this article. For a relatively fair comparison, all the WDs are assumed to use up their energy collected during the WIT stage and transfer at a fixed power, and the two HAPs use MRC scheme to maximize the received SNR.

For this approach, the first duration $\tau$ is allocated as WET and the WDs use TDMA to pass their separate messages directly to their respective HAP for the rest of the time. The EB matrices ${\mathbf{Q}\prime }_1$ and ${\mathbf{Q}\prime }_2$ in the stage of WET are computed by maximizing the minimum received power among the WDs as shown below

$$\begin{array}{c}\underset{\mathbf{Q}\succcurlyeq 0}{max}{\lambda \prime }_1+{\lambda \prime }_2\hfill \\ \mathrm{s}.\mathrm{t}.\mathrm{tr}\left({\mathbf{Q}\prime }_1{\mathbf{A}}_i\right)\le P_1\hfill \\ \mathrm{tr}\left({\mathbf{Q}\prime }_2{\mathbf{B}}_i\right)\le P_2\hfill \\ \mathrm{tr}\left({\mathbf{Q}\prime }_1{\mathbf{A}}_i\right)\ge \lambda \prime ,i=0,\dots ,N-1\hfill \\ \mathrm{tr}\left({\mathbf{Q}\prime }_2{\mathbf{B}}_i\right)\ge {\lambda \prime }_2,i=0,\dots ,N-1\hfill \end{array}$$

(26)

Let ${\mathbf{Q}\prime }_1^{*}$ and ${\mathbf{Q}\prime }_2^{*}$ represent the problem’s (equation (26)) optimal solution. The WDs’ collected energy can be represented as

$$E_{i_{\mathrm{HTT}}}^{\mathrm{EB}}=\eta \tau [\mathrm{tr}\left({\mathbf{A}}_i{\mathbf{Q}\prime }_1\right)+\mathrm{tr}\left({\mathbf{B}}_i{\mathbf{Q}\prime }_2\right)],i=0,\dots ,N-1$$

(27)

Then the WDs transfer their information to their corresponding HAP one by one, where the transmission of each WD spends $\theta =(T-\tau \delta -t_0)/N$ amount of time. The ith WD’s combiner output SNR is

$$\begin{array}{c}\multicolumn{1}{c}{{\gamma }_i^{(4)}=\frac{|{\mathbf{a}}_i{|}^2{P}_{i_{\mathrm{HTT}}}^{\mathrm{EB}}}{N_0}=\frac{\eta \tau h_i[\mathrm{tr}\left({\mathbf{A}}_i{\mathbf{Q}\prime }_1^{*}\right)+\mathrm{tr}\left({\mathbf{B}}_i{\mathbf{Q}\prime }_2^{*}\right)]}{\theta N_0}}\\ \multicolumn{1}{c}{i=0,\dots ,N-1}\end{array}$$

(28)

In consequence, the WDs’ data rates at the two HAPs are

$$R_{i_{HTT}}^{EB}=\theta {\log }_2(1+{\gamma }_i^{(4)}),i=0,\dots ,N-1$$

(29)

Numerical results

This section evaluates our proposed novel system model’s throughput performance for WPCN by simulation software MATLAB to simulate. All figures below show various approaches of the performance for the minimum data rate or optimal sum throughput. The Power cast TX91501-3W transmitter and P2110 Power harvester are, respectively, adopted as energy transmitter at HAP₁ and HAP₂ with transmitting power $P_1=P_2=3\mathrm{watts}(W)$ and energy receiver at each WD with energy harvesting efficiency $\eta =0.51$ in all simulations (please see the detailed product specifications on the website of Power cast Co. http://www.powercastco.com). Except as otherwise noted, it is assumed that the number of antennas for both HAP₁ and HAP₂ and noise power in the bandwidth under consideration for all receivers are $M=5$ and $N_0={10}^{-10}W$ , respectively.^29–31,35 A path loss model is kept for the average channel gain between any two points, either HAP₁ (HAP₂) or a WD.^29–31,35 For instance, make $d_{H,i}$ represent the distance from the HAPs to the ith WD, thus ${\delta }_i^2=G_A(3\times {10}^8/4\pi d_{H,i}{f}_c{)}^{d_D}$ , where $d_D$ expresses the path loss factor during the period of WET DL and WIT UL with set as 2, ¹⁹ $G_A=2$ , and $f_c=915\mathrm{MHz}$ . Except as otherwise noted, let us suppose that 50 WDs are evenly distributed within a circle cell of radius r, and d is the distance from the center of the circle to HAP₁. Each point in the figures below is the average of 1000 for the independent WD positions. ⁴

Subsequently, we consider two schemes of selecting CHs by cluster-based cooperation, that is, the WD nearest HAP in the same cell as the CH (CCHAP), or the WD nearest to the center of the cell in the same cell as the CH (CCCH), where the former and the latter are, respectively, called CCHAP with two CHs and CCCH with two CHs for short. Besides, the WDs closest to their corresponding centers are selected as the CHs.^29–31,34

In Figure 4, we compare user fairness (the maximum–minimum throughput or average minimum data rate) among all the WDs achieved by our proposed model for the system and multi-antenna clustering-collaboration interactive communication with the benchmark scheme IT with two HAPs in Section Benchmark method by fixing the cell radius r = 6 m when the distance d varies. Specifically, sum throughput (spectral efficiency) is also compared.

Figure 4.

Performance comparison of the various transmission methods when r = 3 m and the cluster-to-HAP₁d changes: (a) maximum–minimum throughput and (b) sum throughput.

Unsurprisingly, the data rates for all three schemes go down as d goes up. However, as shown in Figure 4(a) and (b), our proposed scheme (CCCH with two CHs) for the maximum–minimum and sum throughput performance is the best of the three schemes. For instance, in Figure 4(a), when d = 5 m, CCCH with two CHs and CCHAP with two CHs are, respectively, over 2 and 1 times more than the benchmark scheme, when d adds up to 12 m, the throughput for the IT with two HAPs is approximated to 0, while the proposed method CCCH with two CHs can still keep a fairly high optimal throughput. This indicates that our proposed system model and clustering-collaboration interactive communication have obvious performance advantages when the distance from the cluster to HAP₁ is reversely far away. This is in part due to the doubly-near-far problem, which reduces some far-off WDs’ data rate severely; however, our proposed scheme can efficiently help to relay the information of those far-off WDs.

Figure 5 demonstrates the influence of intra-cluster communication links on the throughput performance by setting d = 9 m and changing the cell radius r. As seen from Figure 5, with the increase of r, the proposed scheme’s performance is performed the best among the other two schemes; for example, in Figure 5(a) and (b), when r = 3 m, our proposed scheme’s maximum–minimum and sum throughput performance are, respectively, over 3 and 2 times larger than those of the benchmark method. Moreover, as r increases, the other two methods’ throughput has a little change, but ours can remain reversely a high throughput. This means adopting EB technology at multi-antenna HAPs and clustering-collaboration interactive communication are necessary and helpful to enhance the system’s minimum throughput when r is relatively big.

Figure 5.

Performance comparison of the various transmission methods when d = 9 m and the radius of the cluster r changes: (a) maximum–minimum throughput and (b) sum throughput.

Finally, Figure 6 demonstrates the stability of throughput performance as the number of N WDs ranges from 50 to 100 with an increase. In general, we fix d = 9 m and r = 6 m. As can be observed from Figure 6(a) that all schemes’ maximum and minimum throughput decreases with the increase of N. The reason is that the average transmission time assigned per WD is shorter, and thus the worst-performing WD’s data rate decreases. More specifically, as the number of N WDs increases from 50 to 100, the decrease in maximum–minimum throughput is steady, whereas the maximum–minimum throughput decreases significantly when N increases further. However, Figure 6(b) shows the sum throughput rises as N goes up in spite of the probable decrease of the data rate per individual. This suggests that there exists a trade-off for the throughput of between each individual WD and aggregate network. In practice, even so, it can be still observed that our proposed method has a fairly high-performance gain compared to the benchmark method, in which in the case of relatively large networks (such as N = 100), the worst-performing WD can still keep an extremely high data rate.

Figure 6.

Performance comparison of the various transmission methods when the number of N WDs changes: (a) maximum–minimum throughput and (b) sum throughput.

Conclusion

In this article, a novel WPCN system model consisting of two HAPs with multiple antennas and a single antenna with N WDs is studied. A new interactive communication protocol for clustering collaboration with multiple antennas is used to improve throughput fairness. EB technology at the multi-antenna two HAPs is adopted for achieving directional energy transfer to equilibrate the WDs’ diversified energy consumption levels, especially the high-power consumption of both CHs. Through the joint optimization of EB design, the allocation of transfer time between HAPs and WDs, the transmitting power of two CHs, and the problem of optimal maximum–minimum throughput among WDs are formulated. Extensive simulation results demonstrate that the proposed system model and multi-antenna clustering-collaboration interactive communication with TDMA can significantly improve user fairness and spectrum efficiency in various scenarios compared with representative benchmark methods.