Open AccessArticle

Ambient Backscatter-Based User Cooperation for mmWave Wireless-Powered Communication Networks with Lens Antenna Arrays

Rongbin Guo

^1,2

Rui Yin

^1,3,

Guan Wang

^1,2,

Congyuan Xu

⁴ and

Jiantao Yuan

^1,3,*

College of Computer Science and Technology, Zhejiang University, Hangzhou 310058, China

School of Information and Electrical Engineering, Hangzhou City University, Hangzhou 310015, China

Zhejiang Engineering Research Center of Building’s Digital Carbon Neutral Technology, Hangzhou 310015, China

⁴

College of Information Science and Engineering, Jiaxing University, Jiaxing 314001, China

Author to whom correspondence should be addressed.

Electronics 2024, 13(17), 3485; https://doi.org/10.3390/electronics13173485

Submission received: 11 August 2024 / Revised: 30 August 2024 / Accepted: 1 September 2024 / Published: 2 September 2024

(This article belongs to the Special Issue Recent Advances in High-Performance Wireless Power Transfer Technologies)

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Abstract

With the rapid consumer adoption of mobile devices such as tablets and smart phones, tele-traffic has experienced a tremendous growth, making low-power technologies highly desirable for future communication networks. In this paper, we consider an ambient backscatter (AB)-based user cooperation (UC) scheme for mmWave wireless-powered communication networks (WPCNs) with lens antenna arrays. Firstly, we formulate an optimization problem to maximize the minimum rate of two users by jointly designing power and time allocation. Then, we introduce auxiliary variables and transform the original problem into a convex form. Finally, we propose an efficient algorithm to solve the transformed problem. Simulation results demonstrate that the proposed AB-based UC scheme outperforms the competing schemes, thus improving the fairness performance of throughput in WPCNs.

Keywords:

ambient backscatter; user cooperation; WPCNs; lens antenna array

1. Introduction

1.1. Motivation

With the continuous evolution of wireless networks, sixth-generation communication (6G) is expected to realize ultrabroadband, ubiquitous connectivity, and integrated sensing and communication, which will enable many significant application scenarios such as internet of things (IoT), smart transportation, monitoring of the environment, and so on [1,2,3]. It is estimated that the number of global network terminals will hit 125 billion by 2030, and the number of IoT connections per cubic meter could reach up to 100 [4]. Limited by device size and deployment environment, some IoT devices are energy constrained. Therefore, future communication networks will benefit greatly from low-power technologies, not only by improving spectrum efficiency but also by being highly desirable.

In this regard, wireless energy transfer (WET), which can receive power wirelessly through radio-frequency (RF) transmission, has the potential to supply ample energy to wireless systems with limited power. Furthermore, the seamless integration of WET and wireless connectivity has become a popular area of research, known as wireless-powered communication networks [5,6]. A harvest-then-transmit (HTT) protocol is suggested in [7] for WPCNs, where users initially collect energy from RF signals sent by a hybrid access point (HAP) in the downlink (DL), and subsequently, send their information to the HAP in the uplink (UL). However, users located far from the HAP harvest much less energy than those close to it, yet they must consume more energy to transmit data back to the HAP, creating a ‘doubly near–far’ user unfairness problem. With consideration of the fairness issue, user cooperation is an effective approach, in which the user far from the HAP cooperates with their adjacent user to transmit signals to the HAP.

Several UC schemes for WPCNs have been developed based on different models [8,9,10]. Optimal energy beamforming and time assignment were designed by the authors in [8] to explore the performance limit of system information transmission with two single-antenna users and an HAP. The authors in [9] considered a reconfigurable intelligent surface (RIS)-assisted UC in a WPCN. Then, they collaboratively optimized the distribution of transmit time and power for both users, as well as the coefficients of the passive array for reflecting wireless energy and information signals in order to maximize the shared minimum throughput of the system. In [10], the authors collaboratively optimized the allocation of time, power, and energy beamforming vectors to maximize the energy efficiency (EE) in a scenario containing two UC users and a separated power station and information receiver.

One significant problem with current user collaboration schemes is the excessive overhead involved in exchanging information among users. Specifically, a new low-cost ambient backscatter communication (AmBC) technique [11] allows users to transmit information by passively backscattering environmental RF signals, thus achieving device battery conservation. Compared to the HTT mode, IoT devices operating in backscatter mode exhibit reduced power consumption [12]. In AmBC systems, a backscatter device (BD) utilizes ambient signals that are already modulated by surrounding RF sources such as Wi-Fi access points, TV towers, or cellular network base stations for communication [13]. The BD changes the backscattered signal by alternating between two modes: a mode for backscattering, when the BD antenna is short-circuited; and a mode for transmission, when the BD antenna is open-circuited. These modes are used to indicate bit ‘0’ and bit ‘1’. Typically, the backscatter receiver (BR) is equipped with an energy detector (ED) [14] to determine the received power levels of AmBC signals, and then, associate them with the corresponding transmitted signals from the BD. As a result, the AmBC system is efficient in terms of energy as it does not require active RF signal transmission, and it also makes efficient use of the spectrum by sharing it with ambient RF sources. Actually, except for ambient backscatter (AB), there are two types of backscatter modes: bistatic backscatter (BB), for which the RF emitter and BR can be separately deployed; and monostatic backscatter (MB), for which the RF emitter and BR are colocated [15]. The AB mode device communicates by modulating and reflecting ambient signals, eliminating the need for dedicated spectrum and energy unlike the other two types [16].

Nonetheless, ambient backscatter communication relies on the unpredictable nature of data traffic to generate the necessary excitation signal for IoT devices utilizing backscattering. As a result, WPCN systems should utilize energy-efficient technologies such as mmWave multiple-input multiple-output (MIMO) communication to provide active RF signals. MmWave MIMO has emerged as a crucial technology for future cellular networks due to the availability of abundant spectrum resources at higher frequencies and its high energy efficiency with beamforming. Furthermore, mmWave technology is suitable for various short-range wireless communication scenarios like IoT because of its short wavelength and wide frequency band.

1.2. Related Work

The combination of mmWave-based communication systems and WPCNs has garnered significant interest in recent research. In [17], the authors studied the WPT performance of the mmWave band with a typical low-power device. In comparison to lower frequencies, WPCN in mmWave bands has the capability to offer improved energy transfer coverage when using optimal parameters. Additionally, the efficiency of WPT in a massive mmWave WPCN was studied by the authors in [18], and simulation results showed that mmWave WPT outperformed WPCNs operating at lower frequencies. The authors in [19] introduced a more practical non-linear energy harvesting model in a massive mmWave WPCN system and analyzed the potential performance of WPT. The study in [20] examined the probability of beam outage and energy outage for a mmWave WPCN using a random energy beamforming scheme, while the arrangement of energy receivers was based on the homogeneous Poisson point process (HPPP). Then, the authors analyzed the optimal performance of a mmWave WPCN system. In [21], the authors jointly designed the transmit power, beamforming, and power split coefficient for the optimization of transmission performance of a mmWave-based WPCN with imperfect channel state information (CSI). By exploiting the advantages of multiple antennas, energy beamforming can be adopted to transfer energy signals to all users in a mmWave WPCN. Nevertheless, the traditional fully digital beamforming methods lead to excessive power usage and RF chain expenses. In [22], we equip an HAP with a discrete lens array (DLA) [23], which reduces the complexity and cost of the RF hardware as well as improving the power budget due to the lens’s energy-focusing capability [24]. A typical DLA mainly contains an electromagnetic lens and a corresponding antenna array, with elements located in the lens’s focal region. The lenses can execute variable phase shifts for incident signals at different points of the lens aperture to obtain an angle-dependent energy-focusing result [23]. The DLA can transform the traditional mmWave MIMO channels into beamspace channels equivalently with angle-dependent energy-focusing abilities. As the beamspace channels of mmWave MIMO systems are sparse, only a small quantity of beams are needed. In mmWave MIMO systems, each beam needs a single RF chain, so the DLA can reduce the cost of RF chains effectively. Furthermore, the phase shifters of the mmWave MIMO system are replaced by a switching network with DLA, which decreases the complexity and cost of the hardware. However, the UC scheme for user fairness issues with DLA needs to be further considered.

1.3. Our Contributions

Based on our previous work [22], in this paper, we consider an AB-based UC scheme in a mmWave WPCN with multiple antennas on the HAP. In order to ensure fairness for users, we initially establish an optimization problem aimed at maximizing the minimum rate of two users through the joint design of power and time allocation. To address this nonconvex issue, we introduce auxiliary variables and transform the original problem into a convex form. Subsequently, an efficient algorithm is proposed to solve the problem. Simulation results show that compared to traditional UC schemes using active communication, the passive AB-based UC scheme with DLA can effectively improve the throughput performance of energy-constrained devices in mmWave WPCNs. This particular scenario has not been previously explored.

1.4. Notation and Paper Organization

The remainder of this paper is structured as follows. Section 2 introduces the UC system model based on AB and formulates the optimization problem. The algorithm is proposed in Section 3. Our experimental results are analyzed in Section 4, and the paper concludes in Section 5.

Notation: In this document, the symbol

a_{i j}

in lowercase represents the element at position

(i, j)

in matrix

A

. Bold uppercase and lowercase letters

A

and

a

represent a matrix and a vector, respectively. The symbols

A^{T}

A^{H}

{| | A | |}_{2}

, and

Tr (A)

denote the transpose, conjugate transpose, Frobenius norm, and trace of matrix

A

, respectively. The symbol

I_{K}

refers to the identity matrix of size

K \times K

, while

E {\cdot}

denotes an expectation operation.

2. System Model and Problem Formulation

We consider a mmWave WPCN with one HAP and two single-antenna users (

U_{1}

and

U_{2}

). The HAP is equipped with a DLA, which includes

M_{t}

antennas and one RF chain. The network topology is depicted in Figure 1, and for simplicity, we assume that these three nodes are arranged in a linear configuration. The HAP has a fixed power supply, while the two users must harvest energy from the signals transmitted by the HAP during the DL WET phase. The harvested energy is stored in an energy buffer (e.g., rechargeable battery), after which the users transmit information during the UL wireless information transmission (WIT) phase.

2.1. Channel Model

We hypothesize that WET and WIT function within an identical frequency range, and there is channel reciprocity between the DL and UL. The beamspace channel matrix,

\tilde{H}

, is derived from the physical spatial MIMO channel:

\begin{matrix} \tilde{H} = [{\tilde{h}}_{1}, {\tilde{h}}_{2}] = [{Uh}_{1}, {Uh}_{2}], \end{matrix}

(1)

where the matrix

U \in C^{M_{t} \times M_{t}}

represents the discrete Fourier transformation (DFT) corresponding to DLAs at the HAP, and

h_{k} \in C^{M_{t} \times 1}

is the channel vector between the HAP and user k in the spatial domain. The DFT matrix

U

comprises of steering vectors for

M_{t}

orthogonal beams distributed across the entire angular domain, i.e.,

\begin{matrix} U = {[a (φ_{1}), a (φ_{2}), \dots, a (φ_{M_{t}})]}^{H}, \end{matrix}

(2)

where the spatial directions

φ_{m}

are normalized as

φ_{m} = \frac{1}{M_{t}} (m - \frac{M_{t} + 1}{2})

, where

m = 1, 2, \dots, M_{t}

. The corresponding array-steering vectors

a (φ_{m})

are defined as

a (φ_{m}) = \frac{1}{\sqrt{M_{t}}} {(e^{- j 2 π φ_{m} i})}_{i \in I}

, with

M_{t} \times 1

dimensions. Here, the index set of array elements is denoted by

I = {i - (M_{t} - 1) / 2 | i = 0, 1, \dots, M_{t} - 1}

In a typical multi-path setting, if we assume transmission, the channel can be expressed as

\begin{matrix} h_{k} = β_{k}^{(0)} a (ϕ_{k}^{(0)}) + \sum_{l = 1}^{L} β_{k}^{(l)} a (ϕ_{k}^{(l)}), \end{matrix}

(3)

where

β_{k}^{(0)} a (ϕ_{k}^{(0)})

and

β_{k}^{(l)} a (ϕ_{k}^{(l)})

represent the channel vectors for the direct line-of-sight (LoS) and the l-th non-line-of-sight (NLoS) paths between the HAP and user k, respectively. Additionally,

β_{k}^{(0)} (β_{k}^{(l)})

denote the complex channel gains, while

ϕ_{k}^{(0)} (ϕ_{k}^{(l)})

represent the corresponding spatial directions. For simplicity, we only consider azimuth angles of departure (AoD), assuming that the elevation AoD is zero due to practical validity when users are much higher than their height difference compared to the distance from the HAP. The extension to a 3D scenario is straightforward and does not affect the nature of the problem. We assume that the beamspace channel matrix

\tilde{H}

is perfectly estimated by the HAP [22,24,25].

2.2. The Protocol Description

As depicted in Figure 1, the system functions through four stages. During the initial phase, lasting

τ_{1}

, the HAP sends out an energy signal with a constant power

P_{1}

. The energy signal received by user k can be represented as

\begin{matrix} y_{u k}^{(1)} = \sqrt{P_{1}} {\tilde{h}}_{k}^{H} f_{t} s_{1} + n_{u k}, \end{matrix}

(4)

in which

s_{1}

, satisfying

E {s_{1}^{H} s_{1}} = 1

, is the transmitted signal;

{\tilde{h}}_{k} \in C^{M_{t} \times 1}

is the beamspace channel vector between the HAP and user k;

f_{t} \in C^{M_{t} \times 1}

is the beam selection vector with only one non-zero element 1; and

n_{u k} \sim CN (0, σ_{0}^{2})

is the additive zero-mean circular complex Gaussian noise at user k, where

σ_{0}^{2}

denotes the noise variance.

The HAP transmits energy to all users using beam selection in order to enhance WET. We choose the beam with the highest magnitude [23] to maximize power transfer for each user. It is assumed that the energy harvested from noise

n_{d k}

can be disregarded. Therefore, the anticipated energy harvested by user k can be represented as

\begin{matrix} E_{u k}^{(1)} = η P_{1} τ_{1} {| {\tilde{h}}_{k}^{H} f_{t} s_{1} |}^{2}, \end{matrix}

(5)

where the energy-converting efficiency,

0 < η < 1

, is assumed fixed and equal for all users.

In the second phase, with

τ_{2}

amount of time,

U_{1}

harvests energy from an incident signal transmitted by the HAP, and also backscatters a different fraction of the incident signal to

U_{2}

to transmit “0” or “1”. As a result,

U_{2}

employs non-coherent detection methods such as the energy detector [11] to interpret the transmitted bit. When

U_{1}

sends a “0”, only the energy signal from the HAP is received by

U_{2}

\begin{matrix} y_{u 2, 0}^{(2)} = \sqrt{P_{1}} {\tilde{h}}_{2}^{H} f_{t} s_{2} + n_{u 2}, \end{matrix}

(6)

where

s_{2}

, satisfying

E {s_{2}^{H} s_{2}} = 1

, is the transmitted signal. On the other hand, when

U_{1}

transmits a bit “1”,

U_{2}

receives a combination of signals from both the HAP and

U_{1}

, i.e.,

\begin{matrix} y_{u 2, 1}^{(2)} = \sqrt{P_{1}} {\tilde{h}}_{2}^{H} f_{t} s_{2} + μ β_{12} \sqrt{P_{1}} {\tilde{h}}_{1}^{H} f_{t} s_{2} + n_{u 2}, \end{matrix}

(7)

where

μ

is the signal attenuation coefficient due to the reflection at

U_{1}

, and

β_{12}

denotes the channel coefficient between

U_{1}

and

U_{2}

We apply a power splitting scheme in

U_{2}

, i.e., the received RF signal is split into two parts, with a constant splitting factor

γ \in [0, 1]

. Accordingly, the

γ

part of the RF signal power is harvested, and the remaining

(1 - γ)

part is used for information decoding (ID). The circuit of ID introduces an extra noise,

n_{e} \sim CN (0, σ_{1}^{2})

. We assume

n_{e}

is independent of

n_{u k}, k = 1, 2

. As a result, the signal at the ID receiver and energy decoder can be written as

\begin{matrix} y_{u 2, I}^{(2)} = \sqrt{1 - γ} y_{u 2}^{(2)} + n_{e}, y_{u 2, E}^{(2)} = \sqrt{γ} y_{u 2}^{(2)}, \end{matrix}

(8)

where

y_{u 2}^{(2)} = y_{u 2, 1}^{(2)}

when

U_{1}

backscatters “1”, and

y_{u 2}^{(2)} = y_{u 2, 0}^{(2)}

when

U_{1}

transmits “0”. We assume that “0” and “1” are transmitted with equal probability without loss of generality. Then, we can obtain the harvested energy by

U_{2}

, which is given by

\begin{matrix} E_{u 2}^{(2)} = & \frac{1}{2} η γ τ_{2} (E [| y_{u 2, 1}^{(2)} |^{2}] + E [| y_{u 2, 0}^{(2)} |^{2}]) \\ = & \frac{1}{2} η γ P_{1} τ_{2} (2 | {\tilde{h}}_{2}^{H} f_{t} s_{2} |^{2} + μ^{2} β_{12}^{2} | {\tilde{h}}_{1}^{H} f_{t} s_{2} |^{2}) . \end{matrix}

(9)

Note that here we assume the signal backscattered from

U_{1}

is uncorrelated with the signal received directly from the HAP due to the random modulation during the backscatter phase. Additionally, the battery level of

U_{1}

remains constant because the energy usage from operating the backscatter transmitter is negligible compared to the energy harvested during this phase. We also assume a fixed backscattering data rate

R_{b}

bps, and the sampling rate of the backscatter receiver at

U_{2}

N_{b} R_{b}

, which means the receiver takes

N_{b}

samples of each bit. We are able to calculate the probability of bit error (BER)

P_{b}

when employing an optimal energy detector for decoding the received single-bit data [14]:

\begin{matrix} P_{b} = \frac{1}{2} e r f c [\frac{(1 - γ) P_{1} μ^{2} \sqrt{N_{b}} β_{12}^{2} {| {\tilde{h}}_{1}^{H} f_{t} s |}^{2}}{4 ((1 - γ) σ_{0}^{2} + σ_{1}^{2})}] . \end{matrix}

(10)

The process of communication can be represented as a binary symmetric channel, with its capacity measured in bits per channel use, i.e.,

\begin{matrix} C_{b} = 1 + P_{b} log P_{b} + (1 - P_{b}) log (1 - P_{b}) . \end{matrix}

(11)

And the effective bit rate from

U_{1}

U_{2}

can be expressed as

\begin{matrix} R_{12}^{(2)} = C_{b} R_{b} τ_{2} . \end{matrix}

(12)

In the third phase, of duration

τ_{3}

U_{1}

transmits information to the HAP and

U_{2}

simultaneously by exhausting the energy harvested in the first phase. The average transmit power of

U_{1}

is given by

\begin{matrix} P_{3} = E_{u 1}^{(1)} / τ_{3} = η P_{1} τ_{1} {| {\tilde{h}}_{1}^{H} f_{t} s_{1} |}^{2} / τ_{3} . \end{matrix}

(13)

The received signal at the HAP and

U_{2}

can be expressed as

\begin{matrix} y_{u 0}^{(3)} = \sqrt{P_{3}} f_{r}^{T} h_{1} s_{3} + n_{u 0}, y_{u 2}^{(3)} = β_{12} \sqrt{P_{3}} s_{3} + n_{u 2}, \end{matrix}

(14)

where

f_{r}^{T} \in C^{1 \times M_{t}}

is the beam selection vector which chooses the largest element of the UL channel

h_{1}

, just like

f_{t}

;

s_{3}

, satisfying

E {| s_{3} |^{2}} = 1

, is the complex base-band signal of

U_{1}

; and

n_{u 0} \sim CN (0, σ_{0}^{2})

denotes the receiver noise at the HAP.

In the last phase,

U_{2}

first transmits

U_{1}

’s signal to the HAP with power

P_{41}

and time

τ_{41}

; after that,

U_{2}

transmits its own signal to the HAP with power

P_{42}

and time

τ_{42}

. We can acquire the total energy consumed by

U_{2}

in the last phase constrained by the energy harvested in the first and second phases:

\begin{matrix} P_{41} τ_{41} + P_{42} τ_{42} \leq E_{u 2}^{(1)} + E_{u 2}^{(2)} . \end{matrix}

(15)

We also have a total time constraint of time allocations

τ ≜ (τ_{1}, τ_{2}, τ_{3}, τ_{41}, τ_{42})

\begin{matrix} τ_{1} + τ_{2} + τ_{3} + τ_{41} + τ_{42} \leq T, \end{matrix}

(16)

where T represents the length of time during which the channel remains unchanged. For simplicity, we set

T = 1

. Then, the achievable rates of transmitting

U_{1}

’s signal from

U_{1}

U_{2}

and the HAP in the third phase, and from

U_{2}

to the HAP in the last phase, can be written as

\begin{matrix} R_{12}^{(3)} = τ_{3} {log}_{2} (1 + \frac{P_{3} β_{12}^{2}}{σ_{0}^{2}}), \end{matrix}

(17a)

\begin{matrix} R_{10}^{(3)} = τ_{3} {log}_{2} (1 + \frac{P_{3} {| f_{r}^{T} h_{1} |}^{2}}{σ_{0}^{2}}), \end{matrix}

(17b)

\begin{matrix} R_{10}^{(4)} = τ_{41} {log}_{2} (1 + \frac{P_{41} {| f_{r}^{T} h_{2} |}^{2}}{σ_{0}^{2}}) . \end{matrix}

(17c)

Thus, the achievable rates of

U_{1}

and

U_{2}

within the duration

T = 1

can be obtained [8]:

\begin{matrix} R_{1} = \min (R_{12}^{(2)} + R_{12}^{(3)}, R_{10}^{(3)} + R_{10}^{(4)}), \end{matrix}

(18a)

\begin{matrix} R_{2} = τ_{42} {log}_{2} (1 + \frac{P_{42} {| f_{r}^{T} h_{2} |}^{2}}{σ_{0}^{2}}) . \end{matrix}

(18b)

2.3. Problem Formulation

We optimize the power and time allocation of

U_{1}

U_{2}

, and the HAP under the max–min throughput criterion. This involves designing a joint optimization problem:

\begin{matrix} \max_{P, τ} \min (R_{1}, R_{2}) \end{matrix}

(19a)

\begin{matrix} s . t . τ_{1}, τ_{2}, τ_{3}, τ_{41}, τ_{42} \geq 0, \end{matrix}

(19b)

\begin{matrix} P_{41}, P_{42} \geq 0, \end{matrix}

(19c)

\begin{matrix} (13), (15), (16), \end{matrix}

(19d)

where

P ≜ (P_{41}, P_{42})

. Note that when we set

τ_{2} = 0

, the original problem (19) reduces to the case of a conventional UC scheme without AB. Furthermore, if we set

τ_{2} = τ_{41} = 0

, (19) reduces to a case of WPCN without UC, which means the far user

U_{1}

does not cooperate with the near user

U_{2}

to transmit its information to the HAP.

3. Problem Transformation

Problem (19) is nonconvex due to the multiplicative terms in constraint (15), so we introduce auxiliary variables

V ≜ {V_{1}, V_{2}}

, satisfying

V_{1} = P_{41} τ_{41}

and

V_{2} = P_{42} τ_{42}

, to deal with coupled variables

{P_{41}, τ_{41}}

and

{P_{42}, τ_{42}}

. Then,

R_{12}^{(3)}

and

R_{10}^{(3)}

in the original problem can be rewritten as functions of

τ

and

{V_{1}, V_{2}}

. In addition, as

P_{3}

is defined in (13),

R_{10}^{(4)}

and

R_{2}

can be re-expressed as functions of

τ

\begin{matrix} R_{12}^{(3)} = τ_{3} {log}_{2} (1 + \frac{δ_{1} τ_{1}}{τ_{3}}), \\ R_{10}^{(3)} = τ_{3} {log}_{2} (1 + \frac{δ_{2} τ_{1}}{τ_{3}}), \\ R_{10}^{(4)} = τ_{41} {log}_{2} (1 + \frac{V_{1} δ_{3}}{τ_{41}}), \\ R_{2} = τ_{42} {log}_{2} (1 + \frac{V_{2} δ_{3}}{τ_{42}}) . \end{matrix}

(20)

where

\begin{matrix} δ_{1} = \frac{η P_{1} β_{12}^{2} {| {\tilde{h}}_{1}^{H} f_{t} s |}^{2}}{σ_{0}^{2}}, \\ δ_{2} = \frac{η P_{1} | {\tilde{h}}_{1}^{H} f_{t} {s |}^{2} {| f_{r}^{T} h_{1} |}^{2}}{σ_{0}^{2}}, \\ δ_{3} = \frac{| f_{r}^{T} h_{2} |^{2}}{σ_{0}^{2}} \end{matrix}

(21)

are all constants. We also introduce an auxiliary variable R satisfying

R \leq \min (R_{1}, R_{2})

. Then, we can transform the original problem (19) into an equivalent form expressed as

\begin{matrix} \max_{V, τ} R \end{matrix}

(22a)

\begin{matrix} s . t . R \leq R_{12}^{(2)} + R_{12}^{(3)}, \end{matrix}

(22b)

\begin{matrix} R \leq R_{10}^{(3)} + R_{10}^{(4)}, \end{matrix}

(22c)

\begin{matrix} R \leq R_{2}, \end{matrix}

(22d)

\begin{matrix} V_{1} + V_{2} \leq E_{u 2}^{(1)} + E_{u 2}^{(2)}, \end{matrix}

(22e)

\begin{matrix} τ_{1} + τ_{2} + τ_{3} + τ_{41} + τ_{42} \leq 1, \end{matrix}

(22f)

\begin{matrix} τ_{1}, τ_{2}, τ_{3}, τ_{41}, τ_{42} \geq 0, \end{matrix}

(22g)

in which

R_{12}^{(3)}

R_{10}^{(3)}

R_{10}^{(4)}

, and

R_{2}

are all concave functions. As

E_{u 2}^{(1)}

and

E_{u 2}^{(2)}

are affine functions of

τ_{1}, τ_{2}

, we can find that problem (22) is convex, which can be addressed with existing convex optimization tools and algorithms, e.g., the CVX tool [26] and the interior point method. Finally, when we obtain the solution of (22), the optimal solution of

P

can be obtained with

P_{41} = V_{1} / τ_{41}

and

P_{42} = V_{1} / τ_{42}

4. Simulation Results

In this section, We consider a mmWave WPCN consisting of one HAP and two single-antenna users. The system configuration is defined by the following choice of parameters: the HAP is equipped with a DLA, comprising

M_{t} = 64

antennas and one RF chain. A prototype lens antenna array has been fabricated, based on which the preliminary measurement results have verified the angle-dependent energy focusing capabilities of lens arrays [27]. The power of the HAP

P_{1}

is set to 0 dBW. The noise power of all receivers

σ_{0}^{2}

is set to −100 dBW, and the noise power of the ID circuit

σ_{1}^{2}

is set to −100 dBW. The energy-converting efficiency

η = 0.6

. The power splitting factor of

U_{2}

γ = 0.8

and the signal attenuation coefficient is

μ = 0.8

[20]. We also choose two transmitting rates of AB for comparison, i.e.,

R_{b} = 10

Mbps and

R_{b} = 1

Mbps, and the corresponding sample rate of AB is six times that of

R_{b}

, i.e.,

N_{b} = 6

. The channel model parameters are set as [28] (1) one LoS link and

L = 2

NLoS links; (2)

ϕ_{k}^{(0)}

and

ϕ_{k}^{(l)}

obey the uniform distribution within

[- \frac{1}{2}, \frac{1}{2}]

; (3) the LOS channel gain

{(β_{k}^{(0)})}^{2} = G {(\frac{c}{4 π d_{u k} f_{c}})}^{2}

, where

G = M_{t}

is the antenna power gain,

c = 3 \times 10^{8}

m/s is the speed of light,

d_{u k}

is the distance between user k and the HAP, and

f_{c} = 30

GHz is the carrier frequency of the mmWave band. The channel gain between

U_{1}

and

U_{2}

{(β_{12}^{(0)})}^{2} = G {(\frac{c}{4 π d_{12} f_{c}})}^{2}

, where

d_{12} = d_{u 1} - d_{u 2}

is the distance between

U_{1}

and

U_{2}

. We set the NLOS channel gain

β_{k}^{(l)} = 0.1 β_{k}^{(0)}

In the rest of this section, we compare the max–min rate performance versus

P_{1}

M_{t}

d_{u 1}

, and

d_{u 2}

for different schemes, i.e., the AB-based UC schemes with

R_{b} = 10

Mbps and

R_{b} = 1

Mbps (shown as

R_{b} = 1

and

R_{b} = 10

in the simulation results, respectively), a UC scheme without AB (shown as “Without AB” in the simulation results), and a conventional scheme without UC (shown as “Without UC” in the simulation results). In Figure 2, we change the transmitting power of the HAP

P_{1}

from 1 W to 4 W. We can observe that the performances of all schemes are improved with increasing transmitting power

P_{1}

, and the proposed AB-based UC schemes have better performance than other competing schemes. The scheme with

R_{b} = 10

has a better performance than the scheme with

R_{b} = 1

, owing to the higher

R_{b}

reducing the power consumption of information transmission between

U_{1}

and

U_{2}

more.

In Figure 3, we change the number of antennas at the HAP

M_{t}

from 8 to 64. We can observe that the performances of all schemes are improved with an increasing number of antennas

M_{t}

, benefiting from the energy capability of the lens array. Similarly, the proposed AB-based UC schemes have better performance than other competing schemes, which shows the AB technology can improve the performance of the UC system.

In Figure 4, we set

P_{1} = 4 W

M_{t} = 64

, and

d_{u 2} = 2

m, and change

d_{u 1}

from 4 m to 7 m. We find that the performance of all schemes decreases as

d_{u 1}

grows longer; this is because the channel between

U_{1}

and HAP is attenuated more severely as

d_{u 1}

increases. Upon observation, it is evident that the efficiency of UC schemes utilizing AB declines at a slower rate compared to other schemes. This indicates that passive AB usage can effectively lower energy consumption, and consequently, enhance throughput performance. Therefore, the simulation results illustrate the benefits of implementing AB to enhance the throughput performance of UC schemes in WPCNs.

In Figure 5, we set

P_{1} = 4 W

M_{t} = 64

, and

d_{u 1} = 5

m, and change

d_{u 2}

from 1 m to 4 m. We can find that the performance of the scheme without UC hardly changes with

d_{u 2}

, as its performance is mainly limited by the weak channel between the HAP and the farther user

U_{1}

. On the other hand, the performance of AB-based UC schemes increases as

d_{u 2}

grows shorter; this is because when

d_{u 2}

decreases, the distance between

U_{1}

and

U_{2}

increases, thus

U_{1}

needs more energy to transmit actively to the helping

U_{2}

, and the use of passive AB can effectively reduce the energy consumption, and thus, improve the throughput performance.

5. Conclusions

In this paper, we have considered an AB-based UC scheme in a mmWave WPCN with lens antenna arrays. In particular, to solve the ‘doubly near–far’ user unfairness problem, we have formulated an optimization problem to maximize the minimum rate of two users by jointly designing the power and time allocation of the HAP and users. After that, we have introduced auxiliary variables and transformed the original problem into a convex form. Then, we have proposed an efficient algorithm to solve the transformed problem. Furthermore, we have compared the max–min rate performance versus the transmission power of the HAP, the number of HAP antennas, and the distance between two users and the HAP for different schemes. The simulation results have demonstrated that the proposed AB-based UC scheme with DLA outperforms the competing schemes, thus improving the throughput fairness performance in the mmWave WPCN with lower costs for RF hardware and a lower power budget.

Author Contributions

Conceptualization: R.G. and R.Y.; methodology: R.G. and R.Y.; software: J.Y. and C.X.; investigation: R.G., G.W., and J.Y.; resources: R.G. and R.Y.; data curation: J.Y. and C.X.; writing—original draft preparation: R.G. and J.Y.; writing—review and editing: R.G. and R.Y.; visualization: R.G. and G.W.; funding acquisition: R.G. and R.Y. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported in part by the China Postdoctoral Science Foundation under Grant 2023M743063 and the Zhejiang Provincial Postdoctoral Scholarship under Grant ZJ2022107, in part by the National Natural Science Foundation of China under Grant 61771429, Grant 62302197 and Grant 62271438, Zhejiang Provincial Natural Science Foundation of China under Grant LQ23F020006.

Data Availability Statement

Dataset available on request from the authors.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

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Figure 1. System model and transmission protocol for UC.

Figure 2. Performance of different schemes.

Figure 3. Performance of different schemes.

Figure 4. Performance of different schemes.

Figure 5. Performance of different schemes.

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Guo, R.; Yin, R.; Wang, G.; Xu, C.; Yuan, J. Ambient Backscatter-Based User Cooperation for mmWave Wireless-Powered Communication Networks with Lens Antenna Arrays. Electronics 2024, 13, 3485. https://doi.org/10.3390/electronics13173485

AMA Style

Guo R, Yin R, Wang G, Xu C, Yuan J. Ambient Backscatter-Based User Cooperation for mmWave Wireless-Powered Communication Networks with Lens Antenna Arrays. Electronics. 2024; 13(17):3485. https://doi.org/10.3390/electronics13173485

Chicago/Turabian Style

Guo, Rongbin, Rui Yin, Guan Wang, Congyuan Xu, and Jiantao Yuan. 2024. "Ambient Backscatter-Based User Cooperation for mmWave Wireless-Powered Communication Networks with Lens Antenna Arrays" Electronics 13, no. 17: 3485. https://doi.org/10.3390/electronics13173485

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Ambient Backscatter-Based User Cooperation for mmWave Wireless-Powered Communication Networks with Lens Antenna Arrays

Abstract

1. Introduction

1.1. Motivation

1.2. Related Work

1.3. Our Contributions

1.4. Notation and Paper Organization

2. System Model and Problem Formulation

2.1. Channel Model

2.2. The Protocol Description

2.3. Problem Formulation

3. Problem Transformation

4. Simulation Results

5. Conclusions

Author Contributions

Funding

Data Availability Statement

Conflicts of Interest

References

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