In this paper, we investigate IRS-aided user cooperation (UC) scheme in millimeter wave (mmWave) wireless-powered sensor networks (WPSN), where two single-antenna users are wireless powered in the wireless energy transfer (WET) phase first and then cooperatively transmit information to a hybrid access point (AP) in the wireless information transmission (WIT) phase, following which the IRS is deployed to enhance the system performance of the WET and WIT. We maximized the weighted sum-rate problem by jointly optimizing the transmit time slots, power allocations, and the phase shifts of the IRS. Due to the non-convexity of the original problem, a semidefinite programming relaxation-based approach is proposed to convert the formulated problem to a convex optimization framework, which can obtain the optimal global solution. Simulation results demonstrate that the weighted sum throughput of the proposed UC scheme outperforms the non-UC scheme whether equipped with IRS or not.

The rapid expansion of the number of mobile devices has brought higher requirements for wireless applications, such as more extensive radio coverage, lower latency, higher data transmission rates and higher security, while the emergence of sixth-generation (6G) wireless technologies can perfectly meet such demands [

Also, energy harvesting (EH), as one of the main techniques to power future 6G wireless networks, has been introduced as an efficient method that allows wireless devices to capture the energy from external environments [

To improve the radio coverage and signal quality in a green way, an intelligent reflecting surface (IRS) has been proposed to reshape the signal propagation environment via passive reflecting arrays [

Recently, some research on IRS-aided wireless powered sensor networks (WPSN) has been studied in [

To tackle the issue of the uplink transmission of WDs in WPCNs depending on the harvested energy from the downlink, Wang et al. [

Integrating the IRS technology with sensor networks can achieve a self-sustaining system, specifically by embedding the IRS to the existing WPSN to reflect energy and information signals to improve the wireless energy transfer (WET) and wireless information transfer (WIT) capabilities of the WPSN. Also, to achieve a better performance with the IRS-assisted scheme, we consider a mmWave WPSN UC system in the uplink, i.e., one user not only completes his own signal transmission task, but also assists other users in completing signal transmission as a relay. Different from the existing works on the IRS-aided WPCN system, the research of transmission strategies in an IRS-assisted WPSN systems with UC in the mmWave band has not been made yet. We summarize our contributions as follows:

First, an IRS has been used to improve the performance of the WPSN system with UC in the mmWave channel, where two single-antenna wireless devices can harvest energy radiated by a hybrid access point (AP) to support the separate information transmission to the AP. Here, the IRS play a role in promoting the system performance of the downlink wireless energy harvesting and the uplink wireless information transmission by energy and information reflection for the IRS, respectively.

Second, it aims to maximize the weighted sum-rate through jointly optimizing the power, the time slots allocation and the IRS phase shift of the WET and WIT is used to evaluate the performance of the proposed system model. Since the original problem is non-convex with respect to the coupled variables of the power and the IRS phase shift, it is hard to solve directly.

Finally, to deal with the non-convexity of the original formulated problem, the semidefinite programming relaxation (SDR) technique is applied to convert the weighted sum-rate maximization (WSRM) problem to a convex optimization framework, which can obtain the global optimal solution. Simulation results proved that the IRS and the UC can improve the system performance compared with the two latest benchmarks.

The rest of the paper is organized as follows.

As shown in _{2} is used as a relay between WU_{1} and AP in the meantime. An IRS with _{k}, where _{k}, WU_{1} and WU_{2},

For the mmWave channel of AP to IRS, IRS to WU_{k},

_{k}, AP _{k},

_{k}, _{k} was donated as

The time of the WIT phase is _{1} and WU_{2} can transmit information signals directly to the AP simultaneously, and WU_{2} can act as a passive relay, reflecting some information signals from WU_{1} to AP. As shown in

In the first sub-phase, i.e., _{1} transmits the information signal to the AP and WU_{2} using the harvested energy (i.e., WU_{1} _{1} _{1} is reflected to the AP and WU_{2} via the IRS (i.e., WU_{1} _{1} _{2});

In the second sub-phase, i.e., _{2} first decodes WU_{1}’s information signal and then forwards it to the AP and the IRS (i.e., WU_{2} _{2}

In the third sub-phase, i.e., _{2} _{2}

In the first sub-phase, the harvested energy obtained in WET is used in WET and the transmit power of WU_{1} is

Then, the information signal received at AP and WU_{2} are expressed respectively as

_{1} with _{2} with variance

In the second sub-phase, the signal received at AP given by

_{2} within the subphase, _{2} associated with WU_{1}’s information. Then, the achievable direct rates from WU_{2} to the AP are expressed as

The information signals transmitted from WU_{1} to AP have four different paths, where the signal of AP in the first path is the direct link from WU_{1} _{2} with proposed UC scheme (i.e., WU_{2} _{2} with UC scheme via IRS to AP (i.e., WU_{2} _{1} to AP is given by

In the third sub-phase, the information signal received at AP is written as

The energy obtained by WU_{2} in

According to the above transmission process, the time period

Using the derivation and definition from the previous step, a WSRM problem is formulated based on a UC scheme and then solved by jointly optimizing the phase shift matrices, time allocation, and power allocation. First, the WSRM problem is given by

For the non-convexity of problem (P1), we can introduce some transformation forms for the phase shift matrices to tackle it. So, we have

_{1} in the first sub-phase. Taking the similar operations for

Then, introducing auxiliary variables

Define

We further define

Accordingly, by introducing another auxiliary variable

Due to the rank-one constraint causing the problem to be non-convex, so we use the SDR approach to remove this constraint, then (P1) can be reformulated as

Here, the problem

Combined with the above derivation, we can further obtain the optimal values as

The rank-one solution may be obtained from the relaxed WSRM (P3). So we employ the eigenvalue decomposition for

The simulation results are presented to evaluate the performance of the user cooperation scheme in IRS-aided mmWave WPSN. The illustration of the system is shown in _{k} are on the same level, and the distance between the IRS and this horizontal line is 4 meters and the distance between AP and IRS is

Parameters | Characteristic |
---|---|

Path loss exponent | 2 |

Noise power | |

Preference constants | |

Number of multipaths in mmWave channel | |

Constant in path loss | |

Energy harvesting efficiency |

IRS+UC: IRS helps WUs to harvest energy through reflection in the WET phase. In the WIT phase, IRS reflects signals from WUs to AP, and WU_{2} can receive and secondary transmit signals from WU_{1} to AP as a relay in the UC scheme.

Non IRS+UC: Following [

IRS+Non UC: Following [

Non IRS+Non UC: There are no IRS and UC schemes in the system.

We first evaluate the sum throughput _{1} in _{1} will be influenced, which will affect the sum throughput. In this simulation,

In order to observe the sum throughput improvement with increasing

Finally, the impact of the elements number

In this paper, we proposed a UC scheme for IRS-aided mmWave WPSN. The WSRM problem is formulated to maximize the weighted sum throughout by jointly optimizing the phase shift matrix, time slots, and power allocation. Some efficient variable substitutions and SDP relaxation are introduced to convert the original non-convex problem into a convex problem that is easy to tackle. Finally, numerical results confirm that the weighted sum throughput of our proposed UC scheme is greater than that of non UC whether equipped with IRS or not.

This work was supported in part by the open research fund of National Mobile Communications Research Laboratory, Southeast University (No. 2023D11), in part by Sponsored by Program for Science & Technology Innovation Talents in Universities of Henan Province (23HASTIT019), in part by Natural Science Foundation of Henan Province (232300421097), in part by the Project funded by China Postdoctoral Science Foundation (2023T160596, 2020M682345), in part by the Henan Postdoctoral Foundation (202001015).

This work was supported in part by the open research fund of National Mobile Communications Research Laboratory, Southeast University (No. 2023D11), in part by Sponsored by program for Science & Technology Innovation Talents in Universities of Henan Province (23HASTIT019), in part by Natural Science Foundation of Henan Province (20232300421097), in part by the project funded by China Postdoctoral Science Foundation (2020M682345), in part by the Henan Postdoctoral Foundation (202001015).

The authors confirm contribution to the paper as follows: study conception and design: Yonghui Lin, Zhengyu Zhu; data collection: Yonghui Lin, Zhengyu Zhu; analysis and interpretation of results: Yonghui Lin, Zhengyu Zhu; draft manuscript preparation: Yonghui Lin. All authors reviewed the results and approved the final version of the manuscript.

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The authors declare that they have no conflicts of interest to report regarding the present study.