[ technique. Through numerical results, AoI-metric and energy

harvesting requirements of the network are analyzed versus 1 different parameters such as number of antennas at BS, size v of STAR-RIS, and transmitted power to highlight how we can 6 improve two-fold performance of the system by utilizing STAR7 RIS compared to the conventional RIS structure. 7

Index Terms—Age of information, energy harvesting, simul2 taneously transmitting and reflecting-reconfigurable intelligent .0 surface, optimization methods. 2 1 I. INTRODUCTION 3 :v E variety of self-powered devices that has gained significant 2 NERGY harvesting is a highly appealing technology for a i interest. Internet of things (IoT) is one example of such sysXtems which are entangled with the energy harvesting feature. a However, if energy harvesting procedure takes a long period, r the user’s performance/experience may not be acceptable due to the delays [1]. Moreover, some other emerging applications, such as cooperative autonomous driving also require fresh and real-time status information [2]. Therefore, energy harvesting and data freshness are two important features in the forthcoming wireless networks.

One of the key technology to improve performance of a wireless system, e.g. spectral-efficiency, energy-efficiency and coverage, is the reconfigurable intelligent surface (RIS). By controlling the phase and/or amplitude of each elements of RIS, one can control the wavefront or equivalently manipulate the wireless propagation channel to enhance the performance [3]. Recently, a promising version of RIS, known as simultaneously transmitting and reflecting RIS (STAR-RIS) has evolved, wherein each element of the RIS can partly reflect and/or transmit the waveform while individually controlling amplitudes and phases of transmitted and reflected parts. Compared to the conventional RIS, one of the main advantages of STAR-RIS is enhancing the coverage from half-space to full-space [4].

Numerous studies on STAR-RIS assisted wireless networks are published in the literature. In [5], a wireless powered IoT network based on a STAR-RIS is studied which indicates the STAR-RIS enhances energy harvesting and information transfer for the considered setup. Also, a wireless-powered mobile edge computing system aided STAR-RIS is investigated in [6], where an STAR-RIS is deployed to assist the energy transfer in the downlink as well as the task offloading in the uplink. Recently, STAR-RIS assisted simultaneous wireless information and power transfer (SWIPT) system is studied in [7]. The trade-off between information users and energy users is investigated through a multi-objective optimization problem.

On the other hand, age of information (AoI), a new metric to measure freshness of information, is defined as the amount of time elapsed from the generation of a previous successfully transmitted status update packet [8]. AoI is becoming one of the key metrics in telecommunication systems which has been investigated and analyzed for different systems and scenarios [9]. For instance, average peak of AoI for a twohop relay wireless power transfer based system is studied in [10], wherein a source and a relay capture their required power by harvesting from received signal transmitted from a power station. Moreover, [11] has investigated potential impact of the conventional RIS in SWIPT system on minimizing sum-AoI.

Most of available studies on STAR-RIS mainly have focused on achievable rate and energy efficiency improvements of a system, and information freshness analysis in presence of STAR-RIS aided SWIPT networks is not studied in the literature. Therefore, in this paper, we present a STAR-RIS assisted SWIPT system in presence of two types of users: 1- Information users (IUs) that require fresh information 2- In the ES protocol, all STAR-RIS elements are able to Energy users (EUs) which ask for energy harvesting from operate in transmitting and reflecting modes at the same a base station. Also, thanks to the STAR-RIS and 360 de- time by splitting the energy. In contrast, for the MS case, gree coverage, in contrast to the conventional RIS technique, each element can operate only in transmitting or reflecting one can support users in front and behind of the STAR- mode. The TaRCs of a generic STAR-RIS are denoted by RAIoSI, sausbjwecetll.toTheunse,rgwye hsaturvdeystminignimcoinzsintrgainotfs afvoerradgieffseuremn-t wΦhkEeS/rMeS³ tm=, ³ drmia* g([p0,³ 11k]efjoθr1k ,E.S. .a,nqd ³ ³ kMtm,e³jθrmMk )*,{ " 0k, 1 }* f{ortM,rS},, STAR protocols. A non-convex problem is formulated to and » mt, » mr * [0, 2Ã ) , " m * M ; These parameters represent optimize transmit beamforming, phase shifts, and the proposed amplitude and phase shift of the m-th element, respectively. It scheduling scheme. The problem is solved by a successive is worth noting that the amplitude parts of TaRCs are subject convex approximation (SCA) based alternating optimization to law of energy conservation, i.e. ³ tm + ³ rm = 1 [4, 12]. (AO) algorithm. Moreover, numerical results for different protocols of STAR-RIS are evaluated and indicate performance improvements compared to that of the conventional RIS. B. Signal Transmissions and Receptions

Organization: Section II represents the proposed system BS sends tIk(n)=ωk(n)xIk(n) and rkE(n) = ϑk(n)xkE (n) to model, STAR-RIS configuration and defines AoI formulation. IUk and EUk, wherein ωk(n) * CNt×1 and ϑk(n) * CNt×1 Section III introduces the optimization problem and specifies denote beamforming vectors for IUk and EUk, respectively. the proposed algorithm. Section IV presents the numerical Also, information and energy signals are presented by xIk(n) > results, and section V concludes the paper. CN ( 0, 1 ) and xkE (n) > CN ( 0, 1 ), respectively. By assuming

Notations: tr(F ) denotes trace of matrix F , F 0 declares maximum power constraint Po at the BS, we have trhoawt Fan disja-tphocsoitliuvmenseimsir-edperfiesneitnetemdabtryixF, [ain,dj]a.nxelesmpeecnitfiiensit-hthe X ωk(n) 2 + X ϑk(n) 2 f Po. ( 3 ) Euclidean norm of the complex-valued vector x, and real part k∈{t,r} k∈{t,r} of x is R{x}. Probability of a random variable x is denoted by Therefore, the single-antenna k-th information user receives PGra{uxs}si,aanndraandzoemro-vmaeriaanblaendisuxn i>tC-vNaria(n0c,e1c).omplex symmetric ykIU(n) = fkH (n)ΦkES/MS(n)G(n)tIk(n) + nIkU, ( 4 )

A downlink STAR-RIS-aided SWIPT wireless system depicted in Fig. 1, in which a base station (BS) with Nt antennas, by utilizing the STAR-RIS, transmits signals towards singleantenna energy users and information users. The STAR-RIS is equipped with M elements and is utilized to improve performance and coverage of the system by tuning transmitting and reflecting coefficients (TaRCs). As depicted in the figure and without loss of generality and for simplicity, it is assumed that two energy users, i.e. EUt and EUr, and two information users IUt and IUr are located in the transmission and reflection regions of STAR-RIS, respectively.

Also, we consider one information stream per information user and one energy stream for each energy user. Therefore, the BS sends energy signals and status update packets to the energy users and the information users over energy and information channels, respectively. It is assumed that energy channels are orthogonal to information channels to control interference over the information channel and enhance signalto-noise ratio (SNR). Moreover, it is assumed that there are N time slots indexed by n * { 1, . . . , N }, and there is one information channel per time slot. Thus, the scheduling policy to support information users at the BS is constrained by st(n) + sr(n) f 1, sk(n) * { 0, 1}, " k * { t, r}, ( 1 ) ( 2 ) where sk(n) denotes scheduling state at time slot n for IUk.

To present numerical results, it is assumed that the Cartesian coordinates of STAR-RIS, EUr, IUr, EUt, IUt and BS are ( 8, 0 ), ( 10, 2 2 ), ( 12, 2 2 ), ( 10, 2 ), ( 12, 2 ) and (0, 0), respectively. Probabilities of the packet arrivals are » k = 0.6, the number of time slots is N = 100, and the noise variance is à I2,k = 1. The path loss exponents for information and energy users are ³ i = 2.2 and ³ e = 2, respectively. We also assume a stronger channel for the energy users than that of the information users. The geometric path-loss and random phase are considered for channel simulation as F = p(1/d)αq, where d represents a relative distance and q = ejφ denotes a random phase shift with a uniform distribution over 0, 2à .

Fig. 2 depicts average sum-AoI versus SNR threshold ³ th for Po = 3, M = 32 and Nt = 4. Average sum-AoI increases Algorithm 1 SCA method for addressing optimization problem given in ( 16 ) Input: Initial values for ωk(0)(n) and ϑ(k0)(n), Channel coeffitcoielenrtasnGce, ëu=kH ,1a0n−d3.fkH . Maximum power Po. Initial value for 1: for i = 1, 2, . . . do 2: For given ωk(i)(n), ϑ(ki)(n), " k update ϕk(n) and sk(n) by solving P2.1. 3: for j = 1, 2, . . . do 4: For given ϕk(n) and sk(n), solve the problem P2.2 to update value of ωk(i+1)(n) and ϑ(i+1)(n) k 5: Until: Convergence of ωk(n), ϑk(n) and sk(n) 6: end for 7: Until Convergence of ϕk(n) and sk(n) .

8: end for Output: The optimal values: ϕk(n), sk(n), ωk(n) and ϑk(n). with ³ th because, with greater demands for communication quality, successful transmission is more challenging to achieve. Besides, the average sum-AoI increases by increasing the energy harvesting threshold from E = 2 30 to E = 2 10 [dB], since power allocation and beamforming must be adjusted to meet the requirements of energy users. So, there is a compromise between the average sum-AoI and the harvested energy of energy users. Additionally, compared to MS protocol, ES protocol shows better performance with the same parameters. Also, ES and MS based STAR-RIS always outperforms the conventional RIS structure.

In Fig. 3, average sum-AoI versus transmit power Po is plotted for E = 2 20 [dB], M = 32 and Nt = 4. By increasing Po, SNR is improved and due to higher chance of successful delivery, average sum-AoI is decreased. Also, the difference between the performance of ES and MS protocols, and conventional RIS becomes more significant as ³ th increases.

The average sum-AoI versus number of antennas is illustrated in Fig. 4. It demonstrates that increasing the number of antennas Nt from 4 to 20 at the BS improves the average sumAoI, with Po = 3, E = 2 20 [dB], and M = 32. Similarly, in Fig. 5, the average sum-AoI is decreased dramatically by increasing the number of STAR-RIS elements M from 16 to 128, with Po = 3, E = 2 20 [dB], and Nt = 4. Therefore, based on the energy harvesting and data freshness requirements, one can select number of antennas at the BS and configure the STAR-RIS size and policy.

We explored average sum-AoI optimization in SWIPT networks with the assistance of STAR-RIS. An AO algorithm was proposed to cope with the non-convexity of the optimization problem. STAR-RIS TaRCS are optimized by problem transformation, and beamforming vectors optimization at the BS is performed by SCA algorithm. Numerical results highlighted that the performance of the proposed algorithm for ES and MS protocols is more beneficial than that of the conventional RIS, and the ES protocol outperforms the MS one. Also, numerical results show a trade-off between the average sum-AoI and the

Fig. 4: Average sum-AoI versus the number of antennas. harvested energy constraint. Increasing the number of antennas at the BS, and especially the number of STAR-RIS elements can improve performance of the system.