We propose techniques for optimizing transmit beamforming in a full-duplex multiple-input-multiple-output (MIMO) wireless-powered communication system, which consists of two phases. In the first phase, the wireless-powered mobile station (MS) harvests energy using signals from the base station (BS), whereas in the second phase, both MS and BS communicate to each other in a full-duplex mode. When complete instantaneous channel state information (CSI) is available, the BS beamformer and the time-splitting (TS) parameter of energy harvesting are jointly optimized in order to obtain the BS-MS rate region. The joint optimization problem is non-convex, however, a computationally efficient optimum technique, based upon semidefinite relaxation and line-search, is proposed to solve the problem. A sub-optimum zero-forcing approach is also proposed, in which a closed-form solution of TS parameter is obtained. When only second-order statistics of transmit CSI is available, we propose to maximize the ergodic information rate at the MS, while maintaining the outage probability at the BS below a certain threshold. An upper bound for the outage probability is also derived and an approximate convex optimization framework is proposed for efficiently solving the underlying non-convex problem. Simulations demonstrate the advantages of the proposed methods over the sub-optimum and half-duplex ones.
In this paper, we propose a full-duplex relay (FDR) based on a zero-forcing beamforming (ZFBF) for a multiuser MIMO relay system. The ZFBF is employed at the base station to suppress both the self-interference of the relay and the multiuser interference at the same time. Numerical results show that the proposed FDR can enhance the sum rate performance as compared to the half-duplex relay (HDR), if sufficient isolation between the transmit and receive antennas is ensured at the relay.
In this paper, full-duplex radios are used to continuously update the channel state information at the transmitter, which is required to compute the downlink precoding matrix in MIMO broadcast channels. The full-duplex operation allows leveraging channel reciprocity for open-loop uplink training to estimate the downlink channels. However, the uplink transmission of training creates interference at the downlink receiving mobile nodes. We characterize the optimal training resource allocation and its associated spectral efficiency, in the proposed open-loop training based full-duplex system. We a…
In this paper we explore the use of full-duplex radio to improve the spectrum efficiency in a two-way relay channel where two sources exchange information through an multi-antenna relay, and all nodes work in the full-duplex mode. The full-duplex operation can reduce the overall communication to only one phase but suffers from the self-interference. Instead of purely suppressing the self-interference, we aim to maximize the end-to-end performance by jointly optimizing the beamforming matrix at the relay which uses the amplify-and-forward protocol as well as the power control at the sources. To…
A full-duplex two-way relay channel with multiple antennas is considered. For this three-node network, the beamforming design needs to suppress self-interference. While a traditional way is to apply zero-forcing for self-interference mitigation, it may harm the desired signals. In this paper, a design which reserves a fraction of self-interference is proposed by solving a quality-of-service constrained beamforming design problem. Since the problem is challenging due to the loop self-interference, a convergence-guaranteed alternating optimization algorithm is proposed to jointly design the rela…
In this paper, we deal with the performance analysis of full-duplex relaying in decode-&-forward cooperative networks with multiple-antenna terminals. More specifically, by analyzing the end-to-end statistics, we derive the accurate closed-form expressions of the end-to-end outage probability for both transmit and receive ZFBF scheme over Rayleigh fading environments. Some selected results show some interesting observations useful for system designers. Specifically, we observe that the outage performance can be improved by adopting the joint ZF-based precoding with different antenna configurat…
In this paper, we studied the joint sparse beamforming and power control for network-assisted full duplex (NAFD) in large-scale distributed antenna system (L-DAS), where the remote antenna units either be operating in half-duplex mode or full-duplex mode are all connected to the central processing unit (CPU) via high-speed backhaul links. With joint processing at CPU, NAFD could achieve truly flexible duplex, including flexible half-duplex and full-duplex. Cross-link interference and the finite-capacity backhaul are the main problems of NAFD in L-DAS. To solve these problems, we aim to maximiz…
We consider the full-duplex (FD) two-way amplify-and-forward relay system with imperfect cancelation of loopback self-interference (SI) and investigate joint design of relay and receive beamforming for minimizing the mean square error under a relay transmit power constraint. Due to loopback channel estimation error and limitation of analog-to-digital converter, the loopback SI cannot be completely canceled. Multiple antennas at the relay can help loopback SI suppression but beamforming is required to balance between the residual SI suppression and the desired signal transmission. Moreover, the…
In this paper, we investigate the problem of two-way relay beamforming optimization to maximize the achievable sum-rate of a simultaneous wireless information and power transfer (SWIPT) system with a full-duplex (FD) multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay. In particular, we address the optimal joint design of the receiver power splitting (PS) ratio and the beamforming matrix at the relay node given the channel state information (CSI). Our contribution is an iterative algorithm based on difference of convex (DC) programming and one-dimensional searching to achieve …
Multiple transmitting antennas can considerably increase the downlink spectral efficiency by beamforming to multiple users at the same time. However, multiuser beamforming requires channel state information (CSI) at the transmitter, which leads to training overhead and reduces overall achievable spectral efficiency. In this paper, we propose and analyze a sequential beamforming strategy that utilizes full-duplex base station to implement downlink data transmission concurrently with CSI acquisition via in-band closed or open loop training. Our results demonstrate that full-duplex capability can…
In this paper, we present and study a digital-controlled method, called SoftNull, to enable full-duplex in many-antenna systems. Unlike most designs that rely on analog cancelers to suppress self-interference, SoftNull relies on digital transmit beamforming to reduce self-interference. SoftNull does not attempt to perfectly null self-interference, but instead seeks to reduce self-interference sufficiently to prevent swamping the receiver's dynamic range. Residual self-interference is then cancelled digitally by the receiver. We evaluate the performance of SoftNull using measurements from a 72-…
We model the self-interference in a multiple input single output (MISO) full-duplex two-way channel and evaluate the achievable rate region. We formulate the boundary of the achievable rate region termed as the Pareto boundary by a family of coupled, non-convex optimization problems. Our main contribution is decoupling and reformulating the original non-convex optimization problems to a family of convex semidefinite programming problems. For a MISO full-duplex two-way channel, we prove that beamforming is an optimal transmission strategy which can achieve any point on the Pareto boundary. Furt…
Incorporating full duplex operation in Multiple Input Multiple Output (MIMO) systems provides the potential of boosting throughput performance. However, the hardware complexity of the analog self-interference canceller scales with the number of transmit and receive antennas, thus exploiting the benefits of analog cancellation becomes impractical for full duplex MIMO transceivers. In this paper, we present a novel architecture for the analog canceller comprising of reduced number of taps (tap refers to a line of fixed delay and variable phase shifter and attenuator) and simple multiplexers for …
We study the beamforming optimization for an intelligent reflecting surface (IRS)-aided full-duplex (FD) communication system in this letter. Specifically, we maximize the sum rate of bi-directional transmissions by jointly optimizing the transmit beamforming and the beamforming of the IRS reflection. A fast converging alternating algorithm is developed to tackle this problem. In each iteration of the proposed algorithm, the solutions to the transmit beamforming and the IRS reflect beamforming are obtained in a semi-closed form and a closed form, respectively. Compared to an existing method ba…
We derive the optimal signaling for a multiple input multiple output (MIMO) full-duplex two-way channel under the imperfect transmit front-end chain. We characterize the two-way rates of the channel by using a game-theoretical approach, where we focus on the Pareto boundary of the achievable rate region and Nash equilibia (NE). For a MISO full-duplex two-way channel, we prove that beamforming is an optimal transmission strategy which can achieve any point on the Pareto boundary. Furthermore, we present a closed-form expression for the optimal beamforming weights. In our numerical examples we q…
We solve a sum rate maximization problem of full-duplex (FD) multiuser multiple-input multiple-output (MU-MIMO) systems. Since additional self-interference (SI) in the uplink channel and co-channel interference (CCI) in the downlink channel are coupled in FD communication, the downlink and uplink multiuser beamforming vectors are required to be jointly designed. However, the joint optimization problem is non-convex and hard to solve due to the coupled effect. To properly address the coupled design issue, we reformulate the problem into an equivalent uplink channel problem, using the uplink and…
Full Duplex (FD) communication can revolutionize wireless communications as it avoids using independent channels for bi-directional communications. This work generalizes the point-to-point FD communication in millimeter wave (mmWave) band consisting of K-pairs of massive MIMO FD nodes operating simultaneously. We present a novel joint hybrid beamforming (HYBF) and combining scheme for weighted sum-rate (WSR) maximization to enable the coexistence of massive MIMO FD links cost-efficiently. The proposed algorithm relies on alternative optimization based on the minorization-maximization method. M…
We consider a full-duplex decode-and-forward system, where the wirelessly powered relay employs the time-switching protocol to receive power from the source and then transmit information to the destination. It is assumed that the relay node is equipped with two sets of antennas to enable full-duplex communications. Three different interference mitigation schemes are studied, namely, 1) optimal 2) zero-forcing and 3) maximum ratio combining/maximum ratio transmission. We develop new outage probability expressions to investigate delay-constrained transmission throughput of these schemes. Our ana…
Consider a two-way communication scenario where two single-antenna nodes, operating under full-duplex mode, exchange information to one another through the aid of a (full-duplex) multi-antenna relay, and there is another single-antenna node who intends to eavesdrop. The relay employs artificial noise (AN) to interfere the eavesdropper's channel, and amplify-forward (AF) Alamouti-based rank-two beamforming to establish the two-way communication links of the legitimate nodes. Our problem is to optimize the rank-two beamformer and AN covariance for sum secrecy rate maximization (SSRM). This SSRM …
In this paper, we consider a non-orthogonal multiple access cognitive radio network, where a full-duplex multi-antenna relay assists transmission from a base station (BS) to a cognitive far user, whereas, at the same time, the BS transmits to a cognitive near user. Our objective is to enlarge the far-near user rate region by maximizing the rate of the near user under a constraint that the rate of the far user is above a certain threshold. To this end, a non-convex joint optimization problem of relay beamforming and the transmit powers at the BS and cognitive relay is solved as a semi-definite …
Although the hardware complexity of the analog self-interference canceller in full duplex Multiple Input Multiple Output (MIMO) designs does not necessarily scale with the number of transceiver antennas, exploiting the benefits of analog cancellation in massive MIMO systems with hundreds of antenna elements is still quite impractical. Hybrid Analog and Digital (A/D) beamforming architectures have been lately considered as a candidate technology for realizing massive MIMO transceivers with very large number of antenna elements, but with much fewer numbers of Radio Frequency (RF) chains. In this…
Security is a critical issue in full duplex (FD) communication systems due to the broadcast nature of wireless channels. In this paper, joint design of information and artificial noise beamforming vectors is proposed for the FD simultaneous wireless information and power transferring (FD-SWIPT) systems with loopback self-interference cancellation. To guarantee high security and energy harvesting performance of the FD-SWIPT system, the proposed design is formulated as a secrecy rate maximization problem under energy transfer rate constraints. Although the secrecy rate maximization problem is no…
This paper studies the joint optimization problem of two-way relay beamforming, the receiver power splitting (PS) ratio as well as the transmit power at the sources to maximize the achievable sum-rate of a simultaneous wireless information and power transfer (SWIPT) system with a full-duplex (FD) multiple-input multiple-output (MIMO) amplify and forward (AF) relay, assuming perfect channel state information (CSI). In particular, our contribution is an iterative algorithm based on the difference of convex programming (DC) and one dimensional searching to achieve the joint solution. Simulation r…
Physical layer security is a key issue in the full duplex (FD) communication systems due to the broadcast nature of wireless channels. In this paper, the joint design of information and artificial noise beamforming vectors is proposed for the FD simultaneous wireless information and power transferring (FD-SWIPT) systems. To guarantee high security and energy harvesting performance of the FD-SWIPT system, the proposed design is formulated as a sum information transmission rate (SITR) maximization problem under information-leakage and energy constraints. In addition, we consider the fairness iss…
Reconfigurable intelligent surfaces (RIS) have drawn considerable attention recently due to their controllable scattering elements that are able to direct electromagnetic waves into desirable directions. Although RISs share some similarities with relays, the two have fundamental differences impacting their performance. To harness the benefits of both relaying and RISs, a multi-user communication system is proposed in this paper wherein a relay and an RIS cooperate to improve performance in terms of energy efficiency. Using singular value decomposition (SVD), semidefinite programming (SDP), and…
In this paper, we propose a joint transceiver beamforming design to simultaneously mitigate self-interference (SI) and partial inter-node interference for full-duplex multiple-input and multiple-output ad-hoc network, and then derive the transmission capacity upper bound (TC-UB) for the corresponding network. Condition on a specified transceiver antenna's configuration, we allow the SI effect to be cancelled at transmitter side, and offer an additional degree-of-freedom at receiver side for more inter-node interference cancellation. In addition, due to the proposed beamforming design and imper…
Beamforming design has been widely investigated for integrated sensing and communication (ISAC) systems with full-duplex (FD) sensing and half-duplex (HD) communication. To achieve higher spectral efficiency, in this paper, we extend existing ISAC beamforming design by considering the FD capability for both radar and communication. Specifically, we consider an ISAC system, where the base station (BS) performs target detection and communicates with multiple downlink users and uplink users reusing the same time and frequency resources. We jointly optimize the downlink dual-functional transmit si…
In this paper, we investigate the physical layer security of a full-duplex base station (BS) aided system in the worst case, where an uplink transmitter (UT) and a downlink receiver (DR) are both equipped with a single antenna, while a powerful eavesdropper is equipped with multiple antennas. For securing the confidentiality of signals transmitted from the BS and UT, an artificial noise (AN) aided secrecy beamforming scheme is proposed, which is robust to the realistic imperfect state information of both the eavesdropping channel and the residual self-interference channel. Our objective functi…
In this paper, a novel full-duplex non-coherent (FD-NC) transmission scheme is developed for massive multiple-input multiple-output (mMIMO) systems using analog beamforming (ABF). We propose to use a structured Grassmannian constellation for the non-coherent communications that does not require channel estimation. Then, we design the transmit and receive ABF via the slow time-varying angle-of-departure (AoD) and angle-of-arrival (AoA) information, respectively. The ABF design targets maximizing the intended signal power while suppressing the strong self-interference (SI) occurred in the FD tra…
This paper investigates a multiuser multiple-input single-output (MISO) full-duplex (FD) system for simultaneous wireless information and power transfer (SWIPT), in which a multi-antenna base station (BS) simultaneously sends wirelessly information and power to a set of single-antenna mobile stations (MSs) using power splitters (PSs) in the downlink and receives information in the uplink in FD mode. In particular, we address the joint design of the receive PS ratio and the transmit power at the MSs, and the beamforming matrix at the BS under signal-to-interference-plus-noise ratio (SINR) and t…
In this paper, we present a novel scenario for directional modulation (DM) networks with a full-duplex (FD) malicious attacker (Mallory), where Mallory can eavesdrop the confidential message from Alice to Bob and simultaneously interfere Bob by sending a jamming signal. Considering that the jamming plus noise at Bob is colored, an enhanced receive beamforming (RBF), whitening-filter-based maximum ratio combining (MRC) (WFMRC), is proposed. Subsequently, two RBFs of maximizing the secrecy rate (Max-SR) and minimum mean square error (MMSE) are presented to show the same performance as WFMRC. To …
This letter studies a wireless-powered amplify-and-forward relaying system, where an energy-constrained relay node assists the information transmission from the source to the destination using the energy harvested from the source. We propose a novel two-phase protocol for efficient energy transfer and information relaying, in which the relay operates in full-duplex mode with simultaneous energy harvesting and information transmission. Compared with the existing protocols, the proposed design possesses two main advantages: i) it ensures uninterrupted information transmission since no time switc…
In this paper, we investigate the secrecy capacity of a point-to-point, full-duplex (FD) wirelesly powered communication system in the presence of a passive eavesdropper (EVE). The considered system is comprised of an energy transmitter (ET), an energy harvesting user (EHU), and a passive EVE. The ET transmits radio-frequency energy, which is used for powering the EHU as well as for generating interference at the EVE. The EHU uses the energy harvested from the ET to transmit confidential messages back to the ET. As a consequence of the FD mode of operation, both the EHU and the ET are subjecte…
This paper considers a cloud radio access network (C-RAN) where spatially distributed remote radio heads (RRHs) communicate with a full-duplex user. In order to reflect a realistic scenario, the uplink (UL) and downlink (DL) RRHs are assumed to be equipped with multiple antennas and distributed according to a Poisson point process. We consider all participate and nearest RRH association schemes with distributed beamforming in the form of maximum ratio combining/maximal ratio transmission (MRC/MRT) and zero-forcing/MRT(ZF/MRT) processing. We derive analytical expressions useful to compare the a…
This paper studies optimal resource allocation in the wireless-powered communication network (WPCN), where one hybrid access-point (H-AP) operating in full-duplex (FD) broadcasts wireless energy to a set of distributed users in the downlink (DL) and at the same time receives independent information from the users via time-division-multiple-access (TDMA) in the uplink (UL). We design an efficient protocol to support simultaneous wireless energy transfer (WET) in the DL and wireless information transmission (WIT) in the UL for the proposed FD-WPCN. We jointly optimize the time allocations to the…
In this paper, we compare two common modes of duplexing in wireless powered communication networks (WPCN); namely TDD and FDD. So far, TDD has been the most widely used duplexing technique due to its simplicity. Yet, TDD does not allow the energy transmitter to function continuously, which means to deliver the same amount of energy as that in FDD, the transmitter has to have a higher maximum transmit power. On the other hand, when regulations for power spectral density limits are not restrictive, using FDD may lead to higher throughput than that of TDD by allocating less bandwidth to energy an…
This paper studies intelligent reflecting surface (IRS)-aided full-duplex (FD) wireless-powered communication network (WPCN), where a hybrid access point (HAP) broadcasts energy signals to multiple devices for their energy harvesting in the downlink (DL) and meanwhile receives information signals in the uplink (UL) with the help of IRS. Particularly, we propose three types of IRS beamforming configurations to strike a balance between the system performance and signaling overhead as well as implementation complexity. We first propose the fully dynamic IRS beamforming, where the IRS phase-shift …
In this paper, a wireless powered communication network (WPCN) consisting of a hybrid access point (H-AP) and multiple user equipment (UEs), all of which operate in full-duplex (FD), is described. We first propose a transceiver structure that enables FD operation of each UE to simultaneously receive energy in the downlink (DL) and transmit information in the uplink (UL). We then provide an energy usage model in the proposed UE transceiver that accounts for the energy leakage from the transmit chain to the receive chain. It is shown that the throughput of an FD WPCN using the proposed FD UEs ca…
For a self-sustaining wireless communication system in Internet-of-Things (IoT) networks, energy harvesting (EH) can be implemented at each user node as a constant renewable power supply source. Hence, an investigation into the use of wireless powered communication network (WPCN) protocols to facilitate communication between an access point (AP) and multiple mobile users (MUs) is presented in this paper. The AP has multiple antennas and operates in the full-duplex (FD) mode. The MUs, on the other hand, have single antennas and works in the half-duplex (HD) mode. Each MU communicating with the …
In this paper, we investigate the capacity of a point-to-point, full-duplex (FD), wirelessly powered communication system impaired by self-interference. This system is comprised of an energy transmitter (ET) and an energy harvesting user (EHU), both operating in a FD mode. The ET transmits energy towards the EHU. The EHU harvests this energy and uses it to transmit information back to the ET. As a result of the FD mode, both nodes are affected by self-interference. The self-interference has a different effect at the two nodes: it impairs the decoding of the received signal at the ET, however, …
This letter considers the secure communication in a reconfigurable intelligent surface (RIS) aided full duplex (FD) system. An FD base station (BS) serves an uplink (UL) user and a downlink (DL) user simultaneously over the same time-frequency dimension assisted by a RIS in the presence of an eavesdropper. In addition, the artificial noise (AN) is also applied to interfere the eavesdropper's channel. We aim to maximize the sum secrecy rate of UL and DL users by jointly optimizing the transmit beamforming, receive beamforming and AN covariance matrix at the BS, and passive beamforming at the RI…
The optimal resource allocation scheme in a full-duplex Wireless Powered Communication Network (WPCN) composed of one Access Point (AP) and two wireless devices is analyzed and derived. AP operates in a full-duplex mode and is able to broadcast wireless energy signals in downlink and receive information data in uplink simultaneously. On the other hand, each wireless device is assumed to be equipped with Radio-Frequency (RF) energy harvesting circuitry which gathers the energy sent by AP and stores it in a finite capacity battery. The harvested energy is then used for performing uplink data tra…
In this correspondence, we consider an amplify-and-forward relay network in which relayed information is overheard by an eavesdropper. In order to confound the eavesdropper, a wireless-powered jammer is also considered which harvests energy from a multiple-antenna source. We proposed a new secure beamforming scheme in which beamforming vector is a linear combination of the energy beamforming (EB) and information beamforming (IB) vectors. We also present a new closed-form solution for the proposed beamforming vector which is shown to achieve a higher secrecy rate as compared to the trivial EB a…
In this paper, we consider a wireless communication network with a full-duplex hybrid access point (HAP) and a set of wireless users with energy harvesting capabilities. The HAP implements the full-duplex through two antennas: one for broadcasting wireless energy to users in the downlink and one for receiving independent information from users via time-division-multiple-access (TDMA) in the uplink at the same time. All users can continuously harvest wireless power from the HAP until its transmission slot, i.e., the energy causality constraint is modeled by assuming that energy harvested in the…
Millimeter wave (mmWave) full-duplex (FD) is a promising technique for improving capacity by maximizing the utilization of both time and the rich mmWave frequency resources. Still, it has restrictions due to FD self-interference (SI) and mmWave's limited coverage. Therefore, this study dives into FD mmWave MIMO with the assistance of reconfigurable intelligent surfaces (RIS) for capacity improvement. First, we demonstrate the angular-domain reciprocity of FD antenna arrays under the far-field planar wavefront assumption. Accordingly, a strategy for joint downlink-uplink (DL-UL) channel estimat…
This paper investigates the passive beamforming and deployment design for an intelligent reflecting surface (IRS) aided full-duplex (FD) wireless system, where an FD access point (AP) communicates with an uplink (UL) user and a downlink (DL) user simultaneously over the same time-frequency dimension with the help of IRS. Under this setup, we consider three deployment cases: 1) two distributed IRSs placed near the UL user and DL user, respectively; 2) one centralized IRS placed near the DL user; 3) one centralized IRS placed near the UL user. In each case, we aim to minimize the weighted sum tr…
Full Duplex (FD) radio has emerged as a promising solution to increase the data rates by up to a factor of two via simultaneous transmission and reception in the same frequency band. This paper studies a novel hybrid beamforming (HYBF) design to maximize the weighted sum-rate (WSR) in a single-cell millimeter wave (mmWave) massive multiple-input-multiple-output (mMIMO) FD system. Motivated by practical considerations, we assume that the multi-antenna users and hybrid FD base station (BS) suffer from the limited dynamic range (LDR) noise due to non-ideal hardware and an impairment aware HYBF ap…
We consider a full-duplex (FD) decode-and-forward system in which the time-switching protocol is employed by the multi-antenna relay to receive energy from the source and transmit information to the destination. The instantaneous throughput is maximized by optimizing receive and transmit beamformers at the relay and the time-split parameter. We study both optimum and suboptimum schemes. The reformulated problem in the optimum scheme achieves closed-form solutions in terms of transmit beamformer for some scenarios. In other scenarios, the optimization problem is formulated as a semi-definite re…
Integrated Sensing and Communication (ISAC) has attracted substantial attraction in recent years for spectral efficiency improvement, enabling hardware and spectrum sharing for simultaneous sensing and signaling operations. In-band Full Duplex (FD) is being considered as a key enabling technology for ISAC applications due to its simultaneous transmission and reception capability. In this paper, we present an FD-based ISAC system operating at millimeter Wave (mmWave) frequencies, where a massive Multiple-Input Multiple-Output (MIMO) Base Station (BS) node employing hybrid Analog and Digital (A/…
Full-duplex (FD) systems have emerged as an es- sential enabling technology to further increase the data rate of wireless communication systems. The key idea of FD is to serve multiple users over the same bandwidth with a base station (BS) that can simultaneously transmit and receive the signals. The most challenging issue in designing an FD system is to address both the harmful effects of residual self-interference caused by the transmit-to-receive antennas at the BS as well as the co- channel interference from an uplink user (ULU) to a downlink user (DLU). An efficient solution to these prob…
User scheduling, beamforming and energy coordination are investigated in smart-grid powered cellular networks (SGPCNs), where the base stations are powered by a smart grid and natural renewable energy sources. Heterogeneous energy coordination is considered in SGPCNs, namely energy merchandizing with the smart grid and energy exchanging among the base stations. A long-term grid-energy expenditure minimization problem with proportional-rate constraints is formulated for SGPCNs. Since user scheduling is coupled with the beamforming vectors, the formulated problem is challenging to handle via sta…
