We propose and analyze secret key generation using intelligent reflecting surface (IRS) assisted wireless communication networks. To this end, we first formulate the minimum achievable secret key capacity for an IRS acting as a passive beamformer in the presence of multiple eavesdroppers. Next, we develop an optimization framework for the IRS reflecting coefficients based on the secret key capacity lower bound. To derive a tractable and efficient solution, we design and analyze a semidefinite relaxation (SDR) and successive convex approximation (SCA) based algorithm for the proposed optimization. Simulation results show that employing our IRS-based algorithm can significantly improve the secret key generation capacity for a wide-range of wireless channel parameters.
Physical layer key generation (PLKG) can significantly enhance the security of classic encryption schemes by enabling them to change their secret keys significantly faster and more efficient. However, due to the reliance of PLKG techniques on channel medium, reaching a high secret key rate is challenging in static environments. Recently, exploiting intelligent reflecting surface (IRS) as a means to induce randomness in static wireless channels has received significant research interest. However, the impact of spatial correlation between the IRS elements is rarely studied. To be specific, for t…
The IEEE Signal Processing Society is proud to announce the eighth edition of the Signal Processing Cup: an exciting challenge to control a wireless propagation environment using an intelligent reflecting surface. An intelligent reflecting surface is a two-dimensional array of metamaterial whose interaction with electromagnetic waves can be controlled, e.g., by tuning the impedance variations over the surface. These surfaces might be used in the sixth generation (6G) mobile technology to direct wireless signals from a transmitter towards a receiver, to raise the communication performance. The …
The work analyzed the positioning of IRS over the coverage region of micro cell to derive optimal placement location to support cell-edge Internet of Things (IoT) devices with a favorable signal-to-interference plus noise ratio (SINR). Moreover, the work derived that the implementation of IRS significantly enhances energy efficiency notably reducing the transmit power of the micro cell base station.
Millimeter wave communication is eminently suitable for high-rate wireless systems, which may be beneficially amalgamated with intelligent reflecting surfaces (IRS), relying on beam-index modulation. Explicitly, we propose three different architectures based on IRSs for beam-index modulation in millimeter wave communication, which circumvent the line-of-sight blockage of millimeter wave frequencies. We conceive both the optimal maximum likelihood detector and a low-complexity compressed sensing detector for the proposed schemes. Finally, the schemes conceived are evaluated through extensive si…
Reconfigurable intelligent surface (RIS) based communications have emerged as a new paradigm. This letter proposes a differential reflecting modulation (DRM) scheme for RIS based communication systems. In DRM, information bits are jointly carried by the activation permutations of the reflecting patterns and the phases of the transmitted signals, leading to that DRM can work without any channel state information (CSI) at the transmitter, RIS or receiver. In other words, DRM can release the intricate and resource-consuming channel estimation in the transmission process. Simulation results show t…
Vehicular communication is an important application of the fifth generation of mobile communication systems (5G). Due to its low cost and energy efficiency, intelligent reflecting surface (IRS) has been envisioned as a promising technique that can enhance the coverage performance significantly by passive beamforming. In this paper, we analyze the outage probability performance in IRS-assisted vehicular communication networks. We derive the expression of outage probability by utilizing series expansion and central limit theorem. Numerical results show that the IRS can significantly reduce the o…
Intelligent reflecting surface (IRS) is envisioned as a promising solution for controlling radio propagation environments in future wireless systems. In this paper, we propose a distributed intelligent reflecting surface (IRS) assisted multi-user millimeter wave (mmWave) system, where IRSs are exploited to enhance the mmWave signal coverage when direct links between base station and users are unavailable. First, a joint active and passive beamforming problem is established for weighted sum-rate maximization. Then, an alternating iterative algorithm with closed-form expressions is proposed to t…
This paper investigates the use of a reconfigurable intelligent surface (RIS) to aid point-to-point multi-data-stream multiple-input multiple-output (MIMO) wireless communications. With practical finite alphabet input, the reflecting elements at the RIS and the precoder at the transmitter are alternatively optimized to minimize the symbol error rate (MSER). In the reflecting optimization with a fixed precoder, two reflecting design methods are developed, referred as eMSER-Reflecting and vMSER-Reflecting. In the optimization of the precoding matrix with a fixed reflecting pattern, the matrix op…
We investigate the use of an intelligent reflecting surface (IRS) in a millimeter-wave (mmWave) vehicular communication network. An intelligent reflecting surface consists of passive elements, which can reflect the incoming signals with adjustable phase shifts. By properly tuning the phase shifts we can improve link performance. This is known as phase optimization or passive beamforming. We consider the problem of rate maximization in the uplink, which utilizes an IRS. However, using an IRS brings more challenges in terms of channel estimation. We propose two schemes to reduce the channel esti…
In this letter, an intelligent reflecting surface (IRS) enhanced full-duplex MIMO two-way communication system is studied. The system sum rate is maximized through jointly optimizing the source precoders and the IRS phase shift matrix. Adopting the idea of Arimoto-Blahut algorithm, the non-convex optimization problem is decoupled into three sub-problems, which are solved alternatingly. All the sub-problems can be solved efficiently with closed-form solutions. In addition, practical IRS assumptions, e.g., discrete phase shift levels, are also considered. Numerical results verify the convergence…
We analyze the outage probability of an intelligent reflecting surface (IRS)-assisted communication network. A tight upper bound on the outage probability is formulated based on the Chernoff inequality. Furthermore, through an exact asymptotic (a large number of reflecting elements) analysis based on a saddlepoint approximation, we derive closed-form expressions of the outage probability for systems with and without a direct link and obtain the corresponding diversity orders. Simulation results corroborate our theoretical analysis and show the inaccuracies inherent in using the central limit t…
We propose a new secure transmission scheme which uses directional modulation (DM) with artificial noise and is aided by the intelligent reflecting surface (IRS). Specifically, the direct path and IRS-enabled reflect path carry the same confidential signal and thus can be coherently added at the desired position to maximize the total received power, while the received signals at other positions are distorted. We derive a closed-form expression for the secrecy rate achieved by the proposed scheme. Using simulation results, we show that the proposed scheme can achieve two-dimensional secure tran…
We propose a novel concept of hybrid relay-reflecting intelligent surface (HR-RIS), in which a single or few elements are deployed with power amplifiers (PAs) to serve as active relays, while the remaining elements only reflect the incident signals. The design and optimization of the HR-RIS is formulated in a spectral efficiency (SE) maximization problem, which is efficiently solved by the alternating optimization (AO) method. The simulation results show that a significant improvement in the SE can be attained by the proposed HR-RIS, even with a limited power budget, with respect to the conven…
In this paper, we derive the uplink achievable rate expression of intelligent reflecting surface (IRS)-aided millimeter-wave (mmWave) systems, taking into account the phase noise at IRS and the quantization error at base stations (BSs). We show that the performance is limited only by the resolution of analog-digital converters (ADCs) at BSs when the number of IRS reflectors grows without bound. On the other hand, if BSs have ideal ADCs, the performance loss caused by IRS phase noise is a constant. Finally, our results validate the feasibility of using low-precision hardware at the IRS when BSs…
In this letter, the use of intelligent reflecting surface (IRS) to enhance the physical layer security of downlink wireless communication is investigated. Assuming a single-antenna legitimate user and a multi-antenna eavesdropper, we propose an effective algorithm to jointly optimize the active and passive beamforming. In the proposed algorithm, the optimal transmit beamforming vector at the BS under fixed IRS phase shifts is derived, and a low-complexity algorithm based on fractional programming (FP) and manifold optimization (MO) is proposed to obtain near optimal IRS phase shifts. Simulatio…
This letter studies a cloud radio access network (C-RAN) with multiple intelligent reflecting surfaces (IRS) deployed between users and remote radio heads (RRH). Specifically, we consider the uplink transmission where each RRH quantizes the received signals from the users by either point-to-point compression or Wyner-Ziv compression and then transmits the quantization bits to the BBU pool through capacity limited fronthhual links. To maximize the uplink sum rate, we jointly optimize the passive beamformers of IRSs and the quantization noise covariance matrices of fronthoul compression. An join…
Cognitive radio (CR) is an effective solution to improve the spectral efficiency (SE) of wireless communications by allowing the secondary users (SUs) to share spectrum with primary users. Meanwhile, intelligent reflecting surface (IRS), also known as reconfigurable intelligent surface (RIS), has been recently proposed as a promising approach to enhance energy efficiency (EE) of wireless communication systems through intelligently reconfiguring the channel environment. To improve both SE and EE, in this paper, we introduce multiple IRSs to a downlink multiple-input single-output (MISO) CR syst…
In this paper, we introduce an intelligent reflecting surface (IRS) to provide a programmable wireless environment for physical layer security. By adjusting the reflecting coefficients, the IRS can change the attenuation and scattering of the incident electromagnetic wave so that it can propagate in a desired way toward the intended receiver. Specifically, we consider a downlink multiple-input single-output (MISO) broadcast system where the base station (BS) transmits independent data streams to multiple legitimate receivers and keeps them secret from multiple eavesdroppers. By jointly optimiz…
Malicious jamming launched by smart jammer, which attacks legitimate transmissions has been regarded as one of the critical security challenges in wireless communications. Thus, this paper exploits intelligent reflecting surface (IRS) to enhance anti-jamming communication performance and mitigate jamming interference by adjusting the surface reflecting elements at the IRS. Aiming to enhance the communication performance against smart jammer, an optimization problem for jointly optimizing power allocation at the base station (BS) and reflecting beamforming at the IRS is formulated. As the jammi…
Intelligent reflecting surface (IRS) has emerged as a revolutionizing solution to enhance wireless communications by intelligently changing the propagation environment. Prior studies on IRS are based on an ideal reflection model with a constant amplitude and a variable phase shift. However, it is difficult and unrealistic to implement an IRS satisfying such ideal reflection model in practical applications. In this letter, we aim to investigate the phase-amplitude-frequency relationship of the reflected signals and propose a practical model of reflection coefficient for an IRS-aided wideband sy…
In this paper, we consider channel estimation for intelligent reflecting surface (IRS)-assisted millimeter wave (mmWave) systems, where an IRS is deployed to assist the data transmission from the base station (BS) to a user. It is shown that for the purpose of joint active and passive beamforming, the knowledge of a large-size cascade channel matrix needs to be acquired. To reduce the training overhead, the inherent sparsity in mmWave channels is exploited. By utilizing properties of Katri-Rao and Kronecker products, we find a sparse representation of the cascade channel and convert cascade ch…
In this paper, we study an intelligent omni-surface (IOS)-assisted downlink communication system, where the link quality of a mobile user (MU) can be improved with a proper IOS phase shift design. Unlike the intelligent reflecting surface (IRS) in most existing works that only forwards the signals in a reflective way, the IOS is capable to forward the received signals to the MU in either a reflective or a transmissive manner, thereby enhancing the wireless coverage. We formulate an IOS phase shift optimization problem to maximize the downlink spectral efficiency (SE) of the MU. The optimal pha…
This paper investigates an intelligent reflecting surface (IRS) aided cooperative communication network, where the IRS exploits large reflecting elements to proactively steer the incident radio-frequency wave towards destination terminals (DTs). As the number of reflecting elements increases, the reflection resource allocation (RRA) will become urgently needed in this context, which is due to the non-ignorable energy consumption. The goal of this paper, therefore, is to realize the RRA besides the active-passive beamforming design, where RRA is based on the introduced modular IRS architecture.…
In this paper, a three-dimensional (3D) geometry based stochastic model (GBSM) for a massive multiple-input multiple-output (MIMO) communication system employing practical discrete intelligent reflecting surface (IRS) is proposed. The proposed channel model supports the scenario where both transceivers and environments move. The evolution of clusters in the space domain and the practical discrete phase shifts are considered in the channel model. The steering vector is set at the base station for the cooperation with IRS. Through studying statistical properties, the non-stationary properties ar…
In this paper, secure wireless information and power transfer with intelligent reflecting surface (IRS) is proposed for a multiple-input single-output (MISO) system. Under the secrecy rate (SR) and the reflecting phase shifts of IRS constraints, the secure transmit beamforming at access point (AP) and phase shifts at IRS are jointly optimized to maximize the harvested power of energy harvesting receiver (EHR). Due to the non-convexity of optimization problem and coupled optimization variables, firstly, we convert the optimization problem into a semidefinite relaxation (SDR) problem and a sub-o…
Malicious jamming launched by smart jammers can attack legitimate transmissions, which has been regarded as one of the critical security challenges in wireless communications. With this focus, this paper considers the use of an intelligent reflecting surface (IRS) to enhance anti-jamming communication performance and mitigate jamming interference by adjusting the surface reflecting elements at the IRS. Aiming to enhance the communication performance against a smart jammer, an optimization problem for jointly optimizing power allocation at the base station (BS), and reflecting beamforming at th…
Intelligent reflecting surface (IRS) has emerged as a promising and revolutionizing technology for future wireless networks. Most existing IRS studies focus on simple cooperative systems which usually have a single frequency band. In realistic non-cooperative multi-band networks, however, the existing IRS designs may be not applicable or have severe performance degradation. Thus, in the complex network environment, it is more rational to consider IRSs as public resources to be dynamically allocated to appropriate users. In this paper, we first introduce the auction theory to tackle the resourc…
In a wireless system with Intelligent Reflective Surfaces (IRS) containing many passive elements, we consider the problem of channel estimation. All the links from the transmitter to the receiver via each IRS elements (or groups) are estimated. As the estimation performance are dependent on the setting of the IRS, we design an optimal channel estimation scheme where the IRS elements follow an optimal series of activation patterns. The optimal design is guided by results for the minimum variance unbiased estimation. The IRS setting during the channel estimation period mimics a series of discret…
This paper first describes the introduction of 6G-empowered V2X communications and IRS technology. Then it discusses different use case scenarios of IRS enabled V2X communications and reports recent advances in the existing literature. Next, we focus our attention on the scenario of vehicular edge computing involving IRS enabled drone communications in order to reduce vehicle computational time via optimal computational and communication resource allocation. At the end, this paper highlights current challenges and discusses future perspectives of IRS enabled V2X communications in order to impr…
Maneuvering target sensing will be an important service of future vehicular networks, where precise velocity estimation is one of the core tasks. To this end, the recently proposed integrated sensing and communications (ISAC) provides a promising platform for achieving accurate velocity estimation. However, with one mono-static ISAC base station (BS), only the radial projection of the true velocity can be estimated, which causes serious estimation error. In this paper, we investigate the estimation of the true velocity of a maneuvering target with the assistance of an intelligent reflecting su…
As one of the key technologies for the sixth generation (6G) mobile communications, intelligent reflecting surface IRS) has the advantages of low power consumption, low cost, and simple design methods. But channel modeling is still an open issue in this field currently. In this paper, we propose a three-dimensional (3D) geometry based stochastic model (GBSM) for a massive multiple-input multiple-output (MIMO) communication system employing IRS. The model supports the movements of the transmitter, the receiver, and clusters. The evolution of clusters on the linear array and planar array is also…
Millimeter wave (mmWave) communications are evolving as a promising technology to meet the ever increasing data rate requirements. However, high directivity and severe path loss make it vulnerable to blockages, which could be frequent in indoor or urban environments. To address this issue, intelligent reflecting surfaces (IRSs) are introduced to provide additional adjustable reflected paths. Most prior works assume that elements of IRSs have an infinite phase resolution, which is difficult to be realized in practical systems. In this paper, IRSs with low-resolution phase shifters are considere…
As a means to control wireless propagation environments, the use of emerging and novel intelligent reflecting surfaces (IRS) is envisioned to enhance and broaden many applications in future wireless networks. This paper is concerned with a point-to-point IRS-assisted millimeter-wave (mmWave) system in which the IRS consists of multiple subsurfaces, each having the same number of passive reflecting elements, whereas both the transmitter and receiver are equipped with massive antenna arrays. Under the scenario of having very large numbers of antennas at both transmit and receive ends, the achiev…
In this letter, we investigate an intelligent reflecting surface (IRS) aided device-to-device (D2D) offloading system, where an IRS is employed to assist in computation offloading from a group of users with intensive tasks to another group of idle users. We propose a new two-timescale joint passive beamforming and resource allocation algorithm based on stochastic successive convex approximation to minimize the system latency while cutting down the heavy overhead in exchange of channel state information (CSI). Specifically, the high-dimensional passive beamforming vector at the IRS is updated i…
Full-duplex (FD) transmission has already been regarded and developed as a promising method to improve the utilization efficiency of the limited spectrum resource, as transmitting and receiving are allowed to simultaneously occur on the same frequency band. Nowadays, benefiting from the recent development of intelligent reflecting surface (IRS), some unique electromagnetic (EM) functionalities, like wavefront shaping, focusing, anomalous reflection, absorption, frequency shifting, and nonreciprocity can be realized by soft-controlled elements at the IRS, showing the capability of reconfiguring…
In this paper, unmanned aerial vehicles (UAVs) and intelligent reflective surface (IRS) are utilized to support terahertz (THz) communications. To this end, the joint optimization of UAV's trajectory, the phase shift of IRS, the allocation of THz sub-bands, and the power control is investigated to maximize the minimum average achievable rate of all the users. An iteration algorithm based on successive Convex Approximation with the Rate constraint penalty (CAR) is developed to obtain UAV's trajectory, and the IRS phase shift is formulated as a closed-form expression with introduced pricing fact…
In this paper, we consider the weighted sum-power minimization under quality-of-service (QoS) constraints in the multi-user multi-input-single-output (MISO) uplink wireless network assisted by intelligent reflecting surface (IRS). We perform a comprehensive investigation on various aspects of this problem. First, when users have sufficient transmit powers, we present a new sufficient condition guaranteeing arbitrary information rate constraints. This result strengthens the feasibility condition in existing literature. Then, we design novel penalty dual decomposition (PDD) based and nonlinear e…
Intelligent reflecting surfaces (IRSs) are envisioned to provide reconfigurable wireless environments for future communication networks. In this paper, both downlink and uplink IRS-aided non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA) networks are studied, in which an IRS is deployed to enhance the coverage by assisting a cell-edge user device (UD) to communicate with the base station (BS). To characterize system performance, new channel statistics of the BS-IRS-UD link with Nakagami-$m$ fading are investigated. For each scenario, the closed-form expressions for the …
In this paper, we study an intelligent reflecting surface (IRS)-aided wireless secure communication system for physical layer security, where an IRS is deployed to adjust its surface reflecting elements to guarantee secure communication of multiple legitimate users in the presence of multiple eavesdroppers. Aiming to improve the system secrecy rate, a design problem for jointly optimizing the base station (BS)'s beamforming and the IRS's reflecting beamforming is formulated given the different quality of service (QoS) requirements and time-varying channel condition. As the system is highly dyn…
An intelligent reflecting surface (IRS) at terahertz (THz) bands is expected to have a massive number of reflecting elements to compensate for the severe propagation losses. However, as the IRS size grows, the conventional far-field assumption starts becoming invalid and the spherical wavefront of the radiated waves should be taken into account. In this work, we consider a spherical wave channel model and pursue a comprehensive study of IRS-aided multiple-input multiple-output (MIMO) in terms of power gain and energy efficiency (EE). Specifically, we first analyze the power gain under beamfocu…
In this paper, non-orthogonal multiple access (NOMA) networks assisted by multiple intelligent reflecting surfaces (IRSs) with discrete phase shifts are investigated, in which each user device (UD) is served by an IRS to improve the quality of the received signal. Two scenarios are considered according to whether there is a direct link between the base station (BS) and each UD, and the outage performance is analyzed for each of them. Specifically, the asymptotic expressions for the upper and lower bounds of the outage probability in the high signal-to-noise ratio (SNR) regime are derived. Foll…
In this letter, secure beamforming in a multiple intelligent reflecting surfaces (IRSs)-aided millimeter-wave (mmWave) system is investigated. In this system, the secrecy rate is maximized by controlling the on-off status of each IRS as well as optimizing the phase shift matrix of the IRSs. This problem is posed as a joint optimization problem of transmit beamforming and IRS control, whose goal is to maximize the secrecy rate under the total transmission power and unit-modulus constraints. The problem is difficult to solve optimally due to the nonconvexity of constraint conditions and coupled …
In this paper, the intelligent reflecting surface (IRS)-aided unmanned aerial vehicle (UAV) communication system is studied, where the UAV is deployed to serve the user equipment (UE) with the assistance of multiple IRSs mounted on several buildings to enhance the communication quality between UAV and UE. We aim to maximize the energy efficiency of the system, including the data rate of UE and the energy consumption of UAV via jointly optimizing the UAV's trajectory and the phase shifts of reflecting elements of IRS, when the UE moves and the selection of IRSs is considered for the energy savi…
Intelligent reflecting surfaces (IRSs)-assisted wireless communication promises improved system performance, while posing new challenges in channel estimation (CE) due to the passive nature of the reflecting elements. Although a few CE protocols for IRS-assisted multiple-input single-output (MISO) systems have appeared, they either require long channel training times or are developed under channel sparsity assumptions. Moreover, existing works focus on a single IRS, whereas in practice multiple such surfaces should be installed to truly benefit from the concept of reconfiguring propagation env…
In this paper, we consider the weighted sum-power minimization under quality-of-service (QoS) constraints in the multi-user multi-input-single-output (MISO) uplink wireless network assisted by intelligent reflecting surface (IRS). We perform a comprehensive investigation on various aspects of this problem. First, when users have sufficient transmit powers, we present a new sufficient condition guaranteeing arbitrary information rate constraints. This result strengthens the feasibility condition in existing literature. Then, we design novel penalty dual decomposition (PDD) based and nonlinear e…
In this paper, we study the high-resolution channel estimation problem for intelligent reflecting surface (IRS)-assisted millimeter wave (mmWave) multiple-input-multiple-output (MIMO) communications, which is a prerequisite to guarantee further high-rate data transmission. Considering the typical sparsity of mmWave channels, we formulate the cascaded channel estimation problem from a sparse signal recovery perspective, and then propose a novel two-step cascaded channel estimation protocol to estimate the cascaded user-IRS-base station channel with high-resolution for IRS-assisted mmWave MIMO c…
Intelligent reflecting surface (IRS) is a promising solution to build a programmable wireless environment for future communication systems. In practice, an IRS consists of massive low-cost elements, which can steer the incident signal in fully customizable ways by passive beamforming. In this paper, we consider an IRS-aided multiuser multiple-input single-output (MISO) downlink communication system. In particular, the weighted sum-rate of all users is maximized by joint optimizing the active beamforming at the base-station (BS) and the passive beamforming at the IRS. In addition, we consider a…
The past years have witnessed increasing research interest in achieving passive human localization with commodity WiFi devices. However, due to the fundamental limited spatial resolution of WiFi signals, it is still very difficult to achieve accurate localization with existing commodity WiFi devices. To tackle this problem, in this paper, we propose to exploit the degree of freedom provided by the Intelligent Reflecting Surface (IRS), which is composed of a large number of controllable reflective elements, to modulate the spatial distribution of WiFi signals and thus break down the spatial res…
Reconfigurable intelligent surface (RIS) has emerged as a cost- and energy-efficient solution to enhance the wireless communication capacity. However, recent studies show that a very large surface is required for a RIS-assisted communication system; otherwise, they may be outperformed by the conventional relay. Furthermore, the performance gain of a RIS can be considerably degraded by hardware impairments such as limited-resolution phase shifters. To overcome those challenges, we propose a novel concept of hybrid relay-reflecting intelligent surface (HR-RIS), in which a single or few elements …
In recent years, intelligent reflecting surface (IRS) has emerged as a promising technology for 6G due to its potential/ability to significantly enhance energy- and spectrum-efficiency. To this end, it is crucial to adjust the phases of reflecting elements of the IRS, and most of the research works focus on how to optimize/quantize the phase for different optimization objectives. In particular, the quantized phase shift (QPS) is assumed to be available at the IRS, which, however, does not always hold and should be fed back to the IRS in practice. Unfortunately, the feedback channel is generall…
This paper considers symbol-level precoding (SLP) for multiuser multi-input single-output (MISO) downlink transmission with the aid of intelligent reflecting surface (IRS). Specifically, by assuming one-bit transmitted signals at the base station (BS), which arises from the use of low-resolution DACs in the regime of massive transmit antennas, a joint design of one-bit SLP at the BS and the phase shifts at the IRS is proposed with a goal of minimizing the worst-case symbol error probability (SEP) of the users under the PSK modulation. This joint design problem is essentially a mixed integer no…
Reconfigurable intelligent surfaces (RISs) have emerged as a cost- and energy-efficient technology that can customize and program the physical propagation environment by reflecting radio waves in preferred directions. However, the purely passive reflection of RISs not only limits the end-to-end channel beamforming gains, but also hinders the acquisition of accurate channel state information for the phase control at RISs. In this paper, we provide an overview of a hybrid relay-reflecting intelligent surface (HR-RIS) architecture, in which only a few elements are active and connected to power am…
