STAR-RISs: Simultaneous Transmitting and Reflecting Reconfigurable Intelligent Surfaces

Recently, the concept of smart radio environments and reconfigurable intelligent surfaces (RISs) has received heated discussion in the research community. It is envisioned that the RISs can assist wireless communication networks by intelligently controlling part of the radio environment [1, 2, 3]. Specifically, the RIS is a two-dimensional structure that consists of a large number of low-cost elements. These elements are of sub-wavelength sizes and are reconfigurable in terms of their electromagnetic responses. There are diverse applications of introducing RISs into wireless networks, including but not limited to energy efficiency enhancement [4], multi-user support [5], visible light communication [6], and robotic communication [7].

Despite these advantages, existing research contributions [3, 4, 5, 6] mainly considered the employment of the reflecting-only RISs, which brings extra topological constraints to the wireless system. Specifically, to receive signals from the reflecting-only RISs, users have to be on the same side as the transmitter. To mitigate this drawback and to facilitate more flexible system designs of the RIS-assisted network, in this letter, we propose the concept of simultaneous transmitting and reflecting RISs (STAR-RISs). From a manufacturing perspective, the proposed new RISs can be implemented using various metasurface-based designs. For example, NTT DOCOMO, INC. recently announced a dynamic metasurface achieving dynamic manipulation of both reflection and penetration in a highly transparent package [8]. Other successful implementations achieving manipulation of transmission and reflection are also reported, including graphene-based dynamic metasurfaces [9] and multi-layer metasufaces [10].

However, existing research contributions [8, 9, 10] mainly focused on the designing of metasurface prototypes or studying particular physical properties of the designed surface. There is a lack of communication models for the STAR-RISs that are both physically-compliant and mathematically-tractable. To facilitate the research on STAR-RISs in the field of wireless communications, we separately present a general hardware model and two channel models for the near-field region and the far-field region. Base on the field equivalence principle[3], the proposed hardware model characterizes each STAR-RIS element by the transmission and reflection coefficients. The channel model gives the closed-form formulation of channel gains in terms of the transmission and reflection coefficients, as well as the geometric settings of the system. Base on the proposed models, we analyze and compare the diversity gain of the STAR-RISs and conventional RISs. Our numerical results confirm that the STAR-RIS can significantly extend the coverage and achieve full diversity order on both sides of the surface, yielding a superior performance gain over conventional RISs.

As shown in Fig. 1, a schematic representation of the structure of STAR-RISs is presented. Base on the field equivalence principle [3], as the STAR-RIS elements are excited by the incident signal, the transmitted and reflected signals can be equivalently treated as waves radiated from the time-varying surface equivalent electric currents $\bm{J}_{p}$ and magnetic currents $\bm{J}_{b}$ (also referred to as the bound currents). Within each element, the strengths and distribution of these surface equivalent currents are determined by the incident signal $s_{m}$ as well as the local surface averaged electric and magnetic impedances $Y_{m}$ and $Z_{m}$. Assume that the STAR-RIS produces both transmitted and reflected signals with the same popularization. At the $m$th element, these signals can be expressed as:

where $T_{m}$ and $R_{m}$ are the transmission and reflection coefficients of the $m$th element, respectively. According to the law of energy conservation, for passive STAR-RIS elements, the following constraint on the local transmission and reflection coefficients must be satisfied:

According to electromagnetic theory, the phase delays of both the transmitted and reflected field are related to $Y_{m}$ and $Z_{m}$. In Fig. 1, the reconfigurability of the element is reflected in the change of the surface impedances, since the transmission and reflection coefficients of the $m$th element is related to the surface impedances as: $T_{m}=\frac{2-\eta_{0}Y_{m}}{2+\eta_{0}Y_{m}}-R_{m}$, and $R_{m}=-\frac{2(\eta_{0}^{2}Y_{m}-Z_{m})}{(2+\eta_{0}^{2}Y_{m})(2\eta_{0}+Z_{m})}$, where $\eta_{0}$ is the impedance of free space [11]. From the perspective of metasurface design, supporting the magnetic currents is the key to achieve independent control of both the transmitted and reflected signals. According to [12], single-layered RISs with non-magnetic elements can only produce identical radiation on different sides, which is referred to as the symmetry limitation. By introducing the equivalent surface electric and magnetic currents into the model, the proposed hardware model is able to independently characterize the transmission and reflection of each element. To facilitate the design of the STAR-RISs in wireless communication systems, we rewrite these coefficients in the form of their amplitudes and phase shifts as follows:

where $\beta^{T}_{m},\beta^{R}_{m}\in[0,1]$ are real-valued coefficients satisfying $\beta^{T}_{m}+\beta^{R}_{m}\leq 1$, and $\phi^{T}_{m},\phi^{R}_{m}\in[0,2\pi)$ are the phase shifts introduced by element $m$ for the transmitted and reflected signals, $\forall m\in\{1,2,\cdots,M\}$.

Base on the proposed hardware model, in this section, we study the communication channels of the STAR-RISs. As shown in Fig. 2, a downlink STAR-RIS-assisted multi-user wireless network is considered, where the transmitter (Tx) and receivers (Rx) are equipped with a single antenna, and the STAR-RIS consists of $M$ reconfigurable elements. The users are divided into two groups. Users in group T are located on the opposite side with the transmitter with respect to the STAR-RIS, and thus, they can only receive signals transmitted by the STAR-RIS. Users in group R and the transmitter are located on the same side of STAR-RIS. At the STAR-RIS, signals are transmitted and reflected towards these two groups of users simultaneously. Let $h^{\chi}_{k}$ denote the direct link between the transmitter and receiver $k$ in group T or in group R, where the notation $\chi\in\{T,R\}$ is an indicator representing “$T$” for receiver in group T or “$R$” for receiver in group R. Let $g^{\chi}_{k}$ denote the channel between the transmitter and receiver $k$ through STAR-RIS transmission or reflection.

To concisely highlight the benefits of STAR-RISs, in this section, we present a comparison between the following two RISs with specific configurations:

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  STAR-RIS: All STAR-RIS elements share a common value for the power ratio between the transmitted signal and the reflected signal. However, the phase delays of each element can be independently configured.

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  Conventional RIS: A composite smart surface consist of reflecting-only and transmitting-only RISs, each with $M_{t}$ and $M_{r}$ elements, respectively.

In the following, we compare the performance of the STAR-RIS with the conventional RIS and demonstrate the benefit of deploying STAR-RISs in wireless systems. The power ratio between transmitted and reflected signals is fixed as $\beta^{T}/\beta^{R}$, for all elements¹¹1It is worth mentioning that for STAR-RISs, there is a trade-off between the received power of receivers in group T and group R by changing the power ratio. Including these power ratios in the optimization can further improve the performance of the system.. Consider a multi-user network assisted by an STAR-RIS or a conventional RIS. We assume that Tx and the STAR-RIS can be positioned with a line-of-sight (LoS) Tx-RIS link. The receivers are all located in the far-field region of the RIS. The direct Tx-Rx links follows Ricean distribution as: $h^{\chi}_{k}\sim\mathcal{R}(K^{\chi}_{d},\Omega^{\chi}_{d})$, and the links between each STAR-RIS element and receivers ($r^{\chi}_{k,m}$) are identically and independently distributed, following Ricean distribution as: $r^{\chi}_{k,m}\sim\mathcal{R}(K^{\chi}_{s},\Omega^{\chi}_{s})$. According to the proposed far-field channel model for STAR-RISs, the signal-to-noise ratio (SNR) of receiver $k$ for the case of STAR-RIS or conventional RIS can be expressed as $\gamma^{\mu}_{k}={|H^{\mu}_{k}|^{2}w^{2}_{k}}/{\sigma^{2}_{0}}$, where $\mu\in\{S,C\}$ is an indicator representing “$S$” for the corresponding quantities in the STAR-RIS case, or “$C$” in the conventional RIS case, $H_{k}$ is the overall channel for receiver $k$, $w_{k}$ denotes the power allocation for the message of receiver $k$ at the transmitter, and $\sigma_{0}^{2}$ is the power spectrum density of the Gaussian white noise at receiver $k$. According to our proposed far-field channel model, the overall channel of receiver $k$ in group T or group R can be expressed as:

where $\bm{\Phi}^{T}_{S}=\text{diag}(T_{1},\cdots,T_{M})$, $\bm{\Phi}^{R}_{S}=\text{diag}(R_{1},\cdots,R_{M})$, $\bm{\Phi}^{T}_{C}=\text{diag}(0,\cdots,0,T_{M-M_{t}+1},\cdots,T_{M})$, and $\bm{\Phi}^{R}_{C}=\text{diag}(R_{1},\cdots,R_{M_{r}},0,\cdots,0)$. For the case of STAR-RIS, under a transmit SNR $\gamma_{t}$ and target SNR at receiver $\gamma_{k}$, the outage probability can be formulated as follows:

where $\beta^{T}/\beta^{R}$ is the power ratio between transmission and reflection for STAR-RIS elements. For the case of conventional RIS, the outage probability is:

Note that the summation in (11) has $M_{t}$ terms for $k$ in group T and $M_{r}$ terms for $k$ in group R. In the following, we compare the best achievable diversity orders of receivers for STAR-RISs and conventional RISs.

In the following remark, we consider the diversity order defined through outage probability as follows:

In this section, we numerically demonstrate our proposed models to compare the coverage of the STAR-RISs and the conventional RISs. Then, we simulate the outage probabilities of receivers severed by STAR-RISs and the conventional RISs to verify our analytical results. The geographical setup is shown in Fig. 3(a), where the RIS is positioned at the origin in the $z=0$ plane. We simulate a $16\times 16$ STAR-RIS, where spacing of each element is chosen as $\lambda/2$, and a conventional RIS with $M_{t}=M_{r}=128$.
In Fig. 3, we compare the coverage of the proposed STAR-RIS with conventional RISs by simulating their radiation patterns. The simulation is carried out as follows: Base on (6), we calculate the channel gain of each point on the plane $\Sigma_{e}$. For STAR-RIS, we set $\beta^{T}=\beta^{R}=1$. The phase shift configurations of both the STAR-RIS and conventional RIS is chosen according to the cophase condition [3]. Specifically, the target angles of the transmitted signal and the reflected signal are set as $7.6^{\circ}$ and $16.6^{\circ}$, respectively. As illustrated in Fig. 3(b), the power density of the STAR-RIS is significantly higher near the target angles, forming a beam-like radiation pattern. In contrast, in Fig. 3(c), the transmitted and reflected beams of the conventional RIS are less focused with weaker channel gains. This observation is consistent with our analytical results presented in Section. IV. Moreover, it can be observed that the angular distribution of power density has an irregular pattern which highly depends on the distance in the near-field region, while in the far-field region, a fixed radiation pattern can be observed. These observations of the radiation patterns are consistent with the results of the two proposed channel models.
Fig. 4 shows the channel gain obtained by the $16\times 16$ STAR-RIS. The power ratio between transmission and reflection is set to $2$:$3$. For the horizontal axis, $d$ denotes the distance between the receiver and the center of STAR-RIS. The signal is reflected to the region where $d>0$, and transmitted to the region where $d<0$. In the simulation, we assume that the receiver moves on both sides of STAR-RIS, along a straight line in $\Sigma_{e}$ with an angle of $60^{\circ}$ with respect to the normal direction of STAR-RIS. As illustrated in Fig. 4, the dash-dotted blue line represents the channel gains calculated using the near-field channel model without considering the leaning factor. In other words, we assume $F(\theta^{T}_{m})=F(\theta^{R}_{m})=1$. The solid red line represents the channel gains calculated using the near-field channel model with leaning factor $F(\theta^{\chi}_{m})=(1+\cos\theta^{\chi}_{m})/2$. The dashed black line represents the channel gains calculated using the far-field channel, according to (5). It can be observed that results for the near-field model start to approach the far-field model after the receiver is several wavelength away from STAR-RIS. Within the near-field region, the far-field model fails to provide a physically meaningful result as the channel gain tends to infinity when the distance approaches zero.

In this letter, the concept of STAR-RISs is proposed. A general hardware model and two channel models were proposed. To evaluate the performance of STAR-RISs, we derived expressions for the asymptotic behaviour of the outage probability. Numerical simulations demonstrated the differences between the channel gains in the far-field and the near-field region and verified our proposed channel models. It is also demonstrated that the proposed STAR-RISs can extend coverage and achieve higher diversity order on both sides of the surface, compared to conventional RISs. Base on the proposed models, the joint optimization of transmission and reflection beamforming of the STAR-RISs constitutes an interesting topic for future research.