Beyond Intelligent Reflecting Surfaces: Reflective-Transmissive Metasurface Aided Communications for Full-dimensional Coverage Extension
Shuhang Zhang, Hongliang Zhang, Boya Di, Yunhua Tan, Zhu Han, Lingyang Song
aa r X i v : . [ ee ss . SP ] S e p Beyond Intelligent Reflecting Surfaces:Reflective-Transmissive MetasurfaceAided Communications forFull-dimensional Coverage Extension
Shuhang Zhang,
Student Member, IEEE , Hongliang Zhang,
Member, IEEE , BoyaDi,
Member, IEEE , Yunhua Tan, Zhu Han,
Fellow, IEEE , and Lingyang Song,
Fellow, IEEE
Abstract
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 ina reflective way, the IOS is capable to forward the received signals to the MU in either a reflectiveor a transmissive manner, thereby enhancing the wireless coverage. We formulate an IOS phase shiftoptimization problem to maximize the downlink spectral efficiency (SE) of the MU. The optimal phaseshift of the IOS is analysed, and a branch-and-bound based algorithm is proposed to design the IOSphase shift in a finite set. Simulation results show that the IOS-assisted system can extend the coveragesignificantly when compared to the IRS-assisted system with only reflective signals.
Index Terms
S. Zhang, Y. Tan, and L. Song are with Department of Electronics, Peking University, Beijing 100871 China (email: { shuhangzhang, tanggeric, lingyang.song } @pku.edu.cn).H. Zhang is with Department of Electronics, Peking University, Beijing 100871 China, and also with Department of ElectricalEngineering, Princeton University, Princeton, NJ 08544 USA (email: [email protected]).B. Di is with Department of Electronics, Peking University, Beijing 100871 China, and also with Department of Computing,Imperial College London, London SW7 2BU, U.K. (email: [email protected]).Z. Han is with Electrical and Computer Engineering Department, University of Houston, TX 77004, USA, and also with theDepartment of Computer Science and Engineering, Kyung Hee University, Seoul 02447 South Korea (email: [email protected]). Intelligent omni-surface, IOS phase shift design, coverage extension.
I. I
NTRODUCTION
With the development of meta-surfaces, the intelligent reflecting surface (IRS) is consideredas a promising technique for future communications, since it is cost-effective to achieve a highspectral and energy efficiency [1]. The IRS contains a large number of elements with controllableelectromagnetic responses that can shape the propagation environment into a desirable form [2],thus enhancing the quality of the communication links [3]. In the literature, some initial workshave studied the utilization of wave-reflective IRS to assist the wireless communication networks.In [4], a joint power allocation and continuous phase shift design has been studied in a reflectiveIRS-assisted system to maximize energy efficiency. In [5], the achievable data rate of a reflectiveIRS-assisted communication system has been evaluated, and the effect of limited phase shiftson the data rate has been investigated. However, in the existed works, the signal arrived at theIRS is considered to be reflected completely. As a result, the receivers on the other side of theIRS are shielded, which leads to an incomplete wireless coverage.In this paper, we study an intelligent omni-surface (IOS), whose received signals can be trans-mitted and reflected to both sides concurrently. We utilize the IOS in a communication system toextend the service coverage for downlink transmissions. The IOS provides an ubiquitous wirelesscoverage for the mobile user (MU) on its either side, and the propagation environment of theMU can be adjusted via the phase shifts of the electrically controllable elements on the IOS.The implementation of the IOS-assisted communication system has also brought some newchallenges.
First , the power of reflective and transmissive signals of the IOS may not besymmetric, i.e., the channel model of the reflective signal and the transmissive signal canbe different. Therefore, the studies on the reflective IRS-assisted communications cannot beapplied directly in the IOS-assisted ones.
Second , the direct communication link from the basestation (BS) to the MU may exist concurrently with the reflective and transmissive links in theIOS-assisted communication system. Such a superposition impact of multiple communicationlinks should be considered for IOS phase shift design.To deal with the above challenges, we first propose a novel model for the IOS with a con-trollable electromagnetic response on both sides, and then introduce its physical characteristics.Based on the channel model of the proposed IOS, we formulate a downlink communicationspectral efficiency (SE) maximization problem, where an IOS is utilized to improve the SE of a
Bottom layerTop layer
Feedline
Via hole Ground
PatchPin diodes
Fig. 1. Schematic structure of an IOS element.
MU by proper phase shift design. The optimal solution to the IOS phase shift is analysed, anda branch-and-bound algorithm is proposed to design the IOS phase shifts in a finite set. Theperformances in terms of coverage and SE improvement are provided by simulations.The rest of this paper is organized as follows. In Section II, we introduce the IOS. In Section III,we present an IOS-assisted downlink communication system, including the channel model andthe SE, and formulate a SE maximization problem with IOS phase shift design. An IOS phaseshift design algorithm is provided in Section IV. Numerical results in Section V evaluate theperformance of the proposed algorithm. Finally, we draw the conclusions in Section VI.II. I
NTELLIGENT O MNI -S URFACE
The IOS is a two-dimensional array of electrically controllable IOS elements. Each element inthe IOS is of the same size, with δ x being the width and δ y being the height, and is composed ofmultiple metal patches and N D PIN diodes assembled on dielectric substrates. As shown in Fig. 1,the metal patches are connected to the ground via PIN diodes, and can be switched between ON and OFF states according to the applied bias voltages, based on which a unique phase shift canbe added to the transmissive and reflective signals. There are N D possible phase shifts in totalfor each element. For generality, we assume that a subset of possible phase shifts are available,which is referred to as the available phase shifts set , denoted by S a = { , · · · , S a } . We denotethe phase shifts of the m th element by s m ∈ S a . We can control the PIN diodes to generate S a patterns of phase shifts for each element, with a uniform interval ∆ ψ m = πS a [5]. The possiblephase shift value can be given as l m ∆ ψ m , where l m is an integer satisfying ≤ l m ≤ S a − .The phase shift of the IOS is defined as the vector of the phase shifts of all IOS elements,i.e., s = ( s , . . . , s M ) , where M denotes the number of IOS elements. When a signal arrivesat an IOS element from either side of it, a part of the signal transmits through the elements as Arrival signal Departure signal
Destination Z X Y IOS element m (m) (m) (m) (m) Source
Fig. 2. Illustration for the angles of arrival and departure signals for a IOS element. the transmissive signal , and the other part of the signal is reflected as the reflective signal [6].The phase shift of the IOS determines the waveform of the transmissive and reflective signalsconcurrently.As illustrated in Fig. 2, we denote the direction of the arrival signal from the source node to el-ement m , and the direction from element m to the destination node by ξ A ( m ) = ( θ A ( m ) , φ A ( m )) and ξ D ( m ) = ( θ D ( m ) , φ D ( m )) , respectively. The influence of element m on the arrival signal isdenoted by a complex number g m , which we refer to as the power gain of the signal. The valueof g m for a transmission link is affected by the direction of the arrival signal from the sourcenode, i.e., ξ A ( m ) , the direction of the departure signal to the destination node, i.e., ξ D ( m ) , andthe element phase shifts s m . The experimental equation of the corresponding power gain can beexpressed as [7] g m ( ξ A ( m ) , ξ D ( m ) , s m ) = q G m K A ( m ) K D ( m ) δ x δ y | γ m | exp ( − jψ m ) , (1)where G m is the antenna gain of element m , and ψ m is the corresponding phase shift. Variable γ m is the power ratio of the departure signal to the arrival signal. It can either be a function of s m or a constant, which is related to the schematic structure of the IOS element. K A ( m ) and K D ( m ) are the normalized power radiation pattern of the arrival signal and departure signal,respectively. An example of the normalized power radiation pattern is given as following: K A ( m ) = | cos θ A ( m ) | , (2) The departure signal can be either transmissive signal or reflective signal. BS MU IOS
Transmissive link
Direct link MU Reflective link
Possible range of the MU
Move
Fig. 3. System model for the IOS-aided downlink cellular system. K D ( m ) = | cos θ D ( m ) | , θ D ( m ) ∈ (0 , π/ ,ǫ | cos ( π − θ D ( m )) | , θ D ( m ) ∈ ( π/ , π ) , (3)where ǫ is a constant parameter that describes the power ratio of the transmissive signal to thereflective signal . III. S YSTEM M ODEL AND P ROBLEM F ORMULATION
In this section, we first describe an IOS assisted single MU downlink system, and thenintroduce the channel model and SE of the IOS-assisted system. Finally, we formulate a downlinkSE maximization problem by optimizing the IOS phase shift.
A. Scenario Description
As shown in Fig. 3, we consider a downlink transmission scenario in an indoor environment,which consists of one BS and one MU. We assume that the MU is randomly located in arange denoted by L . Due to the severe channel fading and complicated scattering in the indoorenvironment, the MU may suffer low quality of service of the communication link to the BS.To tackle this problem, we deploy an IOS in the indoor environment. The power of the receivedsignals at the MU can be improved with either the transmissive signal or the reflective signal ofthe IOS, and the type of the received signal from the IOS is determined by the current locationof the MU. The IOS can be viewed as an antenna array far away from the BS, inherently capable The value of ǫ is determined by the material of the IOS element [8], which needs to be performed before the IOS deployment.Therefore, the distribution of the MU should be estimated before the IOS deployment. of realizing beamforming via the IOS phase shift design, which will be introduced in detail inSection III-C. B. Channel Model
The channel from the BS to the MU consists of two parts: the direct path from the BS to theMU bypassing the IOS, and the reflective-transmissive channel that goes through the IOS. Thedetailed descriptions of the direct path and the reflective-transmissive channel are given in thefollowing.
1) Direct Path Bypassing the IOS:
The channel model of the direct path from the BS to theMU is similar to the one in conventional cellular networks, which can be formulated as a Ricianchannel. The channel of the direct path from the BS to the MU can be written by h D = r κ κ h LoSD + r
11 + κ h
NLoSD , (4)where κ is the Rician factor indicating the ratio of the LoS component to the non-line-of-sight (NLoS) one, and h LoSD and h NLoSD are the LoS and NLoS components of the direct path,respectively. According to [9], the LoS component of the normal channel between the BS and theMU can be given as h LoSD = q G tx G rx d − αBS,MU exp ( − j πλ d BS,MU ) , where G tx is the transmissionantenna gain of the BS antenna, G rx is the receiving antenna gain of the MU, d BS,MU is thedistance from the BS to the MU, and α is the path-loss parameter. Similarly, the NLoS componentcan be written as h NLoSD = P L ( d BS,MU ) h SS , where P L ( · ) is the channel gain for the NLoScomponent, and h SS ∼ CN (0 , denotes the small-scale NLoS components.
2) Transmissive-Reflective Channel via the IOS:
As introduced in Section II, the departuresignal of the IOS contains two parts: transmissive signal and reflective signal. The location of theMU determines whether it receives the transmissive signal or the reflective signal. The channelfrom the BS to the MU via the IOS can be considered as the sum of M channels from the BSto the MU via every IOS element. Since the BS-IOS-MU link is much stronger than the NLoSones, the channel from the BS to the MU via each IOS element can be modeled as a Racianchannel. The channel gain from the BS to the MU via IOS element m is given as h m = r κ κ h LoSm + r
11 + κ h
NLoSm . (5)The LoS component of h m can be expressed as h LoSm = λ p G tx F txm G rx F rx exp (cid:16) − j π ( d BS,m + d m,MU ) λ (cid:17) (4 π ) d BS,m d m,MU × g m ( ξ A ( m ) , ξ D ( m ) , s m ) , (6) where λ is the wave length corresponding to the carrier frequency, G tx and G rx are antennagains of the BS and the MU, respectively, F txm is the normalized power gain of the BS antennain the direction of the m -th IOS element, F rxm is the normalized power gain of the MU in thedirection of IOS element m , d BS,m and d m,MU are the distances from the IOS element m to theBS and to the MU, respectively. g m ( ξ Ak ( m ) , ξ D ( m ) , s m ) is the power gain of the signal towardthe MU via IOS element m , which is given in (1). The NLoS component of h m can be writtenas h NLoSm = P L ( d BS,m ) P L ( d m,MU ) h SS , (7)where P L ( · ) is the channel gain for the NLoS component, and h SS ∼ CN (0 , denotes thesmall-scale NLoS component.In summary, the channel gain from the BS to the MU can be written as h = M X m =1 h m + h D , (8)where the first term represents the superposition of the transmissive-reflective channel of the M IOS elements, and the second term is the direct path.
C. Spectral Efficiency with IOS Phase Shift Design
In this part, we introduce the IOS phase shift design, with which the power of the signalreceived by the MU can be improved significantly. According to (8), the received signal at theMU can be expressed as z = M X m =1 h m x + h D x + n, (9)where n is the additive white Gaussian noise (AWGN) at the MU with zero mean and σ as thevariance, and x denotes the transmitted signal with | x | = 1 .The downlink SE of the MU can be defined as the data rate in bits per second per Hz, whichis given as R = log (cid:18) P | h | σ (cid:19) , (10)where P is the transmission power of the BS, which is given as a constant in this paper. D. Problem Formulation
In this part, we formulate an IOS phase shift design problem to maximize the average downlinkSE of the system. As shown in (6) and (10), the SE of the MU is determined by its locationand the phase shift of the IOS s . Given the MU location l , the signal-to-noise ratio at the MUscan be added instructively with proper IOS phase shift design, and the SE can be improved. In IOS IRS (a) x (m) y ( m ) y ( m ) (b) x (m) Signal from BS
Signal from BSHigh SE on both sides of the IOS
High SE on left side of the
IRS
Low SE on right side of the IRS
Spectral efficiency (bit/sec/Hz) Spectral efficiency (bit/sec/Hz)
Fig. 4. Simulation for maximum SE. (a) IOS system. (b) IRS system. the following, we aim to maximize the SE of the MU randomly distributed in the range of L by optimizing the phase shift of IOS s , and then the problem can be formulated as max s R, ∀ l ∈ L , (11a) s.t. s m ∈ S a , m = 1 , , · · · M. (11b)Constraint (11b) is the feasible set for the phase shifts of each IOS element.IV. IOS P HASE S HIFT D ESIGN
In this section, we first relax the variable in problem (11) and discuss the SE maximizationproblem with continuous IOS phase shifts, and then propose a branch-and-bound based algorithmto design the IOS phase shift in finite set S a . A. Continuous IOS Phase Shift Design
As shown in (4), the channel of the direct path is not affected by the phase shift of the IOS,and thus we only need to optimize the SE of the BS-IOS-MU link. Moreover, the BS-IOS-MUlink is modeled as a Racian channel given in (5), whose NLoS component is not affected bythe phase shift of the IOS. Therefore, problem (11) can be simplified as maximizing the SE ofthe LoS component of the BS-IOS-MU link, which is shown as max s log P | P Mm =1 h LoSm + h D | σ ! , ∀ l ∈ L , (12a) s.t. s m ∈ S a , m = 1 , , · · · M. (12b)Problem (12) is an integer optimization problem, which cannot be solved by the optimizationmethods for continuous variables. In the following, we first solve the problem with s being relaxed to a continuous variable, and then we propose a branch-and-bound based algorithm todesign the discrete phase shift for each IOS element. Proposition 1:
When the power ratio of the departure signal to the arrival signal γ m isconsidered as a constant, the optimal phase shift of each element satisfies ψ m = 2 πλ ( d BS,MU − d BS,m − d m,MU ) , m = 1 , · · · , M. (13) Proof.
See Appendix A.
B. Finite IOS Phase Shift Design
The optimal solution proposed in Proposition 1 cannot be obtained by the IOS elements with afinite set of phase shift S a . For IOS element m , we denote its optimal phase shift by ψ optm . For IOSelement m , its phase solution to problem (11) is one of the two consecutive phase shifts of s m and s m +1 , which satisfies ψ m ≤ ψ optm ≤ ψ m +1 . In the following, we propose a branch-and-boundbased algorithm to solve the IOS phase shift design in the finite set S a efficiently.The solution space of IOS phase shift s can be considered as a binary tree structure. Eachnode of the tree contains the phase shift of all the IOS elements, i.e., s = ( s , . . . , s M ) . Atthe root node, all the variables in s are unfixed. The value of an unfixed variable at a fathernode can be either s m or s m +1 , which branches the node into two child nodes. The objective ofthe proposed algorithm is to search the tree for the optimal solution of problem (11) with thefollowing three steps. Step 1: Initialization.
We first set a random IOS phase shift, and the corresponding SE isgiven as the lower bound of the solution.
Step 2: Bound Calculation.
We then start to search the optimal solution from the root node.On each node we first evaluate the upper bound of the objective function with variable relaxation,and the upper bound can be calculated with the phase shift solution proposed in Proposition 1.
Step 3: Variable Fixation.
In this step, we prune the branches whose upper bounds arebelow the value of the current solution. When a solution that outperforms the current solutionis found, we replace the current solution with the new one, and continue the branch-and-boundalgorithm. The phase shifts of an element is fixed when only one feasible value satisfies thebound requirements.The algorithm terminates when all the element phase shifts are fixed, and the correspond-ing current solution is the final solution of problem (11). The proposed algorithm that solvesproblem (11) is summarized as Algorithm 1. Algorithm 1:
IOS Phase Shift Design Algorithm. Initialization:
Compute an initial solution s to problem (12) and set the SE as the lowerbound R lb While
Not all nodes are visited or pruned Calculate the upper bound of the current node R ub If R ub < R lb : Prune this branch If Variable s m is fixed: Go to the node with s m Else
Generate two new nodes by setting an unfixed variable at s m and s m +1 Go to a node that has not been visited or pruned If The current node has a corresponding SE R curr : If R curr > R lb : R lb = R curr Output: s ; V. S IMULATION R ESULTS
In this section, we evaluate the performance of the IOS assisted system with the proposedalgorithm in an indoor environment, and compare it with the IRS assisted system as proposedin [12], [13] and the conventional cellular system. In the IRS assisted system, the IRS onlyreflects the signals from the BS to the MU, and no transmissive signal is considered. In theconventional cellular system, we only consider the direct link from the BS to the MU. In oursimulation, we set the height of the BS and the center of the IOS as 2 m, and the distancebetween the BS and the IOS being 500 m. The MU is randomly deployed within a circle ofradius 2 m centering at the IRS, and the results present below are the average performance ofover 10000 instances of the Monte Carlo simulation. The maximum transmit power of the BS P B is 40 dBm, the power of the AWGN is -96 dBm, and the IOS element separation is 0.03 m.The power ratio of the transmissive signal to the reflective signal ǫ is set as 1, the number ofphase shifts for each IOS element is set as S a = 4 .Fig. 4 shows the maximum SE of the MU on different locations, with the BS on the left sideof the surface. An IOS/IRS with the length of 4 m and the height of 0.6 m is deployed at theline segment ((0,-2),(0,2)), and the BS is deployed at (-500,0). In the IOS system, the SE oneither side of the surface can be improved. A higher SE can be obtained when the MU is closerto the center of the IOS, where the reflective-transmissive channel has a better quality. In the Size of IOS ( M)
10 20 30 40 50 60 70 80 S pe c t r a l E ff i c i en cy ( b i t/ s / H z ) Fig. 5. Size of IOS vs. SE.
IRS system, the MU has a high SE only when it is on the left side of the surface.Fig. 5 depicts the relation between the average SE of the MU and the size of the IOS. Theaverage SE is defined as the expectation of SE R with the random distribution of the MU. TheIOS is considered as a square array with √ M elements on each line and each row. The SEincreases with the number of IOS elements, and the growth rate gradually slows down with theIOS size. An IOS with × elements improves the average SE for about 20 times whencompared to the conventional cellular system, while an IRS of the same size only improves theaverage SE for about 12 times. The performance difference between the two systems is causedby the service coverage. The IOS can improve the average SE of the MU on either side of thesurface, while the IRS can only improve that of the MU on one side.VI. C ONCLUSIONS
In this paper, we have studied an IOS-assisted downlink system. The IOS is capable to enhancethe received signal of the MU on either side of it with IOS phase shift design. We have formulatedan IOS phase shift design problem to maximize the SE of the system. The optimal phase shiftsof the IOS elements have been solved, and an algorithm that designs the IOS phase shift in thefinite set has been proposed. Simulation results have shown that the IOS significantly extends theservice coverage of the BS when compared to the IRS. An IOS with a larger size can providea higher SE for the MU, while the growth rate reduces with more IOS elements. A PPENDIX AP ROOF OF P ROPOSITION max s E (cid:0) | h | (cid:1) ,s.t. ≤ ψ m < π, m = 1 , , · · · M. (14)We then substitute (4) and (5) into (8). Given that h NLoSm is zero mean and is independent fordifferent elements, (14) can be converted to E ( | h | ) = P Mm =1 (cid:16) κ κ A exp (cid:16) − j π ( d BS,m + d m,MU ) λ (cid:17) exp ( − jψ m ) + κ P L ( d BS,m ) P L ( d m,MU ))+ κ κ P L
LoS exp (cid:16) − j π ( d BS,MU ) λ (cid:17) + κ P L ( d BS,MU ) , where A = λ √ G tx F txm G rx F rx × √ G m K A ( m ) K D ( m ) δ x δ y | γ m | (4 π ) d BS,m d m,MU is not affected by the phase shift of the IOS. P L
LoS is the LoS pathloss of the direct link, and
P L ( d BS,MU ) is the NLoS pathloss of the direct link, which are also not affected by the phase shiftof the IOS. To maximize (14), the phase shift term of each element exp (cid:16) − j (2 π ( d BS,m + d m,MU )+ ψ m ) λ (cid:17) should be consistent with the direct path, i.e., ψ m + π ( d BS,m + d m,MU ) λ = π ( d BS,MU ) λ . Therefore, theoptimal solution of element m satisfies ψ m = 2 πλ ( d BS,MU − d BS,m − d m,MU ) . (15)R EFERENCES [1] M. Renzo, M. Debbah, D. Phan-Huy, A. Zappone, M. Alouini, C. Yuen, V. Sciancalepore, G. C. Alexandropoulos, J. Hoydis,H. Gacanin, J. Rosny, A. Bounceur, G. Lerosey, and M. Fink, “Smart Radio Environments Empowered by ReconfigurableAI Meta-surfaces: An Idea Whose Time Has Come,”
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