Ranking Based Beam Training for XLRIS

Ranking Based Beam Training for XLRIS Ahmed M. Nor Electrical Engineering Department Aswan University Aswan, Egypt [email protected] Department of Electrical Engineering Pontifical Catholic University of Rio de Janeiro Rio de Janeiro, Brazil Seyed Salar Sefati Telecommunications Department National University of Science and Technology POLITEHNICA Bucharest Bucharest, Romania [email protected] Abdelrhman Y. Soliman Electrical Engineering Department Aswan University Aswan, Egypt [email protected] Abstract—Extremely large-scale reconfigurable intelligent surface (XLRIS) is pivotal for 6G millimeter wave and terahertz networks, enhancing performance and coverage by creating alternative links between the base station and the user equipment (UE). However, their passive nature and near-field (NF) propagation characteristics resulting from large XLRIS aperture size make passive beamforming (PBF) a complex process. Traditional beam training (BT) methods, e.g., exhaustive search (EX) based NF codebooks (NFCB), incurs high overhead and complexity. Multistages approaches risk outage and misalignment, meanwhile position-based codebooks require frequent and complex redesigns in multi-user or mobile scenarios, limiting their practicality. To overcome these challenges, this paper proposes a novel rankingbased beam training (RBT) approach. By leveraging available UE position information, the RBT scheme intelligently ranks all codewords in the conventional NFCB based on their similarity to the UE’s location. Then, instead of a long EX, the system only tests the top Ncranked candidates’ beams, dramatically reducing training space and required power for BT. Numerical results demonstrate the practicality and the efficiency of the RBT which obtains close performance to the optimal EX based NFCB approach with significant reduction in the overhead. Index Terms—Extremely large-scale RIS, near-field communication, beam training, ranking-based BT, 6G networks. I. INTRODUCTION 6G networks are rapidly progressing depending on the promising technology of reconfigurable intelligent surface (RIS) [1], [2]. More, specifically, the extremely large-scale version of RISs, which is called XLRIS [1], [3], is widely employed as electromagnetic wave reflecting surface in outdoor and urban scenarios, where it is deployed in buildings fronts. These XLRIS consists of massive number of adjustable passive elements to preserve energy consumption. By configuring the XLRIS elements’ amplitude and phase, in what is called passive beamforming (PBF) [2], [4], the incident signal on XLRIS can be redirected to another direction, where targeted user equipments (UEs) exist. This characteristic is utilized to provide alternative line of sight (LOS) link when the main LOS path between the base station (BS) and the UE is blocked due to different type of obstacles, i.e., when blockage phenomenon occurs [1], [2], [5]. Moreover, it serves as a helpful link, if This work is supported by FAPESP, MCTIC, and CGI in Brazil, under project no. 2023/00579-0. the main LOS link exists. Employing XLRIS significantly improves system performance such as data rate, coverage, readability and energy efficiency particularly in challenging environments in 6G networks [1], [4]. However, due to XLRIS passive nature, the PBF task is highly complicated as the elements cannot be used for exchanging control signal, hence the BS-XLRIS and XLRISUE channels cannot directly be estimated [1]. Moreover, with massive number of XLRISs elements, estimating the full channels needs long delay, high complexity and overhead. Utilizing codebooks (CBs) based PBF approaches have been recently adopted to relax complexity and reduce overhead, and simultaneously overcome the limitation of estimating the full channel [2], [4]. Nevertheless, XLRIS has a special structure which makes the physical aperture grows and increases the Rayleigh distance. Hence, the electromagnetic wave propagates in the near-field (NF) region making far-field based CBs inefficient for passive beamforming [3]. The authors in [3] proposed conventional near-field codebook (NFCB) then suggested exhaustive search (EX) for beam training (BT) for XLRIS. But, due to high overhead and complexity, they further developed NF based hierarchical based codebook (NFHCB) approach for PBF, where BT is done in two phases. In [6], the authors proposed NF rainbow based BT approach benefiting from the spatial features in wideband signals. The authors in [7], [8], [9], [10] developed different two-phases hierarchical and multi-BT schemes to relax full traditional NFCB complexity. Though lower overhead and delay reduction, HCB and multi-stages based approaches suffer outage and misalignment issues, mainly if the first stage fails to detect a promising codeword and sequentially the following stages will be ineffective, also they still requires high overhead. The authors in [11] proposed positioning based CB (PCB) for XLRIS PBF. However, this PCB needs to be frequently reconstructed to handle mobility and multiuser scenarios. Moreover, the system shall redesign this PCB at each new frame based on associated UEs positions. Hence, this PCB needs additional system complexity even if the PCB size is small which makes PCB [11] in inefficient solution. In this paper, to existing BT schemes’ limitations, we propose a ranking based beam training (RBT) approach to UE y x XLRIS Reflected link 𝐡r BS-XLRIS link Blocked link G BS UEs plane Fig. 1: XLRIS aided downlink communication systems. significantly reduce the beam training overhead by leveraging user equipment (UE) position information. In RBT approach, instead of exhaustively testing all possible NFCB codewords, the system first retrieves the UE’s position, then calculates distances’ vector between this UE position and the prestored positions associated with each beam codeword in the conventional codebook. The algorithm ranks all codewords based on these calculated distances and shrinks the searching space to only top Ncpromising candidates beams to identify the best beam for transmission. The RBT reaches near optimal achievable rate performance with lower overhead than other BT solutions, where RBT needs only Ncbeams for BT. Hence, the RBT scheme is a practical solution for reducing BT time and power consumption without compromising performance. The paper is organized as: Section II and III presents system and channel model, and NFCB design and training steps. The proposed RBT is demonstrated in Section IV. Section V and VI present the numerical results and conclusion of the paper. II. SYSTEM AND CHANNEL MODEL In this work, as shown in Figure 1, we consider an XLRIS aided downlink system where a fixed base station (BS) equipped with Mantennas serves a single-antenna UE via the assistant of XLRIS, as the direct BS-UE link is fully blocked. The XLARIS is a planar surface consist of N=Nx×Ny passive elements and is centered at the origin. Let G∈CN×Mand h∈C1×Ndenote the BS-XLRIS and XLRIS-UE channels, respectively. The XLRIS is a diagonal RIS, hence the XLRIS phase shift matrix Θ= diag(θ), where θ= [θ1, θ2, . . . , θN]Tis the XLRIS PBF vector and θn= γnejϕn, here the nth element amplitude is γn∈[0,1] and phase is ϕn∈[0,2π). The BS active beamforming vector is v∈CM×1and the transmitted symbol to the UE is s. Thus, the received signal at the UE can be presented as r=h Θ G v s+zn,(1) where zn∼ CN (0, σ2)is complex Gaussian noise. As a result of fixed BS and XLRIS locations, active beamforming, i.e., configuring v, is assumed to be done [2], [4]. Hence, the focus is conducting the PBF training process to align the reflected XLRIS beam with the main path between the XLRIS and UE. A. Near-Field Channel Model The Rayleigh distance in RIS-aided systems is Z=2D2 RIS λ, where DRIS refers to the RIS aperture and λdenotes the signal wavelength. The XLRIS has a large aperture DRIS enlarging the Rayleigh distance and makes the reflected signal by XLRIS pointing to the near-field region instead of far-field region [3], [12] . Hence, the spherical wave model shall be adopted. The nth XLRIS element coordinate is (xnx, yny,0), where xnx=nx−Nx+1 2dRand yny=ny−Ny+1 2dR, where dRis elements spacing, nx= 1, ..., Nxand ny= 1, ..., Ny. Noting that all coordinates are normalized by the wavelength. Let (xr, yr, zr)denotes the coordinate corresponding to the main XLRIS-UE path scatter, hence the XLRIS-UE channel in the near-field can be expressed as hr NF =αrcT(xr, yr, zr),(2) where αris the XLRIS-UE path gain and c(xr, yr, zr)is the array steering vector which presented as c(xr, yr, zr) = he−j2πDr(1,1), . . . , e−j2πDr(Nx,Ny)iT ,(3) in which Dr(nx, ny) = p(xr−xnx)2+ (yr−yny)2+z2 r. Similarly, let (xG, yG, zG)denotes the coordinate corresponding to the main BS-XLRIS path scatter, hence the BSXLRIS channel in the NF can be expressed as hG NF =αGcT(xG, yG, zG),(4) where αGis the BS-XLRIS path gain, meanwhile the array steering vector c(xG, yG, zG) = he−j2πDr(1,1), . . . , e−j2πDr(Nx,Ny)iT , where DG(nx, ny) = p(xG−xnx)2+ (yG−ynx)2+z2 G. Hence, the effective cascaded BS-XLRIS-UE channel can be expressed as ¯ hNF =αr.αG.¯ c(xG, yG, zG),(xr, yr, zr),(5) where ¯ c(xG, yG, zG),(xr, yr, zr)=he−j2πD(1,1),..., (6) e−j2πD(1,Ny), . . . , e−j2πD(Nx,1), . . . , e−j2πD(Nx,Ny)iT , in which D(nx, ny) = DG(nx, ny) + Dr(nx, ny). Note that the selected optimal beam, if EX is employed for NFCB, depends on the scatters corresponding to the UE. Hence, imagine that the UE exact position is known, i.e., the scattering point (xr, yr, zr)is known, hence the BT process will not be needed, however that cannot be obtained. III. CONVENTIONAL NFCB DESIGN AND BEAM TRAINING In this section, we briefly present the NFCB design steps and beam training method that are proposed in [3], as this traditional CB is the base for our proposed RBT approach. In the conventional NFCB for XLRIS, the entire considered three-dimensional (3D) space, i.e., the environment space covered by the XLRIS, is divided into several sampled points in the x-y-zcoordinate system considering sampling step ∆. The NF cascaded array steering vector ¯ cof the NF cascaded channel ¯ hNF is determined by the sum of the distance from (xG, yG, zG)to the XLRIS and the distance from (xr, yr, zr) to the XLRIS, hence each codeword for XLRIS is related to these pair of sampled points in the x-y-zcoordinate system. Let Prrefers to the collection of the sampled points corresponding to (xr, yr, zr), and can be presented as Pr=     (xr s, yr s, zr s)       xr s=Xr min, Xr min + ∆xr, . . . , Xr max; yr s=Yr min, Y r min + ∆yr, . . . , Y r max; zr s=Zr min, Zr min + ∆zr, . . . , Zr max      (7) where ∆xr,∆yr, and ∆zrare the NFCB sampling step on the x-, y-, and z-axes for Pr, respectively. Using any sampled point (xr s, yr s, zr s)alongside BS scattering point (xG, yG, zG), the effective sampled distance between the two scattering points Ds(nx, ny)is expressed similar to D(nx, ny). Using Ds(nx, ny), the sampled steering vector ¯ csis computed as in (6), then the NFCB Fis constructed as F= [F,¯ cs]after passing through all possible scattering combinations without repetition. The work in [3] discussed NFCB design in details. For BT, the system search along all Fcodewords, then receiving feedback from UE indicating the received signal strength obtained from each codeword, thereafter it selects the optimal beam achieving the the highest signal strength. The NFCB contains Fcodewords, where each fcodeword has corresponding positioning record for the sampled point p[f]=(xr s, yr s, zr s), that are used for constructing this codeword. The NFCB is large as the sampling points are huge due to the network coverage, causing high searching overhead and long delay. Thus, to reduce this, we propose a lower overhead ranking based beam training approach in the next section. IV. PROPOSED RANKING BASED BT APPROACH In the proposed RBT, the system ranks the NFCB codewords corresponding to the targeted UE position to determine the best beam for serving a certain UE by . To do so, the system retrieve the UE position u= (xu, yu, zu). Then, it computes the metric or similarity based distances vector d= [d[1], d[2], ..., d[F]] between the UE position vector uand the vector of each codeword positioning record, i.e., p[f],∀f∈F, that are used for building the NFCB considering ∆ = 10. Note that the UE position is obtained using available Wi-Fi signal, which has accuracy error of 2.5 m [13]. Thereafter, the system ranks the codewords based on their calculated distances and searches only on the first Nccodewords to determine the best codeword to be used for the UE in the transmission period. Nc, which is the number of searching beams in RBT approach, is a design parameter that depends on the trade-off between the required performance and acceptable overhead. As we will show in the numerical result section, Ncis small comparable to NFCB size, which highly reduces the training overhead. Several metric or similarity distances are used to rank the NFCB codewords, in this work, we use Euclidean, Cosine, Correlation, Hamming, and Chebyshev distances, then, we study the RBT performance when using each distance. In the following, we present the equations used for computing d[f]using each distance. The metric distances, i.e, Euclidean Algorithm 1 Proposed Ranking based Beam Training 1: Input: u,p[f],∀f∈F, and Nc. 2: Output: Selected best codeword f∗ 3: Initialize distance vector d=0. 4: for f= 1 →Fdo 5: Compute the distance d[f](u,p[f]) according to the utilized distance using (8), (9), (10), (11) or (12). 6: Append d[f]to d. 7: end for 8: Rank Fcodewords according to ascending order of d[f]. 9: Select top Nccodewords for candidate search. 10: Search the Nccandidates to find out the best codeword f∗that achieves the highest received power. distance dEuc[f], Hamming distance dHam[f]and Chebyshev distance dChev[f]can be expressed, respectively, as dEuc[f](u,p[f]) = p(xu−xr s)2+ (yu−yr s)2+ (zu−zr s)2,(8) dHam[f](u,p[f]) = 1 31{xu=xr s}+1{yu=yr s}+1{zu=zr s},(9) dChev[f](u,p[f]) = max n|xu−xr s|,|yu−yr s|,|zu−zr s|o.(10) The similarity distances, i.e., Cosine distance dCos[f]and Correlation distance dCorr[f]are expressed, respectively, as dCos[f](u,p[f]) = 1 −xuxr s+yuyr s+zuzr s px2 u+y2 u+z2 up(xr s)2+ (yr s)2+ (zr s)2, (11) dCorr[f](u,p[f]) = 1 −P3 i=1(ui−¯u)(pi−¯p) qP3 i=1(ui−¯u)2qP3 i=1(pi−¯p)2 . (12) where ¯uand ¯pare the means of uand p[f], respectively. Algorithm 1 summarizes the proposed RBT approach steps. The computational complexity of the proposed algorithm is mainly dominated by computing distances which requires O(3F)time and ranking the Fdistances that needs O(Flog F)time. The search among the top Nccandidates adds O(Nc)considering constant-time for received power evaluation. Therefore, the overall complexity is O(3F+Flog F+Nc), with an additional memory cost of O(F)for storing the distance vector. The computational complexity and memory storage are law comparable to the benefits obtained by employing the proposed RBT scheme as we will further clarify. V. NUMERICAL RESULTS In this section, we provide numerical results to present the proposed RBT approach performance comparable to the conventional NFCB beam training and the optimal channel state information (CSI) based beamforming schemes, though it is impractical to be applied due to XLRIS size. In the simulations, system parameters are M= 64 and N=Nx×Ny= 128 ×4 = 512. The path gains are modeled as αG∼ CN (0,1) and αr∼ CN (0,1). The adjacent XLRIS elements space dR= 1/2[12]. The BS is fixed at (- 50,0,-10) and XLRIS is at (0,0,0) in x-y-z coordinates system, 5 10 15 20 25 30 35 40 45 50 16 16.5 17 17.5 18 Number of candidate beams Nc Achievable rate in (bits/s/Hz) CSI NFCB NFHCB Euclidian-RBT Manhattan-RBT Chebyshev-RBT Cosine-RBT Correlation-RBT (a) −5 0 5 10 13 14 15 16 17 18 19 20 SNR Achievable rate in (bits/s/Hz) CSI NFCB NFHCB Euclidian-RBT Manhattan-RBT Chebyshev-RBT Cosine-RBT Correlation-RBT (b) 10 15 20 25 30 35 40 45 50 101 102 103 Sampling step ∆ Number of beams NFCB NFHCB RBT (c) Fig. 2: (a) Achievable rates against different number of candidate beams when SNR = 5 dB and ∆ = 10, (b) achievable rate versus SNR considering Nc= 10, and (c) beam training overhead versus sampling step ∆. meanwhile the UE is assumed to be located within a 3D region bounded by [0,200],[−25,25], and [−25,−5].s= 1 and v=f∗/M, thus, the effective transmitted symbol becomes ¯s= 1. The signal-to-noise ratio (SNR) is defined as 1/σ2. Figure 2a presents the achievable rate of RBT approaches versus number of candidate beams and comparable to benchmark CSI, NFCB and NFHCB based approaches, considering SNR = 5dB and ∆ = 10. Figure 2a shows that the proposed RBT approach, considering Euclidean, Manhattan and Chebyshev distances, can obtain nearly the same achievable rate as the traditional NFCB based approach with much less number of candidate beams, Ncalmost 20, where Euclidean based RBT approach is leading other distances based RBT schemes. Moreover, it needs only 10 candidate beams to overcome the NFHCB based scheme achievable rate. Noting that similarity based RBT approaches require higher overhead to approach the same performance as distances based RBT schemes. In the following, we consider the RBT approaches with Nc= 10. Figure 2b presents the achievable rate of the proposed RBT approaches comparable to CSI, NFCB and NFHCB based approaches considering different SNR values. It is clear that Euclidean based RBT approach is leading over other RBT schemes and NFHCB based scheme and its performance is close to conventional NFCB based approach. Finally, Figure 2c discusses the training overhead in terms of the number of searching beams for the proposed RBT approaches comparable to NFCB and NFHCB based approaches versus sampling steps. The proposed RBT approach requires only 10 candidate beams, which is nearly 4% of the overhead required for NFCB in case of ∆ = 10, and is less than the required beams for other approaches even if lower sampling step is considered. For example, the number of searching beams for the NFCB based approach with ∆ = 25 is 10-times of the required RBT candidate beams. VI. CONCLUSION This paper has introduced a novel ranking-based beam training (RBT) approach that effectively addresses the critical challenge of BT overhead in XLRIS systems. 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