An Electromagnetic Framework for the Deployment of Reconfigurable Intelligent Surfaces to Control Massive MIMO Channel Characteristics
AAn Electromagnetic Framework for the Deployment ofReconfigurable Intelligent Surfaces to Control Massive MIMOChannel Characteristics
Debdeep Sarkar, Said Mikki and Yahia AntarNovember 2019
Abstract
In this paper, we deploy a full-wave FDTD paradigm to investigate the effect of reconfig-urable intelligent surface (RIS) – switchable frequency-selective surfaces (FSS) – on genericmassive MIMO uplink channel’s eigenspace structure. We place an RIS based on two switch-able FSS layers in the vicinity of a 64-element massive MIMO base-station (BS) array, servinga cluster of four fixed user equipment (UE) units. Utilizing an electromagnetic tool basedon time-averaged Poynting flow developed recently by the authors, we demonstrate how theillumination of BS-array aperture can be controlled by the intentional deployment of variousswitching states in the RIS placed near the BS. We show that such supplementary RIS struc-tures may assist the wireless link engineer in deterministically “customizing” the uplink channelbehaviour by selectively enhancing/suppressing certain channel eigenvalues.
Massive MIMO (multiple-input multiple-output) systems have demonstrated promising perfor-mance in terms of spectral, energy and hardware efficiency, which has established it as one of thekey underlying technologies for the sub-6 GHz and mm-wave wireless networks (5G/6G) of futuregeneration [1]-[3]. Currently active research on massive MIMO technology is seeing the emergenceof futuristic concepts like “extremely large aperture arrays” (ELAAs), “cell-free massive MIMO”and “large intelligent surface” (LIS), pushing the engineers to look into the spatial correlation andchannel-modelling aspects from an advanced electromagnetic perspective [4]-[5]. Traditionally, re-searches on massive MIMO channel modelling have been either experimental/empirical [6]-[8], orbased on simplified assumptions like simplified uncorrelated Rayleigh fading models or ray-tracingtracing approach. With a large number of antennas being accommodated both in the base-stations Debdeep Sarkar (Corresponding Author) and Yahia Antar are with the Royal Military College, PO Box 17000,Station Forces Kingston, Ontario, K7K 7B4, Canada (Emails: [email protected] ; [email protected]). Said Mikki is with University of New Haven, West Haven, Connecticut, 300 Boston Post Rd, 06516, USA (Email:[email protected]). c (cid:13) a r X i v : . [ phy s i c s . a pp - ph ] N ov BS) as well as user-equipments (UEs), it has become crucial for correlation analysis/channel-modelling to extract the complete electromagnetic (EM) knowledge by incorporating effects of theimpinging spherical wave-fronts of near-field illumination, port-to-port mutual coupling as well asrelative BS-element polarization [9]. The problem of far-field spatial correlation analysis in MIMOsystems having multiple interacting elements with arbitrary relative pattern and polarization, canbe analytically handled by utilizing infinitesimal dipole models (IDMs) in conjunction with “cross-correlation Green’s functions” (CGFs) [10]-[13]. However, it is important to utilize full-wave EMsimulation techniques like the finite-difference time-domain (FDTD) method in channel-modelling,in order to properly account for the port-to-port mutual coupling, spherical wave-front illuminationand near-field correlation scenarios [14]-[19].Figure 1: Vision for “wireless 2.0” [20]-[25]: Schematic diagram showing use of reconfigurableintelligent surfaces (RISs) in conjunction with massive MIMO base-station (BS) arrays servinga dense cluster of user-equipments (UEs) in a “smart-radio” environment. The massive MIMOconfiguration is a uniform rectangular array (URA) of M = M V M H elements, with respectiveinter-element spacings d H and d V along y and z directions [13].At this juncture, it is interesting to note that the so-called “massive MIMO 2.0” for smartwireless environments envisions the application of switchable/tunable frequency selective surfaces(FSSs), often termed as “reconfigurable intelligent surface (RIS)”, as an alternative to active relays[4]-[5], [20]-[25]. Such RIS is typically based on periodically arranged low-cost scatterers/reflectors This is conceptually similar to classic reflectarrays [26], or the idea of coding meta-surfaces [27]. passive
FSS, but do not demonstrate the channel eigenspace manipulation via reconfigurability/switchability in the FSS. Therefore in this paper, we first determine the channel matrix for the UE-to-BS massiveMIMO uplink ( H = H uplink ) following the FDTD-based EM-approach of [28], and consequentlystudy the impact of RIS on the eigan-value distribution of the Gram matrix G = H H H . We consider FDTD framework based on Cartesian coordinate system with cubical spatial grids(∆ x = ∆ y = ∆ z = ∆ = 12 mm) and time-step ∆ t = 18 . × × x, y and z directions.Fig. 2 demonstrates the FDTD simulation paradigm for the complete system under considera-tion, having: (i) massive MIMO BS-antenna array of M = 64 elements ( M V = M H = 8, d V = 8∆and d H = 3∆, see Fig. 1) along yz -plane, (ii) assembly of N = 4 UE antennas along y -axis withuniform spacing of 5∆, and (iii) RIS consisting of two FSS layers along the xz -plane. The BSantenna elements are reflector-backed short-dipoles having end-fire directional patterns, while theUE antennas are short-dipoles with omni-directional radiation, both having the same polarization(along z -direction, see Fig. 2). Both the UE antenna and the BS-exciter elements are modelled bythree infinitesimal dipoles (IDs) [28], while the reflector for the BS-element consists of five IDs (Fig.2). The UE-assembly along xy -plane is kept at z = z −
20∆ (slightly offset downward), where z = 85∆ lies in the mid-way of the computational volume (see Fig. 2).Note that we deal with the UE-to-BS uplink channel H = H uplink for the time-being, implyingthat the BS-array operates in the receiving mode, i.e. all the exciter dipoles are maintained atmatched load termination [28]. The UEs are excited by a modulated Gaussian pulse v in ( t ) via theirDelta feed-gap: v in ( t ) = exp (cid:20) − ( t − t ) σ (cid:21) sin (2 πf t ) , (1)where modulating signal frequency f is 2.5 GHz, with parameters t = 70∆ t and σ = 15∆ t .When one UE is excited, the others are terminated by matched load. To make the transient effectsdie down completely, the FDTD time-marching simulation is run for T max = 400∆ t . Note that, thedistance d along x -axis between the UE-assembly and the massive MIMO BS-array is chosen at70∆ = 7 λ , where λ = c/f and c is the speed of EM wave in free-space.3igure 2: Full-wave FDTD simulation setup comprising of: (i) 64-element massive MIMO BS-arrayconsisting of directional elements (reflector-backed short dipoles), (ii) an assembly of 4 UEs havingomni-directional elements (short dipoles) and (iii) an RIS with two FSS layers. The zoomed viewsrepresent the infinitesimal dipole model (IDM) representation of UE and BS antenna elements. Theparameters d = 70∆ and d = 18∆, where ∆ is the cubical FDTD grid-size.Figure 3: (a) Normalized | S avg | distribution (see (2)) along xy -plane ( z = z center − G = H H H , where H is the complete FDTD-computed channelmatrix for the reference system without RIS. 4o visualize the EM-wave propagation from the UEs to the illuminated massive MIMO BS-arrays, we plot the 2D profiles of time-averaged Poynting vector magnitude | S avg | given by: S avg = S avg ( r ) = 1 T max (cid:90) T max S ( r , t ) dt, (2)where the Poynting vector S = S ( r , t ) = E ( r , t ) × H ( r , t ) is computed via standard grid-interpolationtechniques using local electric and magnetic fields (i.e. E ( r , t ) and H ( r , t )) generated by FDTDsimulations [28]. Fig. 3(a) shows the normalized | S avg | -distribution along the xy -plane ( z = z center − v in ( t ), in the system of Fig. 2 without considering any RIS.Now to compute the frequency-domain M × N channel matrix H at f , we first excite theUE antenna- j (where j = 1 , , . . . , N ), then record the channel response signals h ij ( t ) at the BSantenna- i (where i = 1 , , . . . , M ), and finally Fourier transform the temporal signals h ij ( t ). Fig.3(b) shows the eigenspace of the resulting N × N Gram-matrix G = H H H (superscript H indicatesHermitian) for the UE-array to-BS uplink without any RIS. Fig. 3(b) confirms that there are N = 4dominant eigen-channels and the corresponding eigenvalues are gradually decreasing in order.Figure 4: (a) Possible practical implementation scheme for the switchable FSS-layers constitutingthe RIS structure of Fig. 2. (b) Four switching states of the FSS layers, which can be realized byuse of PIN diodes and suitable biasing mechanism. In the FDTD code, we use connected wires forswitch ON, and disconnected wires for switch OFF, for EM simulation purpose. The RIS as shown in Fig. 2 is typically mounted in a wall to provide additional paths to the UE-emitted signal for illuminating the BS massive MIMO array aperture. In our analysis we consider5he RIS two be consisting of two FSS layers, each consisting of z -directed thin PEC-wires havingperiodicity 2∆ along x -direction. The location of RIS relative to the UE-assembly and BS-arrayis specified by the parameters d and d (see Fig. 2). To realize the reconfigurability practically ,we need to load the wires with PIN diodes and control their ON-OFF condition by proper biasingcircuitry (as depicted in the possible schematic of Fig. 4(a)).Figure 5: Using UE-4 as the excited element, normalized | S avg | distribution along xy -plane ( z = z center − V and V . Two important points mustbe mentioned here: (i) many other states apart from the ones (1 to 4, as shown in Fig. 4(b))can be realized, but are not taken up for this particular work, (ii) in the FDTD simulations, wesimply use the EM-aspects only and emulate the ON- and OFF-states of the switches as connectedand disconnected PEC wires respectively. For our analysis, we choose FSS-2 in Fig. 2 in a fixedstate-1 (see Fig. 4), while vary the FSS-1 in four states 1 to 4, and re-compute the M × N channelmatrix H for all scenarios using same method discussed in the previous section. Fig. 5 illustrates One can find discussions on practical realization of such structures by utilizing thin microstrip-lines printed onlow-loss substrates or by capillaries filled with liquid-metal technology (See [29]-[30]). G = H H H (where H is the uplink channel matrix) forthe RIS-based systems (using State-1 to State-4 for FSS layer-1, see Fig. 6), with respect to thereference system (i.e. without RIS).how these various FSS-states leads to different S avg -configurations, and illuminates the BS massiveMIMO-array aperture in different ways. Interestingly, when both FSS-1 and FSS-2 are in State-1of Fig. 4(b), the RIS would behave like a simple PEC wall for the frequency of interest. However,it should be remembered that the presence of a simple PEC wall instead of an RIS provides a fixed reflected beam, while variable FSS switching states in the RIS provide an opportunity to obtaindifferent illumination-profiles of the BS-array for the same UE location.To quantify the effects of RIS we compute eigenvalue difference (similar to [28]), by subtractingthe eigenvalues of G = H H H without the RIS (i.e. reference case, see Fig. 3) from the eigenvaluesof G = H H H with the RIS-wall. It is clearly observed that the lower eigenvalues are enhancedin value for some specific switching configurations and State-3 in our analysis shows the mostpromising effect. Considering a fixed assembly of 4 UEs, the present paper uses a full-wave FDTD simulation approachin uplink channel modelling for an RIS-enabled 64 element massive MIMO BS-array of reflector-backed dipoles. The eigenvalue difference results of Fig. 6 make it evident that the methodologybased on switchable FSS or RIS has immense potential in tailoring/“customizing” the channeleigenspace (i.e. suppressing/enhancing certain eigen-channels), even for a line-of-sight (LOS) typepropagation scenario.Note that, here we consider the UE and BS antenna-elements to beam same z -directed polar-ization, but other possible combinations can be easily explored in the FDTD simulation paradigm.7urthermore, we only consider only a few possible switching states (see Fig. 4) of top FSS-layerin this work. 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