Figure 1 shows the schematic diagram of a simple transmit-receive SISO communication link using two dipoles separated by a distance d. The length of each dipole is chosen as 0.47λ to ensure near-zero input reactance for the dipoles, where λ = c/f ₀, f ₀ = 3.5 GHz (sub-6 GHz 5G range) being the operating frequency chosen for all simulations, and c = 3 × 108 m/s is the speed of light. To modulate the channel properties, an IRS comprising of N × N array of PEC (perfect electric conductor) loop unit-cells is placed at a distance of s from the transmitting dipole (see Figure 1). One key underlying idea behind the use of IRS near the transmitter, is to control the channel propagation characteristics through the properties of the IRS-unit cells, i.e. the circular PEC loops in our case. The resonant frequency and operating modes of the individual PEC loops are controlled by the radius r of each PEC loop, along with the lumped circuit load Z _Load placed on each loop (see Figure 1). The mutual coupling between the loops are controlled by the center-to-center spacing p between the loops. Note that the PEC loops are essentially thin-wire strips, therefore the width of the strips is kept very small (≈0.01λ). Also, the value of p is fixed as 2r + 2 mm, for the subsequent simulations. Now, note that the total input impedance Z _in,L of each loop can be expressed as: Z i n , L = Z i n , U L + Z Load , (1) where Z _in,UL is the loop input-impedance without any lumped circuit loading, that provides an impedance Z _Load in the series. For most simulations we keep: Z Load = I m Z i n , U L * , so that the input impedance Z _in,L of each individual loop bears only resistive component. Later on, we will demonstrate how the Z _Load can be varied to alter Z _in,L , and systematically control the path-loss behaviour. Now, using the MoM-based MATLAB Antenna toolbox it is possible to compute the transmission coefficient S ₂₁ for the two dipole assembly in presence (as well as absence) of IRS, for different values of d and s.

To estimate the impact of the IRS on the path-loss, we define a metric ΔP (in dB) as follows: Δ P = | S 21 with IRS | − | S 21 no IRS | , (2) where | S 21 with IRS | and | S 21 no IRS | respectively represent the |S ₂₁| (in dB), for the presence and absence of the IRS near the transmit (Tx)-dipole. Note that, if the inter-loop spacing p (see Figure 1) is kept unchanged, the physical aperture area of the IRS can be changed in two ways: either by changing the loop-radius r or by increasing the number of unit-cells through the parameter N. In Figure 2, we try to compare the relative impact of r and N on ΔP, by choosing their values such that the overall physical apertures are of the same range. For better visualization, we use two-dimensional (2D) distributions of ΔP (in dB), by varying the distance d between the transmit and receive dipoles from 0 to 10λ, and s from 0 to 4λ (see Figure 2).

While it is possible to change the reflection/scattering from IRS by changing the size (and consequently the resonant operating modes) of the unit cells, it can not be carried out “real-time” (i.e. using external electronic control signals). One key usefulness of IRS lies in the possibility to tailor the reflection/scattering by varying the lumped circuit loading of the individual IRS unit cells. So far we simply used the Z _Load value to cancel out the input reactance of each loops, but now we focus on varying Z _Load of each unit cell, which alters the ΔP (in dB) distribution (see Figure 4). Practically, this variation in Z _Load (both resistance and reactive parts) can be achieved by using circuit components like Varactor diodes, as well as transistor-based voltage controlled resistor elements. Note that, increasing the resistance value of the input impedance, simply implies that the loop is approaching more towards an open circuit termination condition. However, due to limitations in MATLAB Antenna Toolbox, it was not possible to incorporate negative resistance values to realise an short-circuit termination, especially for the loops having r = 0.1λ having a finite input resistance close to 97 Ω. But, it is indeed possible to provide both inductive and capacitive reactive loads, and it can be seen that the path loss behaviour is significantly changed (Figure 4). In our case, the inductive reactance condition of individual loops appear to be causing a greater path loss compensation as compared to the capacitive reactance condition (Figure 4C and Figure 4D).

Next we consider the impact of IRS location with respect to the transmit and receive dipoles, and compute the corresponding ΔP distributions by varying the loop-radius as well as the individual loop loading through Z _Load . A symmetric configuration is considered (see Figure 5), where the IRS is located at same distance from both transmitting and receiving dipole. Increasing r while keeping N same has the similar qualitative effect as that of the previous asymmetric case (i.e. IRS near the transmitter), but the range of values for ΔP has changed (Figure 5B and Figure 5C). Same observation is valid for the scenarios having different load values in the IRS unit cells (see Figure 6). These analyses based on IRS locations emphasize upon the importance of generating such ΔP variation curves for different IRS locations for same Tx-Rx antenna setup, because the channel properties change drastically with it and it is not possible to make a very general statement.

Finally we demonstrate the role of the mutual coupling between the unit cells, in governing the path loss pattern. We consider the 4 × 4 IRS with r = 0.1λ, but consider the IRS placement to be both asymmetric and symmetric, keeping s = 0.5λ for both cases. To make a proper, comparison we first keep the value of |S ₂₁| for p = 2r + 2 mm as reference i.e. | S 21 ref | . We vary the parameter (p − 2r)/λ as well as d/λ, by keeping r and s fixed, and consequently compute the |S ₂₁| values to obtain a factor ΔG (in dB) as: Δ G = | S 21 | − | S 21 ref | (3)

It can be noticed from the ΔG plots that the symmetric arrangement in Figure 7B is more prone to the mutual coupling effects as compared to the asymmetric case of Figure 7A, especially when the IRS is placed close to the transmitter. However, even for the symmetric arrangement, when we consider the IRS to be placed at greater distance 5λ (see Figure 7C), the impact of mutual coupling on the ΔG subsides significantly.

It should be remembered that communication links operating in sub-6 GHz are not sensitive to blockages when compared to mm-wave signals. Therefore, we extend our MoM based simulation approach to analyse SISO links working at 28 GHz. We use half-wavelength dipoles as both transmitter (Tx) and receiver (Rx) separated by distance d, and the IRS is placed at a distance s from the transmitter as shown in Figure 8. The loop radius values are appropriately scaled with respect to λ, so that the IRS operates in the 28 GHz frequency band. Figure 8 demonstrates the path-loss variations with respect to both Tx-Rx and Tx-IRS distances (i.e. s/λ and d/λ).

It can be observed that the qualitative nature of the two-dimensional ΔP distributions are similar to the ones observed for the sub-6 GHz frequency range. Clearly, the variation in path-loss is quite sensitive to the s/λ, i.e. the distance between the Tx and the IRS. The value of ΔP appears to be oscillating between maximum and minimum values (i.e.). Also, the area of the IRS plays a significant role in shaping the path-loss variation, especially for lower Tx-IRS distances. One can say that to achieve a considerable impact on the pathloss variation with smaller IRS unit-cell size, one has to increase the IRS array (see that the 8 × 8 loop-array based IRS with loop-radius 0.1λ gives very prominent effect on ΔP for lower s/λ values.)

Although the dipole antennas are inherently narrowband structures, it is vital to study their interactions over a wide frequency band, instead of concentrating on the single 28 GHz frequency. We first analyse the variation of PL = S ₂₁ of the Tx-Rx system by keeping the separation d at 10λ (Figure 9A), and varying frequency range from 20–40 GHz. As anticipated, the maximum transmission from Tx-to-Rx can be observed near 28 GHz, i.e. dipole impedance match frequency. But overall there is significant wireless power transfer in the 25–30 GHz frequency range (Figure 9B). After that, we place the IRS (8 × 8 array of loops having radius 0.2λ) at a distance 1.5λ away from the Tx. Figure 9B shows that as the IRS size is increased, greater enhancement of ΔP is observed within the entire frequency range 25–30 GHz. Therefore it is once again reaffirmed that IRS size is a critical factor in governing modifying the pathloss characteristics in IRS assisted communication links. Since the operating mechanism of such IRS is quite similar to classical reflectarray antenna systems, it can be intuitively inferred that the IRS aperture area will play a major role in focusing of reflected power at a desired location; since greater aperture area translates into higher gain in reflectarrays, it is natural that ΔP will increase in presence of larger IRS sizes.

Finally, the underlying advantages of using MoM simulation to achieve insights into the finer details of spatial path-loss variation for IRS-assisted Comm-links are demonstrated by comparing with the theoretical bounds provided in Ozdogan et al. (2020). Figure 10A shows the schematic of a SISO Tx-Rx system separated by distance d, with an IRS of area A _IRS spaced at a distance s. Since the IRS is an N × N array of circular loops having radius r and center-to-center spacing p, the value of A _IRS can be obtained as: A IRS = a b = ( N − 1 ) p + 2 r 2 . (4)

Following equation (19) of Ozdogan et al. (2020), the theoretical bounds on the path-loss can be obtained for the proposed configuration of Figure 10A as: P L theory = G t G r ( 4 π ) 2 A IRS s d 2 ⁡ cos 2 θ i , where tan θ i = d 2 s . (5)

We also numerically compute the | S 21 with IRS | using MoM. Figure 10B and Figure 10B depict how PL _theory and | S 21 with IRS | vary over a range of s/λ and d/λ values.

It is crucial to note that, the theoretical upper bound will assist designers to get an initial guess about how the pathloss will vary for different Tx-Rx and Tx-IRS distances. Note that, the theoretical bound is mainly computed from Friis transmission equation viewpoint and assuming interaction between Tx Rx and IRS via plane wavefronts. However, for radiating near-field regions, it is important to consider the impacts of spherical wavefronts. Therefore, the periodic “ripple-like” variations in the pathloss, especially for varying s/λ while keeping d/λ fixed, are better captured using the full-wave MoM approach (see HYPERLINK Figure 10B and HYPERLINK Figure 10C).