An Efficient Ray-Tracing Approach for the Isolation Assessment of Co-Located Base Station Antennas at mmWave

Numerical evaluation and/or measurement campaigns are currently the only means of evaluating the isolation between antennas; in the former case, the simulation time and computational resources necessary can be burdensome, whereas the latter requires several weeks of work to be completed. Within this context, this article aims at presenting an effective methodology for the evaluation of the isolation between co-located antennas in a rapid computational time. The proposed method is based on the near-field equivalent representation of real antennas (Tx and Rx) combined with the ray tracing method for evaluating the field re-radiated by the source antenna on the receiver, hence the received power. The procedure is general and suitable to any type of antenna with any configuration and number of radiation elements. Moreover, antenna mechanical and electrical details are not needed, since only near field information is needed. Finally, it considers the presence of the support structure and surrounding obstacles. The methodology has been validated by full-wave simulations and measurements, yielding consistent and accurate results with an error that is below 2 dB in most of the cases, up to 6 dB for very low coupling values, indicating a high level of accuracy and reliability.

interconnected over the internet, mobile networks have become an essential part of people's daily lives [2].The number of mobile devices per person has grown exponentially, with an estimated 5.22 billion unique mobile users worldwide [3], whose use ranges from traditional telephony and messaging to educational and entertainment purposes (e.g., audio and video streaming).Consequently, this increasing demand for mobile data traffic has created new challenges for mobile networks, which must constantly improve their performance to keep up with users' evolving needs and expectations [4], [5].
In this article, 5G network was developed, enabling connectivity between people worldwide, providing higher speeds, supporting low-latency transmissions, and greater capacity than 4G LTE networks [6].As a result of such features, remote health care, smart cities, remote control, and vehicle-to-X communications essential for autonomous driving and other innovative services can be achieved [7].
5G technology has been implemented by exploiting the millimeter wave spectrum (mmWave) [8] as it allows for greater bandwidth at higher frequencies and an enhancement in network capacity.Namely, by combining a very large bandwidth with smaller cell sizes, the available spectrum can be fragmented into larger bands for each user, allowing for increased data traffic capacity.
More in detail, the requirements for the 5G network include a capacity of 1000 times greater, a peak data rate under ideal conditions of 10-20 Gbps, a perceived data rate of 100 Mbps, latency less than 1ms, acceptable quality of service also for high mobility transmissions up to 500 km/h [4], [5], [9].Such 5G coverage and connectivity requirements, as well as the need to share the same site by multiple operators, have resulted in the installation of new antennas on existing or new cell towers, with consequent antennas overcrowding on the same radio base station (BS).Unfortunately, closely spaced antennas can lead to a reduction in electromagnetic (EM) isolation between the antennas so resulting in degraded performance of the entire system due to undesirable effects of mutual coupling.
On top of this, one of the newly emerging network entities called integrated access and backhaul (IAB) [10] node is now proposed to operate in a full-duplex (FD) scheme.This means that two information streams (i.e., the uplink UL and the downlink DL) share the same frequency resource, giving various benefits: improve system capacity; decrease latency for access and IAB links; expand UL coverage; and enable flexible and dynamic UL/DL resource adaption based on UL/DL traffic in a resilient way.Multiple sources of interference consequently hamper FD implementation: Self-interference between UL and DL at the FD node; clutter echo; and cross-link interference.Critical enablers for FD nodes include excellent spatial isolation between two antenna panels, beam isolation between Tx/Rx beams, digital/analog self-interference mitigation, and an appropriate approach to finding the ideal Tx/Rx beam pairing for user scheduling.
Thus, the aforementioned restrictions dictate the maximum number of antennas that can be deployed on the same infrastructure, as well as their required separation distances.Furthermore, it is of paramount importance to identify and comprehend the primary EM coupling mechanisms between the antennas.
The majority of literature about the antenna isolation assessment, considered as an intersystem problem between two or more separate antennas, is founded upon far field (FF) and free space (FS) assumptions [11].However, this approach is substantially limited for application in a realistic scenario, such as that of radio BS antennas.This approach is valid assuming that the separation distances between the antennas are sufficiently large to be comparable with the FF distance; in the latter case, the antenna isolation assessment is based on the calculation of the received power using the Friis formula [11], [12].Furthermore, the presence of the support structure invalidates the FS assumption.
Currently, to investigate EM co-siting problems, commercial software can provide hybrid resolution capabilities.Nevertheless, the simulation time and computational resources required can be prohibitive or even impossible to sustain, unless huge computing resources are employed.Alternatively, it is possible to carry out experimental measurements which, on the other hand, require several weeks of work to be completed.In addition, alternative methods have been proposed to estimate mutual coupling and RF interference in antenna systems.For example, Frid et al. [13] suggested an approximative approach to evaluate mutual coupling between antennas on vehicles, considering a line of sight between them; while, Gao et al. [14] presented a method to estimate RF interference without detailed knowledge of the antenna structure, reducing computation time by over 50% using an equivalent model based on the radiation pattern.Moreover, a simple yet effective correction term to the Friis formula has been proposed to improve its accuracy in the Fresnel region [15].However, there is currently a lack of studies examining the isolation analysis between antennas in the presence of obstacles or support structures.
Therefore, this article aims to propose an effective numerical approach to perform a fast isolation assessment of antennas co-located on the same radio BS.The proposed approach takes into account the presence of the support structure and avoids the need for expensive full-wave (FW) simulations or very expensive measurement campaigns due to the long duration and to the needed resources (very high specialized technicians and exclusive instruments operating at the 5G bands).In our previous work [16], we have preliminarily demonstrated the effectiveness of this proposed method.In the following, we detail our proposed methodology focusing on the following advantages: the procedure is general and suitable to any type of antenna with any configuration and number of radiation elements; in addition, it is not necessary to know in advance all the electrical and mechanical details of the antennas but only their EM near fields are needed, obtaining results in very short computation times and employing low computational costs.Finally, the calculation of the received power (and therefore of the antenna isolation) is obtained as an overall quantity, taking into account the beam direction and the polarization.
The rest of this article is organized as follows.Section II presents the problem statement and summarizes the aim of this work; Section III deals with the methodology adopted and the theoretical formulation; in Section IV, numerical and experimental results are presented, compared and discussed.Finally, Section V concludes this article.

II. PROBLEM STATEMENT
Co-siting is the practice of sharing a common site or assembling BS antennas at a few selected common sites in response to new antennas deployment requirements.Different configurations, and related coupling problems, are commonly in place as shown in Fig. 1.However, the presence of one or more antennas at close distance and the complex installation configurations can lead to interference phenomena, reduction of EM isolation between the antennas, and consequent degradation of the overall system performance.Such phenomena can cause various undesirable effects, such as desensitization of the receiver, lower dynamic range of the receiver, and distortions generated inside the front-end circuits of the receiver [17], [18], [19], [20], [21].
Recently two typical cases of relays like Integrated and IAB and network controlled repeater (NCR) have been identified by the 5G new radio (NR) standardization.In particular 3GPP release-17 includes a key feature of IAB like the simultaneous communication with parent nodes and child nodes using spatial division multiplexing or frequency division multiplexing, while 3GPP Release-18 is expected to include NR NCR; in both cases an accurate assessment on coupling between closely spaced antennas is required [22].
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Based on the above-mentioned considerations, an accurate evaluation of physical isolation among nearby antennas is of paramount importance to figure out the maximum number of antennas that can be installed on the same infrastructure as well as their spacing.In addition, it allows us to identify and comprehend the basic EM coupling mechanisms between antennas, so to take additional counter-measures to enhance isolation.
The purpose of this article is therefore to provide a robust and effective simulation methodology capable of assessing the isolation of co-located antennas in a short computational time while accounting for the presence of a support structure.The proposed methodology will be detailed in the following section.

III. PROPOSED ANTENNA ISOLATION ASSESSMENT METHODOLOGY
This section details the proposed methodology for the isolation assessment between the antennas of the 5G BS, taking into account both the theoretical and mathematical aspects; its framework is based on the steps outlined below (see Fig. 2).We resort at first to Huygens's equivalence principle [23], [24], so to obtain a complexity simulation reduction by replacing the detailed antenna model with an equivalent representation.Based on this assumption, it is not necessary to have knowledge in advance of the electrical and mechanical characteristics of the antennas, but only their electric ( E) and magnetic ( H) near fields are needed.Once the equivalent electric and magnetic fields are at disposal, the radiated fields of such equivalent sources are calculated and this calculation of EM fields at a given point can be accelerated through a three-dimensional (3-D) ray-tracing approach that was proved to be highly effective [16].Once the E and H fields over the integration surface are known, the reciprocity theorem [24] enables the calculation of the received power and, consequently, the antenna isolation.All the procedure is detailed in the following sub-sections.

A. Huygens's Equivalent Principle: Near Field Source (NFS) Representation
As earlier mentioned, FW methods can be used to estimate antenna isolation.However, simulating multiple antennas operating simultaneously can be a computationally demanding task that requires significant resources.In addition, the computational challenge becomes particularly severe when the problem at hand is electrically large from an EM point of view, especially at higher frequencies.To address such limitations, we propose an effective strategy that involves replacing the detailed antenna model with an equivalent representation.
Applying Huygens equivalence principle [23], [24] is therefore the initial stage of our approach.It is known as the NFS representation.Currents J s and M s calculated on a fictitious surface surrounding the radiative source are used instead of the actual source.Therefore, the EM field generated outside the fictitious surface by the actual Js and Ms is equal to the original one.In Fig. 3, E 1 and H 1 represent the radiated fields in a homogeneous medium, whereas n represents the outward-pointing normal unit vector out of the surface.
The fields outside of the Huygens' box are uniquely determined by the equivalent source over the entire Huygens' surface.
The major advantage of adopting Huygens Equivalence Principle is that it is not necessary to know in advance the electrical and mechanical features of the antennas; instead, it is sufficient to simulate or measure their EM near fields (i.e., the NFS representations).In addition, the calculation of the EM field radiated by the J s and M s incorporates all distance-dependent factors (1/r, 1/r 2 , and 1/r 3 ), ensuring great accuracy in both far and near (radiative and reactive) field regions.

B. Computation of the EM Field Radiated By J s and M s
The electric J s and magnetic M s equivalent currents calculated at each point of the surface surrounding the radiating source are interpreted as elementary electric and magnetic dipoles.Consequently, the EM field outside the integration surface S is computed as the coherent sum of the fields produced by each pair of elementary dipoles.
The electric and magnetic fields can be determined by using the following equation [25]: where A and F are the vector potentials, defined as follows: where R is the observation point (i.e., the point at which the EM field is computed).
To speed up the calculation of the EM field at a given point, we opted for a 3-D ray-tracing method.In fact, at high frequencies, the concept of rays can be efficiently used to trace the paths followed by EM waves from the transmitting antenna (Tx) to the receiving antenna (Rx) and to calculate the attenuation, taking into account the interaction with the obstacles in its environment.The scenario is realized from a geometric perspective in the first step of the ray-tracing calculation.Then, it computes the rays launched from a source point (Tx) to an observation point (Rx) while interacting with the obstacles present in the scenario.Specifically, the multipath between Tx and Rx is calculated by applying the method of images, [26].The EM field for each ray is then estimated using geometrical optics (GOs), the geometrical theory of diffraction, and its extension, the uniform theory of diffraction (UTD) [26], [27], [28].
In addition, the GO enables the computation of direct rays [i.e., the line of sight (LoS)] and reflected rays (R).In addition, the G/UTD allows the calculation of diffracted rays (D) in case a better accuracy is needed.Finally, the coherent sum of the EM fields is performed based on the following step.
1) Calculating the total E and H fields associated to the rays coming from each Tx point.2) Determining the total E and H fields over the equivalent surface.

C. Isolation Computation: Reciprocity and Reaction Theorems
The final step of the methodology is committed to the calculation of the isolation between antennas.The problem can be defined based on the following premise: two sets of sources, J 1 , M 1 and J 2 , M 2 emitting at the same frequency and existing within a linear, isotropic, but not necessarily homogeneous medium, produce the fields E 1 , H 1 , and E 2 , H 2 , respectively.Assuming that the sources are positioned in a finite region and the fields are observed at the far-field (ideally at infinity), the Reaction theorem [24] allows computing the coupling between a set of fields and a set of sources, which produces another set of fields.
In particular, it relates the reaction (coupling) of the fields E 1 and H 1 produced by the sources J 1 , and M 1 , to the sources − → J 2 and M 2 , generating the fields E 2 and H 2 , and vice-versa.
Formulas follows: Then, the Reciprocity Theorem [24] relates the coupling of the fields E 1 , H 1 to the coupling of the fields E 2 , H 2 , as follows: To this aim, the reaction theorem [29], [30], [31], [32] can be employed to compute the mutual impedance between the two set of sources (Z 21 ) as a function of the fields E 1 , H 1 , generated by the first source and E 2 , H 2 , generated by the second one as follows: where S represents the separation surface between the two antennas in two disjoint regions, and I 11 and I 22 are the terminal current of antenna 1, 2 when they transmit, respectively.
Once the E and H fields are known over the integration surface (see Fig. 4), as described previously, the reciprocity theorem can be used to calculate the received power and, consequently, the antenna isolation.Namely, using the definition of the reciprocity theorem, it is possible to calculate the coupling.
The coupling, defined as the ratio between the received and transmitted power, is expressed by means of the following formula, known as the Hu formula [33]: P r is the power received by the first or second antenna; n is the normal to the integration surface; P t is the power transmitted by the second or first antenna; and S is any surface separating the antennas.E 1 and H 1 are the fields produced over S by the first antenna under the assumption that it is transmitting; Ẽ2 and H2 , are the fields produced over S by the second antenna under the assumption that it is transmitting.P t1 and P t2 are the transmitting powers of the first and second antennas, respectively.
The above formula is a general power transmission formula expressed solely in field quantities; it is valid for matched and lossless antennas (with negligible losses); and it applies to a system where the two antennas can have any size, relative position, and polarization.Also, it is important to highlight that coupling C, expressed by ( 9), represents an "overall coupling." Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
Thus, if the victim antenna is an array, C shows the coupling at the array level, not just that of a single array element.

IV. RESULTS
The proposed methodology has been implemented in a software tool.The input generation is the preliminary phase required to create the methodology input: the Ẽ and H fields produced by a radiating source over the Huygens's equivalent surface (NFS representation) are derived using FW simulations or measurements.
By means of a graphical user interface, it is possible to generate the scenario consisting of the following main elements: a mechanical structure (e.g., a pole or BS tower); the NFS representations E 1 , H 1 of the first radiating source and E 2 , H 2 of the second radiating source; and the integration surface.
The preprocessing enables the computation of equivalent currents J 1 , M 1 and J 2 , M 2 and the generation of the integration surface points.Consequently, the processing phase is the core of the EM simulation: the tool computes the E and H fields over the integration surface resulting from the radiation of the first and second radiating source, respectively.The post-processing phase ends with the computation of the received power, which is required to calculate the isolation value.
In our previous work [16], we performed multiple preliminary tests to validate the reliability of our approach comparing the results to those obtained from commercial software.In this work, we aim to further demonstrate the effectiveness of our simulation approach in the presence of an obstruction (i.e., pole/cell tower).

A. Numerical Test Cases
To validate the accuracy of our numerical approach, we performed numerical tests comparing the results obtained from our methodology with those from commercial software that implements the method of moments (MoM).We designed a 28 GHz Horn antenna, which replicated the radiative characteristics of a standard Horn antenna (SGH2650 [34]).
First, we characterized the performance of the antenna in terms of its electric and magnetic field distributions, as well as its radiative characteristics, by employing a stand-alone configuration.Subsequently, we used the simulation to obtain the NFS representation of the E and H fields.Then, we carried out FW simulations with the two horn antennas to calculate the received power and isolation.
A graphical representation of the stand-alone configuration and a polar gain plot of the Horn antenna are shown in Fig. 5(a) and (b), respectively.As a basic case, two antennas have been simulated in order to evaluate the scattering parameters (S matrix).The off-diagonal term S ij (iࣔj) in our case is the coupling (or isolation) between the two antennas.
Several simulations were performed, both in the absence and in the presence of obstructions.In the latter case, we have designed an obstruction, represented by an aluminum plate measuring 10 cm×10 cm.By fixing the spatial distance between the antenna apertures (equal to 0.5 m), we blocked their line of sight and varied the position of the plate placed between them of a quarter or half of its length.

TABLE I RESULTS: STANDARD MOM VERSUS PROPOSED APPROACH
At the we the same scenario to be evaluated by our method, employing as input data the NFS representation of the E and H fields (taken from stand-alone antenna simulations on commercial software), the 3-D model of the metal plate and the surface integration.Table I gives the results of both the FW simulations and our approach, by positioning the antennas as shown in Fig. 6(a) and (b).The two methods produce consistent results, with the added benefit of reduced memory consumption and optimized simulation time.
Notably, the time required to simulate a single Horn antenna and extract the E and H near fields (of about 2 h) should be taken into account.However, once we obtain the equivalent NFS representations, we can simulate multiple configurations in a short time.
It is worth pointing out that with our approach, the calculation of the EM field radiated by J s and M s (applying the Huygens's equivalence principle) contains all the radial terms 1/r, 1/r 2 and 1/r 3 guaranteeing a high precision in both near and far-field regions (radiative and reactive).Therefore, it is possible to calculate the isolation between two antennas placed at short distances and operating in the NF region of each other in a precise and accurate way.

B. Experimental Test Cases
The last part of our research was devoted to experimentally validate our numerical simulation methodology.
We performed the measurements at the Huawei Technologies Research Center in Milan, inside an mmWave anechoic chamber.First, the measurement setup was defined; it is composed of two standard gain horns (SGH1800 and SGH2650 [25]) and a square pole covered in copper and aluminum, with a height (H) equal to 100 cm and a side (L) equal to 10.6 cm.
The anechoic chamber was equipped as in Fig. 7(a) and (b).D1 is the distance between the center of mass of the pole and the aperture plane of the Horn SGH1800, that is fixed; D2 is the distance between the pole and the aperture plane of the Horn SGH2650, that is able to rotate in the azimuthal plane.The pole can be displaced relative to the line of sight of the two horn antennas of a path (disp) that can be positive or negative according to the inset of Fig. 7(a).If the pole displacement is null, the center of mass of the pole is aligned to the line of sight of the two antennas.Before starting the measurements in presence of the pole, some preliminary measurements were performed without the presence of the pole, so to evaluate the isolation of the two antennas in FS condition.
Since the proposed methodology is based on the modeling of the antennas with the NFS representation, it was necessary to obtain the two near field boxes via full wave simulation.
The above horn antennas were simulated stand-alone, and their radiation patterns were analyzed and compared to datasheet ones to be confident of their modeling.The NFS representation of the sources were subsequently calculated and used in the scenario of our tool, where an integration surface has been interposed between them.
We compared the results obtained with our method, and the experimental measurement of the antennas isolation as a first calibration of the antenna models and our methodology.Table II gives the results obtained during this calibration procedure and the results demonstrate a remarkable level of agreement between the simulated and experimental data, confirming the effectiveness and accuracy of our approach.Subsequently, the square pole has been inserted between the antenna apertures [see Fig. 8(a)) and (b)].Varying the azimuth angle of the BOX NF HORN 2, the isolation values have been acquired step by step and compared with those obtained by our method.All tests have been repeated for the antennas in horizontal and vertical polarization.
Fig. 9 depicts the working principle of 3-D ray tracing by tracing the path of EM waves from the transmitting antenna (Tx) to the receiving one (Rx), taking into account the presence of an obstacle.If the antennas were in FS, only direct rays would arise.Instead, when an obstruction blocks their line of sight, reflected rays arise, and diffracted ones originate from the obstacle edges.
The pole has been positioned by choosing an initial displacement value of −6 cm with respect to the line joining the centers Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.  of the two antennas.Specifically, this displacement was meant to restrict the antennas' line of sight by approximately a quarter of their length.As shown in Fig. 10, the results obtained with our method are superimposed on those acquired during the measurements, and the error between simulation and measurement has been computed for both the polarizations.The error committed by our method is always less than 4 dB.
The last set of measurements have been carried out by reducing the displacement of the pole at a distance of +2 cm and +1.5 cm, with respect to line of sight of the antennas.The aim in this case was to simulate a real obstacle in the measurement  isolations are shown in Fig. 11 for both the displacement values of the pole.The error of our approach is almost always less than 6 dB, and only one direction reveals a greater error for the pole displacement of +2 cm in vertical polarization.However, it was concluded that such error was caused by a misalignment of the transmitting antenna while mechanically rotating inside the anechoic chamber.
The saving in time and resources of the simulation approach compared to the experimental one has not been quantified because it is completely unbalanced in favor of the proposed method.These findings represent a significant achievement, as they demonstrate the potential of our approach to providing an efficient and cost-effective means of analyzing antenna isolation in practical applications, without compromising on accuracy.

V. CONCLUSION
In this article, we presented a reliable and efficient antenna isolation evaluation method.Physical isolation allows us to estimate the most effective number of antennas and their placement on the infrastructure, considering the support structure.The proposed method can be employed as an alternative to a numerical FW method to evaluate isolation between co-located antennas in a short computational time frame.Huygens' Principle of Equivalence enables us to use the near field equivalent representation of the working antennas without knowing their mechanical and electrical characteristics.
To evaluate the accuracy and efficacy of our method, we compared its results to the FW simulation using the MoM in commercial software.We designed and simulated a conventional horn antenna (SGH2650) with and without obstructions.These analyses demonstrated that our method calculate antenna coupling accurately even in the presence of obstructions.We conducted anechoic chamber investigations to validate the dependability and accuracy of our method.In these investigations, a pole was moved to obstruct the line of sight between two horn antennas.Upon comparing the experimental outcomes with our proposed methodology, it was seen that most cases exhibited an error of less than 2 dB.However, for very low coupling values, the discrepancy reached up to 6 dB.It is important to note that only one direction reveals a greater margin of error.However, it is concluded that such error is due to a misalignment of the transmitting antenna.
In summary, we have demonstrated that the proposed method offers a reliable, accurate, and computationally efficient solution for calculating the coupling between antennas, while also considering the potential impact of obstructions or obstacles.The capability of the method to accurately model the effects of obstacles enhances its usefulness in practical applications.

Fig. 1 .
Fig. 1.Example of co-siting practice among two or more antennas.

Fig. 2 .
Fig. 2. Schematic of the robust and effective methodology proposed for the fast isolation assessment of co-located 5G antennas.

Fig. 3 .
Fig. 3. Representation of the application of the Huygens' equivalence principle to a generic radiant source without considering any obstacle in the scene.

Fig. 4 .
Fig. 4. Integration surface where E and H fields are calculated; tracing the rays and knowing the E and H fields due to the two antennas, the coupling is therefore estimated.

Fig. 5 .
Fig. 5. (a) 3-D numerical model of the 28 GHz Horn antenna.(b) Total gain of the Horn antenna at 28 GHz.

Fig. 6 .
Fig. 6.Test case of two 28 GHz Horn Antenna in the presence of an obstacle.(a) FW scenario.(b) Our scenario with the NFS representation.

Fig. 7 .
Fig. 7. (a) Schematic diagram of the experimental set-up inside the anechoic chamber.(b) Experimental set-up of the anechoic chamber: Horn SGH2650 rotating around the vertical axis of the aperture, while Horn SGH1800 is fixed.

Fig. 9 .
Fig. 9. Pictorial representation of the 3-D Ray Tracing approach to trace the paths followed by EM waves from the transmitting antenna (Tx) to the receiving antenna (Rx).

Fig. 10 .
Fig. 10.Measurements vs. Simulation with displacement equal to −6 cm.(a) Isolation of the two antennas in horizontal (HH) polarization.(b) Isolation error between measurement and simulation in HH polarization.(c) Isolation of the two antennas in vertical (VV) polarization.(d) Isolation error in VV polarization.

Fig. 11 .
Fig. 11.Measurements vs. Simulation with displacement equal to +2 cm and 1.5 cm.(a) Isolation of the two antennas in HH polarization.(b) Isolation error between measurement and simulation in HH polarization.(c) Isolation of the two antennas in VV polarization.(d) Isolation error in VV polarization.