@article{ozturk_anjinappa_erden_chowdhury_guvenc_dai_bhuyan_2023, title={Channel Rank Improvement in Urban Drone Corridors Using Passive Intelligent Reflectors}, ISSN={["1095-323X"]}, DOI={10.1109/AERO55745.2023.10115741}, abstractNote={Multiple-input multiple-output (MIMO) techniques can help in scaling the achievable air-to-ground (A2G) channel capacity while communicating with drones. However, spatial multiplexing with drones suffers from rank-deficient channels due to the unobstructed line-of-sight (LoS), especially in millimeter-wave (mmWave) frequencies that use narrow beams. One possible solution is utilizing low-cost and low-complexity metamaterial-based intelligent reflecting surfaces (IRS) to enrich the multi path environment, taking into account that the drones are restricted to flying only within well-defined drone corridors. A hurdle with this solution is placing the IRSs optimally. In this study, we propose an approach for IRS placement with a goal to improve the spatial multiplexing gains, and hence, to maximize the average channel capacity in a predefined drone corridor. Our results at 6 GHz, 28 GHz, and 60 GHz show that the proposed approach increases the average rates for all frequency bands for a given drone corridor when compared with the environment with no IRSs present, and IRS-aided channels perform close to each other at sub-6 and mmWave bands.}, journal={2023 IEEE AEROSPACE CONFERENCE}, author={Ozturk, Ender and Anjinappa, Chethan K. and Erden, Fatih and Chowdhury, Md Moin Uddin and Guvenc, Ismail and Dai, Huaiyu and Bhuyan, Arupjyoti}, year={2023} }
 @article{du_mujumdar_ozdemir_ozturk_guvenc_sichitiu_dai_bhuyan_2022, title={60 GHz Outdoor Propagation Measurements and Analysis Using Facebook Terragraph Radios}, ISSN={["2164-2958"]}, DOI={10.1109/RWS53089.2022.9719957}, abstractNote={The high attenuation of millimeter-wave (mmWave) would significantly reduce the coverage areas, and hence it is critical to study the propagation characteristics of mmWave in multiple deployment scenarios. In this work, we investigated the propagation and scattering behavior of 60 GHz mmWave signals in outdoor environments at a travel distance of 98 m for an aerial link (rooftop to rooftop), and 147 m for a ground link (light-pole to light-pole). Measurements were carried out using Facebook Terragraph (TG) radios. Results include received power, path loss, signal-to-noise ratio (SNR), and root mean square (RMS) delay spread for all beamforming directions supported by the antenna array. Strong line-of-sight (LOS) propagation exists in both links. We also observed rich multipath components (MPCs) due to edge scatterings in the aerial link, while only LOS and ground reflection MPCs in the other link.}, journal={2022 IEEE RADIO AND WIRELESS SYMPOSIUM (RWS)}, author={Du, Kairui and Mujumdar, Omkar and Ozdemir, Ozgur and Ozturk, Ender and Guvenc, Ismail and Sichitiu, Mihail L. and Dai, Huaiyu and Bhuyan, Arupjyoti}, year={2022}, pages={156–159} }
 @article{ozturk_erden_du_anjinappa_ozdemir_guvenc_2022, title={Ray Tracing Analysis of Sub-6 GHz and mmWave Indoor Coverage with Reflecting Surfaces}, ISSN={["2164-2958"]}, DOI={10.1109/RWS53089.2022.9719917}, abstractNote={Indoor coverage and channel modelling is crucial for network planning purposes at mmWave bands. In this paper, we analyzed received power patterns and connectivity in an indoor office environment for sub-6 GHz and mmWave bands using ray tracing simulations and theoretical models over different scenarios. We discussed the effect of using metallic walls instead of regular drywall, base station (BS) location, and open/shut doors. Our results showed that ray tracing solutions are consistent with theoretical calculations, and using reflective walls significantly improves average received power and connectivity at mmWave bands, e.g., for the given floor plan, coverage increases from 86% to 97.5% at 60 GHz band.}, journal={2022 IEEE RADIO AND WIRELESS SYMPOSIUM (RWS)}, author={Ozturk, Ender and Erden, Fatih and Du, Kairui and Anjinappa, Chethan K. and Ozdemir, Ozgur and Guvenc, Ismail}, year={2022}, pages={160–163} }
 @article{ozturk_saka_2021, title={Multilayer Minkowski Reflectarray Antenna With Improved Phase Performance}, volume={69}, ISSN={["1558-2221"]}, DOI={10.1109/TAP.2021.3090533}, abstractNote={We propose a multilayer unit cell consisting of Minkowski fractal-shaped reflector with aperture coupled phasing stubs to obtain a broad phase range for reflectarray antenna with smaller unit cell size and interelement spacing compared with some other studies in the literature. In the study, simulations are conducted using high-frequency structure simulator (HFSS) program with Floquet Port incidence. A unit cell with two cycles of phase range and very low reflection loss is designed. About 21.9% shrinkage is achieved in patch surface area using Minkowski fractals. Subsequently, the proposed unit cell is used to design and fabricate a full-scale 221-element reflectarray antenna. At 10 GHz, the simulation results are compared with the measured data and a good agreement is observed.}, number={12}, journal={IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION}, author={Ozturk, Ender and Saka, Birsen}, year={2021}, month={Dec}, pages={8961–8966} }
 @article{singh_bhattacherjee_ozturk_guvenc_dai_sichitiu_bhuyan_2021, title={Placement of mmWave Base Stations for Serving Urban Drone Corridors}, DOI={10.1109/VTC2021-Spring51267.2021.9448923}, abstractNote={As the use of unmanned aerial vehicles (UAVs) in various commercial, civil, and military applications increases, it becomes important to study the design of aerial drone corridors that can support multiple simultaneous UAV missions. In this work, we study the placement of base stations (BSs) to serve aerial drone corridors while satisfying specific UAV mission requirements, such as the geometrical waypoints for the UAV to fly through and the minimum data rate to be supported along the mission trajectory. We develop a mathematical model of the drone corridor and propose a brute force algorithm that leverages A* search to meet the quality of service (QoS) requirements of the corridor by choosing the minimal set of BS locations from a pre-determined initial set. Using raytracing simulations, BS placement results are presented for various antenna array sizes in a dense urban region in East Manhattan. It was found that, for the scenario under consideration, a single BS equipped with an 8x8 antenna array is sufficient to satisfy the given QoS requirements of the corridor, while two BSs are required when using 4x4 antenna arrays.}, journal={2021 IEEE 93RD VEHICULAR TECHNOLOGY CONFERENCE (VTC2021-SPRING)}, author={Singh, Simran and Bhattacherjee, Udita and Ozturk, Ender and Guvenc, Ismail and Dai, Huaiyu and Sichitiu, Mihail and Bhuyan, Arupjyoti}, year={2021} }
 @article{khawaja_ozdemir_erden_ozturk_guvenc_2020, title={Multiple ray received power modelling for mmWave indoor and outdoor scenarios}, volume={14}, ISSN={["1751-8733"]}, url={https://doi.org/10.1049/iet-map.2020.0046}, DOI={10.1049/iet-map.2020.0046}, abstractNote={IET Microwaves, Antennas & PropagationVolume 14, Issue 14 p. 1825-1836 Research ArticleFree Access Multiple ray received power modelling for mmWave indoor and outdoor scenarios Wahab Khawaja, Corresponding Author Wahab Khawaja wahab.ali@must.edu.pk Department of Electrical and Computer Engineering, North Carolina State University, 890 Oval Dr, Raleigh, NC, 27606 USA Mirpur University of Science and Technology, Mirpur, AJK, PakistanSearch for more papers by this authorOzgur Ozdemir, Ozgur Ozdemir Department of Electrical and Computer Engineering, North Carolina State University, 890 Oval Dr, Raleigh, NC, 27606 USASearch for more papers by this authorFatih Erden, Fatih Erden orcid.org/0000-0002-1708-3063 Department of Electrical and Computer Engineering, North Carolina State University, 890 Oval Dr, Raleigh, NC, 27606 USASearch for more papers by this authorEnder Ozturk, Ender Ozturk orcid.org/0000-0002-6390-8089 Department of Electrical and Computer Engineering, North Carolina State University, 890 Oval Dr, Raleigh, NC, 27606 USASearch for more papers by this authorIsmail Guvenc, Ismail Guvenc Department of Electrical and Computer Engineering, North Carolina State University, 890 Oval Dr, Raleigh, NC, 27606 USASearch for more papers by this author Wahab Khawaja, Corresponding Author Wahab Khawaja wahab.ali@must.edu.pk Department of Electrical and Computer Engineering, North Carolina State University, 890 Oval Dr, Raleigh, NC, 27606 USA Mirpur University of Science and Technology, Mirpur, AJK, PakistanSearch for more papers by this authorOzgur Ozdemir, Ozgur Ozdemir Department of Electrical and Computer Engineering, North Carolina State University, 890 Oval Dr, Raleigh, NC, 27606 USASearch for more papers by this authorFatih Erden, Fatih Erden orcid.org/0000-0002-1708-3063 Department of Electrical and Computer Engineering, North Carolina State University, 890 Oval Dr, Raleigh, NC, 27606 USASearch for more papers by this authorEnder Ozturk, Ender Ozturk orcid.org/0000-0002-6390-8089 Department of Electrical and Computer Engineering, North Carolina State University, 890 Oval Dr, Raleigh, NC, 27606 USASearch for more papers by this authorIsmail Guvenc, Ismail Guvenc Department of Electrical and Computer Engineering, North Carolina State University, 890 Oval Dr, Raleigh, NC, 27606 USASearch for more papers by this author First published: 22 October 2020 https://doi.org/10.1049/iet-map.2020.0046Citations: 2AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Millimetre-wave (mmWave) frequency bands are expected to be used for future fifth generation networks due to the availability of a large unused spectrum. However, the attenuation at mmWave frequencies is high. To resolve this issue, the utilisation of high gain antennas and beamforming mechanisms are widely investigated in the literature. In this work, the authors considered mmWave end-to-end propagation modelled by individual ray sources and explored the effects of the number of rays in the model and radiation patterns of the deployed antennas on the received power. It is shown that taking the dominant two rays is sufficient to model the channel for outdoor open areas as opposed to the indoor corridor which needs five dominant rays to have a good fit for the measurement and simulation results. It is observed that the radiation pattern of the antenna affects the slope of the path loss. Multi-path components increase the received power, thus, for indoor corridor scenarios, path loss according to the link distance is smaller for lower gain antennas due to increased reception of reflected components. For an outdoor open area, the slope of the path loss is found to be very close to that of the free space. 1 Introduction There has been a significant increase in the number of smart communication devices and high data rate applications in the last decade. This trend is expected to grow rapidly in the future [[1]]. However, the available spectrum at the sub-6 GHz band is limited. Higher frequency bands (e.g. millimetre-wave (mmWave) bands) are not heavily utilised, thus, offer larger bandwidths for wireless communication systems. Therefore, research efforts have been concentrated on exploring higher frequencies as an alternative to the sub-6 GHz band. The opening of the mmWave spectrum for mobile usage by FCC [[2]] has given a boost to the current research studies to best utilise these bands. However, mmWave communication suffers from its inherent high free space attenuation as well as high penetration losses. In this work, we used measurements, analytical ray modelling and ray-tracing simulations to model line-of-sight (LoS) characteristics of a mmWave communication channel in a corridor type indoor and open space outdoor environments at 28 GHz frequency band. We analytically calculated received signal properties using the dominant five-ray and two-ray received power models based on first-order reflections for the indoor corridor and outdoor open area, respectively. To compare with our analytical results, measurements were conducted at North Carolina State University using a PXI-based channel sounder platform from National Instruments, and two sets of directional horn antennas with gains 17 and 23 dBi at 28 GHz. The test setup used indoor and outdoor are shown in Figs. 1 and 2, respectively. Fig. 1Open in figure viewerPowerPoint Indoor corridor propagation setup at the basement of Engineering Building II, North Carolina State University Fig. 2Open in figure viewerPowerPoint Outdoor measurement setup at the top floor of a multi-storey car park, Centennial Campus, North Carolina State University The rest of the paper is organised as follows. Readers will find a comprehensive literature review as well as a summary of our contributions in Section 2. Section 3 includes details on received power modelling for indoor and outdoor environments. Section 4 covers experimental and ray-tracing simulations setup. In Section 5, the number of rays and percentage power sum of dominant five rays with a total power of rays is provided. In Section 6, results of measurements, simulations, and calculations for received power are given. In Section 7, a detailed discussion is presented for five-ray and two-ray models. Section 8 provides Ricean K-factor analysis and the paper ends with concluding remarks in Section 9. 2 Literature review and contributions Various approaches have been proposed in the literature to overcome the high attenuation problem at mmWave frequencies [[3], [4]]. A common method is to increase the gain or directivity of the antennas [[5], [6]]. The high directivity is obtained either by beamforming or deploying directional antennas (e.g. horn antennas). In addition to antenna type, material characteristics of the objects in the environment also play an important role in figuring the propagation statistics [[7], [8]]. One way of modelling propagation statistics is by using ray tracing. In the literature, different types of indoor geometries either in LoS or non-LoS (NLoS) scenarios for a wide variety of frequency bands are investigated using ray tracing software [[9]-[12]]. In this work, we modelled the end-to-end propagation as individual ray sources. For the indoor environment, five rays are used in calculations. One is the LoS and four are the reflected rays from two walls, ceiling, and ground. Each ray source contributes to the resulting received power. Contributions of the reflected rays are found to increase with the link distance. This is because when transmitter and receiver antennas are close, reflected fields are rejected by the receiver antenna because of its directional pattern. Together with high Fresnel reflection coefficient values along with the link, we observe an increase in the received power compared to free space, i.e. the slope of the path loss is smaller than that of the free space for indoor. For outdoor open area, two-ray model is found to be sufficient to model the received power and because of the absence of three first-order reflections, no obvious difference between path loss slopes have been detected. The analytical modelling results based on ray sources are compared with measurement and ray-tracing simulation results. We also made a comparative analysis of the measurements with five-ray and two-ray analytical models and ray-tracing simulations with five rays are provided for the indoor environment. The comparative analysis is carried out using z-test of the path loss model parameters. The z-test values indicate that the two-ray model does not provide a close match to the measurement path loss for the indoor corridor. On the other hand, the five-ray model provides a close fit to the measurement data. The ratio of power sum of dominant five rays to power sum of total rays obtained from measurements are also provided in this work. The percentage is greater than 90% for all the scenarios, which indicates that five rays are sufficient for modelling. The Ricean K-factor is also provided to study the contribution of LoS ray and diffuse rays over the link for two different gain antennas. Table 1 shows the related work in the literature, where ray tracing is used. Comparison of the available literature with our work highlights the following distinctions of our work: Propagation modelling based on dominant rays at 28 GHz is considered in our work. Table 1. Related work in the literature on mmWave channel modelling using ray tracing Literature Number of rays Frequency Maximum distance Reported channel statistics [[13]] 2 sub-6 GHz and mmWave 10 km Received power, two-ray model, break point distance based on first Fresnel zone [[14]] 1, 2, 5, 20 100 MHz, 1800 MHz, 2400 MHz 10 km Path loss, two-ray model, effect of first Fresnel zone on path loss exponent [[15]] 2 1.5 GHz 1 km Two-ray model, path loss exponent for vertically and horizontally polarised signals [[16]] 3 3.6 GHz, 10.6 GHz 100 m Path loss, three ray model for UWB propagation [[17]] 3 1900 MHz 400 m Three ray propagation model for PCS and -cellular services [[18]] 62 0.06 THz-1 THz 6 m Distance and frequency selective characteristics, coherence bandwidth, channel capacity, and temporal broadening analysis [[19]] 9 60 GHz 60 m LOS, 25 m NLOS Received power, indoor corridor power distribution comparison with Rayleigh and Rician [[20]] 2, 4, 5 2.4 GHz 50 m Received power analysis in open and closed corridors [[21]] 2, multiple rays 94 GHz 6 m Path loss, multipath analysis [[22]] 2, 4 94 'GHz 1.5 m Received power, multipath analysis for radars [[23]] 2, 4, 6, 10 2.4 GHz 10 m Path loss This study 2, 5 28 GHz 40 m indoor, 100 m outdoor Received power, path loss, the effect of antenna gain, adequacy analysis on number of rays using z-test and Ricean K-factor Five dominant rays were found to be adequate for the indoor corridor propagation modelling whereas, two dominant rays were found to adequately model the open area outdoors. The antenna gain of each individual ray is modelled based on its geometric position from the radiation pattern of the antenna provided in the datasheet. The resolvable distance of the rays compared to the LoS as a function of the link distance is also provided. Smaller than this resolvable distance, the rays will be superimposed coherently with the LoS component. A polarisation-dependent reflection coefficient for different materials is used at 28 GHz. A z-test is also performed for comparison of parameters of two-ray and five-ray path loss models obtained analytically, through ray-tracing simulations and measurements. A commonly occurring scenario for future fifth generation (5G) deployments is closely positioned transmitter and receivers at indoor corridors. This commonly occurring scenario in a typical indoor corridor environment is studied. There are other works in the literature in which five, even more, first-order reflections are taken into account [[18]-[27]]. We only considered rays experiencing the first-order reflection. This is because most of the received power comes from the LoS signal and the first-order reflections. For the purpose of illustration, consider that we have a second-order reflected ray with the same reflection coefficient as the first-order reflected ray, . Then the power contribution of the second-order reflected ray will be times the first order reflected ray. Generally, for common non-metallic surfaces such as walls and ground, hence, the power coming from second-order reflected ray will be smaller than the first-order reflected ray. In addition, rays that we consider as second-order reflections have to undergo longer paths than the first-order reflections as the geometry of a corridor obliges. Let the distance travelled by a first-order reflected ray from the transmitter to the receiver be , and additional distance travelled due to the second reflection. Then, the power of the second-order reflected ray will be smaller than the first-order reflected ray by a factor of due to free space path loss. Overall, the received power due to the second-order reflections will be significantly smaller compared to the first-order reflections and the contribution of the second-order reflections to the total received power will be small. Consequently, third and higher-order reflections will also have small contributions, thus negligible. The difference between first-order and second-order reflections in a similar setup is shown in a previous work, [[3]], as well. Moreover, considering higher-order reflections increases the complexity of the model unnecessarily compared to their contribution to the received power. Therefore, our model based on LoS and first-order reflections provides a robust and simple way to calculate received power in corridors and similar shaped indoor environments. Similarly, for outdoor open area two-ray model is sufficient to model the received power. 3 Received power modelling based on dominant rays for indoor corridor and outdoor open area In this section, we will first discuss antenna radiation pattern effects on propagation. Later, a received power calculation model based on dominant LoS signal and reflected rays in the indoor corridor (five-ray model) is presented. Two-ray model as a special case of the five-ray model is used for outdoor open area. 3.1 Antenna radiation pattern and propagation effects The antenna radiation pattern plays an important role in modelling the propagation characteristics of directional mmWave links. In the model, we used two directional horn antenna sets which have different gains and respective half-power beamwidths (HPBWs) in the azimuth and elevation planes. We represent the 3D antenna gain as a surface area extended on a sphere at a distance d with a given solid angle . The surface area A subtended by the antenna gain at a distance d from the source is , where the solid angle is given as: (1) where is the radiated power from the antenna in spherical coordinates as a function of distance d, elevation, and azimuth angles of and , respectively. is the maximum radiated power. The propagation from the transmitting antenna is modelled as a spherical wavefront. The majority of the radiated power is concentrated over the area covered by the solid angle represented by and , where these two angles represent the antenna HPBWs in the elevation and azimuth planes, respectively. Moreover, if and are small, we can approximate the area extended by and in space as at a fixed distance in the far-field region. The rays lying in this region will have significantly higher gain compared to the rays lying outside this area. 3.2 Ray resolution along the link distance The propagation from the antenna can be considered either as a wavefront propagation or decomposed as ray-based propagation [[28], [29]]. In the case of ray-based propagation, rays are considered to be originating from the transmitting antenna in all directions, where only the rays that interact with physical objects in the environment are taken into account. This is the basic principle of the ray tracing as well. In the case of a rectangular corridor, there are five dominant rays that interact with the surroundings. These rays are LOS, rays reflected from the left and right walls, floor, and ceiling. Theoretically, these rays are distinguishable at every point along the receiver route. The distinguishing characteristics of the individual rays depend on the (i) antenna characteristics at the transmitter and receiver; (ii) the geometry of propagation setup; and (iii) geometry of the environment. Our channel sounder setup can resolve any two rays at a spatial distance represented as , whereas the theoretical ray resolution can resolve rays at any distance. Consider the case of two-ray modelling for a given height of the transmitter and receiver represented as and , respectively (Fig. 3). When the link distance d between the transmitter and receiver is increased such that the difference between the paths travelled by any two rays is smaller than , those rays cannot be resolved, thus can be measured as a superposition. The relevant inequality is as follows: (2) Fig. 3Open in figure viewerPowerPoint Propagation of LoS and GRC from transmitter antenna towards receiver antenna when their heights ( and ) are the same Similarly, for the indoor corridor, the rays reflected from the ground, ceiling, and walls may not be resolvable depending on the link distance d. Fig. 4 shows the difference in path distances of the rays reflected from the ground, ceiling, and walls with respect to the LoS ray. In Fig. 4, the reflected rays are considered to be independent of each other. According to Fig. 4, the ray from the ceiling is the first to get unresolved at 3.1 m compared to ground reflected ray, which gets unresolved at 7 m. The rays from the two walls are not resolvable after 5 m. This indicates that the path of the reflected ray from the ceiling is the smallest compared to the paths of the remaining three rays. Fig. 4Open in figure viewerPowerPoint Difference of ray lengths with the LoS, plotted as a function of link distance 3.3 Received power modelling for indoor corridor The received signal is given by , where represents the transmitted signal, is the impulse response of the channel and is the convolution operation. In case that received and transmitted signals are known, channel impulse response (CIR) could be obtained by applying deconvolution. In this work, we considered the CIR in the indoor corridor (similar to rectangular waveguide). The reason for selecting a corridor is because the future 5G base stations (BSs)/access points (APs) are expected to be deployed in corridors of common building structures (e.g. buildings containing offices or classrooms). The major occupancy in these environments is in the rooms adjacent to the common corridor. Therefore, the BSs/APs are preferred in the corridor to provide optimum coverage to the adjoining rooms and in the corridor itself. Moreover, the indoor corridor can be considered to be a large rectangular room, or a square room (if considered in small portions). Therefore, propagation in this area can help to understand the propagation in other similar environments. The indoor corridor propagation layout is shown in Fig. 5. Based on the 3D geometry shown in Fig. 5, five dominant rays are considered. The characteristics of these rays depend on the antenna radiation pattern at the transmitter and receiver in both azimuth and elevation planes, height of the transmitter and receiver, and distance of the transmitter from the walls, ceiling, and floor for a given receiver position. The height of the transmitter and receiver are kept the same throughout the experiments. The five dominant rays are given as follows: one is the LoS and the other four are the reflected rays from the ground, ceiling, and two walls. Fig. 5Open in figure viewerPowerPoint Layout of the indoor corridor propagation environment As the distance of the receiver increases from the transmitter moving in a straight line received power coming from reflected rays increase as well. Due to the geometry of the test setup, as the link distance increases, reflected rays gets closer to the boresight of the received antenna, thus, captured with a higher gain. As a result of this, the difference between power value calculated taking only free space path loss into account and the five-ray received power increases in favour of the five-ray model. The contribution of the reflected rays to the overall received power is also dependent on the Fresnel reflection coefficients. Reflected rays of more than first-order have a significantly smaller contribution to the received power compared to first-order reflections. Therefore, in our model, we can safely ignore their contributions. Let represent the received LoS component given as: (3) where is the gain of the antenna for the transmitter at elevation and azimuth angles of and , respectively. Similarly, is the gain of the antenna for the receiver at elevation and azimuth angles of and , respectively, represents the delay of the LoS component given by , where c is the speed of the light and d is the distance of the LoS component, represents the phase of the LoS component, represents the dot product between the polarisation unit vectors of the electric field at the transmitter and receiver, respectively. The gain of the antenna for the LoS ray in the azimuth and elevation planes at the transmitter and receiver are given as follows [[30]]: (4) where and represent the direction of departure (DoD) in the elevation and azimuth planes, respectively. Similarly, the direction of arrival (DoA) in the elevation and azimuth planes are given as and . can be expressed as follows: (5) where is the antenna gain and is the relative phase of the component of a ray. If both the transmitter and receiver are aligned to their boresight, then the total gain given in (4) is maximised. Similar to the LoS component, the four dominant received rays reflected from the environment, with the ray index , is expressed as: (6) The reflection coefficient also called Fresnel reflection coefficient for the relative permittivity of the ground material is given as: (7) where the value of Y depends on the polarisation and are given for vertical and horizontal polarisation as follows: (8) If the link distance , then and the gain of the reflected ray approaches to the LoS component gain and the Fresnel reflection coefficient, . Let E represent the average over time, and represent the total received power, then , the coherent addition of the LoS and the reflected rays for , is given as: (9) Equation (9) can be rewritten for d values such that the reflected rays can be resolvable (see Section 3.2, Fig. 4) from each other: (10) From (3), (6), if , and where is the transmitted power. Moreover, for the LoS component, the XPD (cross polarisation discrimination) factor is negligible for vertical–vertical (VV) and horizontal–horizontal (HH) antenna orientations. Similarly, for the reflected rays, the diffuse scattering is small due to smooth reflecting surfaces leading to small XPDs. Therefore, the dot product of the polarisation vectors can be taken as 1 for the LoS and reflected rays. Therefore, the total received power from (9) can be written as follows: (11) where for . Additionally, if the heights of the antennas are not the same and/or not aligned to the boresight, we have additional attenuation due to smaller antenna gain. This attenuation will decrease with the increase in distance between the transmitter and the receiver. Considering the th individual reflected ray at a given link distance, we can write the received power as follows: (12) From (12), it can be observed that the received power of the th reflected ray approaches to the LoS ray at distance when (i) the antenna gains at the transmitter and receiver side are equal to the boresight antenna gains, and (ii) the reflection coefficient is 1. 3.4 Received power modelling for outdoor open area The outdoor open area is selected to study the mmWave propagation with two dominant rays, i.e. LOS and ground reflected component (GRC) with negligible contribution from the surroundings. Therefore, a simple propagation model that only considers two multipath components can accurately characterise the signal propagation. The outdoor open area scenario can be often encountered in parking lots, recreational parks, and highways, among others. The two-ray model can also be considered as a special case of the five-ray model. The two-ray model is used for received power modelling in outdoor open area assuming that antenna heights are significantly high. The contribution of any other rays from far off scatterers is small for the open area and is ignored. In the two-ray modelling, the received power is dependent on the LoS and GRC. Therefore, the total received power is given as follows: (13) where is the phase difference between the LoS and the GRC signals. 3.5 Polarisation effects on the received power The polarisation of electric fields should be taken into account. There are two co-polarised configurations based on antenna orientation used in the measurements, namely VV and HH. The difference in VV and HH antenna orientations is subject to the antenna radiation pattern in the azimuth and elevation planes. However, even though the whole patterns are different in two orthogonal planes, as the HPBWs are the same for both horn antenna sets, no significant difference in the antenna radiation patterns has been observed due to antenna orientation. Cross polarisation of vertical–horizontal (VH) is also introduced to study the XPD factor in the indoor corridor. Considering the channel stationary, we can obtain the XPD factor between the transmitter and receiver as follows: (14) where , and are the received powers for VV, VH and HH antenna orientations, respectively, and E denotes the expected value. A major use of XPD factor is that it helps to study the interaction of the antennas of different beamwidths with the surroundings when cross-polarisation is not negligible. 3.6 Path loss modelling The path loss obtained from the received power measured at different distances from the transmitter are given as follows: (15) An alpha–beta model for the path loss modelling [[31]] is given as: (16) where is the y-intercept in dB, is the slope and X is a random variable and , where expressed in dB is the variance of X. A least square regression is used to fit a regression line (best fit) to the data. 4 Experimental and ray-tracing simulations setup In this section, an indoor and outdoor experimental setup, as well as the ray-tracing simulation setup, are discussed. 4.1 Indoor and outdoor measurement setup Indoor corridor measurements were carried out at the basement of the Engineering Building II, North Carolina State University, shown in Fig. 1. The walls in the corridor are three-layered drywall, the ceiling is Armstrong type ceiling and the ground is a concrete grinded surface. The measurements were carried out using NI mmWave transceiver system operating at 28 GHz. The description of the NI mmWave transceiver system is provided in [[32]]. Two horn antenna sets with gains 17 and 23 dBi were used in the measurements. The HPBWs of 17 dBi antennas are and in the E- and H-planes, respectively. The HPBWs for the 23 dBi antennas in the E- and H-planes are and , respectively. The height of the transmitter and receiver from the ground was fixed to 1.44 m, whereas, the distance of the transmitter and receiver from the ceiling was 0.9 m. The distance from either of the walls to the antennas was 1.24 m. The transmitter was kept at a fixed position, whereas the receiver was moved in a straight line away from the transmitter at constant intervals of 0.3 m starting from 1.9 to 39.7 m. Laser alignment is used between the transmitter and the receiver at every step. The outdoor measurements were carried out at the top floor of a multi-storey car park at North Carolina State University shown in Fig. 2. Similar to the indoor corridor measurements, the transmitter was kept at a fixed place, and the receiver was moved in steps of 5 m beginning from 4.6 to 100 m. The height of the transmitter and receiver was 1.09 m. For both indoor and outdoor measurements, the transmit power has been set to 0 dBm. 4.2 Ray tracing and analytical simulation setup Ray-tracing simulations were carried out using Wireless InSite® software [[33]]. The environment model is shown in Fig. 6. The indoor corridor and the outdoor open area were modelled similar to the real environment with as many details as we could. For the indoor setup, four different material types are used for walls, floor, ceiling, and doors in the ray-tracing simulation environment. The material used for the floor is concrete, whereas, for the ceiling and walls, Armstrong ceiling and drywalls are used, respectively. The relative permittivity of the concrete floor at 28 GHz is 5.31, while it is 3 f}, number={14}, journal={IET MICROWAVES ANTENNAS & PROPAGATION}, publisher={Institution of Engineering and Technology (IET)}, author={Khawaja, Wahab and Ozdemir, Ozgur and Erden, Fatih and Ozturk, Ender and Guvenc, Ismail}, year={2020}, month={Nov}, pages={1825–1836} }