Efficient and accurate ray tracing method for indoor radio wave ...

Curriculum Vitae A S M ZAHID KAUSAR Post Graduate Student and Research Assistant Department of Electrical Engineering University of Malaya, Malaysia. Cell: +6-016-3248190 E-mail: [email protected] Educational Background:  Master of Science (M.Sc.) in Engineering (Master’s by Research) (Intended year of completion is 2013) University: Department of Electrical Engineering, University of Malaya, Malaysia.  Bachelor of Science (B.Sc.) in Electrical & Electronic Engineering, 2009 University: Chittagong University of Engineering & Technology (CUET), Chittagong, Bangladesh. CGPA: 3.31 in scale of 4.00, Ranked: 27th position among the 120 successful students.  Higher Secondary Certificate, 2004 College: Shahid Syed Nazrul Islam College, Mymensingh, Bangladesh Major: Science CGPA: 4.80 in scale of 5.00  Secondary School Certificate, 2002 School: Arjat Atarjan High School, Kishoreganj, Bangladesh. Major: Science CGPA: 4.50 in scale of 5.00 Publication List (Journal and Conference):  A. W. Reza, K. Dimyati, K. A. Noordin, A. S. M. Z. Kausar, and M. S. Sarker. A comprehensive study of optimization algorithm for wireless coverage in indoor area. Optimization Letters. DOI: 10.1007/s11590-012-0543-z, 2012.  A. S. M. Z. Kausar, A. W. Reza, K. A. Noordin, Md. Jakirul Islam, and H. Ramiah. Efficient Radio Propagation Prediction Algorithm Including Rough Surface Scattering with Improved Time Complexity. Progress in Electromagnetic Research-B. Vol. 53, 127-145, 2013.  M. J. Islam, A. W. Reza, K. A. Noordin, K. Dimyati, A. S. M. Z. Kausar and R. Harikrishnan. Efficient and accurate ray tracing method for indoor radio wave propagation prediction in presence of human body movement. Journal of Electromagnetic Waves and Applications. Vo. 27, No. 12, 1566-1586, 2013.  M. J. Islam, A. W. Reza, K. A. Noordin, K. Dimyati, A. S. M. Z. Kausar. Red-black tree based fast and accurate ray tracing for indoor radio wave prediction. Accepted for Vol. 67, No. 9-10 in Frequenz, (in Press).  M. J. Islam, A. W. Reza, K. A. Noordin, K. Dimyati, A. S. M. Z. Kausar. An accelerated and accurate three-dimensional ray tracing using red-black tree with surface

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extraction and object skipping techniques. Turkish journal of electrical engineering & computer sciences 2013. DOI: 10.3906/elk-1212-98, 2013 (in Press). M. J. Islam, A. S. M. Z. Kausar, A. W. Reza, K. A. Noordin. Investigation of the Effect of Human Motion on Indoor Radio Signal Propagation. 2nd International Conference on Power and VLSI Engineering (ICPVE'2013) May 6-7, Kuala Lumpur, Malaysia. Sampad Ghosh, A. S. M. Zahid Kawsar, Muhammad Asad Rahman, Debasish Das. Design and Implementation of Smart Level Crossing System. International J. of Eng. and Tech. Vol. 8, Issue 4, pp. 815-819, December 2011. [Online:http://gscience.gurpukur.com/product_info.php?cPath=5_214_235&products_i d=1174] A. S. M. Z. Kausar, A. W. Reza, K. A. Noordin, Md. Jakirul Islam, and H. Ramiah. An Optimized Binary Space Partitioning Algorithm for Designing Indoor Wireless Radio Network. Under review in Advances in Electrical and Computer Engineering journal. A. S. M. Zahid Kausar, A. W. Reza, K. A. Noordin, K. Dimyati, and M. J. Islam Nearest Object Priority Based Integrated Rough Surface Scattering Algorithm For 3D Indoor Propagation Prediction. Under review in China Communications. A. S. M. Z. Kausar, A. W. Reza, K. A. Noordin, Md. Jakirul Islam, and H. Ramiah. An integrated algorithm of rough surface scattering for 3D indoor wireless network. Under Review in Turkish journal of electrical engineering & computer sciences. A. S. M. Z. Kausar, A. W. Reza, K. A. Noordin, Md. Jakirul Islam, and H. Ramiah. An Optimized Ray Tracing Algorithm and Complexity Analysis for Indoor Wireless Network. Under Review in International Journal of Microwave and Wireless Technology Journal.

Research Interests:  Electromagnetic Field, Antenna Design, Energy Harvesting, Micro Electronics, VLSI, RFID, RFIC, WSN, Nanotechnology, Optical Fiber Communication. Research Experience:  Research Assistant at Department of Electrical Engineering, University of Malaya, Malaysia under the project: “Investigation of the possibility of implementing PSO in radio signal prediction and optimization”. Duration: 15/07/2011 – 31/08/2011  Research Assistant at Department of Electrical Engineering, University of Malaya, Malaysia under the project: “3D Ray Tracing: Indoor ray optical propagation and prediction model”. Duration: 15/09/2011 – 14/09/2012  Research Assistant at Department of Electrical Engineering, University of Malaya, Malaysia under the project: “Green Energy Research: RF energy harvesting for wireless sensor network in indoor and natural environment”. Duration: 15/09/2012 – 14/07/2013  Research Assistant at Department of Electrical Engineering, University of Malaya, Malaysia, under the project: “Brain- Machine Research: Cognitive dynamic systems using brain electromagnetic signals”. Duration: 16/07/2013 -till now

Membership of Professional Institutions:  Student member of IEEE, Membership No.: 92290015 Computer Knowledge:  Operating System: Windows XP, Linux, Windows 7, Windows RT  Programming Language: C#, VB, MATLAB R2009a, C/C++.  Design software: CST Studio suit. Language Skill:  Bengali (Mother tongue)  English (Good command in speaking, reading and writing)  Hindi  Bahasa Melayu Basic Courses Completed: Electrical Circuits-I & II, Computer Programming and Numerical Analysis, Electrical Machines- I & II, Electronics I & II, Electromagnetic Fields I & II, Signal and System, Power Transmission and Distribution of Electrical Power, Measurement and Instrumentation, Electronic Communication, Power System Analysis, Control System, Digital Electronics, Telecommunication Engineering, Microprocessor and Interfacing, Data Communication, Switchgear and Protection, Semiconductor Physics and Devices, Science of Materials, Power Station, Power Electronics, VLSI Technology, Digital Signal Processing, Mobile Cellular communication. Undergraduate Project “Design and implementation of Railway Gate Control system Using Microcontroller”. Supervised By: Prof. Anil Kanti Dhar, Department of Electrical & Electronic Engineering, Chittagong University of Engineering & Technology (CUET), Bangladesh. References Dr. Mahmud Abdul Matin Bhuiyan Associate Professor & Head Department of Electrical & Electronic Engineering Chittagong University of Engineering and Technology, Chittagong 4349 E-mail: [email protected]

Dr. Md. Tazul Islam Professor and Dean Faculty of Mechanical Engineering Chittagong University of Engineering and Technology, Chittagong 4349 E-mail: [email protected]

I, hereby, declare that all the information stated above is correct to the best of my concern.

23.08.2013

Progress In Electromagnetics Research B, Vol. 53, 127–145, 2013

EFFICIENT RADIO PROPAGATION PREDICTION ALGORITHM INCLUDING ROUGH SURFACE SCATTERING WITH IMPROVED TIME COMPLEXITY Abu S. M. Z. Kausar*, Ahmed W. Reza, Kamarul A. Noordin, Mohammad J. Islam, and Harikrishnan Ramiah Department of Electrical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur 50603, Malaysia

Abstract—Precise modeling of radio propagation is necessary for experiencing the benefits of wireless technology for indoor environments. Among many modeling techniques, the ray tracing based prediction models become popular for indoor wireless radio propagation characterization. Though the ray tracing models are popular, their key deficiency is the slower performance. In this paper, an accelerated technique for three dimensional ray tracing using Adelson-Velski and Landis (AVL) tree data structure is introduced. Here, the AVL tree data structure is coupled with the concepts of quadrant eliminating technique (QET) and nearest neighbor finder (NNF) for optimization and fast characterization of indoor wireless communication. Surface intersection scheme (SIS) is also introduced for optimizing the ray-object intersection time. The AVL tree is used for the effective handling of the objects and environments relative information. The QET technique decreases the ray tracing time by omitting unnecessary object, while NNF decreases the ray-object intersection time by finding the nearest object in an efficient technique. For the validation of the superiority of the proposed technique, a detailed comparison is made with the existing techniques. The comparison shows that the proposed technique has 81.69% lower time consumption than the existing techniques.

Received 20 May 2013, Accepted 6 July 2013, Scheduled 15 July 2013 * Corresponding author: Abu Sulaiman Mohammad Zahid Kausar (zahid04eee@hotmail. com).

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1. INTRODUCTION The advent of wireless technology and available low cost wireless transceivers has opened the door of various types of application (such as, personal communication system, wireless local area network, etc.) inside building area. For these applications, proper modeling for indoor radio propagation is essential. Although an indoor wireless communication network can be designed either by estimation through simulation or through extensive field measurements, it is preferable to use estimation through simulation. For estimation through simulation, the ray tracing based methods are very popular and widely used [1–6]. The main problem for the ray tracing based propagation prediction model is the ray-object intersection test. This test consumed the most time and resources in a ray tracing method [7]. Intersection test is performed every time after a new ray is generated and its goal is to determine whether there is a ray-object intersection or not. During intersection test, all of the objects present in the area of concern will be used to identify which one has the actual intersection. Hence, if all objects participate in this test, the ray tracing time consumed will be extremely high. To accelerate the ray tracing technique, various methods such as angular sectoring [8], KD-tree, octree, quad tree [4] and a preprocessing method are proposed [7]. However, the existing models, such as shooting and bouncing ray (SBR) [4], bidirectional path tracing (BDPT) [9], brick tracing (BT) [10], ray frustums (RF) [11], prior distance measure (PDM) [7], and space division (SD) [12] techniques require higher prediction time due to complex algorithms used. Moreover, the prediction accuracy is not so high. Some of the drawbacks of the listed techniques are: double ray counting error in SBR, incorrect result for multiple floor in BDPT, erroneous analytic reflection and transmission coefficient for corner bricks in BT, high intersection test time in BT due to considering all of the brick as a source after first Tx -brick interaction, use of high computer memory for complex environment in RF, increase of execution time due to the use of single list for storing cell id in SD, extra effort and expense for the preprocessing in PDM. Considering all of the drawbacks of the existing technique, this paper introduced a new method based on Adelson-Velski and Landis (AVL) tree data structure, quadrant elimination technique (QET) and nearest neighbor finder (NNF). The AVL tree [13] is used for efficiently handling different information relative to the objects and scenarios. This tree has a lower data searching time, which helps to find a particular object for simulation within a shorter time and thus contributes in reduction of ray tracing time. The QET technique

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helps to choose the quadrant in which the ray-object intersection will possibly occur. The objects of the chosen quadrant will only be considered for ray-object intersection test and the other three quadrants and the objects of those quadrants will be omitted. Thus, QET eliminates the unnecessary objects. The NNF technique finds the actual object, which intersects with the ray from all the object of the chosen quadrant (done by QET) and thus optimizes the ray tracing technique. This optimization uses the ‘Pythagoras Theorem’ and the newly introduced diagonal intersection point (DIP) technique for finding the actual object. Thus, it eliminates the time for the intersection test between the ray and all of the objects of the chosen quadrant. Finally, the surface intersection scheme (SIS) is used for finding the ray-object intersection point, which also optimizes the time by reducing the number of surface during intersection point calculation. 2. SCATTERING MODEL Firstly we are going to present the model we have used for computing rough surface scattering field and then the ray tracing technique will be described with the acceleration techniques. The following model is based on the well-known Kirchhoff Approximation (KA). So the rough surface is decomposed into micro-facets, i.e., into small planes that are locally tangent to the roughness. Figure 1(a) represents an arbitrary tangent plane on a rough profile, and the notations used hereafter for the incident and the scattered fields.

(a)

(b)

Figure 1. (a) Plain and rough surface geometry. (b) Geometry used to define surface elements. Let us consider a rough surface geometry shown in Figure 1(a). The EM field scattered in reflection inside the surface S at the point P 1, can be obtained by Kirchhoff-Helmholtz integral equation. From

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this Kirchhoff approximation the equation can be written as [14] ³ ´ ZZ ¯ ˆ ˆ Er1 = +2ik1 I − Vr Vr · dxP 1 dyP 1 G1 (RP 1 , R) Fr (γP 1,x , γP 1,y ) ×Ei (RP 1 ) Ξr (RP 1 )

(1)

where, Ξr is the illumination function in reflection. · ¸ −LP y +LP y −LP x +LP x xP 1 ∈ ; and yP 1 ∈ ; 2 2 2 2

(2)

In Equation (1), the ‘Green’s function’ is used for describing the propagation of the scattered wave. Its expression is given by [14, 15] Z i dv eiv·(r−rP )+if (v)|z−ζP n | Gα (R, RP ) = (3) 2 f (v) (2π)2 where, v = vx x ˆ + vy yˆ and r = xˆ x + y yˆ with [14] (p vα2 − kvk2 ; if vα2 ≥ kvk2 f (v) = p i kvk2 − vα2 ; if vα2 < kvk2

(4)

Now the ‘Green’s function’ can be approximated by [14] Gα (R, RP ) ∼ =

exp [i (vα R − Vs · RP )] 4πR

(5)

With Vs = Vr for α = 1. Substituting Equation (5) to Equation (1), the ‘scattered field’ can be expressed as [14] Z ¡ ¢ iv1 E0 eik1 R ³¯ ˆ ˆ ´ ∞ Er,1 =+ I− Vr Vr ·Fr γP0 1 × drP 1 ei(Vi−Vr )·RP 1 Ξr (RP 1 ) (6) 2πR R RR where, drP 1 ≡ dxP 1 dyP 1 and Fr (γP0 1 ) is given by [14], with γP0 1,x , 0 γP 1,y given by (vrx − vix ) (7) vrz − viz (vry − viy ) γP0 1,y ≡ − (8) vrz − viz Here, the third coordinate z is used to represent the change of height of the reflected rays after reflection from a rough surface. To define the scattering technique for our simulation environment, we have used the roughness technique proposed by ‘Oren-Nayar’ [16] which is the modification of ‘Lambertian method’ [16]. Figure 1(b) defines the parameter notations, which have been used for describing γP0 1,x ≡ −


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the technique below. In Figure 1(b), θi marks incidence angle and ϕi marks incident azimuth angle while, θr denotes reflected angle and ϕr denotes reflected azimuth angle. The terminology of diffuse reflection is expressed in terms of reflected radiance Lr and incident radiance Li . Now by considering an isotropic surface with V cavities with same facet slop θa and uniform distribution in orientation ϕa , the radiance can be determined as [16] Lr (θr , θi , ϕr − ϕi ; σ) = L1r (θr , θi , ϕr − ϕi ; σ)+L2r (θr , θi , ϕr − ϕi ; σ) (9) A modification has been done based on the term K3 by neglecting inter-reflection. According to ‘Oren-Nayar’ Lr (θr , θi , ϕr − ϕi ; σ) ρ = E0 cos θi (A1 + A2 max[0, cos(θr − θi )] sin α tan β) π

(10)

where, A1 = 1 − 0.5

σ2

σ2 + 0.33

(11)

σ2 (12) σ 2 + 0.09 This simplified Equation (10) has advantages for using in purpose of computer simulation. A2 = 0.45

3. DETAILED RAY TRACING ALGORITHM 3.1. The Proposed QET Technique As ray-object intersection is the most critical part in the ray tracing technique, it is necessary to find the objects which are taking part in intersection test. We have shorted the necessary objects in two different techniques. First we have used the proposed QET to find a group of objects according to the ray direction. Then the NNF will find the nearest object from that particular group of objects and that nearest object will take part in intersection test. These two acceleration techniques will reduce the intersection test time by finding the exact object. As the proposed technique is for 3D, octants have been used in the simulation tool for finding an object using the QET. The graphical representation of octants for QET is a bit complicated. So, here quadrants are used instead of octants to represent the QET. Both of the quadrants and octants are Cartesian coordinates and the basic of octants and quadrants are pretty similar [17]. The coordinate axis x = 0, y = 0 divide the plane into 4 regions called quadrants.

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Similarly, the coordinate planes x = 0, y = 0 and z = 0 divide the space into 8 regions called octants. In the proposed algorithm, interval between two consecutive rays shooting is one degree (1◦ ). That means starting from zero degree it finishes at 359◦ . Now, first divide the surface in four quadrants (I, II, III, and IV) at the Tx position or the position of ray beginning. As we know, that the whole surface covers 360◦ , each of the quadrants covers 90◦ of the surface. That means quadrant I covers 0◦ to 90◦ , II covers 90◦ to 180◦ , III covers 180◦ to 270◦ and IV covers 270◦ to 360◦ or 0◦ . If the Tx position is (X, Y ) then, the objects having a position (> X, < Y ) will be found in I, (< X, < Y ) in II, (< X, > Y ) in III and (> X, > Y ) in IV, where the origin of the simulation space is the top left corner. Now, based on the ray shooting angle, we can identify the quadrant in which the ray is going to travel. So, for first intersection test of that particular ray, the objects of that particular quadrant are enough to be tested. A sample environment is shown in Figure 2, which has 44 different objects, one Tx and one Rx. Suppose, a ray is shooting at an angle of 110◦ (which is in between 90◦ to 180◦ ) from the Tx. Then it is obvious that it will travel to the quadrant II and only the objects having location (< X, < Y ) will be tested for intersection test. In this case, only object 26–43 will have to test for intersection test. That means 17 objects out of 44 have to test. By this way the QET eliminates objects which decrease the burden for next step.

Figure 2. Sample environment showing QET and NNF.

3.2. Proposed NNF Technique By applying the QET technique a group of possible intersecting objects can be found. Most of the objects of this group are parallel to each other. In case of this type of parallel objects, only the nearest object will take part in the intersection test. So, it will not be wise to test


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all of the objects whether they are intersecting or not. It will consume time and will make the ray tracing less efficient. So, for finding this nearest object we have introduced NNF. This technique is divided into two phases. In the first phase, diagonal intersection point (DIP) (point ‘A’ in Figure 3(a)) will be calculated for each of the objects. Then, this DIP will be used to find the distance of that object from the ray source. This will be done for all of the parallel objects. After all, the decision of nearest object will be taken by comparing the distances of the parallel objects from the source ray. The DIP is the point of intersection between two diagonal of a rectangle. Suppose, the surface containing C1, C3, C5, and C7 vertices of an object are in front of the ray source B (X2, Y 2) (Figure 3(a)). Using these four vertices, two diagonals C1C7 and C3C5 can be found. The intersection point between C1C7 and C3C5 will be considered as the DIP for this object. If (x1, y1), (x3, y3), (x5, y5), and (x7, y7) are the coordinates of C1, C3, C5, and C7, respectively, then ‘the intersection point (DIP) A(X1, Y 1) between two diagonals can be found as’ ¯ ¯ ¯ ¯ ¯ ¯ ¯¯ ¯ ¯¯ ¯ ¯ ¯ x1 y1 ¯¯ ¯¯ x1 1 ¯¯ ¯ ¯ ¯ x1 y1 ¯¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ x7 y7 ¯ ¯ x2 1 ¯ ¯ ¯ ¯ x7 y7 ¯ x1 − x7 ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ x y ¯¯ ¯¯ x 1 ¯¯ ¯ ¯ ¯ x y ¯¯ ¯ ¯ ¯ 3 3 ¯ ¯ 3 ¯ ¯ ¯ 3 3 ¯ x −x ¯ ¯ 5 ¯ ¯ ¯ x5 y5 ¯ ¯ x5 1 ¯ ¯ ¯ ¯ x 5 y5 ¯ 3 ¯ ¯ ¯ ¯ ¯ = ¯ X1 = ¯ ¯¯ ¯ x1 − x7 y1 − y7 ¯ ; ¯ ¯ x1 1 ¯¯ ¯¯ y1 1 ¯¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ x3 − x5 y3 − y5 ¯ ¯ x7 1 ¯ ¯ y7 1 ¯ ¯ ¯ ¯ ¯ ¯ ¯ x 1 ¯¯ ¯¯ y 1 ¯¯ ¯ 3 ¯ ¯ 3 ¯ ¯ ¯ x5 1 ¯¯ ¯¯ y7 1 ¯¯ ¯ ¯ ¯ ¯ ¯ ¯ (13) ¯ ¯¯ ¯ ¯¯ ¯ ¯ ¯ x1 y1 ¯¯ ¯¯ y1 1 ¯¯ ¯ ¯ ¯ x1 y1 ¯¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ x7 y7 ¯ ¯ y2 1 ¯ ¯ ¯ x7 y7 ¯ y1 − y7 ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ x y ¯ ¯ y 1 ¯ ¯ ¯ ¯ x y ¯ ¯ 3 3 ¯ ¯ 3 3 ¯ ¯ 3 ¯ ¯ ¯ ¯ ¯ x5 y5 ¯ ¯ y5 1 ¯¯ ¯ ¯ ¯¯ x5 y5 ¯¯ y3 − y5 ¯ ¯ ¯ ¯ ¯ ¯ = ¯ Y 1 = ¯ ¯¯ ¯ x1 − x7 y1 − y7 ¯ ¯ ¯ x1 1 ¯¯ ¯¯ y1 1 ¯¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ x3 − x5 y3 − y5 ¯ ¯ x 7 1 ¯ ¯ y7 1 ¯ ¯ ¯ ¯ ¯ ¯ ¯ x 1 ¯¯ ¯¯ y 1 ¯¯ ¯ 3 ¯ ¯ 3 ¯ ¯ ¯ x5 1 ¯¯ ¯¯ y7 1 ¯¯ ¯ Now the distance between the DIP A(X1, Y 1) and ray source B(X2, Y 2) will be calculated by using the ‘Pythagoras Theorem’. By extending the points A and B, a right angled triangle ABC will be formed (Figure 3(a)). The coordinates of the point C will be (X1, Y 2). Now, by applying the ‘Pythagoras Theorem’ in the right

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(a)

(b)

Figure 3. (a) Distance calculation between ray source and DIP. (b) Intersection point calculation between ray and a surface by using SIS. angled triangle, we found, AB2 = AC2 + BC2 = (Y 2 − Y 1)2 + (X2 − X1)2

(14)

If the distance between A and B is D, then from Equation (11), we found, p D = dX 2 + dY 2 (15) where, dX is the difference between the X-coordinates of A and B and dY is the difference between the Y -coordinates of A and B. According to Figure 2, when a ray shoots in the second quadrant at an angle of 110◦ , the possible intersecting objects are the 28th, 31st, 33rd and 34th objects. These objects are all parallel to each other. The nearest of the four objects has to find out. For this, at first, the DIP of the objects will have to be found and it will be done by using ‘Equation (13)’. Now, suppose the DIP of the 28th, 31th, 33rd, and 34th objects are A, D, E, and F, respectively. At this instant, these points will be used for calculating the distance between the objects and ray source point by using ‘Equation (15)’. Suppose the distances are D1, D2, D3, and D4, respectively. Then by comparing the distances the nearest object will be chosen. In the above case, 34th object is found as the nearest object and this one will now use for an intersection test to find the intersection point. 3.3. Surface Intersection Scheme for Exact Intersection Points After finding the nearest object, the exact ray-object intersection point is calculated by using surface intersection scheme (SIS). Based on this


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intersection point the next ray shooting decision will be taken from this point. The occurrence of reflection or refraction is also dependent on this point. Suppose, from Figure 3(b), the line of the ray P is described by two points Ia (xa , ya , za ), Ib (xb , yb , zb ) and a plane π (in this case the back surface of the 34th object) is determined by 3 non co-linear points P0 (x1 , y1 , z1 ), P1 (x2 , y2 , z2 ) and P2 (x3 , y3 , z3 ). Thus a general point on the line can be represented as [18] L = Ia + (Ib − Ia )t;

t∈R

(16)

Similarly, a general point on the plane π can be found as [18] P = P0 + (P1 − P0 )u + (P2 − P0 )v;

u, v ∈ R

(17)

Now, the point of intersection between the line and the plane can be found by considering L equal to P . This gives the parametric equation Ia + (Ib − Ia )t = P0 + (P1 − P0 )u + (P2 − P0 )v

(18)

After simplification, Ia − P0 = (Ia − Ib )t + (P1 − P0 )u + (P2 − P0 )v Equation (19) can be expressed " # " xa − x0 xa − xb ya − y0 = ya − yb za − z0 za − zb

(19)

in matrix form as x1 − x0 x2 − x0 y1 − y0 y2 − y0 z1 − z0 z2 − z0

#"

t u v

# (20)

The value of the constant t, u, and v can be found by inverting the Equation (20). " # " # " # t xa − xb x1 − x0 x2 − x0 −1 xa − x0 u = ya − yb y1 − y0 y2 − y0 ya − y0 (21) v za − zb z1 − z0 z2 − z0 za − z0 By plugging the value of t in ‘Equation (16)’ or putting the value of u and v in ‘Equation (17)’, the intersection point Pint (X, Y, Z) can be found. Using ‘Equation (17)’, the intersection point between ray and the 34th object of Figure 2 can be calculated. Now, this intersection point will act as the source for that particular ray for finding the next ray-object intersection point. Reflection, refraction or diffraction will occur at that point according to the object property and the ray will proceed to a particular direction. Based on that direction, again QET will apply at the intersection point and next object will be found for a ray-object intersection by applying the NNF technique. This process will continue and at the end, the ray will be count either as a valid signal received by Rx or an invalid signal.

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In this study, when a ray hits on any transparent object, a refracted ray will be generated. For other kind of objects, the reflected ray will be generated. The diffracted ray is generated when a ray hits on an edge of an object. In case of reflection and refraction, Snell’s law [19] is used to find the direction of rays. In case of diffraction the matter is somewhat different and it is described briefly here. Suppose that, Ri is the origin of the incident ray, P is the point ~ is of diffraction, Rd is the end point of the diffracted ray, and S the direction vector. So, ‘the direction of the diffracted ray’ can be calculated by the following equation [20]: −−→ ~ −−→ −−−→ P Ri · S = P Rd · (−S) (22) ~ is oriented such that S ~ ×W ~ =N ~ , where Here, the direction vector S ~ is a vector that lies in the plane of one of the two surfaces of the W ~ is the unit vector. wedge and N 4. COMPLEX ANALYSIS For M number of objects, the search operation of an AVL tree can be implemented in O(log2 M ) time. Let, M is the number of objects, N is the number of surfaces of each 3D object, and S is the intersection testing time for the proposed method. If R numbers of intersections are required to predict each significant ray, then the total intersection testing time can be calculated by the following equation: Sproposed = R × N × O(log2 M ) (23) Moreover, according to QET, the proposed method can omit a significant amount of objects during each intersection test. Let, MQET be the average number of omitted objects due to QET. Now, Equation (23) becomes: Sproposed = R × N × O(log2 (M − MQET )) (24) Furthermore, the NNF technique also skips objects during intersection test. Suppose, MNNF be the number of objects skipped by NNF technique. Thus, ‘the equation for intersection time’ will be Sproposed = R × N × O(log2 (M − MQET − MNNF )) (25) In addition, the SIS technique ignores 4 of the 6 surfaces from each object. That means, only 2 surfaces or 1/3 of the surfaces have to consider for intersection test, which also reduces the intersection time. Thus, Equation (25) becomes N Sproposed = R × × O(log2 (M − MQET − MNNF )) (26) 3


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As, cuboids have 6 surfaces, N can be replaced by 6. In that case, Equation (26) becomes Sproposed = 2R × O(log2 (M − MQET − MNNF ))

(27)

Table 1 shows the time complexity for the proposed technique and the existing technique; from where, it is obvious that the proposed technique has a lower time complexity. Table 1. Time complexity for finding a significant ray for different techniques. Technique Proposed SBR BT BDPT RF

PDM

SD

Time Complexity 2R × O(log2 (M − MQET − MNNF )) R × N × O(log2 (M − MMT ); where MMT are the skipped objects due to mailbox technique R × N × O(M ) R × N × O(M ) R × N × O(log2 (M − 2H ); where 2H is the order of quad tree R × N × O(M − MPDM − MBSM ); where MPDM and MBSM are the objects skipped due to prior distance measures and bounding spheres method, respectively. R × N × O(M − MSD ); where MSD are the objects skipped by space division

5. CALCULATION OF RECEIVED POWER AND PATH LOSS The received power at a point is calculated by using Friis transmission formula. For 3D modeling, 3D directivity data of transmitting and receiving antennas are required, which can be interpolated from measurement data along the E and H-planes [21]. When the source is smashed by the back-traced ray, ‘the received power’ can be obtained by [11] PR = |VR |2 /Z0

(28)

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where, v ´ ³  u u hR,υ θˆR + hR,υ φˆR u X  ¥Q ¦ u Z0 ¯ i or T¯i or D ¯ i )e−jkSi  (29) · A(S , S )( R VR = λu GR (θR , φR )· i−1 i q  t 4π hT,v θˆT +hT,h φˆT −jkR T · ηP G (θ , φ ) e T T T 4π R and Z0 is the characteristic impedance of a receiver and GR (θR , φR ) the gain along the ray direction. Unit vectors θˆR and φˆR represent vectors along the elevation and azimuth directions seen from the receiving antenna coordinate, respectively. The values hR,v and hR,h represent the polarization components. For indoor environment, the average ‘path loss’ PL (dB) for a transmitter and receiver with separation d can be represented as [22] µ ¶ d P L (dB) = P L(d0 ) + 10n log +ξ (30) d0 where, PL(d0 ) is the propagation loss at the reference distance d0 (1 m in our case), n is the propagation exponent, and ξ is a zero-mean Gaussian distributed random variable that represents the deviation from the mean value. 6. RESULTS AND DISCUSSION With the preceding acceleration algorithms, a computer code in C# is developed to verify the efficiency. The code is implemented basically for three dimensional objects and the coordinate vectors have three components. To evaluate the performance of the proposed technique, a comparison is made with the existing methods. The comparison is made between the proposed technique and the SBR, BT, BDPT, RF, PDM and SD techniques. The drawbacks of the existing techniques have been described in Section 1. For proper comparison, five (5) different environments are chosen (one of them is shown in Figure 2). The environments are different by means of a number of objects. Some are mostly complex and some are moderate. Measurements are done in ten (10) different sampling points for each environment, by changing the Tx and Rx positions. For fair comparison, the same environments are used and all experimental settings are kept equivalent. The results obtained from 10 different sampling points of Figure 2 are represented graphically in Figure 4. Table 2 represents the overall results for all five environments. The detail of the simulation process is as follows. First, with measured antenna radiation patterns, a three dimensional radiation pattern is interpolated and stored in the memory to save the

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Figure 4. Comparison in terms of time. Table 2. Combined results for all five environments.

Proposed SBR BT RF PDM SD

1 142 407 352 365 646 422

2 106 347 304 321 633 376

Time 3 99 331 292 311 621 361

4 115 369 316 342 657 398

5 134 428 365 375 691 434

calculation time. For example, bow-tie antennas of broad bandwidth at 2.4 GHz center frequency are used. The maximum gain of the antenna is 2.3 dBi. The material constants for the walls are εr = 9 and σ = 0 : 02 [S/m]. The same antennas are used for the transmitter and the receiver. According to Figure 4, the proposed algorithm shows lower time consumption for ray tracing execution. The drawbacks of the existing techniques as described before in Section 1 have been removed to decrease the time. Here, AVL tree is used for ray tracing, which decreases the time by arranging the object details in an organized approach. The QET technique also minimizes a huge amount of time by neglecting unused objects in a logical manner. The NNF and the SIS techniques reduce the ray-object intersection test time. Thus, the overall execution time becomes lower than the existing techniques. Results for all five different environments are represented in Table 2. From the results, we observe that, the proposed algorithm shows 68.35% lower time consumption than SBR algorithm, 63.38% lower than BT, 65.30% lower than RF technique, 81.69% lower than PDM method, and 70.10% lower than SD technique.

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6.1. The Effect of Rough Surface Scattering and the Optimization Techniques In this proposed technique rough surface scattering is included with ray tracing technique. Scattering factor (SF) is the key feature which has impact on scattering simulation. The reflection angle changes with respect to specular reflection due to roughness of the surface and this consequence is used in the proposed technique. Here, SF is considered as a measure of surface roughness. SF has a key impact on scattering angle. When the SF increases, the scattering angle also increases. Thus the chance of ray-object interaction increases and it increase the number of predicted rays along with the prediction time. Figure 5 shows the effect of SF on time. 3.45% increased time is needed for the increase of SF from 4 to 8 and 9.48% increased time for SF of 20. So, we can say that scattering has an effect on the time of the ray tracing technique. 260

Time (ms)

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SF = 20 SF = 8 SF = 4

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Figure 5. Change of the prediction time for different scattering factor. Figure 6 shows the effect of scattering and the proposed optimization techniques on the ray tracing time. Here a comparative study is presented for showing the improvement of the proposed technique step by step. From Figure 6, after including the scattering in the ray tracing technique the time decreases 4.65% in average compared to without scattering (AVL) ray tracing. Furthermore, 11.68% time reduction for the inclusion of QET optimization technique and 31.55% reduction for the inclusion of both QET and NNF techniques. Figure 6 also shows a comparison of AVL tree with Projective Scheme (PS) technique [23] and Astigmatic Beam Tracing (ABT) technique [24]. The PS technique has been used BSP tree and ABT technique has been used a beam tree. From the comparison we found that, ray tracing with AVL tree shows 20.26% less time consumption than the PS technique and 8.73% less time consumption than ABT technique. By comparing with the overall proposed technique, we

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Figure 6. Effect of scattering and the proposed optimization techniques on time. found that the proposed technique has 45.41% less time consumption than the PS and 37.53% less than ABT. Though, the ABT technique uses binary tree data structure, it stores the information about path length, curvature radius, spreading factor etc. for electromagnetic field computation [24]. So, it needs to store information for almost all of the generated rays, which results in more time consumption. On the other hand, the PS technique uses BSP tree which has a worse case time complexity of O(n) for n number of nodes. With this time complexity, PS needs a higher amount of time. Furthermore, comparison with ray tracing models which have included scattering is also covers by Figure 6. Here, the proposed technique is compared with Diffuse Scattering (DS) [25] and Effective Roughness (ER) [26] models. The outcome of the comparison is that the proposed technique has 33.07% lower time requirement than DS and 30.46% lower than ER. Form the above discussion it is clear that the inclusion of AVL tree, scattering and the proposed optimization techniques are significantly reducing the ray tracing time. Although the DS and ER technique considered scattering as the proposed technique, the proposed optimization techniques make the proposed tool less time consuming. 6.2. The Influence of Tx-Rx Separation and Height Distance between Tx and Rx and the height of Tx has a great influence on ray prediction. Here this influence has been presented graphically. Figure 7 shows the effect of Tx -Rx separation on the path loss, which is an important parameter of ray prediction technique. From the figure it is obvious that the path loss is increasing as the increasing the distance between Tx -Rx. It is also representing that, all of the considered techniques are showing a matching path loss over distance.

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Figure 7. Distance vs path loss curve. *

Received Power (dBm)

-5 -10 -15

Tx = 0 m Tx = 0.5 m

-20

Tx = 1 m Tx = 1.5 m

-25

Tx = 2 m -30

1

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Figure 8. Change of received power with height. This matching result verifies the proposed technique. In Figure 8, the influence of height of the Tx is presented in terms of received power. The figure reflects that, as the Tx height is increasing, the amount of received power is also increasing. As an example, when the Tx is in ground the average received power is −20.1 dBm and it increases to −7.7 dBm for 2 m height. 7. CONCLUSION During a ray tracing procedure, huge computation time is required for the ray-object intersection test and the data storing and retrieving procedure. In terms of overcoming these shortcomings, this study presents a new propagation prediction technique for indoor environment, where, AVL tree is used for data storing and retrieving process and QET and NNF techniques are used for accelerating the overall ray tracing process. The SIS technique used for finding the intersection point also optimizes the ray-object intersection


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test. Investigations between the proposed and the existing methods demonstrated that the proposed method has lower time complexities. The results obtained reveal that the proposed technique has improved the performance in terms of lower computational time of about 81.69%. With this accomplishment, it is anticipated that the proposed propagation prediction technique has a huge potential to be used as an indoor wireless systems prediction tool. ACKNOWLEDGMENT This research work is supported by the University of Malaya High Impact Research (HIR) Grant (No. UM.c/625/1/HIR/MOHE/ENG/51) sponsored by the Ministry of Higher Education (MOHE), Malaysia. REFERENCES 1. Liu, Z.-Y. and L.-X. Guo, “A quasi three-dimensional ray tracing method based on the virtual source tree in urban microcellular environments,” Progress In Electromagnetics Research, Vol. 118, 397–414, 2011. 2. Athanasiadou, G. E., A. R. Nix, and J. P. McGeehan, “A microcellular ray-tracing propagation model and evaluation of its narrow-band and wide-band predictions,” IEEE Journal on Selected Areas in Communications, Vol. 18, No. 3, 322–335, 2000. 3. Sarker, M. S., A. W. Reza, and K. Dimyati, “A novel raytracing, technique for indoor radio signal prediction,” Journal of Electromagnetic Waves and Application, Vol. 25, Nos. 8–9, 1179– 1190, 2011. 4. Tao, Y. B., H. Lee, and H. J. Bao, “Kd-tree based fast ray tracing for RCS prediction,” Progress In Electromagnetics Research, Vol. 81, 329–341, 2008. 5. Mphale, K. and M. Heron, “Ray tracing radio waves in wildfire environments,” Progress In Electromagnetics Research, Vol. 67, 153–172, 2007. 6. Tayebi, A., J. Gomez, F. M. Saez de Adana, and O. Gutierrez, “The application of ray-tracing to mobile localization using the direction of arrival and received signal strength in multipath indoor environments,” Progress In Electromagnetics Research, Vol. 91, 1–15, 2009. 7. Alvar, N. S., A. Ghorbani, and H. R. Amindavar, “A novel hybrid approach to ray tracing acceleration based on pre-processing

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Efficient and accurate ray tracing method for indoor radio wave propagation prediction in presence of human body movement a

a

a

a

M.J. Islam , A.W. Reza , K.A. Noordin , A.S.M.Z. Kausar & H. Ramiah

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Faculty of Engineering, Department of Electrical Engineering , University of Malaya , Kuala Lumpur , 50603 , Malaysia Published online: 18 Jul 2013.

To cite this article: M.J. Islam , A.W. Reza , K.A. Noordin , A.S.M.Z. Kausar & H. Ramiah (2013) Efficient and accurate ray tracing method for indoor radio wave propagation prediction in presence of human body movement, Journal of Electromagnetic Waves and Applications, 27:12, 1566-1586, DOI: 10.1080/09205071.2013.820653 To link to this article: http://dx.doi.org/10.1080/09205071.2013.820653

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Journal of Electromagnetic Waves and Applications, 2013 Vol. 27, No. 12, 1566–1586, http://dx.doi.org/10.1080/09205071.2013.820653

Efficient and accurate ray tracing method for indoor radio wave propagation prediction in presence of human body movement M.J. Islam, A.W. Reza*, K.A. Noordin, A.S.M.Z. Kausar and H. Ramiah Faculty of Engineering, Department of Electrical Engineering, University of Malaya, Kuala Lumpur 50603, Malaysia


(Received 26 March 2013; accepted 25 June 2013) Due to the attractive features of millimeter band, its uses are greatly expanding in the indoor wireless communication systems. As the distance between the transmitter and receiver is much shorter in indoor environments than that of the outdoor environments, the radio wave paths of the millimeter band frequencies are highly influenced by the building materials as well as by the human movements. Ray tracing is widely used method to characterize the radio wave propagation for the planning and establishment of the indoor wireless network. Precise object modeling for the real environment and computational burden are the two classical problems of the propagation model. Because, large number of rays that travels in a complex and convoluted indoor environment must be traced. Therefore, an accurate and efficient ray tracing method is proposed here, which is based on the surface separation, object address distribution, and surface skipping techniques. The proposed approach considers the effects of human body movement to provide a realistic estimation of the wave propagation. Hence, an approximated human body model is used to simulate the activities of humans, whereas three-dimensional (3-D) cube or cuboids are used for the remaining objects of the simulation environment. To prove the superiority, complexity analysis and detailed comparisons between the proposed and existing methods are presented in this paper. The results obtained will be of great interest for the proposed ray tracing method that involves human motion within the simple and complex indoor environments.

1. Introduction Due to the widespread of telecommunications applications, recent years have shown an increasing interest in wireless networks that are utilizing millimeter band because of low cost and high data rate wireless communications. One of the disadvantages of this type of networks is that the received signal quality is highly influenced by the human body blockage.[1–6] As the network performance fully depends on the received signal quality, accurate predictions of the transmitted signals in the presence of the human body movement are therefore essential for this type of network deployment. In order to investigate the influence of human movements on radio wave propagation, some millimeter wave range channel propagation (using measurement incorporated with ray tracing) have been found in the literature.[7–10] Among these models, the traditional ray tracing algorithms are used to characterize the radio wave propagation for the simple indoor environments. To characterize the realistic complex indoor environments, *Corresponding author. Email: [email protected] Ó 2013 Taylor & Francis


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these methods are not suitable in terms of accuracy and computational efficiency. Therefore, an efficient and more accurate ray tracing algorithm is needed that will yield a minimum amount of computation time for sufficiently accurate simulation. This study proposed a new ray tracing method for the realistic indoor environments, where the motion of the human body is taken into account. To model the environment, data structures using C Sharp Object Oriented Programming are used to store the geometric properties and information about the objects and rays in the simulation environment. These data structures work independently in the simulation software, enabling easy to implement, and will make the characterization of indoor environments more flexible. The main contributions of this study are the accurate ray path prediction and reduction of the computation time. For the accurate ray path prediction, surface separation together with the calculation of the accurate direction of reflected, refracted, and diffracted propagated waves are considered in the proposed model. Moreover, object address distribution, surface skipping, and Red-Black tree data structure are used as new acceleration techniques in the proposed model. The proposed model is compared with the image,[7] Ray Launching (RL),[8] Space Volumetric Partitioning (SVP),[11] and Angular Z-Buffer (AZB) [11,12] methods and provides satisfactory results and good agreement with the proposed model. The proposed ray tracing method is described in Section 2, comprehensive complexity analysis is given in Section 3, and results and discussions are presented in Section 4, followed by a conclusion in Section 5. 2. Object modeling and ray tracing method Ray tracing [13] is vastly used in radio wave propagation prediction. One of the problems of ray tracing is the computational burden because of excessive ray-object intersection test. Hence, with the intension of reduction of ray prediction time, a new 3-D ray tracing for the complex indoor environment (including human body motion) is explored in this study. Before describing the proposed method, some essential tools have been described below. 2.1. Object and human body modeling The objects of the simulation environment (walls, partitions, and furniture) have been constructed by 3-D cubes or cuboids, which are shown in Figure 1(a). Whereas, an approximation of 2-D human body is illustrated in Figure 1(b), where head, hand, and body are represented by 2-D rectangles. Conversely, a 3-D version of the proposed human body model is projected in Figure 1(c). Here, we have used a 3-D rectangle limit to simplify the proposed body model. Khafaji et al. [7] have presented a human body model whose height of the rectangle limit is 1.70 m, whereas both width and depth is 0.305 m. It can be observed that the width and depth of the human body are not equal in size; therefore, this study used the average height, width, and depth of the rectangle limit of the proposed human body model which is 1.70, 0.56, and 0.305 m, respectively. 2.2.

Object address distribution technique

In ray tracing models, extensive search of ray-object intersections is needed to accomplish the ray tracing in 3-D planner spaces and thus, a huge amount of computation time is spent here. To reduce the computation time, object address distribution technique coupled with the Red-Black tree data structure is presented in this section. In this study, the object addresses are distributed according to the space splitting technique


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Figure 1. (a) Walls and partitions presented by 3-D cube or cuboids (b) approximated 2-D model of a human body (c) simplified 3-D representation of a human body model bounded by the 3-D rectangle limit.

(a technique that splits the entire simulation space to a given number of small rectangles, as illustrated in Figure 2). After splitting the simulation area, the information of newly formed rectangles has to store in the Red-Black tree nodes, as shown in Figure 3. Afterwards, at the time of object creation in the simulation space, each object is to be stored first in an object holder (shown at the bottom side of Figure 3). Then, the corresponding address of these objects will be stored in the pointers of the desired tree nodes, that is to say, object address distribution technique. For instance, referring to Figure 2, Object 1 exists on the Rectangle 1 and Rectangle 4; if it is stored in an object holder at position 1, then the address of this object is needed to store in the tree Node 1 and Node 4, as shown in Figure 3. Likewise, Object 2 exists on the Rectangle 5 and Rectangle 6 and if it is stored in an object holder at position 2, then this address will be stored in Node 5 and Node 6 of the Red-Black tree.

Figure 2.

Illustration of the objects exists on some splitting area.



Figure 3.

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Illustration of object address distribution technique.

This study selects Red-Black tree for storing the splitting part of the simulation area and corresponding object addresses. Because the worst case computational complexity of the object retrieval operation of a Red-Black tree is Oðlog2 N Þ,[14] where N is the number of split parts (small rectangles) of the simulation environment. However, an object holder having N split parts needed OðN Þ time in the worst case. The whole operation described above is done before the ray tracing process. Therefore, it does not affect the simulation time of the proposed ray tracing method. 2.3.

Surface separation and calculation of intersection point

At the beginning of ray tracing, rays are launched from the location of Tx at any angle h. Afterwards, an intersection test is performed to identify the intersection point on an object surface. To do this easily and accurately, the surface separation technique is introduced here. Based on the quadrant of rays, the particular surfaces are separated from the 3-D objects (humans, walls, partitions, and furniture) to determine the intersection point. For example, if a ray travels into the first quadrant, then this ray will possibly hit left/bottom surface of a 3-D object and thus, it will be sufficient to separate these surfaces from the 3-D object for the intersection test, as demonstrated in Figure 4. Similarly, for the second quadrant, right/bottom surface will be separated from a 3-D object. Top/bottom and Top/left surface will be separated from a 3-D object in the case of the third and fourth quadrant, respectively, that means, for each intersection test, only two surfaces are taking part in the intersection tests, namely surface skipping technique. Referring to Figure 4, a ray travels into the first quadrant and another ray travels into the second quadrant with respect to its origin, and thus, the bottom surface is first separated from the 3-D object to find out the intersection point (P) on it. To determine the ray and polygon intersection, many methods can be found in the literature. The simplest way is: (i) Perform an intersection test between the ray and the plane containing the polygon. If the intersection point does not exist on it, then finish the procedure. (ii) Afterwards, a point in polygon test is needed to determine whether it is inside the polygon or not.


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Illustration of separated surfaces of a 3-D object and intersection point.

In this study, we have ignored both these steps and directly perform the intersection test between the ray and polygon (separated surface), because we know each coordinate of 3-D objects that are used in the simulation environment and therefore, a significant amount of intersection time is saved by the proposed method. Detail of the intersection point calculation is given below. ~ originated from the P0 ðx0 ; y0 ; z0 Þ and if it is incident at a Given a ray P ¼ P0 þ U V, given polygon (separated surface) with m vertices of P1 ðx1 ; y1 ; z1 Þ through Pm ðxm ; ym ; zm Þ, then the intersection point Pðx; y; zÞ on this ray is calculated by the following equations: x ¼ x1 þ U ðx2 x1 Þ

ð1Þ

y ¼ y1 þ U ðy2 y1 Þ

ð2Þ

z ¼ z1 þ U ðz2 z1 Þ

ð3Þ

If the surface normal of the polygon is denoted by ~ S and the direction vector is denoted ~ðm; n; oÞ, the intersection point between the ray and the polygon will be computed by V by solving the implicit equation ðP P1 Þ ~ S¼0

ð4Þ

We can get the value of scalar parameter U of Equations (1–3) by following way

U¼

ðP1 P0 Þ ~ S ~ ~ V S

ð5Þ

where “.” is a dot product. The intersection point P is calculated by substituting the U value of Equation (5) into Equations (1–3). Based on the object properties and


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intersection type, this point (P) will be used to build either reflected, refracted ray, or diffracted ray for this simulation, as well-presented in Figure 5.

2.4. Direction of reflected, refracted, and diffracted ray The building materials and the existed objects inside the buildings influence the indoor radio wave propagation. A simple movement of interior objects can change the entire propagation paths of reflected, refracted, and diffracted rays. Therefore, an accurate calculation is needed to determine the direction of these rays. In this study, the direction of the propagated rays will be calculated using physics and vector geometry. [15,16] In Figure 5(a), ray Ri incident at point P on an object surface. The smallest positive angles of incidence, reflection and refraction, and the normal vector ~ S are hi , hr , and ht . Let ~ ni , ~ nr , and ~ nt be the unit vectors along with the direction of incident, reflected, and refracted ray, respectively, with ~ S being the normal vector at point P. For any of these angles h and any direction vector n, the direction of the reflected ray can be calculated using the following equation: ~ ni ð~ ni ~ SÞ~ S ð~ ni ~ SÞ~ S ¼~ ni 2ð~ ni ~ SÞ~ S nr ¼ ½~

ð6Þ

Figure 5. Illustration of (a) reflection and refraction of incident ray within a wall (b) diffraction of incident ray from an approximated human body model.

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where “.” represents the dot product. In the case of refracted ray, when a ray enters a denser medium, it will refract towards the normal vector. According to the Snell’s law, if a ray moves from one medium to another, the law of refraction takes the form n1 sin hi ¼ n2 sin ht ) sin ht ¼

n1 sin hi n2

ð7Þ

where n1 and n2 are the refraction index of the first and second medium, respectively. According to Figure 5(a), the direction of the refracted ray can be calculated as ~ nt Þjj þ ð~ nt Þ ? nt ¼ ð~

ð8Þ


After some simplifications, it can be expressed as 0

1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 n1 n1 n1 ~ S ni @ cos hi þ 1 ð1 cos2 hi ÞA~ nt ¼ ~ n2 n2 n2

ð9Þ

On the other hand, the direction of the diffracted ray as shown in Figure 5(b) is calculated by the following equation [17] !

!

PRi ~ S ¼ PRd ð~ SÞ

ð10Þ

where Ri is the origin of the incident ray, Rd is the end point of the diffracted ray, P is the intersecting point of the incident ray, and ~ S is the edge direction vector. Here, the ~ ¼N ~ , where W ~ is a vector that edge direction vector ~ S is oriented such that ~ SW ~ exists on the plane of one of the two polygons of the wedge and N is the unit vector.

2.5. Determination of closest intersection point based on the nearest valid rectangle detection When a launched ray is passed in any direction of the 3-D space, it may intersect more than one object. Therefore, it is needed to find out the closest object intersection of the ray. To do this, the closest intersection can be calculated by the following procedure: (i) By using the algorithm stated in Figure 6, perform intersection tests between the ray (Rstart) and objects that exist in the Rectangle 3, from where this ray is originated as shown in Figure 7(a). If any intersection is found in the origin of the rectangle, then skip the next step. (ii) Otherwise, perform intersection tests between this ray and rectangles (stored in the Red-Black tree as demonstrated in Figure 3), for searching the valid rectangles (2 and 4). Those rectangles are called valid rectangles that contain objects and must intersect with the ray. Once rectangles are found, store them in a list as the first nearest Rectangle 4 in the first position, then the second nearest Rectangle 2 in the second positions, and so on. Afterwards, retrieve the objects from the object holder (as predicted in Figure 3) by using the object addresses stored in the first nearest Rectangle 4, as presented in



Figure 6.

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Algorithm of the closest intersection point detection within a single rectangle.

Figure 7(b). Perform intersection test between the ray and these objects. In can be seen from Figure 7(b) that the ray (Rstart) does not intersect with the object in the Rectangle 4 and therefore, object in the second nearest Rectangle 2 is taking part in intersection tests for finding the closest intersection point (CI) as presented in Figure 7(c). If multiple intersections are found within a single rectangle as shown in Figure 8, then the closest intersection point (CI1 ) can be identified based on the distance from the ray’s emanating point. Referring to Figure 8, a ray starts at Rstart and ends at Rend . This ray intersects with two objects at CI1 and CI2 , respectively. According to the closest distance of origin of the ray, CI1 is the closest intersection of this ray, because the distance between Rstart and CI1 is closer than the distance between CI2 and Rend , that is, d1 \d2 \d. 2.6.

Ray tracing method

In the proposed simulation, human body is presented similar to a wall, partition, or furniture with identical surfaces, and these surfaces could reflect, refract, and diffract the propagated waves. The simulations are carried out by change of the location of each movable object (human). Initially, all objects are placed in their desired locations of the simulation space, where each object has a fixed location. Among these objects, only the location of the movable objects (humans) is modified by the predefined speed and


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Figure 7.

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Closest intersection point detection based on the valid rectangle detection.

Figure 8. The closest intersection point CI1 identified based on the distance from the ray’s emanating point.

direction before the simulation. Afterwards, the simulation results will be obtained by a regular time interval, which will provide the ability to recompute the simulation parameters and current location of the moving objects. For ray tracing in a particular time interval, this study considers an indoor environment, as presented in Figure 9. According to the space splitting technique, the simulation area is divided into six similar sized rectangles, the ID’s (1 through 6) of which are enclosed by the red background rectangles, as shown in Figure 9. Information of these rectangles and corresponding object addresses are kept in a Red-Black tree, as mentioned in Section 2.2. Ray tracing begins with launching rays in each possible direction in the simulation space. After building a ray, the traveling quadrant of the launched ray is calculated by using the incident angle h. When the incident angle h is in between 0 and 90°, 91 and 180°, 181 and 270°, and 271 and 359°, then this ray will travel the first, second, third,



Figure 9.

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Illustration of the proposed ray tracing in an indoor environment.

and fourth quadrant, respectively. In Figure 9, the transmitter and receiver are placed in the Rectangle 6 and Rectangle 4, respectively. It is clear that four significant rays reached the receiver by multiple reflections and each ray is composed of multiple ray segments. For instance, Ray 1 is formed by three ray segments TxA, AB, and BRx. To efficiently build up the ray segment TxA, the proposed algorithm first calculated the traveling quadrant of the ray segment TxA. Then, based on the procedure (i) stated in the previous section, it performs the intersection tests between the ray segment TxA and objects exist in the Rectangle 6. During the intersection test, particular surfaces are taken out one after another from the retrieved objects based on the surface separation technique, as described in Section 2.3. After that, intersection test has been done between this ray and separated object surface. It can be seen from Figure 9 that Ray 1 does not intersect with any object exists in the Rectangle 6. Therefore, the procedure (ii) is applied to find out the closest intersection point A. According to the procedure (ii) as described in the previous section, a search operation is performed within the Red-Black tree for finding the valid rectangles. In this situation, Rectangle 1, Rectangle 2, and Rectangle 5 are the valid rectangles, because they are intersected with the ray segment TxA. Afterwards, objects exist in the Rectangle 5 have to retrieve from the object holder by using the object addresses stored in the valid Red-Black tree nodes of valid Rectangle 5. In this case, also Ray 1 does not intersect with any object exists in this rectangle and therefore, objects in Rectangle 2 have to retrieve from the object holder by using the object addresses stored in Red-Black tree Node 2. After applying procedure (i), the closest intersection is found on the Object 17 and therefore, it will stop the searching operation within the Rectangle 1. It can be seen from Figure 9 that only 12 objects (2, 6, 7, 8, 9, 12, 13, 15, 17, 18, 20, and 21) are taking part in the intersection test. Based on the object property and intersection type, this intersection point is used as an origin of the reflected, refracted, or diffracted ray. The reflected ray is generated, when the ray segment hits the object surface.


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Diffracted ray is generated when the ray segment hit the sharp edge of an object, and refracted ray is generated when the ray hits the transparent objects. It is evident that the ray segment TxA hits the object surface, which is not a receiver and thus, a new ray segment AB has to be built. The direction of the reflected, refracted, and diffracted ray is calculated by using Equations (6), (9), and (10), respectively. To build up the ray segment AB, the proposed algorithm sequentially follows the procedures (i) and (ii). For the ray segment AB, only 9 objects (1, 2, 3, 4, 5, 6, 15, 16, and 19) are taking part in the intersection test and the closest intersection point B is found on Object 1. A new reflected ray BC has to build from the closest intersection point B. Therefore, the proposed algorithm applies the procedure (i) to find out the closest intersection point C. In this case, only 4 objects (1, 15, 16, and 19) exist in the Rectangle 4 are taking part in the intersection test. The ray segment BC intersects with the receiver, therefore, the entire ray path is considered as a significant ray path that originates from the transmitter and reached the receiver after multiple reflections. Therefore, another ray is needed to launch from the position of Tx to trace the next ray, and so on. In general, an intersection point can be found by testing each object surface of an indoor environment. Therefore, a total of 21 6 = 126 intersection tests is needed to find a single intersection point for the general ray tracing algorithm. Referring to Figure 9, three intersection points are needed to find the Ray 1 and thus, at least (3 126) = 378 intersection tests are required for the general ray tracing algorithm. Conversely, a total of (24 + 18 + 8) = 50 intersection tests is needed for the Ray 1 by using the proposed ray tracing algorithm because of the object address distribution and surface skipping techniques, which is 7.56 times less than the general algorithm. Figure 10 shows two different ray tracing scenarios (Figure 10(a) taken from the initial location of movable objects and Figure 10(b) taken by automatically moving the movable objects in other locations) generated by the proposed ray tracing method. In Figure 10, the locations labeled by Tx and Rx represent the transmitter and receiver, respectively and objects within the black circle are the humans. It can be observed from Figure 10(a) that 67 significant signals reached the receivers. However, 57 significant signals reached the receivers (as shown in Figure 10(b)) by following different propagation paths when the humans have changed their location. The proposed ray tracing method is projected in Figure 11. 3.

Complexity analysis

The proposed method uses object address distribution technique along with Red-Black tree data structure for the reduction of ray tracing time, where a significant amount of ray tracing time can be minimized by using the Red-Black tree. Because, the computational complexity for insertion, deletion, or searching of an object can be shown to be Oðlog2 N Þ. Based on this, the time complexity of the proposed method is given below. According to the object address distribution technique, if N number of objects is uniformly distributed over the simulation area, then on average N′ number of objects exists in a particular rectangle R, where R is the number of splitting parts (small rectangles) of the simulation space that are stored in the Red-Black tree. Therefore, N′ number of objects has S ¼ N0 s

ð11Þ



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Figure 10. Illustration of ray tracing (a) when movable objects are placed at their initial locations (b) after automatically moved to the new locations.

surface planes, where s is the number of surfaces of each object. The average number of objects N′ can be calculated using the following equation: N 0 ¼ N =R

ð12Þ

If r number of reflections is involved in a significant ray, the computational complexity of the proposed method is calculated by the following equation: r Oðlog2 R þ SÞ

ð13Þ

In this study, the surface skipping technique is applied to leave out the unnecessary object surfaces and thus, it will further reduce the ray tracing time of the proposed method. If s′ number of surfaces out of a total s number of surfaces takes part in intersection tests, then the total number of surface planes can be expressed as S 0 ¼ N 0 s0

ð14Þ

Finally, using Equations (13) and (14), the time complexity of the proposed method can be expressed as

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Figure 11.

Proposed recursive ray tracing algorithm.

r Oðlog2 R þ S 0 Þ

ð15Þ

On the other hand, ray tracing model in [7] is developed to demonstrate the effect of human movement on the wave propagation in a typical indoor environment. Here, the ray tracing algorithm (based on the image method) [18] is used for the characterization of the radio wave propagation. Hence, the time complexity of the image method for r number of reflections can be expressed as [19]


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OðS r Þ

ð16Þ

where S ¼ ðN sÞ surface planes in an environment. Moreover, another model described in [8] is also used to investigate the characteristics of the radio wave propagation in a living room under the influence of human movement. The RL algorithm is used in the ray tracing simulator that also involved to characterize the wave propagation in indoor environments. However, the time complexity for r number of reflections of the RL method is


r OðSÞ

ð17Þ

Because, every surface plane (S ¼ N s) is involved in the ray-object intersection test. One of the earlier techniques to reduce the number of ray-surface intersection tests is the SVP method.[11] According to [11], the 3-D space surrounding the environment is divided into voxels. All the voxels together constitute a volume that contains the environment. For each voxel, the surfaces that lie totally or partially inside are determined. This information is stored in the SVP matrix, which will be interrogated repeatedly in the intersection tests. According to this algorithm, let the simulation space is divided into R voxels and stored in a matrix M. During the intersection test, SVP method searches for a desired voxel among the R voxels, which needs OðRÞ

ð18Þ

computational time in the worst case. If on an average N′ number of objects exists in each voxel, then it can be calculated by using the following equation: N 0 ¼ N =R

ð19Þ

For r number of reflections, the worst case time complexity of the SVP method is calculated by the following equation: r OðR þ S 0 Þ

ð20Þ

where S 0 ¼ N 0 s. Another accelerated ray tracing method, namely AZB is presented in [11,12]. For a given source, the AZB technique divides the simulation space into some angular regions. Using an arrangement similar to the SVP method, they are called anxels as an abbreviation for angular elements. Afterwards, the surfaces of the scene that lie in each anxel are determined. The information about the anxel and corresponding surfaces is stored in the AZB matrix. According to this method, the number of angular region (AR ) is calculated by the following equation AR ¼

360 No of anxels

ð21Þ

During the intersection tests, this method retrieves the surfaces from the angular region AR that are stored in AZB matrix M. For r number of reflections, AZB method spends r OðAR þ S 0 Þ

ð22Þ

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Table 1.

M.J. Islam et al. Time complexity of the proposed and existing ray tracing algorithms.

Algorithm

Worst case time complexity

Image method [7] RL method [8] SVP method [11] AZB [12] Proposed method

OðS r Þ r OðSÞ r OðR þ S 0 Þ r OðAR þ S 0 Þ r Oðlog2 R þ S 0 Þ

time in the worst case, where S′ is the number of surfaces in a particular angular region (AR ). In order to compare the proposed and existing methods, a comparison of time complexity is projected in Table 1. It is obvious that the time complexity of the proposed method is much better than the time complexity of the existing methods because of the Red-Black tree data structure, object address distribution, surface skipping, and smart object searching techniques, as described earlier. 4.

Results and discussion

The simulation environment is implemented over Visual Studio 2008 software. The results of various scenarios are compared with the same hardware configuration. For the simplicity, the results and discussion part is divided into two subsections. In the first subsection, comparisons based on the ray prediction accuracy (predicted rays) and ray prediction time will be presented. On the other hand, the impact of the human movement on the received rays, computation time, and received power will be presented in the next subsection. 4.1. Performance evaluation The proposed method is compared with the image,[7] RL,[8] SVP,[11] and AZB [12] methods. All simulations have been done for two different environments: first one is a simple environment as shown in Figure 9 and the second one is a very complex environment as shown in Figure 10. The obtained results confirm the precedence of the proposed algorithm. The image method is accurate, because it can guarantee that all the specular paths up to a given order will be found, but it suffers from inefficiency. When the number of walls, partitions, and furniture involved is large and there are many reflections, refractions, and diffractions for a single path from transmitter to receiver, this method suffers from a large computation time. On the other hand, the accuracy of the RL method is significantly reduced for those rays that are traveling long distances from the transmitter. In this condition, such ray tracers may miss important interactions and thus, it can be said that the RL technique is suffering from accuracy in terms of ray prediction. The proposed method is developed for better performance with respect to both ray prediction accuracy and computational efficiency. It can predict all specular paths up to a given order because of rays that are launched in each possible direction in the 3-D indoor environment. Moreover, the proposed method first searches the Red-Black tree for finding the valid rectangles, then objects exist within these rectangles and only two surfaces of each object take part in the intersection test. Therefore, none of the intersections have been missing during the intersection tests, which ensures that the proposed method is more accurate than the existing methods. On the other hand, the computation time of the

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proposed method remains at a minimum level because of the object address distribution, surface skipping, and smart object searching techniques, as mentioned in subsections 2.2, 2.3, and 2.5, respectively. In addition, it can be said from the complexity analysis that the proposed method can reduce a huge amount of ray prediction time compared to the existing ray tracing methods used in [7,8,11,12]. As the accuracy (number of predicted rays) is same with the image and SVP methods, Figure 12 shows a comparison, which is based on the predicted rays and corresponding computation time that considers the human body moving parallel to the line-of-sight (LOS) paths in two different indoor environments, as shown in Figures 9 and 10, respectively. It is observed from Figure 12(a) that the proposed method predicts the higher amount of rays compared to the RL (it is about 4 and 16%) and AZB (it is about 2.28 and 2.67%) methods, when the simulation was carried out in a simple and complex indoor environment, respectively. According to Figure 12(b), the proposed method is 69.30 and 91.47% (on average) faster than the RL and image methods, when the simulation was carried out in the simple and complex indoor environment, respectively. The SVP method spends 29 and 32.5% more computational time than the proposed method for simple and complex indoor environment, respectively. Because, the only surfaces that must be tested for intersection are stored in the voxels matrix pierced by the ray and search operation of those surfaces from voxels matrix follows the linear search time instead of the logarithmic search time. Conversely, the AZB method takes almost the same amount of computational time with the SVP method in the case of the simple indoor environment, while takes additional 14.95% computational time for the complex indoor environment.

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Figure 13.

Model of LOS blocking by a human body in a complex indoor environment.

For a given number of anxels, the efficiency of the angular partitioning decreases when the size of the scene increases. This is because, far away from the source, the area that occupies each anxel will be large so that it could contain a large number of surfaces and therefore increases the computational time. Moreover, it can be observed from Figure 12(b) that the proposed method relatively obtaining the constant time for two different environments and the simulation time does not directly follow the number of objects in the indoor environment. 4.2.

Effect of human movements

To demonstrate the human movement effect on the received rays and subsequent computation time, this study considers a single floor of dimension 20 m 32 m having multiple furnished rooms, as shown in Figure 13. During the simulation, the Tx and Rx have remained in a fixed position. The presented human body model as illustrated in subsection 2.1 is used to simulate the human activity in the indoor environments. The reflection and transmission coefficient is calculated from [20]. The diffraction coefficient of the proposed and existing methods is calculated by using Uniform Theory of Diffraction.[17] A semi-spherical antenna operating at 60 GHz with 15 dB gain and radiating 10 mW is used for both the Tx and Rx. Detailed specifications of the indoor environment used in the proposed simulation software are estimated in Table 2.

4.2.1. Effect of single human movement for different distances between human and Rx To investigate the effect of single human movements for different distances between human and Rx, simulation starts at d = 1 m and ends at 1 m on the other end of the path, as presented in Figure 13. In order to show the different situations on the received rays and their computation time for the proposed and existing ray tracing algorithms used in [7,8,11,12], the results for a single human moving with different distance D from the receiver (Rx) are deliberated and plotted in Figure 14. It can be observed from Figure 14(a),

Journal of Electromagnetic Waves and Applications Table 2.

Specifications of the simulation environment.

Name

Materials

Human Outer wall Outer wall Inner wall Door Table

Human body Brick Glass Brick Glass Wood

(a)

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Permittivity ðer Þ

1.70 2.8 2.8 2.8 2.8 0.9

0.56 – – – – –

0.305 0.21 0.21 0.1 0.04 0.04

1.0 5.2 3.0 5.2 3.0 3.0

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Figure 14. Received rays and their computation time variations due to human movement for different distances between the human and Rx.

snapshot index 15–25 are the situations so that the center of the human body is on the LOS paths, therefore, the received rays are rapidly falling down, and large variations on the received rays are obtained for two different distances between the human body and Rx. The obtained results also show that the proposed method always predicts the higher amount of rays than the RL and predicts almost the same amount of rays as the image, SVP, and AZB methods. Conversely, it can be observed from Figure 14(b) that the existing methods took more time than the proposed method. Moreover, deviations on computation time are obtained (as shown in Figure 14(b)) when the distance between human and Rx is changed from 1 meter to 2 meters while the computation time remains constant for the proposed method. Therefore, we may summarize that the human body movement at different distances between human and Rx has less effect on the computation time of the proposed method due to the object address distribution, surface skipping, and smart object search techniques.

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Figure 15. Received rays and their computation time variations for the multiple humans moving parallel or perpendicular to the LOS path.

4.2.2.

Effect of the multiple human movements

A comparison based on the ray prediction and computation time for different human movements is shown in Figure 15, where different numbers of humans moving parallel or perpendicular to the LOS paths in the indoor environment are taken into account. This simulation result is also taken from the indoor environment, as shown in Figure 13. To show the different situations on the received rays for different ray tracing algorithms, the results of random multiple human movement with different distances from the receiver (Rx) are calculated here. From this figure, it can be observed that the predicted rays for the proposed method increases with the number of humans compared to the RL method, while predicting almost the same amount of rays with the other three methods, as shown in Figure 15(a). Conversely, the computation time remains same with the different number of humans, as shown in Figure 15(b). The reason is that the proposed method launches rays in each possible direction and predicts all significant propagation paths that we already described in subsection 4.1. Moreover, a comparison based on the received power is demonstrated in Figure 16, where different number of human movements is taking into account. It can be observed from Figure 16 that variations on the received power are obtained for different ray tracing algorithms. This is because, most of the rays reached the receiver through multiple reflections, refractions, and diffractions, and contribute to the received power in indoor environment. These rays may follow the different propagation paths based on the technique used in the different ray tracing algorithms. Therefore, differences in the received rays are observed for the different ray tracing algorithms that also make a difference on the received power.


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Figure 16. Comparison based on the received power for different number of humans while moving parallel or perpendicular to the LOS path.

According to Figure 16(a), the proposed method predicts almost the same amount of the received power as image, SVP, and AZB methods, while better prediction results obtained in the case of the RL method, when six humans are moving in parallel and perpendicular to the LOS path. On the other hand, the proposed method offers almost the same prediction results than the image and SVP methods, whereas better received power is obtained compared to the RL and AZB methods, as shown in Figure 16(b), when nine humans are moving in parallel and perpendicular to the LOS path. 5. Conclusion In this paper, an accelerated and accurate ray tracing method is proposed for the real-life indoor environment, which is able to estimate the influence of human motion on indoor radio wave propagation. In order to prove the superiority of the proposed ray tracing method, this study compares the proposed method with the image and RL methods as well as with faster ray tracing approaches, such as SVP and AZB, and found that the proposed method yields better performance in different scenarios. This is because, the proposed method launched rays in each possible direction and used a faster object searching technique based on the object address distribution and surface skipping techniques. As a result, none of the intersections are missed during the ray tracing and thus, the minimal computation time is consumed by the proposed method for sufficiently accurate simulation. The proposed ray tracing method can be efficiently used to characterize the wave propagation (at millimeter band frequencies) in a given realistic single-storied building having multiple furnished room indoor scenario. Acknowledgements This research work is supported by the University of Malaya High Impact Research (HIR) Grant (No. UM.c/HIR/MOHE/ENG/51) sponsored by the Ministry of Higher Education (MOHE), Malaysia.

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