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Int. J. Electron. Commun. (AEÜ) 66 (2012) 439– 447

Contents lists available at SciVerse ScienceDirect

International Journal of Electronics andCommunications (AEÜ)

jou rn al h omepage: www.elsev ier .de /aeue

n efficient two-dimensional ray-tracing algorithm for modeling of urbanicrocellular environments

anjay Soni ∗, Amitabha Bhattacharyaepartment of Electronics and Electrical Communication Engineering, IIT Kharagpur, West Bengal, India

r t i c l e i n f o

rticle history:eceived 30 April 2011

a b s t r a c t

In this work, an efficient ray-tracing approach based on decomposition of visibility-tree into sub-tree hasbeen compared with the conventional approach. The comparison is done in the context of both the com-

ccepted 11 October 2011

eywords:eterministic propagation modelicrocellular scenario

putational complexity and accuracy of the ray-tracing algorithm. Three independent urban scenarios areconsidered for this comparison. It is observed that the efficient approach based on use of sub-tree reducesthe computational complexity significantly. Further, the proposed ray-tracing algorithm is applied to amicrocellular environment to compute rms delay spread and the results are compared with availablemeasurements.

ay tracingniform theory of diffraction (UTD)

. Introduction

Due to ever-demanding high-data rate by mobile customersn 3 G/4 G networks (e.g. in 4 G, significantly higher bit rate than

Mbps with typically 100 Mbps as maximum), there is great inter-st in multiple-input multiple-output (MIMO) technology whichnhances channel capacity by taking advantage of the multipathadio channel [1,2]. This technology uses adaptive antenna ele-ents whose performance strongly depends on the directional

roperty of channel (such as delay spread, angular spread). Thisequires accurate modeling of the propagation channel [3].

Among different propagation models available, deterministicodels are most preferable prediction tool as they can give accu-

ate prediction in various kinds of scenarios without any need of theumbersome measurement [4,5]. Deterministic model based on theay approximation of electromagnetic field is most suitable whenhe scattering body is electrically large. Thus, ray model finds widepplications in the urban scenarios where buildings are involved.

The main hurdle in successful implementation of ray-tracingool for commercial purposes is the enormous computation timeaken by the computer programme. In the literature, variouspproaches have been suggested to enhance the speed of the ray-racing tool. For instance, in [6], it is shown that some ray paths areommon between transmitter (Tx) and receiver (Rx). Thus, they can

e computed by determining the ray path only once. This is doney decomposing the ray paths in four categories Tx–Rx, Tx–D, D–D,–Rx where D stands for diffraction. The ray trajectory between Tx

∗ Corresponding author. Tel.: +91 1368 228030; fax: +91 1368 228062.E-mail addresses: sanjoo.ksoni@gmail.com, amitabha@ece.iitkgp.ernet.in

S. Soni).

434-8411/$ – see front matter © 2011 Elsevier GmbH. All rights reserved.oi:10.1016/j.aeue.2011.10.005

© 2011 Elsevier GmbH. All rights reserved.

and Rx is established by appropriately concatenating the elementsof the above categories. In [7], the proposed method overcomesthe problem of the Shooting-and-Bouncing (SBR) method’s require-ment of tracing all of the rays to the receiver emitted by thetransmitter by noting that most of the emitted rays do not reachthe receiver. In [8], simplification of input database is proposed.In this approach, the two nearby buildings with same heights arejoined. Second approach is to reduce input database by selecting“active set” of buildings and discarding rest of the buildings. In [9],Carluccio et al. uses modified Newton search algorithm for tracingthe multiple diffracted paths assuming a series of arbitrarily placedwedges that are completely visible to each other.

When the height of the building is much larger than the heightof the transmitter and the receiver, the ray-tracing tool can be sim-plified to trace the ray paths only in the horizontal plane and henceinput database of the buildings does not require height informa-tion of the buildings. In such scenarios, the predicted results oftwo-dimensional ray-tracing are shown to be adequate [10–12].

Image-based two-dimensional ray-tracing algorithm is pre-sented in [13]. This algorithm is based on ray-tube method andit uses visibility-tree (VT) of the building scenario to construct theray paths. It is fast in the sense that it does not require any testing toexamine whether the selected ray-path in the VT of building layoutis valid or not. However, this method requires redundant com-putation time to compute children of images and virtual sources,which is very time consuming. In [14] a more efficient approachto implement the ray-tracing tool using VT has been presented.The approach is based on VT and pre-processing of the data before

actual ray-tracing tool is run. One of the main challenges faced inimplementing the ray-tracing tool is the sharp rise in the com-putational complexity with the increase in the order of scattering[9,12].

440 S. Soni, A. Bhattacharya / Int. J. Electron. Commun. (AEÜ) 66 (2012) 439– 447

y tree

mwdasccit

tbdsaS

2

2

woiaisowo

tFTdrdsviIr

Fig. 3. This VT is prepared up to third-order scattering with the rootof tree as transmitter. The whole VT is divided into number of sub-trees. For simplicity, only three sub-trees at scattering level-1 areshown in Fig. 3. These are sub-tree1, sub-tree2 and sub-tree3. These

Fig. 1. An example of a building scenario and its visibilit

In this paper, the comparison between an efficient ray-tracingethod based on decomposition of VT into sub-tree has been doneith conventional ray-tracing method. The comparison has beenone in the context with computational complexity as well asccuracy of algorithm both. For this purpose, three microcellularcenarios of Ottawa city, Bern city and Fribourg city have beenonsidered. It is observed that ray-tracing tool based on sub-treeoncept results in considerable reduction in computational time. Its further observed that there is a moderate rise in the computa-ional complexity with the increase in the scattering order.

The paper is organized as follows. Section 2 describes brieflyhe concept of sub-tree, their construction. This also includes arief discussion on the propagation model, the extension of two-imensional model to three-dimensional model and rms delaypread. Section 3 presents the comparison between predictions andvailable measurements of both path loss and rms delay spread.ection 4 concludes the work.

. Proposed ray tracing algorithm

.1. Construction of visibility-tree

The scheme of the propagation environments considered in thisork can be observed in Fig. 1. Fig. 1(a) is a two-dimensional view

f a multiple building environment where Tx and Rx are consideredn the same plane. To determine the valid ray path from Tx to Rx in

given scenario, the use of VT is an effective approach [13]. Fig. 1(b)llustrates an example of the construction of the VT of the buildingcenario shown in Fig. 1(a). There are basically two kinds of sec-ndary sources generated: (i) image source (IS) at the surface of aall (ii) virtual source (VS) at the corner. These are called children

f Tx.Each of the secondary sources can now produce its own children

hat contain both image source and virtual source. For example, inig. 1(b), IS1 at I-order level generates k children VS1, VS2 . . . VSk.hey are called II-order sources. This recursion continues till theesired scattering order is reached. To determine the ray path, aeceiver is tested if it lies in the shadow region of a given child atesired scattering order. If Rx lies in the visibility region of the childource, then, the backward ray path from Rx to Tx can be traced and

alid ray-path can be determined without doing shadow-test. Fornstance, in Fig. 1 if Rx lies in the lit region of image source IS1 atI order, then, the II-order ray path is Rx–IS1–VSm–Tx as shown ined colour. Therefore, we note that construction of VT for a given

: (a) 2D view of building scenario and (b) visibility-tree.

scenario plays a crucial role in the determination of a ray path. Inthe VT, it is the determination of the valid children of a given sourcethat takes most of the computational time. Once the children up tothe desired scattering levels are obtained, determination of the raypath is done simply by moving in backward direction from Rx toTx.

2.2. Construction of sub-tree

In the ray-tracing algorithm based on sub-tree, we decomposethe visibility-tree of a given scenario into a number of sub-treeswhich can be generated from the building database irrespectiveof the position of Tx in the scenario. Therefore, the required VTof a given scenario is nothing but simply a concatenation of thesestored sub-trees. In order to elaborate this approach, we considera simplified two-building scenario as shown in Fig. 2.

We note that there are eight corners and eight faces of this twobuildings scenario. Image source at the face and virtual source atthe corner are denoted as ISj

iand VSj

irespectively where i is the

index number of the image/virtual source and j is the scattering-order. The VT corresponding to this building scenario is shown in

Fig. 2. Simplified two-building scenario (2D view).

S. Soni, A. Bhattacharya / Int. J. Electron. Commun. (AEÜ) 66 (2012) 439– 447 441

Table 1Number of virtual sources with increase in the order of the scattering for a particularscenario of Fig. 2.

Scattering order VS1 VS2 VS3 VS4 VS5

I-Order 1 1 1 1 1II-Order 3 2 3 4 3III-Order 10 11 5 11 6IV-Order 21 34 35 30 37

sptsaa

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sititcnoa

Table 2Look-up table showing the range of the children and their number.

Index No. Total No. of children Range

IS VS IS VS

1. n1 m1 1 − S1 1 − U1

2. n2 m2 (S1 + 1) − S2 (U1 + 1) − U2

N∑

ub-trees are independent of visibility-tree and hence they can berepared independently using building database. Note that sub-ree2 contains sub-tree1 as its subset. Similarly, sub-tree3 containsub-tree1 as its subset. Therefore, once the subtree1 is preparednd stored, it can be directly used in the construction of sub-tree2nd sub-tree3. It is interesting to note that children of VSj

iand chil-

ren of VSki are exactly same. Therefore, children of VSj

iobtained

y processing the building database can be used at any scatteringrder. As we go down to the higher scattering level, this situations more often encountered where sub-tree, prepared once usinguilding database, can be employed more frequently. Table 1 showsn example of how the number of VS increases as we go down thecattering order, establishing the above mentioned fact clearly. Thisesults in great saving in computation time by avoiding computa-ion of higher order sources. This also results in moderate rise inomputational complexity while going from Nth scattering level toN + 1)th scattering level as will be shown in Section 3.

Considering Fig. 2 once again, there will be eight sub-trees corre-ponding to eight corners of the buildings. The root of the sub-trees always the virtual source. Similarly, we can construct the sub-rees with image source as the root of the sub-tree provided thesemage sources are the children of the virtual source. This is dueo the reason that if they are the children of the virtual source atorner, only then their position will be fixed in the building sce-ario. These sub-trees are constructed irrespective of the position

f the transmitter and the receiver in the buildings scenario. Welso note from Fig. 3 that the length of the sub-tree can be as long

Fig. 3. Decomposition of visib

3. n3 m3 (S2 + 1) − S3 (U2 + 1) − U3

– – – – –N nN mN (SN−1 + 1) − SN (UN−1 + 1) − UN

as we require depending on the scattering order. Fig. 5 shows theflowchart for the ray-tracing method based on sub-tree.

2.3. Preparation of look-up table

We note that there are N sub-trees possible for the buildingscenario with N corners shown in Fig. 2. Each of the sub-tree hasits root as virtual source as shown in Fig. 5. We store the firstorder IS children of all sub-trees in a matrix IMAGE SOURCE (i,J),i = 1, 2,. . .P;j = 1,2 where P is the total image source children of allsub-trees. Similarly, We store the first order VS children of all sub-trees in a matrix VIRTUAL SOURCE (i,J), i = 1,2,. . .Q; j = 1, 2 where Qis the total virtual source children of all sub-trees. In order that themain ray-tracing program picks up suitable children of a sub-tree,we have to define corresponding range of children belonging to aparticular sub-tree. Therefore, we store the information about thisrange in a look-up table shown in Table 2.

The first column of the table shows the index number of cornerpoints of the building. For each index number of corner point, thenumber of image and virtual sources are listed in columns II andIII. The range of IS and VS are given in fourth and fifth columnsrespectively. Though this table incorporates the first order childrenof all sub-trees, the table can be extended to incorporate the totalchildren of desired scattering order of all sub-trees.

SN =i=1

ni (1)

ility-tree into sub-trees.

442 S. Soni, A. Bhattacharya / Int. J. Electron. Commun. (AEÜ) 66 (2012) 439– 447

Fig. 4. Multiple diffractions and reflections from building.

Fig. 5. Flowchart for proposed ray-tracing algorithm.

tron. Commun. (AEÜ) 66 (2012) 439– 447 443

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Table 3Comparison between conventional and new approach for prediction of path loss fordifferent number of building walls.

No. of walls Available approach(computation time) (s)

New approach(computation time) (s)

20 4.9 1.86

¯

S. Soni, A. Bhattacharya / Int. J. Elec

N =N∑

i=1

mi (2)

here N is total number of corner points of the given map, ni ishe total number of image children of ith sub-tree, mi is the totalumber of virtual children of ith sub-tree.

.4. Computation of field at receiver

In the free space, the electric field in the direction of (�, �) in thear field of transmitting antenna at a distance of r is given by [15]:

(r, �, �) = [E0,�(�, �)e� + E0,�(�, �)e�]exp(−jˇr)

r(3)

here

0,(�,�)(�, �) =√

PT �0

2�g(�,�)(�, �) (4)

here PT is the average transmitted power, �0 is the intrinsicmpedance of the free space and g(�,�) is the antenna gain in (�,) direction. Let E� and E� be the � and � components of the fieldt receiver. Then, the total field at receiver is given by

total = E� × e� + E� × e� (5)

It may be noted that for vertically polarized antenna (in this case,he vertical field component will be parallel to wall surface), E� wille much greater than E� .

Fig. 4 shows the multiple diffractions and reflections scenariorom the buildings. Consider, for example, a multiple scatteringcenario where the field reflects N times before the first diffrac-ion, Q times between two diffractions and M times after secondiffraction. The � component of field at receiver is given by [15]

� = E0,�(�, �)exp(−jˇrTR)

rTR

N∏n=1

R⊥n Ds(1)

√rT1

r12(rT1 + r12)

Q∏q=1

R⊥q Ds(2)

×√

rT1 + r12

r2R(rT1 + r12 + r2R)

M∏m=1

R⊥m (6)

here R⊥i

is the reflection coefficient of ith surface with perpendicu-ar polarization, rT1, r12, r2R, rTR are the distances as defined in Fig. 4.arameter Ds is the diffraction coefficient (with soft polarization)nd it is defined in [17].

After combining all the received multipath components coher-ntly (with phase), the total power is given by

R = �2

8��0

∣∣∣∣∣N∑

i=1

[E�,i × g� + E�,i × g�

] ∣∣∣∣∣2

(7)

here � wave number; �0 is instrinsic impedance of free space; Ns number of multipath components received at Rx

If the receiving antenna is vertically polarized, which is generallyhe case in mobile communication, and then the received power isiven as

R = �2

8��0

∣∣∣∣∣N∑

i=1

[E�,i × g�

] ∣∣∣∣∣2 (8)

nd path loss is given as

L(dB) = PT (dB) − PR(dB) + GT,max(dBi) + GR,max(dBi) (9)

42 34 8.372 167 28

2.5. Extension of 2D approach to 3D approach

Conversion of 2D ray path to 3D ray path can be done followingthe approach discussed in [6]. Propagation environment for singlebuilding scenario and double building scenario are shown in Fig. 6.Fig. 6 (a) depicts 2D ray model and its corresponding 3D ray model.We note that there are two possible 3D ray paths Ray-1′ and groundreflected ray path called Ray-1′′ corresponding to one 2D ray path.These 3D ray paths are computed using approach in Fig. 7. We notethat x1 + x2 = d and x1/x2 = ht/hr. From these two equations, we cancompute ground reflection point. In order the compute the heightof diffraction point E for Ray-1′, we can use

EF

d1= (ht − hr)

(d1 + d2)(10)

Fig. 6(b) shows another scenario where 2D Rays Ray-1 and Ray-2 corresponds to 3D rays Ray-1′, Ray-1′′ and Ray-2′ respectively.These rays can be determined using the approach discussed in Fig. 7.In order to include the possibility of roof top Ray-3, 2D ray-tracingtool needs to be modified to check if the Ray-3 exists or not. This canbe done by comparing the height of the building with the height ofthe intersection point A using previous approach. If the height ofthe building is lesser, then, this ray will exist otherwise, this will beblocked.

2.6. Delay spread

The delay spread is a measure of multipath richness of a channel.R.M.S delay spread is given by [21]

�� =

√∑Ni=1(ti − t)2

P∑Ni=1Pi

=√∑N

i=1(ti)2P∑N

i=1Pi

− (t)2 (11)

where ti is the arrival time of ith multipath and it is calculated asti = Li/c, Li is the total distance of ith multipath and c is the speed ofthe light. The parameter i is mean delay time and is defined as

i =∑N

i=1 t × P∑Ni=1Pi

(12)

where N is total number of multipath for given position of Tx andRx.

3. Results and discussion

3.1. Application of the proposed ray-tracing algorithm to Ottawacity

In this section, the overall performance of proposed ray-tracingis analyzed. As two-dimensional ray-tracing is suitable for micro-cellular scenario, we took microcellular environment (Ottawa city)for which measurement was carried out by Whitteker [16]. In a

particular region (core) of this city, there are 15 buildings and total72 walls. This urban scenario is presented as 2D view in Fig. 8. Themeasurement was carried out along the Bank St. and Tx is at 263Laurier St. and frequency of operation was considered as 910 MHz.

444 S. Soni, A. Bhattacharya / Int. J. Electron. Commun. (AEÜ) 66 (2012) 439– 447

) single-building and (b) double-building.

pcduml[pa

Fig. 6. Propagation environment: (a

In our calculations, reflected and diffracted fields are com-uted using the Fresnel reflection coefficient and the diffractionoefficient of El-Sallabi et al. [17]. In all the prediction results, con-uctivity of � = 0.001 S/m and relative permittivity of εr = 7 weresed. The value of εr is consistent with the range 5 ≤ εr ≤ 7 by directeasurement [3] and the value of � is consistent with [18]. Path

oss predictions were obtained using both the available approach of13] and the proposed ray-tracing method. Table 3 shows the com-

arison between available two-dimensional ray-tracing and newpproach for the prediction of path loss for different number of

Fig. 7. Conversion of 2D ray to 3D rays.

Fig. 8. Map of Ottawa city.

walls of buildings of the scenario depicted in Fig. 8. Total time takento process the database for constructing sub trees is 30 s.

It can also be noted that using available ray-tracing approach

[13], there is an exponential growth in the computation time (CT)as the number of walls increases. On the other hand, the propor-tion by which the CT increases for the proposed approach is muchslower. It is because of more frequent use of sub-trees in the higher

Table 4Comparison between conventional and new approach for prediction ofpath loss at RX using conventional and new approach (Intel Core2quadCPU,Q9400@2.66 GHz,3.24 GB RAM): complete simulation (CT = computationtime).

Prediction order Conventional approach New approach

CT (s) No. of sources CT (s) No. of sources

2 Refl, 2 Diffr 4.5 1687 2.58 11843 Refl, 2 Diffr 167 62,578 28 23,281

S. Soni, A. Bhattacharya / Int. J. Electron. Commun. (AEÜ) 66 (2012) 439– 447 445

posed

oNcdcdcavctlmewsupibaapai

Fig. 9. Comparison between path loss obtained using pro

rder of scattering levels. This reduces computational load fromth to (N + 1)th scattering level. Table 4 shows the comparison ofomputation time for the complete simulation of path loss pre-iction at a given Rx location. The comparison is shown for twoases: (i) 2 reflections and 2 diffractions, (ii) 3 reflections and 2iffractions. It can be noted that the proposed method results inomputation time reduction by more than 80 percent. This tablelso gives the details of total number of sources (Image source plusirtual sources) in both the cases. This gives an indication of theomputational complexity. It is also quite obvious from the tablehat for conventional cases, there is sharp rise in the computationaload (almost 35 times) whereas using proposed method, there is a

oderate rise in computational load (almost 11 times). Here, thextent of improvement is not claimed to be same for all cases (asill be seen in the following example), but in any case it does repre-

ent adequate improvement. Though the comparison is shown onlyp to 3 reflections and 2 diffractions, it is quite obvious that pro-osed method will give drastic reduction in the computational load

n the higher scattering order as well. Fig. 9 shows the comparisonetween predicted results obtained using proposed method andvailable measurement [16]. Simulation results obtained based onvailable ray-tracing method [13] is also included for comparison

urpose. We note that both are exactly same. The prediction resultvailable elsewhere [6] is also included for comparison. This results reported to be generated using 5 reflections and 2 diffractions. We

Fig. 10. Map of Bern City [11,12].

ray-tracing algorithm and available measurement [16].

note that both the results (i.e. proposed result and Daniela result)are almost same with some discrepancy in the lower part of theplot. That may be due to lesser number of reflections order used inthe proposed algorithm.

3.2. Application of the proposed ray-tracing algorithm in Berncity

We consider another example of microcellular scenario of Berncity (Switzerland) for which measurement is available in [12]. Inthe region of interest of this city, there are 23 buildings with 103walls. The frequency of operation is 1.89 GHz. Conductivity and rel-ative permittivity of the wall were considered to be � = 0.001 S/mand εr = 5 respectively as reported in [12,18]. The map for Bern cityis shown in Fig. 10. The transmitter is located at ‘src2’ (See Fig. 10)and the receiver movement is along Rodtmatt St. Comparison ofthe proposed ray-tracing algorithm with available approach [13]is presented in Tables 5 and 6. In Table 5, the comparison is madewith respect to increase in the number of walls. Here, it is noted thatcomputation time using new approach is significantly lower thanthat required using available approach. In ray-tracing algorithm,scattering order in ray-tracing engine was set to 3 reflections and2 diffractions. Table 6 shows complete simulation for calculationof the field at the given receiver location. Here, comparison is donewith the increase in the scattering order. We note that there is dras-tic reduction in computational load with the increase in scatteringorder. Fig. 11 shows the comparison of path loss prediction usingproposed ray-tracing algorithm and available measurement [12].In this path loss prediction result, our ray-tracing program also

included the transmission through the building, scattering fromtree [19, Eqs. (13) and (16)] and knife-edge model [20, Section V].This result shows that there is no compromise on the predictionaccuracy of the proposed ray-tracing algorithm.

Table 5Comparison between conventional and new approach for prediction of path loss fordifferent number of building walls in Bern city.

No. of walls Available approach(computation time) (s)

New approach(computation time) (s)

20 5.62 2.7669 416 64103 1132 118

446 S. Soni, A. Bhattacharya / Int. J. Electron. Commun. (AEÜ) 66 (2012) 439– 447

Table 6Comparison between conventional and new approach for prediction of path lossat RX of Bern city (Intel Core2quad CPU,Q9400@2.66 GHz, 3.24 GB RAM): completesimulation.

Prediction order Conventional approach New approach

CT (s) No. of sources CT (s) No. of sources

2 Refl, 2 Diffr 16 4048 6 2677

C

3F

bwfiTotrtcTptnta

Fa

Fa

Table 7Comparison between conventional and new approach for the prediction of path lossin Fribourg city (Intel(R) Pentium (R) Dual CPU T 3400 @ 2.16 GHz,1.96 GB of RAM):complete simulation (no. of RX points taken along receiver route is 80).

Prediction order Conventional approach New approach

CT (s) No. of sources CT (s) No. of sources

2 Refl, 2 Diffr 46 15,440 38 15,680

3 Refl, 2 Diffr 1132 232,545 118 66,380

T, computation time.

.3. Application of the proposed ray-tracing algorithm inribourg city

Finally, the proposed ray-tracing algorithm is applied to Fri-ourg city [11, Fig. 3]. Measurement route is shown by red colour forhich measurement was carried out by Rizk et al. [11]. Operating

requency taken is 1.8 GHz. Relative permittivity and conductiv-ty were considered to be εr = 5 and � = 0.0001 S/m respectively.able 7 shows the comparison of computation time for predictionf path loss in the receiver route between the conventional andhe proposed algorithm. Total number of Rx samples taken in theeceiver route is 80. We note that almost 50% percent computationime is saved. Here, computation time reduction is not as signifi-ant as in the two cases reported in the previous two subsections.his is due to lesser number of buildings involved in the path lossredictions. From the above two examples, it is quite obvious thathe advantage of the proposed algorithm is more significant when

umber of buildings involved in simulation is large. Fig. 12 showshe comparison of path loss obtained using proposed algorithm andvailable measurement [11]. Significant gap between prediction

ig. 11. Comparison of path loss obtained using proposed ray-tracing algorithm andvailable measurement [12].

ig. 12. Comparison of path loss obtained using proposed ray-tracing algorithm andvailable measurement [11].

3 Refl, 2 Diffr 448 144,640 260 145,760

CT, computation time.

and measurement in the lower part of the result is possibly due toignoring scattering from tree as shown in [19]. In the figure, predic-tion using available ray-tracing approach [13] is also included. Thisis exactly same as that obtained using proposed algorithm. Thus,we note that there is no compromise with prediction accuracy inthe proposed algorithm.

3.4. Application of proposed algorithm to compute delay spreadof multipath channel

Delay spread is a measure of variety of multipath related effectsof a channel. In this section, we present a comparison betweenthe mean rms delay spread obtained using the proposed two-dimensional ray-tracing model and available measurements. Wealso incorporate the prediction results presented by El-Sallabi [3]using VPL method. The propagation scenario for this analysis isshown in Fig. 13. For the prediction results, the wall conductivityand relative permittivity were chosen to be 0.001 S/m and 5 respec-tively. Frequency of operation is chosen as 2.154 GHz. Descriptionof measurement scenario is presented in [3]. Figs. 14 and 15 showthe predicted rms delay spread results (in ns) and available mea-surements for the route CD and GH route of the scenario in Fig. 13.We note that there is a wide range of fluctuations in the measure-ments. As explained in [3], this is due to the fact that each arrivingray is assumed to have time dependency that is delayed versionof PN sequence used in the measurement. Predictions presented in[3] follow the same details of the measurements. Hence we can seethe significant fluctuations in the VPL based prediction results. Inthe lack of these details, we followed the simple approach based

on (12) to obtain the rms delay spread. It can be observed thatthe proposed prediction gives reasonably fair estimates of the rmsdelay spread using two-dimensional ray tracing in the multipathenvironment.

Fig. 13. Map of Helsinki city [3].

S. Soni, A. Bhattacharya / Int. J. Electron. C

Fig. 14. Comparison of rms delay spread with available measurements [3] for theroute CD.

Fr

4

rmweapmro

[

[

[

[

[

[

[

[

[

[

ig. 15. Comparison of rms delay spread with available measurements [3] for theoute GH.

. Conclusion

In this paper, we have presented an efficient two-dimensionalay-tracing algorithm for the characterization of urban environ-ent. Computation time of proposed technique was comparedith available ray-tracing approaches to validate it’s computational

fficiency. The accuracy of the proposed algorithm was tested bypplying the algorithm to various microcellular scenarios and com-

aring the path loss, rms delay spread, thus obtained, with availableeasurements. Further, using the proposed technique, a moderate

ise in the computational complexity with increase in the scatteringrder was observed.

[

[

ommun. (AEÜ) 66 (2012) 439– 447 447

Acknowledgment

The authors are thankful to Prof. S. Sanyal, Department ofElectronics and Electrical Communication Engg. IIT Kharagpur, forvaluable suggestion.

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[2] Cerasoli C. The use of ray tracing models to predict MIMO performance in urbanenvironments. In: IEEE Military Communications Conference. 2006.

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