TIME DELAY SPREAD AT 2.1 GHZ AROUND REGULAR AND CHAFLANE STREET CORNERS FOR MICROCELLULAR C

where E0 is the emitted field strength, k is the wave number and r is the propagation path length. For reflected rays, E reflected = R E 0 − jkr2 e r2 (2)
Fig. 2 Delay profile for P1 in the Rectangular Corner.
τA =
ቤተ መጻሕፍቲ ባይዱ
∑ τ P(τ )
i i i =1 N
N
∑ P(τ )
i i =1
(6)
Where τi is the arriving time of a ray, P(τi) is the power (in linear units) associated to the ray received at τi. The Root Mean Square delay spread is evaluated with the next formula:
where R is the reflection coefficient and r2 the path length between the source and the receiver. Apart from the polarization of the incident wave, the reflection coefficient in our model depends on the angle of incidence, the permittivity and the conductivity. The formulation given in [3] has been used for the reflection coefficient. For diffracted rays, E diffracted = E 0 − jks ' s' e D e − jks s(s + s' ) s' (3)
τ RMS =
∑ (τ
i =1
N
i
− τ A ) 2 P(τ i )
N
Fig. 3 Delay profile for P2 in the Rectangular Corner. (7) First of all, two results were calculated for each corner configuration. One before the cross, P1, and another one after the turning, P2. These points are situated in Fig. 1 for both rectangular and Chaflane street corners. Figures 2 and 3 give the results of the Power Delay Profile in positions P1 and P2 for the rectangular street corner. corner . As it can be seen from the figures and as expected, both Mean Excess Delay and RMS Delay Spread are greater for P2. RMS Delay Spread decreases from 52 to 37 ns after turning the corner. Now, figures 4 and 5 provide the simulation results of the Power Delay Profile for the rectangular street corner. corner in positions P1 and P2. Again, results suggest same results as before, Mean Excess Delay and RMS Delay Spread increase in P2.. RMS Delay Spread increases from 52 to 77 ns. However, the behaviour of Power Delay Profile is different. In the chaflane corner case, delay spread is bigger due to the reflection of rays on the chaflane walls.
0-7803-7589-0/02/$17.00 ©2002 IEEE
PIMRC 2002
propagation model, the diffraction coefficients for finite conductivity wedges found in [6] are applied. For diffracted/reflected rays, E D −R = E 0 − jks ' s' e DR e − jks s' s(s + s' ) (4)
Abstract – A ray tracing model based on the application of the uniform theory of diffraction (UTD) and geometrical optics (GO) for modeling the propagation in the microcellular urban scenarios has been implemented. This model has been used to analyze the behavior of the rms delay spread while turning a corner in two street-corner environments- regular and chaflane street corners. The study of the environment of the two corners shows that there exist important differences between both street corners. Keywords – regular and chaflane street corners; microcell; path loss; power-delay profile; propagation and modelling; ray tracing I. INTRODUCTION The performance of a mobile radio communication system depends on the radio propagation environments, which are stretching from in-house areas up to large rural areas. Hence wave propagation has been analyzed for the whole range of macro-, micro- and pico-cells scenarios in rural and urban environments [1, 2]. For microcellular communications in urban environments, while the propagation characteristics of conventional street corners (Fig. 1(a)) have been already analyzed [3-5], it has not been the same for chaflane crossings (Fig. 1(b)). In this work, a deterministic model based on ray-tracing and the Uniform Theory of Diffraction (UTD) is used to analyze RMS delay-spread at 2.1 GHz around two street corner environments –regular and chaflane street corners-. II. ANALYTICAL MODEL In the ray-tracing engine, the following ray categories have been considered: 1- Direct ray between the transmitter and the receiver. 2- Reflected. 3- Corner Diffracted. 4- Corner diffracted / reflected. 5- Reflected / Corner diffracted. Besides, this 2D model adds ground reflection for each contribution. Fig. 1 Geometry of (a) Regular corners and (b) Chaflane street corners. The electric field of a ray arriving at the receiving antenna is calculated using the following formulas. For the direct ray, E direct = E o − jkr e r (1)
The total electric field is calculated as follows:
E total =
∑∑
i =1