Unit 1: The wireless channel

Transcription

1 Unit 1: The wireless channel Wireless communications course Ronal D. Montoya M. August 16, /21

2 Outline I 1. Ten ray model (TRM) Premises Ray components Overhead view Equations 2. General ray tracing model (GRT) Overview Diffraction model Scattering model 2/21

3 Ten ray model - Premises I Model for urban microcells developed by Amitay. This model assumes rectilinear streets with buildings along both sides of the street and Tx and Rx antenna heights that are close to street level. The building-lined streets act as a dielectric canyon to the propagating signal. Theoretically, an infinite number of rays can be reflected off the building fronts to arrive at the receiver. The rays may also be back-reflected from buildings behind the Tx or Rx. 1. Ten ray model (TRM) 3/21

4 Ten ray model - Premises II The signal paths corresponding to more than three reflections can generally be ignored (some of the signal energy is dissipated with each reflection). The street layout is relatively straight, back reflections are usually negligible also. Experimental data show that a model of ten reflection rays closely approximates signal propagation through the dielectric canyon. 1. Ten ray model (TRM) 4/21

5 TRM - Components I The TRM incorporates all paths from zero to three reflections paths: Line of sight (LOS). The ground-reflected (GR). the single-wall reflected (SW). The double-wall reflected (DW). The triple-wall reflected (TW). The wall-ground reflected (WG). the ground-wall reflected (GW). 1. Ten ray model (TRM) 5/21

6 TRM - Overhear view Figure: Overhead view of the TRM. 1. Ten ray model (TRM) 6/21

7 TRM - Equations I The received signal r 10r (t) is given by: { } λc r 10r (t) = R 4π [A + B] exp (j2πf ct) B = (1) ( ) Gl u (t) exp j2πl λ c A = (2) l 9 R ( ) G xi u (t τ i ) exp j2π(xi ) λ c (3) x i i=1 1. Ten ray model (TRM) 7/21

8 TRM - Equations II Where: x i : Path length of the ith reflected ray. τ = x i l c : time delay of the ith ray (known as delay spread). G xi : product of antenna gains corresponding to the ith ray direction. G l = G c G d : product of antenna gains in the LOS direction. l: distance between Tx and Rx antennas in the LOS direction. 1. Ten ray model (TRM) 8/21

9 TRM - Equations III If τ << Bu 1 then u (t) u (t τ i ) (narrowband model), the received power of r 10r (t): [ ] [ 2 Gl P r λc = P t 4π l + 9 i=1 ] 2 R i Gxi exp ( j φ i ) (4) x i Where the phase difference between the two received signal components is: φ i = 2π x i l λ c (5) 1. Ten ray model (TRM) 9/21

10 TRM - Equations IV Considerations about the reflection coefficient: For each reflection path, the coefficient R i is either a single reflection coefficient given by the two ray model. If the path corresponds to multiple reflections, the final value is the product of the reflection coefficients corresponding to each reflection. The ɛ r is taken as the ground dielectric, so ɛ r = 15 is used for all the calculations of R i. 1. Ten ray model (TRM) 10/21

11 General ray tracing model - Overview I General Ray Tracing (GRT) can be used to predict field strength and delay spread for any building configuration and antenna placement. The building database (height, location, and dielectric properties) and the Tx and Rx locations relative to the buildings must be specified exactly. The GRT model is not used to obtain general theories about system performance and layout; rather, it explains the basic mechanism of urban propagation. 2. General ray tracing model (GRT) 11/21

12 General ray tracing model - Overview II GRT can be used to obtain delay and signal strength information for a particular Tx and Rx configuration in a given environment. The GRT method uses the same geometrical optics of the TRM, as well as signal components from building diffraction and diffuse scattering. There is no limit to the number of multipath components at a given receiver location. The strength of each component is derived explicitly based on the building locations and dielectric properties. 2. General ray tracing model (GRT) 12/21

13 General ray tracing model - Overview III The LOS and reflected paths provide the dominant components of the received signal (diffraction and scattering losses are high). In regions close to scattering or diffracting surfaces, which may be blocked from the LOS and reflecting rays, these other multipath components may dominate. 2. General ray tracing model (GRT) 13/21

14 GRT - Diffraction model I Diffraction results from many phenomena, including the curved surface of the earth, hilly or irregular terrain, building edges, or obstructions blocking the LOS path between the transmitter and receiver. Diffraction can be accurately characterized using the geometrical theory of diffraction (GTD). The complexity of this approach has precluded its use in wireless channel modeling. Diffraction is most commonly modeled by the Fresnel knife edge diffraction model due to its simplicity. 2. General ray tracing model (GRT) 14/21

15 GRT - Diffraction model II The diffracting object is assumed to be asymptotically thin, which is not generally the case for hills, rough terrain, or wedge diffractors. In particular, this model does not consider diffractor parameters such as polarization, conductivity, and surface roughness, which can lead to inaccuracies. 2. General ray tracing model (GRT) 15/21

16 GRT - Diffraction model Figure: Knife-edge diffraction model. 2. General ray tracing model (GRT) 16/21

17 GRT - Diffraction model equations I Considerations: d + d : distance traveled by the diffracted ray. φ = 2π d+d λ c : phase shift of the diffracted ray. h is relative small respect to d and d. The signal must travel an additional distance relative to the LOS path of approximately given by: d = h2 2 d + d dd (6) 2. General ray tracing model (GRT) 17/21

18 GRT - Diffraction model equations II With phase shift respect to the LOS path: φ = 2π d = pi λ c 2 υ2 (7) Where the Fresnel-Kirchoff diffraction parameter υ is given by: υ = h 2 (d + d ) λ c dd (8) 2. General ray tracing model (GRT) 18/21

19 GRT - Diffraction model equations III Computing this diffraction path loss is fairly complex, requiring the use of Huygen s principle, Fresnel zones, and the complex Fresnel integral. The resulting diffraction loss cannot generally be found in closed form. Approximations for knife-edge diffraction path loss (in db) relative to LOS path loss are given by Lee: 2. General ray tracing model (GRT) 19/21

20 GRT - Diffraction model equations IV 20 log 10 [ υ] 0.8 υ < 0 20 log 10 [0.5 exp ( 0.95υ)] ] 0 υ < 1 L (υ) = 20 log 10 [ ( υ) 2 1 υ < log 10 [0.225/υ] υ > 2.4 (9) 2. General ray tracing model (GRT) 20/21

21 GRT - Scattering model Figure: Scattering model. 2. General ray tracing model (GRT) 21/21