Path loss models

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Path loss models

  1. 1. EE161 Handout #3 March 31, 2009 EE161 Spring 2009 Wireless Communications Path Loss Models The transmitted signal s(t) = u(t)ej(2πft+φ0) , where u(·) is a complex baseband signal, f is the carrier frequency and φ0 is a random initial phase (uniformly distributed between 0 and π). Basic propagation mechanisms 1. Reflection 2. Diffraction 3. Scattering Free space loss The received signal r(t) = u(t) λ √ GtGrej 2πd λ 4πd , where d is the distance, Gt and Gr are the transmit and receive antenna power gains and λ is the wavelength. The received power Pr = Pu λ 4πd 2 GtGr. 1
  2. 2. Ground reflection – Two-path model See figure 2.4 of Goldsmith. r(t) = λ 4π GtGr  u(t)ej 2πd ′ λ d′ + u(t + τ)Rej 2πd ′′ λ d′′   , (1) where d ′ is the LOS distance, d ′′ is the ground reflected distance, τ = d ′′ −d ′ c is the path delay and R = sin θ − √ ǫr − cos2θ sin θ + √ ǫr − cos2θ , for horizontal polarization and R = sin θ − √ ǫr − cos2θ/ǫr sin θ + √ ǫr − cos2θ/ǫr , where θ is the angle of reflection. For d > dc = 4hthr λ , we have Pr ≈ GtGr(hthr)2 d4 Pu, i.e., the signal decays as d−4. For all values of d a reasonable approximation is Pr ≈ GtGrd2 0 d2(1 + (d/dc)2q)1/q Pu, for some values of q and d0. General ray tracing r(t) = λ 4π GtGr  u(t)ej 2πl λ l + i∈all paths u(t + τi)Riej 2πli λ li   . Simplified path loss model Pr = PuK d0 d γ , with γ often between two and six. 2
  3. 3. Log-normal shadowing 10 log10 Pr Pu = 10 log10 K − 10γ log10 d d0 + ψdb, where ψdb is a zero-mean Gaussian random variable. 3

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