# Wireless Physical Layer Concepts: Part II

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1 Wireless Physical Layer Concepts: Part II Raj Jain Professor of CSE Washington University in Saint Louis Saint Louis, MO Audio/Video recordings of this lecture are available at: 4-1

2 Overview Channel Model Path Loss, Fading, Shadowing, Noise d -4 Power Law Fresnel Zones Tapped Delay Line Model Doppler Spread 4-2

3 Wireless Radio Channel Path loss: Depends upon distance and frequency Noise Shadowing: Obstructions Frequency Dispersion (Doppler Spread) due to motion Interference Multipath: Multiple reflected waves Inter-symbol interference (ISI) due to dispersion 4-3

4 Channel Model Channel Base Station Power profile of the received signal can be obtained by convolving the power profile of the transmitted signal with the impulse response of the channel. Convolution in time = multiplication in frequency Signal x, after propagation through the channel H becomes y: y(f)=h(f)x(f)+n(f) Here H(f) is channel response, and n(f) is the noise. Note that x, y, H, and n are all functions of the signal frequency f. 4-4 Subscriber Station

5 Path Loss Power is distributed equally to spherical area 4π d 2 The received power depends upon the wavelength If the Receiver collects power from area A R : Receiving Antenna Gain This is known as Frii's Law. Attenuation in free space increases with frequency. 4-5

6 Path Loss (Cont) In practice the distance exponent is higher: 3.5 to 5.5 (after a breakpoint) n 3.5 to 5.5 In log scale: 4-6

7 d -4 Power Law Using a two-ray model Here, h T and h R are heights of transmit and receive antennas It is valid for distances larger than Note that the received power becomes independent of the frequency. Measured results show n=1.5 to

8 d -4 Power Law (Cont) The transition happens around 100m 4-8

9 Small Scale Fading The signal amplitude can change by moving a few inches Small scale fading + = + = 4-9

11 Shadowing PL( d) db PL( d0) 10 log d = + α + χ d0 χ is a Gaussian random variable with standard deviation σ 2 Power received at the same distance may be random and has log normal distribution Log Normal Shadowing χ 4-11

12 Path Loss 4-12

13 Noise Noise consists of 3 components: 1. Thermal Noise: Proportional to absolute temperature Noise Power Spectral Density N 0 = k B T Where, k B = Boltzman's constant = Joules/Kelvin For a band of width B: Noise Power P n = N 0 B = log 10 (B) dbm at 300 K 2. Spurious Emissions: Car ignition and Electronic devices Decreases at higher frequencies. More noise in urban areas. 3. Receiver Noise: Amplifiers and mixers add noise. Noise generated before the amplifiers also gets amplified 4-13

14 Interference Limited Systems SIR min 4-14

15 Fresnel Zones Draw an ellipsoid with BS and MS as Foci All points on ellipsoid have the same BS-MS run length Fresnel ellipsoids = Ellipsoids for which run length = LoS + iλ/2 At the Fresnel ellipsoids results in a phase shift of i\pi Radius of the ith ellipsoid at distancd d T from the transmitter and d R from the receiver is Free space (d 2 ) law is followed up to the distance at which the first Fresnel Ellipsoid touches the ground 4-15

17 Multipath Power Delay Profile Power Transmitted Power Received Delay τ Delay τ A single impulse results in multiple impulses at different times Delay Spread = Maximum delay after which the received signal becomes negligible = τ max. 4-17

18 Tapped Delay Line Model Delay Line c 1 c2 c 3 c 4 τ 1 τ 2 τ 3 τ 4 Coherence Time = Time for which channel remains same Coherence Bandwidth = Bandwidth for which channel remains same N ht (, τ ) = ci() tδτ ( τi) i=

19 Doppler Spread Power Delay Profile of Channel = Power distribution over time for an impulse signal Doppler Power Spectrum = Power Distribution over frequency for a signal transmitted at one frequency Non-zero for (f-f D to f+f D ) Doppler spread = f D Coherence Time = 1/Doppler Spread If the transmitter, receiver, or intermediate objects move very fast, the doppler spread is larege and coherence time is small 4-19

20 Typical Doppler Spread Carrier Freq Speed Max Doppler Spread Coherence Time 2.5 GHz 2 km/hr 4.6 Hz 200 ms 2.5 GHz 45 km/hr Hz 10 ms 2.5 GHz 100 km/hr Hz 4 ms 5.8 GHz 2 km/hr 10.7 Hz 93 ms 5.8 GHz 45 km/hr Hz 4 ms 5.8 GHz 100 km/hr 537 Hz 2 ms 4-20

21 Summary Path loss increase at a power of 2 to 5.5 with distance. Fading = Changes in power changes in position Fresnel zones = Ellipsoid with distance of LoS+iλ/2 Any obstruction of the first zone will increase path loss Coherence time = Time for which channel remains same Doppler Spread = Frequency Band over which channel remains same 4-21

22 Homework 4 Determine the mean received power at a SS. The channel between a base station at 14 m and the subscriber stations at 4m at a distance of 500m. The Transmitter and Reciver antenna gains are 10dB and 5 db respectively. Use a power exponent of 4. Transmitted power is 30 dbm. 4-22

23 References R. Jain, Channel Models Tutorial,

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