NETW 701: Wireless Communications. Lecture 5. Small Scale Fading

Transcription

1 NETW 701: Wireless Communications Lecture 5 Small Scale Fading

2 Small Scale Fading Most mobile communication systems are used in and around center of population. The transmitting antenna or Base Station (BS) are located on top of a tall building or tower and they radiate at the maximum allowed power. The mobile antenna or Mobile Station (MS) is well below the surrounding buildings.

3 Small Scale Fading Small scale fading is used to describe the rapid fluctuations in the amplitude of the signal over a small period of time or over a short distance. Small scale fading is caused by interference between two or more versions of the transmitted signal which arrive at slightly different times. These waves called multi-path waves that combine at the receiver antenna to give a resultant signal which can vary widely in amplitude and phase.

4 Small Scale Fading Multi-Path in the radio channel creates small-scale fading. The three most important effects are: Rapid changes in signal strength over a small travel distance or time interval. Random frequency modulation due to varying Doppler shifts on different multi-path signals. Time dispersion (echoes) caused by multi-path propagation delays.

5 Factors Affecting Small Scale Fading Multipath Propagation: The presence of reflecting objects and scatters in the channel dissipates the signal energy. Speed of the mobile: The relative motion between the base station and the mobile results in random frequency modulation due to different Doppler shift on each multi-path component Speed of the surrounding object: If these objects are moving, they induce a time varying Doppler shift on multi-path components The transmission bandwidth of the signal

6 Multi-Path Propagation Modeling Power Multi-Path Components τ 0 τ 1 τ 2 Time As the mobile receiver (i.e. car) moves in the environment, the strength of each multi-path component varies 6

7 Multi-Path Propagation Modeling Power Multi-Path Components τ 0 τ 1 τ 2 Time As the mobile receiver (i.e. car) moves in the environment, the strength of each multi-path component varies 7

8 Multi-Path Propagation Modeling Power Multi-Path Components τ 0 τ 1 τ 2 Time As the mobile receiver (i.e. car) moves in the environment, the strength of each multi-path component varies 8

9 Multi-Path Channel The Channel is a filter:

10 Multi-Path Channel

11 Multi-Path Channel Consider a pulse with small width at the input of the channel: After convolution; the channel output is:

12 Multi-Path Propagation Modeling

13 Power Delay Profile Power delay profile : indicates how channel power is distributed along the delay The power delay profile (PDP) gives the strength of a signal received through a multipath channel as a function of time delay. For Small Scale channel modeling, the power delay profile of the channel is found by taking the time average of h b (τ;t) 2 over a local area:

14 Parameters of Mobile Multi-Path Channels The power delay profile (PDP) is used to derive some parameters that can help characterize the effect of the wireless channel on communication signal. We will discuss the following: Time dispersion (spreading) parameters Rms delay spread and mean excess delay Maximum Excess delay or Excess delay spread (X db) Coherence bandwidth Doppler spread and coherence time

15 Time Dispersion Parameters What is delay spread in general?? The delay spread is a measure of the multipath richness of a communications channel. In general, it can be interpreted as the difference between the time of arrival of the earliest significant multipath component (typically the line of sight component) and the time of arrival of the latest multipath components.

16 Time Dispersion Parameters τ k It is a measure of the mean delay of signals. k P P τ k τ k τ k

17 Time Dispersion Parameters (2) Find second moment of the mean excess delay: (3) Calculate the standard deviation to get rms delay spread: describes the dispersion in the time domain due to multipath transmission.

18 Time Dispersion Parameters Maximum Excess Delay (XdB) or Excess Delay Spread (XdB): Time delay during which multi-path energy falls to X db below the maximum (Note that the strongest component does not necessarily arrive at τ 0 ) Example Mean delay of the signal

19 Doppler Shift Consider a mobile moving at a constant velocity v, along a path segment having length d between points X and Y, while it receives signals from a source S as shown in Fig. Δl dcosθ vδt cosθ Phase Difference due to variation in path lengths 2πvΔlt 2πvΔt Δφ cos θ λ λ Doppler Shift is Given by Δl X f d θ v d Note: Assume SX, SY >>d such that angle of arrival is nearly equal at X and Y 1 Δφ 2π Δt v λ cosθ θ Y S

20 Example: Solution: Mile=1.6 kilometers

21

22 Coherence Bandwidth A statistical measure of the range of frequencies over which the channel response is flat in the frequency domain (i.e., a channel which passes all spectral components with approximately equal gain and linear phase): B c 1/ Coherence Bandwidth over which Frequency correlation function > 0.9: B C 1 50σ Coherence Bandwidth over which Frequency correlation τ function > 0.5: B C 1 5σ τ

23 What is meant by Frequency Correlation function?? F.T Reading Only

24 Flat Fading Vs Frequency Selective Fading Flat Fading P(τ) Power Delay Profile B S B C TS στ A Common Rule: T S >10σ t Flat fading τ 0 τ 1 τ N Symbol Time (Digital Communication) T S τ Wireless Channel + Minimal ISI (can be neglected) τ 0τa τ N 24

25 Flat Fading Vs Frequency Selective Fading Frequency Selective Fading B S B C TS στ A Common Rule: T S <10σ t Frequency Selective Fading P(τ) Power Delay Profile τ 0 τ 1 τ 2 τ 3 τ N Symbol Time (Digital Communication) T S τ Wireless Channel + Significant ISI τ 0 τ a τ N 25

26 Flat versus Frequency Selective Fading Flat Frequency Selective

27 Example: Solution: τ k k P P τ k τ k τ k

28 Maximum Excess delay (10 db) is 2 microsec.