Fading Lecturer: Assoc. Prof. Dr. Noor M Khan Department of Electronic Engineering, Muhammad Ali Jinnah University, Islamabad Campus, Islamabad, PAKISTAN Ph: +9 (51) 111-878787, Ext. 19 (Office), 186 (ARWiC Lab) Fax: +9 (51) 8743 email: noor@ieee.org, noormhan@jinnah.edu.p Base Station Mobile Station 1
Mobile Parameters Time delay spread Coherence Bandwidth -> ISI Doppler Spread Coherence Time -> Unstable channel Flat fading Frequency selective fading Fast fading Slow fading
Multi-path Propagation Multi-path smears or spreads out the signal delay spread Causes inter-symbol interference limits the maximum symbol rate Base Statio n Mobile Statio n Transmitted Symbol Received Symbol t 3
Delay Spread Base Station Space Mobile Station Transmitted Symbol Received Symbol t Time 4
Intersymbol Interference Transmitted Symbol of Interest Received Symbol of Interest t Transmitted Symbols Received Symbols t 5
Average Delay Spread Average delay spread τ P(τ 1 ) P(τ ) Multi-path Profile (Discrete) τ a a τ P(τ P(τ )τ ) P(τ 0 ) P(τ ) P(τ ) t τ 0 0 τ τ 1 τ 6
RMS Delay Spread (Discrete) RMS delay spread σ τ τ τ τ a a τ P(τ P(τ )τ ) 7
Average Delay Spread (Continuous Delay Profile) Average delay spread τ P( t) dt 0 Representative delay functions exp uniform τ P( t) P( t) 1 e t t 0 P( t) dt 0 t d and zero elsewhere 8
Measurements Type of Delay Spread d Environment (s) Open area <0. Suburban area 0.5 Urban area 3 9
Coherence Bandwidth Coherence bandwidth B c is a range of frequencies over which the channel can be considered flat passes all spectral components with approximately equal gain and liner phase Bandwidth where the correlation function R T () for signal envelopes is high Therefore two sinusoidal signals with frequencies that are farther apart than the coherence bandwidth will fade independently. 10
Coherence Bandwidth If R T () > 0.9 If R T () > 0.5 B C B C An exact relationship between coherence bandwidth & delay spread does not exist 1 50 1 5 11
Doppler Shift f c broadening from f c to (f c + f m ) f m f c v c v v BS1 1
Doppler Spread & Coherence Time Describes the time varying nature of the channel in a local area Doppler Spread B D, is a measure of the spectral broadening caused by the time rate of change f c broadening from (f c - f m ) to (f c + f m ) If the base-band signal bandwidth is much greater than B D, the effects of Doppler spread are negligible at the receiver 13
Coherence Time Coherence Time is the time domain dual of Doppler spread Doppler spread and coherence time are inversely proportional T C = 1/f m Statistical measure of the time duration over which the channel impulse response is invariant 14
Coherence Time If the coherence time is defined as the time over which the correlation function is above 0.5, then 9 TC 16 fm Rule of thumb for modern digital communication defines TC as the geometric mean of the above two expressions for TC T C 9 16 f m 15
Types of Small-Scale Fading 16
Flat Fading 1 If the mobile radio channel has a constant gain and linear phase over a bandwidth greater than the bandwidth of the transmitted signal - the received signal will undergo flat fading Please, observe that the fading is flat (or frequency selective) depending on the signal bandwidth relative to the channel coherence bandwidth. 17
Flat Fading BS << B C & T S >> 18
Frequency Selective Fading 1 If the mobile radio channel as a constant gain and linear phase over a coherence bandwidth, smaller than the bandwidth of the transmitted signal - the received signal will undergo frequency selective fading Again, the signal bandwidth is wider then the channel coherence bandwidth, causing one or more areas of attenuation of the signal within the signal bandwidth 19
Frequency Selective Fading BS > B C & T S < 0
Fast Fading The channel impulse response changes rapidly within the symbol duration - coherence time < symbol period T S > T c and B S < B D specifies as a fast or slow fading channel does not specify whether the channel is flat fading or frequency selective fading 1
Slow Fading The channel impulse response changes at a rate much slower than the transmitted base-band signal. Doppler spread is much less than the bandwidth of the base-band signal T S << T c and B S >> B D Velocity of the MS and the base-band signaling determines whether a signal undergoes fast or slow fading
Fading in Short Large Doppler Spread Time-Selective Fading Large Delay Spread Frequency-Selective Fading Large Angle Spread Space-Selective Fading 3
Fading in Short Delay Spread Coherence Bandwidth Frequency separation at which two frequency components of Tx signal undergo independent attenuations Doppler Spread Coherence Time Time separation at which two time components of Tx signal undergo independent attenuations 4
Bandwidth Fading (Continued) Flat in Time and Selective in Frequency Selective in both Time and Frequency B c Flat in Time and Frequency Flat in Frequency and Selective in Time T c Time 5
Fast and Slow Fading Fading (Continued) If the channel response changes within a symbol interval, then the channel is regarded FAST FADING Otherwise the channel is regarded as SLOW FADING 6
Fast Fading When? The channel impulse response changes rapidly within the symbol period of the transmitted signal. What? The Doppler Spread causes frequency dispersion which leads to signal distortion. 7
Doppler Spread The Doppler effect (in addition to the fading effect) renders the received pulse to be time-varying The State Transitions are determined from the dynamics of the fading channel (Fading Correlation Function or The Doppler Spectrum) 8
Doppler Spread (Continued) y Scattering Point f : carrier frequency Incoming multipath θ MS v c: speed of light v: mobile speed Line of Sight θ: Angle of motion with x incoming multipath BS 9
Doppler Spread (Continued) f d fv cos c f : carrier frequency c: speed of light v: mobile speed θ: Angle of motion with incoming multipath 30
Doppler Spread (Continued) For the land mobile fading spectrum, The Auto-Correlation Function Doppler Fading Spectrum 31
Doppler Spread (Continued) h is the channel impulse response h has a complex normal distribution with zero mean h is Raleigh distributed Phase φ is uniformly distributed between 0 and π is Chi-square distributed 3
r Rayleigh Fading 1 The received envelope (amplitude) of a flat fading signal is described as a Rayleigh distribution Square root sum r, of two quadrature Gaussian noise signals x I and y Q has a Rayleigh distribution (Papoulis65) x I y Q r r p( r) exp ; (0 ) r 33
Rayleigh Fading 34
Rayleigh Fading PDF 35
Rayleigh Fading 3 r r p( r) exp (0 ) r - rms value of the received voltage signal before envelope detection - time average power before envelope detection The probability that the received signal envelope does not exceed R is given by: P( R) R R Pr( r R) p( r) dr 1 exp 0 36
Rayleigh Fading 4 The median value of r is found by solving 1 r r median median 0 p( r) dr 1.77 Mean and median differ by only 0.55dB 37
Ricean Fading 1 When there is a dominant stationary signal component At the output of an envelope detector - adding a DC component ot the random multi-path ( r r Ar p( r) e I e 0 A ) ; for ( A 0, r 0) 38
Ricean Fading A - pea amplitude of the dominant signal I 0 () - modified Bessel function of the first ind and zero order Described in terms of a Ricean factor, K K A ( db) 10log ( db) 39