Wireless Information Transmission System Lab. Mobile Radio Propagation Channel Models Institute of Communications Engineering National Sun Yat-sen University
Table of Contents Introduction Propagation Path Loss Model Friis Free Space Model Hata Model Large Scale Propagation Model Lognormal Distribution Small scale Propagation Model Multipath Delay Spread vs. Coherent Bandwidth Flat Fading vs. Frequency Selective Fading Narrowband vs. Wideband
Doppler s Effect Table of Contents Doppler s Shift vs. Coherent Time Fast Fading vs. Slow Fading. Rayleigh Distribution Level Crossing Rate Ricean Distribution Fading Counteraction Diversity Schemes 3
Wireless Information Transmission System Lab. Introduction Institute of Communications Engineering National Sun Yat-sen University
Main Components of Radio Propagation Propagation Path Loss. ( ~ /r in free space) Large Scale: Propagation models that predict the strength for an arbitrary separation distance. Small Scale: Propagation models that characterize the rapid fluctuation of the received signal strength over very short travel distance (~λ ) or short time duration (~s). 5
Large-Scale Propagation Models Propagation models that predict the mean signal strength for an arbitrary transmitter-receiver (T-R) separation distance are useful in estimating the radio coverage area of a transmitter. They characterize signal strength over large T-R (transmitter receiver) separation distances (several hundreds or thousands of meters). 6
Small-Scale Propagation Models Small-scale fading is used to describe the rapid fluctuation of the amplitude of a radio signal over a short period of time or travel distance. Fading is caused by interference between two or more versions of the transmitted signal which arrive at the receiver at slightly different time. These waves, called multi-path waves, combine at the receiver antenna to give a resultant signal which can vary widely in amplitude and phase. 7
Small-Scale Propagation Models The received signal power may vary by as much as three or four orders of magnitude (3 or 4 db) when the receiver is moved by only a fraction of a wavelength. Typically, the local average received power is computed by averaging signal measurements over a measurement track of 5λ to 4 λ. Hint : with f = GHz ~ GHz, λ = c f = 3cm ~ 5cm 8
Small-Scale vs. Large-Scale Fading 9
Wireless Information Transmission System Lab. Propagation Path Loss Model Institute of Communications Engineering National Sun Yat-sen University
Free Space Propagation Model The free space propagation model is used to predict received signal strength when the transmitter and receiver have a clear, unobstructed line-of-sight (LOS) path between them. e.g. satellite, microwave ling-of-sight radio link. As with most large-scale radio wave propagation models, the free space model predicts that received power decays as a function of the T-R separation distance raised to some power.
PG t tgrλ Pr ( d) = (4π ) d L P t G G Friis Free Space Equation : transmitted power. P ( d) : received power which is a function of the r t r T - R separation. : the transmitter antenna gain. : the receiver antenna gain. d : the T - R separation distance in meters. L : the system loss factor not related to propagation. λ : the wavelength in meters.
Friis Free Space Equation The gain of an antenna is related to its effective aperture, A e, by: G = 4 A π e λ The effective aperture A e is related to the physical size of the antenna. The miscellaneous losses L (L ) are usually due to transmission line attenuation, filter losses, and antenna losses in the communication system. L= indicates no loss in the system hardware. 3
Log-distance Path Loss Model n d PL( d ) d PL( db) PL( d ) nlog d = + d 4
L 5( urban)( db) = 3.8 log h te a( h Hata Model 69.55 re ) + An empirical formulation of the graphical path loss data provided by Okumura Valid from 5M to 5Mhz. h te : 3m ~ m (base station antenna height) h re : m~m (mobile antenna height) d : T-R separation distance (in km) a (h re ) : correction factor for effective mobile antenna height. 5 + 6.6 log (44.9 f c 6.55 log h te ) log d
Hata Model For small to medium sized city: a( h ) = (.log f.7) h (.56log f.8) db re For large city: For suburban area: For open rural areas: L c ( re) = 8.9(log.54 re). for c 3 a h h db f MHz ( re) = 3.(log.75 re) 4.97 for c 3 a h h db f MHz L5 ( db) = L5 ( urban) [log( f c / 8)] 5.4 ( db) ( urban) re 4.78(log f c ) 8.33log f 5 = L5 c c 4.98 6
Hata Model in PCS Band Extension of Hata model to GHz. L 5 a( h C M h h ( urban)( db) = 46.3+ 33.9 log re ) + (44.9 6.55 log h te )log f c 3.8 log d + = db for medium sized city and suburban areas = 3dB for metropolitan centers f :5MHz ~ MHz te re : 3m ~ m :m ~ m d :km ~ km C M h te 7
Wireless Information Transmission System Lab. Large Scale Propagation Model Institute of Communications Engineering National Sun Yat-sen University
Shadowing Effect Lognormal Distribution When reaching the mobile station, the radio wave will have traveled through different obstructions such as buildings, tunnels, hills, trees, etc. The received signal R, when measured in decibels, has a normal density function. Thus R is described by lognormal distribution. ( ln r m) / σ e ( r ) The PDF of R is: p( r) = πσr ( r < ) d PL ( d ) = PL( d ) + X σ = PL( d ) n X σ d + log + X σ : a zero-mean Gaussian distributed random variable (db) with standard deviation 4 - db. 9
Correlation of Path Loss Shadow Fading: attenuation ζ Correlation of Path Loss: (from Viterbi, Principles of Spread Spectrum Communications) ζ = a ξ + b ξ a + b =, mobile base station E( ζ) = E( ξ ) = E( ξ ) =, mobile base station ( ζ) = ( ξmobile) = ( ξbase station) = σ. Var Var Var
Wireless Information Transmission System Lab. Small Scale Propagation Model Institute of Communications Engineering National Sun Yat-sen University
Small Scale Fading -- Problem : multi-path induces delay spread.
Impulse Response Model of a Multipath Channel A mobile radio channel may be modeled as a linear filter with a time varying impulse response, where the time variation is due to receiver motion in space. The filtering nature of the channel is caused by the summation of amplitudes and delays of the multiple arriving waves at any instant of time. 3
Channel Impulse Response Due to the different multipath waves which have propagation delays which vary over different spatial locations of the receiver, the impulse response of the linear time invariant channel should be a function of the position of the receiver. ydt (, ) = xt ( ) hdt (, ) = x( τ) hdt (, τ) dτ where hdt (, ) is the channel impulse resonse. xt ( ) is the transmitted signal. ydt (, ) is the received signal at position d. 4
Multipath Radio Channel 5
- - -3 - - 3 Baseband Signal - - -3 - - 3 Carrier - - -3 - - 3 Passband Signal 6
- - -3 - - 3 - - -3 - - 3 - - -3 - - 3 7
- - -3 - - 3 - - -3 - - 3 - - -3 - - 3 8
- - -3 - - 3 - - -3 - - 3 - - -3 - - 3 9
- - -3 - - 3 - - -3 - - 3 - - -3 - - 3 3
- - -3 - - 3 - - -3 - - 3 - - -3 - - 3 3
- - -3 - - 3 - - -3 - - 3 - - -3 - - 3 3
- - -3 - - 3 - - -3 - - 3 - - -3 - - 3 33
- - -3 - - 3 - - -3 - - 3 - - -3 - - 3 34
- - -3 - - 3 - - -3 - - 3 - - -3 - - 3 35
- - -3 - - 3 - - -3 - - 3 - - -3 - - 3 36
Multipath Propagation Effect 37
Measured Multipath Power Delay Profiles From a 9 MHz cellular system in San Fancisco. 38
Measured Multipath Power Delay Profiles Inside a grocery store at 4 GHz. 39
Delay Spread Delay spread and coherence bandwidth are used to describe the time dispersive nature of the channel. Received Signal: h( t) = n i= a δ Delay Spread στ corresponds to standard deviation of T i. ( t i Ti ) Excess delay is the relative delay of the i-th multipath component as compared to the first arriving component. 4
4 Time Dispersion Parameters Mean Excess Delay: the first moment of the power delay profile. RMS (root mean square) Delay Spread: the square root of the second central moment of the power delay profile. = = k k k k k k k k k k P P a a ) ( ) ( τ τ τ τ τ (τ ) τ σ τ = = = k k k k k k k k k k P P a a ) ( ) ( τ τ τ τ τ
Time Dispersion Parameters These delays are measured relative to the first detectable signal arriving at the receiver at τ =. The equations in the previous page do not rely on the absolute power level of P(τ), but only the relative amplitudes of the multipath components within P(τ). Typical values of rms delay spread are on the order of microseconds in outdoor mobile radio channels and on the order of nanoseconcds in indoor radio channels. 4
Typical Measured Values of RMS Delay Spread 43
Maximum Excess Delay Maximum Excess Delay (ΧdB) = the time delay during which multipath energy falls to ΧdB below maximum. Maximum Excess Delay (ΧdB) can also be defined as τ x - τ, where τ is the first arriving signal; τ x is the maximum delay at which a multipath component is within X db of the strongest arriving multipath signal. The value of τ x is sometimes called the excess delay spread of a power delay profile. 44
Example of An Indoor Power Delay Profile 45
Coherence Bandwidth Time domain focus on excess delay. Frequency domain focus on coherence bandwidth B c. B c is defined related to rms delay spread /(B c ) B c (Coherence Bandwidth) A statistical measure of the range of frequencies over which the channel can be considered flat (i.e. a channel which passes all spectral components with approximately equal gain and linear phase.). The range of frequencies over which two frequency components have a strong potential for amplitude correlation. Two sinusoids with frequency separation greater than Bc are affected quite differently by the channel. 46
Coherence Bandwidth Version : the bandwidth over which the frequency correlation is above.9 B c = 5 σ τ Version : the bandwidth over which the frequency correlation is above.5 B c = 5 σ τ 47
Types of Small-Scale Fading Based on multi-path time delay spread Flat Fading (narrowband system) BW of signal < BW of channel Delay spread < Symbol period Frequency Selective Fading (wideband system) BW of signal > BW of channel Delay spread > Symbol period 48
Wideband v.s. Narrowband Signal Bandwidth t Signal Bandwidth t wideband f narrow band f 49
Flat Fading Signal undergoes flat fading if T s : reciprocal BW (e.g. symbol period) B s : BW of the TX modulation σ τ : rms delay spread 5 B S << BC and T S >> σ τ B c : Coherence BW
Flat Fading The mobile radio channel has a constant gain and linear phase response over a bandwidth which is greater than the bandwidth of the transmitted signal. The multipath structure of the channel is such that the spectral characteristics of the transmitted signal are preserved at the receiver. The strength of the received signal changes with time, due to fluctuations in the gain of the channel caused by multipath. 5
Flat Fading Typical flat fading channels cause deep fades, and thus may require or 3 db more transmitter power to achieve low bit error rates during times of deep fades as compared to systems operating over nonfading channels. Also known as amplitude varying channel. Also referred to as narrowband channels since the bandwidth of the applied signal is narrow as compared to the channel flat fading bandwidth. The most common amplitude distribution of flat fading channel is the Rayleigh distribution. 5
Frequency Selective Fading Signal undergoes frequency selective fading if B > B and T S < στ S C 53
Frequency Selective Fading The channel possesses a constant-gain and linear phase response over a bandwidth that is smaller than the bandwidth of transmitted signal. The received signal includes multiple versions of the transmitted waveform which are attenuated and delayed in time. The channel induces inter-symbol interference. Certain frequency components in the received signal spectrum have greater gains than others. Also known as wideband channels. M-ray Rayleigh fading model is usually used for analyzing frequency selective small-scale fading. 54
Small Scale Fading -- Problem : moving receiver induces fading effects (Doppler shift) for each ray path. 55
Doppler Effect Doppler is a frequency shift, cause by movement of the mobile antenna relative to the base station - Δf = V/λ (at 5 km/h and 9 MHz, Δf = 8 Hz) f f - f V f + f 56
57 Doppler Shift / Spread θ cosθ cos t v d l = = θ λ π λ π φ cos Phase Change : t v l = = θ λ φ π cos : Doppler Shift v t f d = =
Doppler Spread and Coherence Time Delay spread and coherence bandwidth do not offer information about the time varying nature of the channel caused by either relative motion between the mobile and base station, of by movement of objects in the channel. Doppler spread and coherence time are parameters which describe the time varying nature of the channel in a small-scale. Doppler spread B D is a measure of the spectral broadening caused by the time rate of change of the mobile radio channel and is defined as the range of frequencies over which the received Doppler spectrum is essentially non-zero. When a pure sinusoidal tone of frequency f c is transmitted, the received signal spectrum, called the Doppler spectrum, will be in the range f c -f d to f c +f d, where f d is Doppler shift. 58
Coherence Time Coherence time T c is the time domain dual of Doppler spread and is used to characterize the time varying nature of the frequency dispersiveness of the channel in the time domain. Coherence time is a statistical measure of the time duration over which the channel impulse response is essentially invariant. Coherence time is the time duration over which two received signals have a strong potential for amplitude correlation. 59
Version : T Coherence Time c f m ƒ m : the maximum Doppler shift, ƒ m = ν/λ Version : the time over which the time correlation >.5 T 9 6 c f m Version 3: Geometric mean of version and version. π T c = 9 6πf = m.43 f m 6
Doppler Power Spectrum 6
Types of Small-Scale Fading Based on Doppler Spread Fast Fading High Doppler spread. Coherence time < Symbol Period. Channel variations faster than base-band signal variations Slow Fading Low Doppler spread. Coherence time > Symbol period. Channel variations slower than base-band signal variations 6
Fast Fading T S >T C and B S <B D. The channel impulse response changes rapidly within the symbol duration. The coherence time of the channel is smaller than the symbol period of the transmitted signal. Signal distortion due to fast fading increases with increasing Doppler spread relative to the bandwidth of the transmitted signal. Fast fading only deals with the rate of change of the channel due to motion. In practice, fast fading only occurs for very low data rates (or very fast motion speed). 63
Slow Fading T S <<T C and B S >>B D Channel impulse response changes at a rate much slower than the transmitted baseband signal s(t). The channel may be assumed to be static over one or several reciprocal bandwidth intervals. The Doppler spread of the channel is much less than the bandwidth of the baseband signal. The velocity of the mobile and the baseband signaling determines whether a signal undergoes fast fading or slow fading. 64
Type of Small-Scale Fading 65
Type of Small-Scale Fading 66
Wireless Information Transmission System Lab. Rayleigh Distribution Institute of Communications Engineering National Sun Yat-sen University
Rayleigh Distribution Rayleigh distributions are commonly used to describe the statistical time varying nature of the received envelope of a flat fading signal, or the envelope of an individual multipath component. Envelope of the sum of two quadrature Gaussian noise signals obeys a Rayleigh distribution. 68
Typical Rayleigh Fading Envelope 69
7 Rayleigh Distribution Consider a carrier signal s at a frequency ω and with an amplitude a: The received signal s r is the sum of n waves: exp( t) j a s ω = [ ] [ ] θ θ θ θ θ θ θ θ θ θ ω θ ω sin cos where : sin and cos We have : sin cos ) exp( Define : ) exp( ) exp( where ) ( exp ) ( exp r y r x y x r a y a x jy x a j a j r j a j r t j r t j a s n i i i n i i i n i i i n i i i n i i i n i i i r = = + = + + = = + + = = = = = = =
Rayleigh Distribution Because () n is usually very large, () the individual amplitudes a i are random, and (3) the phases θ i have a uniform distribution, it can be assumed that (from the central limit theorem) x and y are both Gaussian variables with means equal to zero and variance σ x = y Because x and y are independent random variables, the joint distribution p(x,y) is σ The distribution p(r,θ) can be written as a function of p(x,y) : 7 σ x + y p( x, y) = p( x) p( y) = exp πσ σ p ( r, θ ) = J p( x, y)
Rayleigh Distribution x r x r r r J = = r; pr (, θ ) = exp y r y r / / θ cosθ sinθ / / θ sinθ cosθ πσ σ Thus, the Rayleigh distribution has a pdf: π r r exp r pr () = pr (, θ) dθ = σ σ otherwise The probability that the envelope of the received signal does not exceed a specified value R is given by the corresponding cumulative distribution function (CDF) R R P( R) = Pr( r R) = p( r) dr = exp σ 7
Rayleigh Distribution Mean: π r mean = E[ r] = rp( r) dr = σ =. 533σ Variance: σ π σ = [ ] [ ] = r E r E r r p( r) dr π = σ =.49σ Median value of r is found by solving: Mean squared value: Most likely value = max { p(r) } = σ 73 = r median E[ r ] = r p( r) dr = σ r median p( r) dr =.77σ
Rayleigh Probability Density Function 74
Wireless Information Transmission System Lab. Ricean Distribution Institute of Communications Engineering National Sun Yat-sen University
Ricean Fading Distribution When there is a dominant stationary (non-fading) signal component present, such as a line-of-sight propagation path, the small-scale fading envelope distribution is Ricean. s r r x y + scattered waves = r'exp[ j( ω t + θ )] + [( x + = ( x + = A = r sinθ A) + A) + r cosθ jy]exp( y direct waves Aexp( jω t) jω t) r exp[ j( ω t + θ )] 76
77 Ricean Fading Distribution By following similar steps described in Rayleigh distribution, we obtain: ( ) = = = < + =! function. the modified zeroth - order Bessel is cos exp where for r, A for exp ) ( i i i r r r r r i x (x) I d Ar Ar I ) (r Ar I A r r r p θ σ θ π σ σ σ σ π
Ricean Fading Distribution The Ricean distribution is often described in terms of a parameter K which is defined as the ratio between the deterministic signal power and the variance of the multipath. It is given by K=A /(σ ) or in terms of db: A K( db) = log [db] σ The parameter K is known as the Ricean factor and completely specifies the Ricean distribution. As A, K - db, and as the dominant path decreases in amplitude, the Ricean distribution degenerates to a Rayleigh distribution. 78
Ricean Fading Distribution 79
Wireless Information Transmission System Lab. Fading Counteraction Diversity Schemes Institute of Communications Engineering National Sun Yat-sen University
Fading Counteraction Short-Term (small scale) Fading Counteraction: Microscopic diversity. Space diversity - spacing is between receiving antennas. Polarization: orthogonality of the polarized wave components. Angle: directional antenna. Frequency: two or more different carriers. Time: time separation. Hopping: frequency hopping and time hopping. 8
Switched Combining Combining Schemes Pure Selection: the received signals are continuously monitored so that the best signal can be selected. Threshold Selection: the received signals are scanned in a sequential order, and the first signal with a power level above a certain threshold is selected. Gain Combining Maximal Ratio Combining (MRC): each one of the M signals has a gain proportional to its own signal-to-noise ratio. Equal Gain Combining: all of the signals have a gain equal to one. 8