Mobile Radio Propagation 2

Cellular Mobile Communications-

V Mobile Radio Propagation Dr. Nasir D. Gohar

Wireless Communications, Principles and Applications Ch.5 [Small Scale Path Loss] by RAPPAPORT Propagation Characteristics Observed in Macro / Micro Cells by H. L. Bertoni

Mobile Radio Propagation Modeling a Radio Channel: Most difficult part in Radio System Design  Highly unpredictable as compared to fixed wireline media  Transmission path and its parameters keeps changing instantaneously

Changes in path profile Obstructions Environmental changes  Typically done statistically based on field measurements[System Specific]

Physical survey *1 Computer simulation using certain models and terrain data *2

*1

Gives some real picture of the environment and data can be incorporated to new system design and predict its performance

*2

Empirical Models and Terrain data may not be quite updated

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation The Multi-path Environment  The received signal is made up of a sum of attenuated, phase shifted and time delayed versions of the transmitted signal.  Propagation modes include diffraction, transmission and reflection.

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation The Mult-ipath Environment - contd. Assuming receiver is stationary and there is no direct path, the received signal can be expressed as a sum of delayed components or in terms of phasor notation: N

Pulse train

er (t ) = ∑ai p (t − ti ), i =1

N

A single pulse

er (t ) = ∑ ai cos (2πf c + φ i ) i =1

Where: ai is the amplitude of the scattered signal, p(t) is the transmitted signal (pulse) shape, ti is the time taken by the pulse to reach the receiver, N is the number of different paths taken by the signal to reach receiver, and fc is the carrier frequency T.S. Rappaport Ch 4-5

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Mobile Radio Propagation The Multi-path Environment - contd.

a Diffracted wave a b

Antenna

y=a+b

a & b are in phase

b Reflected wave a b

No direct path

Antenna

y=0

a & b are out of phase by π Complete fading

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Fading Is due to multi-path propagation.

With respect to a stationary base station, multipath propagation creates a stochastic standing wave pattern, through which the mobile station moves.

Caused by shadowing:  when the propagation environment is changing significantly, but this fading is typically much slower than the multipath fading.

Modem design is affected mainly by the faster multipath fading, which can be normally assumed6 to T.S. Rappaport Ch 4-5 NDG Notes

Mobile Radio Propagation

Signal strength relative to 1uV (db)

Fading - Types

Slow (Long) Term Fast (Short) Term (Also known as Rayleigh Fading) 30 Fast fading 20

10 Slow fading 0 0

5

10

15

20

25 Distance (λ)

Exact representation of fading characteristics is not possible, because of infinite number of situation.

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation

Fading - Slow (Long) Term Slower variation in mean signal strength as the receiver moves behind buildings and the propagation paths are obscured Variations of up to 20dB will cause handovers and change quality-of-service Caused by shadowing: Terrain configuration: Results in local mean (long term fading) attenuation and fluctuation. The built environment (rural and urban areas etc.), between base station and the mobile unit: Results in local mean attenuation T.S. Rappaport Ch 4-5

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Mobile Radio Propagation

Fading- Fast (Short) Term  Describes the constant amplitude fluctuations in the received signal as the mobile moves.  Caused by multipath reflection of transmitted signal by local scatters (houses, building etc.) Observed over distances = λ/2 Signal variation up to 30 dB. Is a frequency selective phenomenon. Can be described using Raleigh statistics, (no line of sight). Can be described using Rician statistics, (line of sight). Causes random fluctuations in the received power, and also Distorts the pulse carrying the information. T.S. Rappaport Ch 4-5

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Mobile Radio Propagation

Fading- Fast (Short) Term - contd. A received signal amplitude is given as the sum of delayed components. In terms of phasor notation it is given as: N

er (t ) = ∑ ai cos (2πf c + φ i ) i =1

Or N

N

i =1

i =1

er (t ) = cos( 2πf ct ) ∑ ai cos (φi ) − sin( 2πf ct ) ∑ ai sin( φi )

In-phase T.S. Rappaport Ch 4-5

Quadrature NDG Notes

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Mobile Radio Propagation

Fading- Fast (Short) Term - contd. The phaseφi can be assumed to be uniformly distributed in the range (0, 2π), provided the locations of buildings etc. are completely random. This for large N, the amplitude of the received signal is:

er (t ) = X cos( 2πf ct ) − Y sin( 2πf ct ) where

N

N

i =1

i =1

X = ∑ ai cos (φi ), Y = ∑ ai sin(φi )

X and Y are independent, identically distributed Gaussian random variables. T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Fading- Fast (Short) Term - contd. The envelope of the received signal is: 2

2 0.5

A = (X + Y )

Which will be Raleigh distributed.

Rayleigh Probability density function Exponential A or power P T.S. Rappaport Ch 4-5

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Mobile Radio Propagation

Raleigh Distribution If the impulse response h(τ , t) of the mobile radio station is time invariant (without a significant deterministic ) and has zero mean, then the envelope of the impulse response has a Rayleigh Distribution given as:  r2  r  p ( r ) = 2 exp  − 2  σ  2σ 

where σ2 is the total power in the multi-path signal T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Rice Fading  If however the impulse response has a non zero mean then there is a significant component of the direct path (line of sight, specular component) signal and the magnitude of the impulse response has a Ricean distribution

 Ricean distribution is the combination of Rayleigh signal with the direct line of sight signal. The distribution is:

 r 2 + s 2   rs  r I p( r ) = 2 exp  − 2  0 2  σ 2σ   σ  

σ2 is the power of the line of sight signal and I0 is a Bessel function of the T.S. Rappaport Ch 4-5 NDGfirst Notes kind 14

Mobile Radio Propagation Fading

Multi-path create small-scale fading effects

Rapid changes in the signal strength due to movement and/or time Random frequency modulation due to Doppler shift on different multipath propagation paths Time dispersion due to multipath propagation delay T.S. Rappaport Ch 4-5

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Mobile Radio Propagation

V V

V Stationary

V

Field strength

Fast Fading – Cases 1: Stationary Mobile

t

V

Mobile is stationery surrounded by moving cars. The number of fading depends on the : Traffic flow Distance between the mobile and moving cars T.S. Rappaport Ch 4-5

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Mobile Radio Propagation

No scattered signals θ

V

Field strength

Fast Fading – Cases 2: Non-stationary Mobile Signal level

t

The received signal at the mobile is: j ( 2 πf t −βx cos θ) r x = Vt

s = Ae

Amplitude

T.S. Rappaport Ch 4-5

Wave number =2π/ λ Transmitting frequency NDG Notes

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Mobile Radio Propagation  SMALL SCALE MULTI-PATH PROPAGATION  Multi-path reception of several versions of the same transmitted radio signal arriving at certain location [Rx] causes fading effects.

Rapid Fluctuations in Signal Strength [over very short distance or time period] Random Frequency Modulation due to Varying Doppler Shifts on Different Multi-Path Signals Time Dispersion / Echoes due to Multi-Path Propagation Delay

 Multi-path propagation occurs even when there is LOS path  In multi-path channel environment, the received signal at any point would be a vector sum of all the versions/components of the signal, reaching at the point, which may widely differ in magnitude and phase.

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Multipath Channel: Impulse Response Model  A mobile radio channel can be modeled as a linear filter with time varying Impulse Response [IR].  IR contains all the necessary information required to simulate or analyze any type of radio transmission through the channel.  IR is a useful channel characterization which can be used to predict and compare the performance of many mobile communication systems/transmission bandwidths for any given particular channel condition. x(t)

h(t)

y(t)

Fig-1: Impulse Response Model of a LTI system. The output signal y(t) can be obtained from the convolution of the input signal x(t) with the IR = h(t) of the system. If x(t) is band limited signal, y(t) is also band limited regardless h(t) is band limited or not. So, we can assume LTI system to be band limited if the input is band limited. T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Multipath Channel: Impulse Response Model  Suppose an MS is moving along the ground at a constant velocity v.  At a certain fixed location distant d, the system can be assumed as LTI system.  Due to multi-path reception, various multi-path components will have different delays associated with them because of difference in distance covered.  So, the IR of this LTI system is a function of time as well as of distance, i.e. IR = h(d,t)

v spatial position

d

Fig-2: The Mobile Radio Channel as a Function of Time and Space

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Multipath Channel: Impulse Response Model ∝

 y(d, t) = x(t)⊗h(d,t) = ∫ - ∝ x(τ) h(d, t- τ) dτ  y(d, t) = t∫ - ∝ x(τ) h(d, t- τ) dτ when h(d,t) = 0 for t>0.  When MS is moving at a constant speed v, then d = vt, so, y(vt, t) = t∫ - ∝ x(τ) h(vt, t- τ) dτ  Since v is constant, so, y(vt, t) is a function of time, y(t) = t∫ - ∝ x(τ) h(vt, t- τ) dτ = x(t)⊗h(vt,t) = x(t)⊗h(d,t)  As the velocity can be assumed constant over a small time interval (short distance), so, Mobile Radio Channel can be assumed as a time varying multi-path channel where t represents time variation due to MS in motion and τ represents the channel multi-path delay for a fixed value of t. T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Multipath Channel: Impulse Response Model ∝

 y(t) = ∫ - ∝ x(τ) h(t, τ) dτ = x(t)⊗h(t, τ) and r(t) = c(t) ⊗ ½(hb (t, τ) ) x(t)

c(t)

h(t, τ ) = Re { hb (t, τ) exp (jwct)}

h(t, τ ) = ½ hb (t, τ)

y(t)

r(t)

Fig-3: Base band channel response model and its equivalent RI

 Here c(t) and r(t) are the complex envelop of x(t) and y(t) such that x(t) = Re { c(t) exp (j2π fc t)} and y(t) = Re { r(t) exp (j2π fc t)}  Average Power of BP signal x2 (t) = ½ |c(t) |2, over bar denotes ensemble average of stochastic signal. T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Multipath Channel: Impulse Response Model  If τ0 represents the excess time delay of the first arriving multipath signal and then ∆τ = τ1 - τ0 but as τ0 = 0, so, ∆τ = τ1 .  τi = i x . ∆τ , and if there are N multi-path components, then maximum excess delay of the channel is N x ∆τ  This model can be used to analyze the transmitted signals having BW which are less than 1/2 ∆τ  hb (t, τ) = Σ ai (t, τ) exp [j(ωc τi(t)+ φi(t, τ) )] δ (t, τi(t)). Sum over I = 0 to N-1 where ai (t, τ) and τi(t)) are real amplitude and excess delay of ith multipath component at time t.  The power delay profile of the channel is found by taking the spatial average of | hb (t, τ) |2 over a local area.  The received power delay profile is given P(t, τ) ≈ k| hb (t, τ) |2 , k is the gain relating the transmitted power in the probing pulse to the total power received. T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Multipath Channel: Impulse Response Model  If a CW signal is transmitted into the channel, let the complex envelop be given by c(t) = 2, then, instantaneous complex envelop of received signal is given as r(t) = Σ ai exp [jθi(t, τ) )] , summation over i = 0 to N-1 and instantaneous received power is | r(t)|2= |Σ ai exp [jθi(t, τ) )]|2 , summation over i = 0 to N-1

EXERCISE: Do Example-4.2 and Example-4.3 carefully at home.

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Small-Scale Multipath Measurements Channel Sounding Techniques  Used to determine Power Delay Profile/Channel Impulse Response of any channel

Direct RF Pulse System

Fig-01: Direct RF Channel Impulse Response Measurement System

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Small-Scale Multipath Measurements Channel Sounding Techniques Spread Spectrum Channel Impulse Response Measurement System

Fig-02: Spread Spectrum Channel Impulse Response Measurement System

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Small-Scale Multipath Measurements Channel Sounding Techniques Spread Spectrum Channel Impulse Response Measurement System  Advantages Rejects pass-band noise Improves the coverage range of a given Tx power No need of Tx and Rx PN synchronization-thanks to sliding correlator Due to inherent processing gain, Tx power required is considerably less  Disadvantages No real time measurements Measurement time for power delay profile may be relatively excessive Due to non-coherent detection, information about the phases of individual multi-path components is lost

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation 

Important Multi-path Channel Parameters 

The Mean Excess Delay τ : It is also called first moment of the power delay profile and is defined as ………………..E-01



The RMS Delay Spread σ τ : It is the square root of the second central moment of the power delay profile and is given as ………………..E-02

where ………………..E-03

* These delays are measured wrt the first detectable multi-path

signal component arriving at Rx at τ0 = 0. ** Typical values for στ are in usec for outdoor channels and nsec for indoor mobile channels.

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation 

Important Multi-path Channel Parameters 

The Maximum Excess Delay τX : The max. excess delay at which a multi-path component is within X dB from the strongest multi-path component (may not necessarily arriving at τ0 ). Also known as excess delay spread of the power delay profile.

Fig-3: Example of an indoor power delay profile, mean excess delay, rms delay spread and excess delay spread

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation 

Important Multi-path Channel Parameters 

Coherence Bandwidth Bc It is a defined relation derived from the rms delay spread στ. Range of frequencies over which the mobile channel can be considered flat (a channel that passes all frequencies with almost equal gain and linear phase). Bc ≈ 1/ 50 στ [for frequency correlation function of above 0.9] ≈ 1/5 στ [for frequency correlation function of above 0.5]

EXAMPLE-01: A multi-path power delay profile is given in Fig-04. Calculate mean excess delay, rms delay spread, and max. excess delay(10 dB). Estimate the 50% coherence bandwidth of the channel. Would it be suitable for AMPS or GSM without equalizers? T.S. Rappaport Ch 4-5

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Mobile Radio Propagation 

Important Multi-path Channel Parameters 

Doppler Spread BD and Coherence Time TC Describe the time varying nature of the channel in a small-scale region.

BD = fm = v/c * fc, the maximum doppler shift TC ≈ 1/ fm TC ≈ 0.423/ fm [A popular rule of thumb] EXAMPLE-02: Assuming the consecutive samples having high time correlation, calculate the proper spatial interval required for proper small-scale propagation measurements. If the test van runs at v = 120 km/h and fc = 900 MHz, how many samples would be required in 10 m interval. Assuming that measurements can be made in real time, how much time it take to make these measurements. What is Doppler spread for the channel? SOLUTION : Worst case Tc = 9/16 *Pi* fm = 9C/16*Pi* v fc = ? Samples should be taken at a rate less than 0.5 *Tc = ? ∆x = vTc/2 =? So, number of samples reqd. over 10 m distance = 10/ ∆x . T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Types of Small-Scale Fading  Depending on the signal parameters [BW, Symbol Period] and channel parameters [ rms delay spread and Doppler spread], in a multi-path environment transmitted signals under go different kinds of fading:  Multi-path delay spread causes:

Flat Fading : BW of signal < BW of channel and delay spread < symbol period, most common fading, amplitude and phase of the transmitted signal is changed depending upon the multi-path but no frequency shift is observed [spectral characteristics preserved]. Frequency Selective Fading: BW of signal > BW of the channel and delay spread > symbol period

 Doppler Spread leads to

Fast Fading: Higher BD, TC < symbol period, rapid fluctuations of signal strength due to very high variations in channel Impulse Response faster than base-band signal variations Slow Fading: Just opposite to fast fading T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Fading Effects due to Multi-Path Time Delay Spread  Flat Fading: In a multi-path radio channel, signal will undergo a flat fading if Bs << Bc and Ts >> rms delay spread of the channel

Spectral characteristics of the signal remain unchanged. Amplitude and phase of the transmitted signal will change in Flat Fading Channel. [Also known as Amplitude Varying Channel or Narrowband Channel]

Fig-1: Flat Fading Channel Characteristics

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Fading Effects due to Multi-Path Time Delay Spread  Frequency Selective Fading: In a multi-path radio channel, signal will undergo a frequency selective fading if Bs > Bc and Ts < rms delay spread of the channel  Amplitude and phase of the transmitted signal will change as well as spectral characteristics in Frequency Selective Fading Channel. [Also known as wideband Channel]  ROT: Ts < 10 στ will make a channel FSFC.

Fig-2: Frequency Selective Fading Channel Characteristics

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Fading Effects due to Doppler Spread  Fast Fading: In a multi-path radio channel, signal will undergoes a fast fading if Ts > Tc and Bs < BD Channel impulse response changes rapidly within the symbol duration. Leads to frequency dispersion which in turn increases signal distortion.  Slow Fading: In a multi-path radio channel, signal will undergoes a slow fading if Ts << Tc and Bs >> BD Channel impulse response varies at a rate much slower than the transmitted base-band signal. {Static Channel] ** Fast and Slow Fading should not be confused with Large-Scale and Small-Scale fading. T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Fading Effects due to Doppler Spread

Fig-3: Fading of signal as function of Symbol Period and Base-band Signal BW

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation

Classification of the Channels

T.S. Rappaport Ch 4-5

Channel Corelation bandwidth

Signal Bandwidth/

 Time-Flat Channel: A time-invariant channel which remains flat (constant) during at least the transmission time of one symbol.  Frequency-Flat Channel: A frequency non-selective channel in which bandwidth of the transmitted signal Bs is less than coherence bandwidth Bc of the channel.  Flat-Flat Channel: A time-flat and frequency flat channel.  Non-Flat Channel: A time-variant and frequency selective channel Time-Flat Non-Flat

Flat-Flat

Frequenc y-Flat

Fig-4: Classification of the Channels

Symbol Time/Channel Correlation Time

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Mobile Radio Propagation  Link Budget Calculation  Large-Scale Fading  Shadowing Effect  Small-Scale [Fast] Fading

Fig-6: Link Budget Calculation for Fading Channels [AB-2000]

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Statistical Models for Multi-path Fading Channels  Clark’s Model for Flat Fading  Basic Assumptions    

Takes into account only Scattering mechanism No direct line-of-sight path considered A fixed Tx with vertical polarization N azimuthal plane waves with arbitrary phases and angle of incidence and equal average amplitude

Fig-01: N Azimuthal plane waves arriving at random angles

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Statistical Models for Multi-path Fading Channels  Clark’s Model for Flat Fading

Mobile Rx is in motion at velocity v in x-direction. The Doppler shift of nth plane wave arriving at angle is given as fn = v cosα n / λ

It can be shown* that random received signal envelop r has a Rayleigh Distribution given by p ( r ) = (r/ σ 2 ) exp ( - r2 / 2 σ 2 ) for 0 <= r <= ∞ =0 for r < 0

* Derivation follows, as given in the TB pp-178-179 T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Statistical Models for Multi-path Fading Channels  Clark’s Model for Flat Fading  Spectral Shape in Clark’s Model

Gans developed a spectrum analysis for Clark’s Model Total received power at Rx can be expressed as

and instantaneous frequency of the received signal component is given as

And it can be shown* that output spectrum is [see Fig-02]

* Derivation is as given in TB pp-179-180 T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Statistical Models for Multi-path Fading Channels  Clark’s Model for Flat Fading  Spectral Shape in Clark’s Model

Fig-02: Doppler Power Spectrum for an un-modulated CW carrier

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Statistical Models for Multi-path Fading Channels  Clark’s Model for Flat Fading  Simulation of Clark’s Model

Fig-03: Clarke’s Simulator using AM with a [a] Doppler Filter [b] Base-Band Doppler Filter

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Statistical Models for Multi-path Fading Channels  Clark’s Model for Flat Fading  Level Crossing and Fading Statistics

Important statistical parameters useful for designing Error Control Codes Level Crossing Rate (LCR) is expected rate at which Rayleigh fading envelop, normalized to the local rms signal level, crosses a specified level in positive-going direction. And this number is given by

Where r is d (r(t))/dt, p(R,r) is the joint density function of r and r at r = R, and fm is max. Doppler shift, and ρ = R/Rrms Average Fade Duration is the average period of time for which the received signal is below a specified level R. For Rayleigh fading signal it is given by

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Statistical Models for Multi-path Fading Channels  Clark’s Model for Flat Fading  Example-1: For a Raleigh fading signal, calculate N such that ρ = 1 and fm = 20 Hz. If fc = 900 MHz what would be the velocity of the mobile to get this Doppler shift?  Example-2: Calculate the Average fade duration for previous example. Repeat it when threshold level is reduced to ρ

T.S. Rappaport Ch 4-5

= 0.01.

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