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**Mobile Communications**

Part IV- Propagation Characteristics Multi-path Propagation - Fading Professor Z Ghassemlooy School of Computing, Engineering and Information Sciences, University of Northumbria U.K. Z. Ghassemlooy

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Contents Fading Doppler Shift Dispersion Summary Z. Ghassemlooy

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**Fading Is due to multipath propagation. Caused by shadowing:**

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 assumed to be locally wide-sense stationary (WSS). Z. Ghassemlooy

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**Multipath Propagation - Fading**

Diffracted wave Reflected No direct path a b Antenna a b y = a + b Antenna b y = 0 a a & b are in phase a & b are out of phase by Complete fading when 2d/ = n, d is the path difference Z. Ghassemlooy

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**Multipath Propagation - contd.**

For a stationary mobile unit with no direct path, the received signal can be expressed as a sum of delayed components or in terms of phasor notation: Pulse train A single pulse 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 fc is the carrier frequency Z. Ghassemlooy

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**Fading - Types Slow (Long) Term**

Fast (Short) Term (Also known as Rayleigh fading) Signal strength relative to 1uV (db) 10 20 30 Fast fading Slow fading 5 10 15 20 25 Distance () Exact representation of fading characteristics is not possible, because of infinite number of situation. Z. Ghassemlooy

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**Fading - Slow (Long) Term**

Slower variation in mean signal strength (distance 1-2 km) Produced by movement over much longer distances Caused by: - Terrain configuration (hill, flat area etc.): 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 Z. Ghassemlooy

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**Fading - Slow (Long) Term**

Transmitter tn,1 Receiver tk,1 t or d tn,3 tn,2 tk,2 tk,3 tk,4 one subpath LOS path k path n Sr(t) Number of path path attenuation factor for the ith path C. D. Charalambous et al Z. Ghassemlooy

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**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.) - random fluctuations in the received power Observed over distances = /2 Signal variation up to 30 dB. Is a frequency selective phenomenon. Can be described using - Rayleigh statistics, (no line of sight). - Rician statistics, (line of sight). Z. Ghassemlooy

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**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: Or In-phase Quadrature Z. Ghassemlooy

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**Fading- Fast (Short) Term - contd.**

The phase i can be assumed to be uniformly distributed in the range (0, 2), provided the locations of buildings etc. are completely random. For a large N, the amplitude of the received signal is: where X and Y are independent, identically distributed Gaussian random variables. Z. Ghassemlooy

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**Fading- Fast (Short) Term - contd.**

The envelope of the received signal is: Which will be Rayleigh distributed: Assuming all components received have approximately the same power and that all are resulting from scattering. Rayleigh Exponential A or power P Probability density function Where 0< r < , s2 is variance of A (the total received power in the multipath signal). Z. Ghassemlooy

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Ricean Fading If there is one direct component in addition to scattered components, the envelope received multipath is Ricean, where the impulse response has a non zero mean. Ricean distribution = Rayleigh signal + direct line of sight signal. The distribution is: 2 is the power of the line of sight signal and I0 is a Bessel function of the first kind Z. Ghassemlooy

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**Fading- Fast (Short) Term - contd.**

The probability that the realization of the random variable has a value smaller than x is defined by the cumulative distribution function: Applying it to the Rayleigh distribution For small r Z. Ghassemlooy

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**Fast Fading – Cases 1: Stationary Mobile**

5 4 2 1 3 6 t4 t5 t2 t1 t3 t6 v Stationary t Field strength Z. Ghassemlooy

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**Fast Fading – Cases 1 The number of fading depends on:**

Traffic flow Distance between the mobile and moving cars The received signal at the MU is: Z. Ghassemlooy

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**Fast Fading – Cases 1 where**

is additional relative delay (positive or negative) and Thus envelope Z. Ghassemlooy

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Fast Fading – Cases 2 t1(t1) t2(t2) T1 = d1/c T2 = d2/c

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**Fast Fading – Cases 3: Non-stationary Mobile**

Field strength Signal level No scattered signals V The received signal at the mobile is: Wave number =2/ x = Vt Transmitting frequency Amplitude Z. Ghassemlooy

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**Fast Fading – Cases 3: Doppler Frequency**

A moving object causes the frequency of a received wave to change Substituting for and x, the expression for the received signal is The Doppler frequency The received signal frequency Z. Ghassemlooy

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**Fast Fading – Cases 3: Doppler Frequency**

When = 0o (mobile moving away from the transmitter) When = 90o (I.e. mobile circling around) When = 180o (mobile moving towards the transmitter) Z. Ghassemlooy

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**Fast Fading – Cases 4: Moving MU + Stationary Scatterer**

x(t) Voltage Standing Wave Pattern V so(t) t = 0 t = round trip time MU Z. Ghassemlooy

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**Fast Fading – Cases 4 Received signal at the MU: and for q = 0**

Incident signal Reflected signal Fading with zero amplitude occurs when Z. Ghassemlooy

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**Fast Fading – Cases 5: Moving MU and Scatterers**

The resultant received signal is the sum of all the scattered waves from different angles qi depending upon the momentary attitude of the various scatterers. Z. Ghassemlooy

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**Channel Fading Effects**

Transmitting a short pulse over a (i) frequency-selective (time-spread) fading channel: (ii) time-selective (Doppler-spread) fading channel: t Tp Tp + dt Transmitted Received t Tp Transmitted Received Z. Ghassemlooy

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**Effects of Doppler shifts**

Bandwidth of the signal could increase or decrease leading to poor and/or missed reception. The effect in time is coherence time variation and signal distortion Coherence time: Time duration over which channel impulse response is invariant, and in which two signals have strong potential for amplitude correlation Coherence time is expressed by: where fD-max is the maximum Doppler shift, which occurs when q = 0 degrees To avoid distortion due to motion in the channel, the symbol rate must be greater than the inverse of coherence time. 2 16 9 D-max c f T p = Z. Ghassemlooy

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Coherence Distance Coherence distance is the minimum distance between points in space for which the signals are mostly uncorrelated. This distance is usually grater than 0.5 wavelengths, depending on antenna beamwidth and angle of arrival distribution. At the BTS, it is common practice to use spacing of about 10 and 20 wavelengths for low-medium and high antenna heights, respectively (120o sector antennas). Z. Ghassemlooy

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**Coherence Bandwidth (Bc)**

Range of frequency over which channel is “flat” It is the bandwidth over which two frequencies have a strong potential for amplitude correlation Signal bandwidth Bs Freq. Power Describes frequency selective phenomenon of fast fading Coherence Bandwidth Bc Effect of frequency selective fading on the received signal spectrum Z. Ghassemlooy

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**Estimation of Coherence Bandwidth**

Coherence bandwidth is estimated using the value of delay spread of the channel, st For correlation > 0.9 For correlation > 0.5 Typical values of delay spreads for various types of terrain: t c B 02 . t c B 2 . Delay spread figures at 900 MHz Delay in microseconds Urban 1.3 Urban, worst-case Suburban, typical Suburban, extreme Indoor, maximum 0.27 Delay Spread at 1900 MHz Buildings, average Buildings, worst - case 1.47 Z. Ghassemlooy

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**Channel Classification**

Based on Time-Spreading Flat Fading BS < BC Tm < Ts Rayleigh, Ricean distrib. Spectral chara. of transmitted signal preserved Frequency Selective BS > BC Tm > Ts Intersymbol Interference signal not preserved Multipath components resolved Signal Channel freq. BS BC C. D. Charalambous et al Z. Ghassemlooy

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**Fading in Digital Mobile Communications**

If Bs>> Bc, then a notch appears in the spectrum. Thus resulting in inter-symbol interference (ISI). - To overcome this, an adaptive equaliser (AE) with inverse response may be used at the receiver. Training sequences are transmitted to update AE. If Bs<< Bc, then flat fading occurs, resulting in a burst of error. - Error correction coding is used to overcome this problem. Z. Ghassemlooy

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**Multipath Delay Spread**

First-arrival delay (τA) Mean excess delay Z. Ghassemlooy

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**Multipath Delay Spread**

The standard deviation of the distribution of multipath signal amplitudes is called delay spread. For directive antenna is characterized by the rms delay spread of the entire delay profile, which is defined as: where avg = Σj Pj j , j is the delay of the j th delay component of the profile Pj = (power in the j th delay component) / (total power in all components Delay spread varies with the terrain with typical values for rural, urban and suburban areas: ( ) rural s m 2 . urban 3 suburban 5 Z. Ghassemlooy

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**Multipath Delay Spread - Dispersion**

The delay spread limits the maximum data rate: No new impulses should arrive at the receiver before the last replica of the pervious impulse has perished. Otherwise symbol spreads (dispersion) into its adjacent slot, thus resulting in Inter Symbol Interference (ISI) The signal arrived at the receiver directly and phase shifted Distorted signal depending on the phases of the different parts Transmitted symbols Received symbols Z. Ghassemlooy

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**Mitigation Techniques for the Multipath Fading Channel**

Space diversity – Signals at the same frequency using two or three antennas located several wavelengths a part. Antennas are connected to two or three radio receivers. The receiver will the strongest signal is elected Disadvantage: Uses two or more antennas, therefore the need for a large site. Frequency diversity – Signals at different frequencies received by the same antenna very rarely fade simultaneously. Thus the use of several carrier frequencies or the use of a wideband signal to combat fading. A single aerial connected to a number receiver, each tuned to a different frequency, whose outputs are connected in parallel. The receiver with the strongest instantaneous signal will provide the output. Disadvantage: Uses two or more frequencies to transmit the same signal. Z. Ghassemlooy

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**Mitigation Techniques for the Multipath Fading Channel**

Time diversity – Spread out the effects of errors through interleaving and coding Multipath diversity Consider the tapped delay line model of a channel shown previously If multipaths can be put together coherently at the receiver, diversity improvement results This is what the RAKE receiver does (see next viewgraph) Z. Ghassemlooy

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**RAKE Multipath Signal Processing**

R.E. Ziemer 2002 Z. Ghassemlooy

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**System Design and Performance Prediction**

Base station placement dependent on Propagation environment Anticipated geographic distribution of users Economic considerations (minimize number of base stations) Political and public opinion considerations Traffic types (3G) Performance figure of merit Spectrum efficiency for voice: ηv voice circuits/MHz/base station Spectrum efficiency for information: ηi bps/MHz/base station Dropped call rate – fraction of calls ended prematurely Z. Ghassemlooy

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**Summary The random fluctuations in the received power are due to**

fading. If there is a relative motion between transmitter and receiver (mobile) the result is Doppler shift If maximum Doppler shift is less than the data rate, there is “slow” fading channel. If maximum Doppler shift is larger than the data rate, there is “fast” fading channel. Z. Ghassemlooy

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**Questions and Answers Tell me what you think about this lecture**

Next lecture: Modulation Techniques Z. Ghassemlooy

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