EE303: Communication Systems · 2020. 10. 23. · e.g. Body Comms, M2M ,wireless IoT 4 antennas build-in (omnidirectional) For instance: "Bluetooth" which is for short-range applications

EE303: Communication Systems

Professor A. ManikasChair of Communications and Array Processing

Imperial College London

An Overview of Fundamentals: Wireless Channels

Prof. A. Manikas (Imperial College) EE303: Wireless Channels v.19 1 / 60

Table of Contents1 Introduction - Basics

Wireless ChannelsMultipathsResolving MultipathsWireless Systems Classification

2 Wireless SISO ChannelsImportant Wireless Channel ParametersMultipathsPropagation LossFadingDelay Spread, TspreadClassification of Wireless ChannelsChannel Selectivity and Channel CoherenceExamples: Temporal and Frequency SelectivityWireless Channel AnalysisDoppler Power Spectrum of Wireless ChannelPower Delay Profile (PDP) of Wireless ChannelScatterersFading and Path Gain/LossLog-distance Path-Loss ModelLog-Normal DistributionRayleigh, Ricean and Uniform DistributionsNakagami Distribution

ClustersModelling of the Received Scalar-Signal x(t)


Introduction - Basics

Wireless - Very Large DistancesThe 1st wireless system was designed by Guglielmo Marconi(1901) and used to transmit a wireless message across the AtlanticOcean .

Marconi was awarded the Nobel Price in Physics (1909) in recognitionof his contribution to Wireless Telegraphy



Wireless Systems have evolved over the yearsI to the latest developments in Multiple-Input Multiple-Outputwireless systems and technologies and

I to the interconnection of wireless devices into a single all-IPwireless platform .

Due to their flexibility and comfort, today wireless systems are usedto cover even very small distances (short range wireless links)



Wireless - Short Range and Low-Power Wireless Links

1 RF-power several µW up to 100 mW

2 Range several cm upto several hundred meters

3 Operation both indoor and outdoorbattery-operated Tx/Rxe.g. Body Comms, M2M ,wireless IoT

4 antennas build-in (omnidirectional)

For instance: "Bluetooth" which is for short-range applications of high-rate data

communications for distances of several meters (developed by the Bluetooth consortium

of telecommunication and PC technology leaders for eliminating wiring between

computers and peripherals, as well as wireless internet access through cellular phones).

other applications: Security Systems, Emergency Medical Alarms,Computer Accessories

(e.g. mouse, keyboard), RFID (Radio Frequency Identification), WLAN (Wireless Local

Area Networks),Wireless microphones/headphones/speakers; Keyless Entry, Wireless bar

code readers.



Tx - Wireless Channel - RxA wireless system can be partitioned into 3 main parts:

1 Tx (a "source " that sends/transmits some information using wavepropagation)

2 Wireless Channel (the physical propagation paths )3 Rx ( a "sink " that receives the transmitted waves)

and the objective in general isI to increase the communication speed (which is known as channelcapacity)without sacrificing the quality of service (for a given energy +bandwidth)


Introduction - Basics Wireless Channels

Wireless Channels

Wireless Channels are much more diffi cult and hostile than wiredchannels.

1 noise (thermal, sky, etc..)2 unintentional interference from other Tx (multiple accessinterference)

3 intentional (hostile) interference (from Jammers)4 multipaths

I reflectionsI diffractionI refractionI scattering


Introduction - Basics Multipaths

Multipaths



Wireless Channel: Basics (cont.)

Because of multipath reflections (echoes), the channel impulseresponse of a wireless channel looks likes a series of pulses.



Wireless Channels: Basics (cont.)

Note: every path is represented by a complex number β


Introduction - Basics Resolving Multipaths

Resolving Multipaths

The delay spread is a measure of the multipath richness of awireless channel.

I In general, it can be interpreted as the difference between the time ofarrival of the earliest significant multipath component and the time ofarrival of the latest significant multipath components.

In modern wireless systems the aim is to resolve multipaths, toestimate them and finally to utilise them.



Resolving Multipaths (cont.)

Pulse duration = 1Bandwidth (B )

Pulse duration = ↓↓↓ =⇒ Bandwidth (B) = ↑↑↑ =⇒ WB/UWB



Resolving Multipaths (cont.)

To find the number of resolvable paths: we compare delay spreadwith the pulse duration Tc .

I If pulse duration < delay spread ⇒ the channel is defined asFREQUENCY SELECTIVE CHANNEL and

number of resolvable paths =⌊delay spreadpulse duration

⌋+ 1



Resolving Multipaths (cont.)In practice (indoors) the number of pulses that can be distinguished isvery large

ITU-R P.1238-1, “Propag. Data & Prediction

Methods for the Planning of Indoor .... in the

Frequ Range 900 MHz to 100 GHz” 1999.

Delay spread can be quantified through

different metrics:

I The maximum delay spread Tmaxis the total time interval during

which reflections with significant

energy arrive.I The r.m.s. delay spread Trms isthe standard deviation value of the

delay of reflections, weighted

proportional to the energy in the

reflected waves.I The mean delay spread Tmean



Multipaths

Before, multipaths = "unwanted" propagation effect (known as"self interference") ⇒ Aim: to remove multipaths

In modern wireless systems the aim is to resolve them and toutilise them - using the concept of "multipath diversity"

I this is extra energy which increases the received desired energy andthus improves the performance of the system


Introduction - Basics Wireless Systems Classification

Wireless Systems Classification

There are many classifications. For instance:1 according to the bandwidth/carrier: narrowband or wideband2 according to the spreading capabilities: conventional or spreadspectrum

3 according to the number of carriers: single carrier or multicarrier4 according to the "generation": 1G, 2G, 3G , 3G+5 according to the "access": TDMA,FDMA , CDMA ,

The overall aims:I speed = ↑,I but maintaining reliability (quality of service) & spectral effi ciency(EUE,BUE)

The current speed is expected to increase by the utilisation of thenew technology of multiple antennas (MIMO) and this gives rise to anew classification which super-sets all the above.



Some Current Wireless Data Rates



New Wireless Systems ClassificationThis new classification is according to the number of antennasused in both Tx and RX



My TerminologyTerminology-1 (More Representative)1 SISO: Scalar-Input-Scalar-Output Channel2 SIVO: Scalar-Input-Vector-Output Channel3 VISO: Vector-Input-Scalar-Output Channel4 VIVO: Vector-Input-Vector-Output ChannelAlternative TerminologyTerminology-2 (Initial)1 SESE Single-Element (SE) Tx to Single-Element (SE) Rx2 SEME Single-Element (SE) Tx to Multiple-Element (ME) Rx3 MESE Multiple-Element (ME) Tx to Single-Element (SE) Rx4 MEME Multiple-Element (ME) Tx to Multiple-Element (ME) RxTerminology-3 (More Popular)1 SISO: Single-Input-Single-Output2 SIMO: Single-Input-Multiple-Output3 MISO: Multiple-Input-Single-Output4 MIMO: Multiple-Input-Multiple-Output


Wireless SISO Channels

Wireless SISO Channels


Wireless SISO Channels Important Wireless Channel Parameters

Important Wireless Channel ParametersC = Channel Capacity (inf. bits/sec)B = Tx-signal/channel Bandwidth (Hz)Bcoh = Coherence Bandwidth of the Channel(Hz)Itypical examples of coherencebandwidth:Bcoh =

{3 MHz outdoor wireless channel100 MHz indoor wireless channels

BDop = Doppler Spread of the Channel (Hz)Tcs = Duration of a channel symbol (sec)Tspread = multipath spread or delay spread (sec)Tcoh = Coherence time (sec)

B =1Tcs

(1)

Bcoh =1

Tspread(2)

BDop =1Tcoh

(3)


Wireless SISO Channels Multipaths

Multipaths

= h(t)

multipaths: arise fromI reflectionI scatteringI refraction, orI diffraction

of the radiated energy off objects that lie in the propagation path


Wireless SISO Channels Propagation Loss

Propagation Loss


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In a wireless system the received signal is the summation of a numberof paths (ignoring noise).



Impulse response (baseband):

h(t) =L

∑`=1

(1d`

)aexp(jϕ`− j2πFc

d`c︷︸︸︷

τ` )︸︷︷︸β`

δ(t − τ`) (4)

=L

∑`=1

β`δ(t − τ`) (5)

or, equivalently,

= h(t)


manikas

Pencil

Wireless SISO Channels Fading

Fading


Wireless SISO Channels Fading

Sample of a "fading" signal envelope: amplitude in dB versus time orlocation of the antenna. Wave interference of multiple reflectedwaves, each with a different amplitude and phase, causes fluctuationsof the received signal amplitude.

Changing the antenna location or the carrier frequency also changesthe signal amplitude.

This is known as fading


Wireless SISO Channels Delay Spread, Tspread

Delay SpreadThis is the time it takes for light to travel a distance equal to thelongest path minus the shortest pathi.e.

Tspread ≡max∀j{dj} −min

∀j{dj}

c(6)

typical examples of delay spread:I fraction of µs≤ Tspread ≤many µs


Wireless SISO Channels Classification of Wireless Channels

Classification of Wireless ChannelsBy comparing Tcs (or Tc ) with Tspread and/or Tcoh



By comparing B (or Bss ) with Bcoh and/or BDop



Some Comments on Multipath Fading in a Conventional System

I In a conventional mobile cellular system (TDM/FDM) the destructiveinterference is known as multipath or Rayleigh fading.

I This occurs more frequently when the mobile is moving.

I This fading is detrimental to the system performance.

I Thus, in a conventional system Tspread is compared to Tcs

IF{Tspread > Tcs(i.e.Bcoh < B)

}then paths can be separated

ELSE signals are distorted =⇒ FLAT FADING

I Number of resolvable paths in a conventional system:

L =⌊TspreadTcs

⌋+ 1 (7)



Some Comments Multipath Fading in Spread Spectrum Systems:

I Multipath fading exists in Spread Spectrum (or CDMA) Systems aswell but it is significantly lower

I Number of resolvable paths in a SSS or CDMA:

L =⌊TspreadTc

⌋+ 1 (8)



Remember - Frequency Selective Channels:

⇒ h(t) =L

∑`=1

β`δ(t − τ`) (9)


Wireless SISO Channels Channel Selectivity and Channel Coherence

Channel Selectivity and Channel Coherence

Channel Selectivity : A channel has selectivity if it varies as afunction of either time, frequency, or space

Channel Coherence: (opposite of Channel Selectivity)I A channel has coherence if it does not vary as a function of eithertime, frequency, or space over a specified ’window’of interest.

I This is the most important concept in describing wireless channels

I coherence:

temporal coherence -coherence time Tcohfrequency coherence -coherence bandwidth Bcohspatial coherence -coherence distance Dcoh


Wireless SISO Channels Examples: Temporal and Frequency Selectivity

Examples: Temporal and Frequency Selectivity


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Example of effect of transmitting a rect pulse over a TimeSelective Fading Channel



Example of effect of transmitting a rect pulse over a FrequencySelective Fading Channel


Wireless SISO Channels Wireless Channel Analysis

Wireless Channel Analysis


Wireless SISO Channels Doppler Power Spectrum of Wireless Channel

Doppler Power Spectrum of Wireless ChannelWith reference to the following figure

the difference in path lengths from Tx to a moving Rx with velocity vis

∆l = d cos θ = v .∆t︸︷︷︸=d

. cos θ (10)

If λc denotes the wavelength of the carrier, then the phase change inRx-signal due to difference in path length is:

∆ϕ =2π.∆l

λc

(10)=2π.v .∆t. cos θ

λc(11)



Doppler frequency (in Hz): it is defined as the rate of phase changedue to Rx’s motion

f =12π.∆ϕ

∆t=vλccos θ (12)

where fmax ,vλc

(13)

Note that the angle θ is a random which can be viewed as a randomvariable uniformly distributed, i.e.

pdfθ(θ) =12πrect

{θ

2π

}(14)

which imples that f is also a random variable with a cosinedistribution.Based on the above, the Doppler Power Spectrum is

SH (f) ∝12π

∣∣∣∣dθ

df

∣∣∣∣⇒ SH (f) =cons√

1−(

ffmax

)2 (15)


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Note-1:

I a single carrier frequency Fc is broadened to a spectrum(Fc − fmax,Fc + fmax)

I a Tx signal with bandwdith 2B centered at Fc is broadened to abandwidth 2B + 2fmax

Doppler spread BDop is defined as the "bandwidth" of the Dopplerpower spectrum and it is a measure of spectral broadening caused bythe time varying nature of the wireless channel.

Coheret time Tcoh ∝ 1BDop

is used to characterise the time varyingnature of the frequency dispersion of the channel in the time domain.



Note-2:I velocity of a mobile and the signal bandwidth B determine whether asignal undergoes fast or slow fading

I often normalised Doppler frequency

f̂ = fmax.Tcs (16)

is used to specify the fading rate.F f̂ = 10−6 is considered very slow fadingF f̂ = 10−4 is considered quite fast fading

Example:I Carrier frequency Fc of 1GHz ⇒ wavelength λc = c/Fc = 30cm(0.3m)

I if the mobile velocity is 10 m/s (36 km/h) and the symbol rate is 3.3Msymbols/s then

F Doppler frequency: fmax = v/λc ≈ 33Hz , andF normalised Doppler frequency: f̂ = fmax.Tcs = 33/(3.3× 106) = 10−5


Wireless SISO Channels Power Delay Profile (PDP) of Wireless Channel

Power Delay Profile (PDP) of Wireless Channel

In this course, the PDP is denoted by SH (τ)

The PDP gives the intensity of a signal received through a multipathchannel as a function of time delay τ.

I The abscissa is the time delay τ (in units of time) and the ordinate isusually in decibels. It is easily measured empirically and can be used toextract certain channel parameters such as the delay spread.

SH (τ) =FT{ΦH (∆f )}, where ΦH (∆f ) denotes the spaced-frequencyautocorrelation function of the channel.

SH (τ) can be use to estimate the delay spread.

SH (τ) is a special case of the scattering function of the channel



The equations for estimating the mean delay spread and rms delayspread are functions of PDP:

mean : Tmeanor= T spread ,

,∫ Tmax0 τSH (τ)dτ∫ Tmax0 SH (τ)dτ

= cont. case

,

L

∑i=1

τiSH (τi )

L

∑i=1

SH (τi )

= discrete case

(17)

rms : Trmsor= σspread ,

,√ ∫ Tmax

0 (τ−T spread )2SH (τ)dτ∫ Tmax

0 SH (τ)dτ= cont. case

,

√√√√√√√L

∑i=1

(τ−T spread )2SH (τ)

L

∑i=1

SH (τ)

= discrete case

(18)



example of a discrete PDP

Coherence bandwidth is related to the PDP and it is a measure ofthe range of frequencies over which the PDP of the channel is "flat"(i.e. passinf spectral componebts with approx equal gain and linearphase)

50% coherence bandwidth Bcoh is defined as

Bcoh ≈1

5σspread

(19)


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Wireless SISO Channels Scatterers

Scatterers

The figures below show a scatterer-cloud (the l-th scatterer) in twotypical scenarios.

`-th scatterer =Lscat

∑k=1

β`k δ(t − τ`k ). (20)

Lscat = the number of paths related to this scatterer


Wireless SISO Channels Scatterers

If the paths cannot be resolved, that is if

τ`1 ' τ`2 ' .. ' τ`Lscat , τ` (21)

then

`-th scatterer =Lscat

∑k=1

β`k δ(t − τ`k )

=Lscat

∑k=1

β`k δ(t − τ`)

=

(Lscat

∑k=1

β`k

)︸︷︷︸

β`

δ(t − τ`)

= β`δ(t − τ`) (22)

In this case β` =

(Lscat

∑k=1

β`k

)is a random variable and, therefore,

should be described by a probability density function (pdf).Prof. A. Manikas (Imperial College) EE303: Wireless Channels v.19 49 / 60

Wireless SISO Channels Fading and Path Gain/Loss

Log-distance Path Loss Model

Path-Loss(PL) = 10 log10

Watt↓PTx1mW︸︷︷︸

Tx power in dBm

− 10 log10

Watt↓PRx1mW︸︷︷︸

Rx power in dBm

(dB) (23)

= PL0 + 10 log10

(dd0

)a+ PLGaussian (dB) (24)

where

PL0 = the path loss at the reference distance d0 = 1km/1miled = path length

a = path loss exponent

PLGaussian = N(0, σ2).



Notes on PLGaussian = N(0, σ2)

no-fading ⇒ σ = 0

shadow fading or slow fading ⇒ σ > 0 in dB ⇒ PRx=random(log-normal distribution) in Watt.

fast fading caused by multipath propagation, the corresponding pathgain |β`| (i.e. |β`|

2 in Watts) may be modelled as a random variablewith Rayleigh distribution or Ricean distribution.



Log-Normal Distributiona log-normal distribution = a continuous probability distribution of arandom variable x

pdfx(x) =1

xσ√2π

exp

{(ln x − µ)2

2σ2

}(25)



a log-normal random variable = takes only +ve real values.

If x=Normal-distribution ⇒ y = exp(x) = log-normal distribution

if y= log-normal- distribution⇒ x = ln(y)= normal distribution.

A variable might be modeled as log-normal if it can be thought of asthe multiplicative product of many independent random variableseach of which is positive.

In wireless communication:

shadow fading or slow fading⇓

PLGaussian = N(0, σ2) with σ > 0 in dB⇓

PRx = random (log-normal distribution) in Watt.



Fast fading (multipath propagation)

There are two main casesI CASE-1 :

if @ a direct path

then{

pdf of |β`| = Rayleigh distribution

pdf of ]β` = uniform distribution

∣∣∣∣(urban areas & large cells)

I CASE-2 :

if ∃ a direct paththen

{pdf of |β`| = Ricean distribution

pdf of ]β` = uniform distribution

∣∣∣∣ (small cells &

satellite mobile systems)

A better pdf which has more degrees of freedom is the NAKAGAMIdistribution. This enables a better fit to experimental measurementsin urban channels.



Fast fading (multipath propagation)Nakagami Distribution


Wireless SISO Channels Clusters

Clusters

The generation of clusters in a typical urban area is described asfollows:

I Many buildings in a typical urban area generally surround a mobile.I Electromagnetic waves from an MS (Mobile-Station) do not propagatein random directions, but along the streets.

I These waves propagate to a BS (Base-Station) while being reflected orscattered at many points along the street.

I Not all reflected or scattered waves propagate to a BS, but some wavesbolstered by certain conditions will propagate to a BS because manybuildings obstruct the waves.

I Each group of selected waves is recognised as a cluster.



The above will give an impulse response similar to the following





Note that

I if Tspread ,1 < Tcs then the 1st cluster involves a number ofunresolvable paths and becomes one ray/path by itself.

I A similar comment can be made for the 2nd cluster.

I if both clusters involve a number of unresolvable paths then the twoclusters are seen as two resolvable paths.


Wireless SISO Channels Modelling of the Received Scalar-Signal x (t)

Modelling of the Received Scalar-Signal x(t)Consider a single Tx transmitting a baseband signal m(t) via anL-path SISO channel. Based on Equation 9, the received signal x(t)can be modelled as follows:

x(t) = h(t) ∗m(t) + n(t) =(

L

∑`=1

β`.δ(t − τ`)

)∗m(t) + n(t)

⇒ x(t) =L

∑`=1

β`.m(t − τ`) + n(t) (26)

Next consider M transmitters operating at the same time, on thesame frequency band each one with its own SISO channel.In this case we have added the subscript i to refer to the i-th Tx.The received signal x(t) can be modelled as follows:

x(t) =M

∑i=1

L

∑`=1

βi`.mi (t − τi`) + n(t) (27)


EE303: Communication Systems · 2020. 10. 23. · e.g. Body Comms, M2M ,wireless IoT 4 antennas build-in (omnidirectional) For instance: "Bluetooth" which is for short-range applications

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