2. Wireless Communications-RF (one week) (not on exams)

Propagation: Path loss, shadowing, multipath (fading), Doppler Modulation---increasing bit rates (Shannon) Channel capacity (PHY layer) and Networking (Queuing)

capacity Research topic (covered later in this course)

A classical layered networking approach will view the PHY layer as a pure bit carrier, and the Data Link layer (which is composed of a lower half layer the MAC [media access control sublayer and upper half layer the Logical Link Control [LLC] sublayer) as being responsible for providing media access and error-free packets to the PHY layer. Under this model, these, and the other, layers operate in isolation. In contrast, in cross-layer networking the physical and MAC layer (and other layers) share knowledge of the wireless medium with higher layers, in order to provide efficient methods of allocating network resources and applications. In essence, future networks will need to provide "impedance matching" of the instantaneous radio channel conditions and capacity needs with the traffic and congestion conditions found in packet-based networks.

2

Channels and Propagation Models

The Wireless Environment Propagation Basics: carrier frequency, rf spectrum,

wavelength Antennas The Gaussian Channel Path Loss, Multipath, and Shadow Fading Fading Multipath Channels, Delay Spread, Rayleigh and

Rician Channels, Doppler Shift Propagation in Macrocells and Microcells

3

A Wireless Transmitter and Receiver: the RF (Radio Frequency) Channel

A high frequency sinusoidal signal is capable of propagating energy through space. By modulating this signal (e.g., changing its amplitude, frequency, or phase) information can be transmitted from an antenna over the air. For a cellular system we will be interested in transmission in the forward/downlink path[base to mobile] and in the backward/uplink path [mobile to base]. As the terminal moves, the signal amplitude, phase, and frequency will fluctuate randomly, or fade.

A/D speech coding

Channel coding

Bit interleaving

RF Channel

Transmit Path

Encryption

Multiplexing

Modulation

Transmitting radio subsystem

Receiving radio subsystem

Demodulation & equalization

Demultiplexing

D/A speech decoding

Channel decoding

Bit deinterleaving Decryption

Receive Path

Timing and synchronization

Below is a point-to-point link; most wireless networks have many users (terminals/mobiles) and support one-to-many (base go mobile) and many-to-one (mobiles to base) networks

Electromagnetic Spectrum

The Electromagnetic Spectrum covers a very wide range of frequency, from almost DC to gamma rays.

Radio frequency (RF) is a subset of the EM spectrum and is loosely defined as:

The frequency in the portion of the electromagnetic spectrum that is between the audio-frequency portion and the infrared portion. The present practical limits of radio frequency are roughly 10 kHz to 100 GHz. [IEEE Std 100-1988 Standard Dictionary of Electrical and Electronic Terms]

EM (Electromagnetic) waves can propagate in vacuum but not acoustic waves.

4

Frequency Wavelength Relationship

The wavelength of an electromagnetic wave is related to its frequency f by:

Conveniently in practice, we can quickly estimate the wavelength of a frequency given in MHz or GHz by:

fc

= where c = 3x108 m/s (speed of light in vacuum)

)m(fMHz

300=

)mm(fGHz

300=

5

e.g., of 100 MHz is 3 m.

e.g., of 10 GHz is 30 mm.

5

6

Radio Waves: Frequency and Wavelength

Idealized radio waves have a smooth, repetitious shape as they move through time and distance. This shape can be described mathematically as sinusoidal [see (2.1)], and can be characterized by measures of either frequency (Hz) or wavelength. The (carrier) frequency, fc, is the number of repetitions which occur per second; it is inversely related to the time period, T, between repetitions. The wavelength, , is the distance between repetitions. The basic relationships are = c/fc where c is the speed of light [3x108 meters/sec] and fc is the carrier frequency, and the electric field at time, t, and distance, d, from the source are

(2.1) )](cos[22cos),( 00 cdt

dE d)

tf(

dEtdE cc ==

RF Band Names

Band Name Abbr. Frequency Wavelength Examples of Usage Extremely Low Frequency ELF 3-30 Hz 10-100 Mm

Super Low Frequency SLF 30-300 Hz 1-10 Mm power lines

Ultra Low Frequency ULF 0.3-3 kHz 0.1-1 Mm

Very Low Frequency VLF 3-30 kHz 10-100 km submarines

Low Frequency LF 30-300 kHz 1-10 km beacons

Medium Frequency MF 0.3-3 MHz 0.1-1 km AM broadcast

High Frequency HF 3-30 MHz 10-100 m short-wave radio

Very High Frequency VHF 30-300 MHz 1-10 m FM and TV broadcast

Ultra High Frequency UHF 0.3-3 GHz 0.1-1 m TV, WiFi, mobile phones, GPS

Super High Frequency SHF 3-30 GHz 10-100 mm radar, satellites, WLAN data

Extremely High Frequency EHF 30-300 GHz 1-10 mm radar, automotive, data

7

Microwave Band Names

8

Band Name Frequency

L 1-2 GHz

S 2-4 GHz

C 4-8 GHz

X 8-12 GHz

Ku 12-18 GHz

K 18-26 GHz

Ka 26-40 GHz

U 40-60 GHz

8

Frequency/Spectrum Allocation/Management

RF frequency allocation is controlled by: ITU (International Telecommunication Union)

a United Nations agency divides the world into three regions (North/South America,

Europe/Africa, Asia/Australia/NZ) divides the spectrum for re-allocation by individual countries

Country-specific National Bodies, e.g., FCC = Federal Communications Commission (USA) ACMA = Australian Communications & Media Authority

9

Wireless System Frequencies

Frequencies are allocated according to types of application (sometimes called service).

Examples of application include:

Mobile phones (around 900 MHz and higher bands)

WLANs (around 900 MHz, 2.4 GHz and 5.8 GHz)

ISM (Industrial, Medical and Scientific) (same as WLANs plus others)

Variation in frequency allocation is allowed in different nations.

Wireless products from one country may not work, or allowed to be used, in another country.

10

Characteristics of Microwave

Microwave frequency: 300 MHz to 300 GHz wavelength: 1 mm to 1 m

Millimetre (mm) Wave frequency: 30 GHz to 300 GHz wavelength: 1 mm to 10 mm

high frequency, short wavelength component size approaches wavelength

(variation of phase across component) high-gain antennas line-of-sight propagation large bandwidth mm wave highly attenuated by atmosphere and rain

11

Communication Link Design and Performance Issues

Propagation free-space propagation, line-of-sight link, multipath fading

(e.g., 20 dB)

Frii's Transmission Equation:

Link Budget to account for power gains/losses between tx and rx

Link Margin (factor M) to account for unexpected attenuation in a communication

link, after most of other known conditions (factor F2) are considered

modified Frii's equation:

rtt

r GGrP

P 2

4

=

MFGGrP

Prt

t

r 22

4

=

12

Tx

Rx

Multipath

13

A multipath propagation occurs when the signal from an RF transmitter Tx (e.g., a mobile phone) is reflected by buildings and/or other objects, resulting in one or more time-delayed signals arriving at the receiver Rx simultaneously as the direct-path signal.

reflected signal

direct-path signal

13

14

Spectrum Allocation [Carrier Frequency]

VLF = Very Low Frequency UHF = Ultra High Frequency LF = Low Frequency SHF = Super High Frequency MF = Medium Frequency EHF = Extra High Frequency HF = High Frequency UV = Ultraviolet Light VHF = Very High Frequency The relationship between the carrier frequency, f , and wave length is

= c/f , where c is the speed of light 3x108m/s [note: we often use the radian frequency = 2 f

1 Mm 300 Hz

10 km 30 kHz

100 m 3 MHz

1 m 300 MHz

10 mm 30 GHz

100 m 3 THz

1 m 300 THz

visible light VLF LF MF HF VHF UHF SHF EHF infrared UV

optical transmission coax cable twisted pair

Cellular/WLAN (~900 MHz to 5 GHz)

15

Types of Waves

Transmitter Receiver

Earth

Sky wave

Space wave

Ground wave Troposphere

(0 - 12 km)

Stratosphere (12 - 50 km)

Mesosphere (50 - 80 km)

Ionosphere (80 - 720 km)

Source: Eurescom, ING

Frequency Band Impacts Coverage/Capacity Coverage ~ 1/d n (n =2 in free space and n ~3.5-4 in urban areas) ---where d is the distance of the terminal from the antenna

900 MHz

2500 MHz 4600 MHz

2100 MHz

3500 MHz

Urban Environment 16

17

Signal Propagation Ranges

Distance from transmitter

sender

transmission

detection

interference

Transmission range communication possible low error rate

Detection range detection of the signal

possible, but communication may not be possible

due to high error rate Interference range

signal may not be detected

signal adds to the background noise

Path loss and shadowing Self interference

Multipath [Rayleigh] fading Delay Spread: Intersymbol interference (ISI) Doppler Shift [due to motion]

Noise (SNR) Other users

Co-channel interference (CCI) ---at same frequency

Adjacent-channel interference (ACI) Time and Frequency synchronization

Wireless (rf) Channel: Limitations on Performance

Multipath Propagation

Path loss Shadowing Co-channel

interference

Delay spread

The wireless channel is generally unknown at the receiver and may change significantly during a frame --- needs to be estimated and tracked

19

Propagation Modeling Design of spectrally efficient wireless communication systems requires a detailed understanding

of radio propagation. Complete analytical solutions are not possible. The characteristics of the rf [radio frequency] channel vary greatly with the operating frequency

and the mode of propagation [e.g., line of sight (LOS) radio links, diffraction/scatter, and satellite links].

In a cellular system, the collection of base stations [BSs] define the radio coverage area. In satellite/military systems the BSs may be moving and the mobiles may be stationary.

In a macrocellular environment, the BS antennas are usually well elevated above local terrain at ~100m elevation and free of local scatterers and typically non LOS [NLOS] (Rayleigh) propagation will exist. Radio propagation path will exist between a BS and a mobile station [MS], because of natural and man-made objects that are situated between the BS and MS. As a consequence the radio waves must propagate via reflections, diffraction, and scattering In a microcellular environment, the BS antennas are often placed below the building rooftops and a direct line of sight [LOS] path generally exists and propagation will be Ricean.

Base Station

Mobile

Typical Macro-cellular Radio Propagation Environment with Local Scatterers: Rayleigh or Ricean Multipath Propagation

The multiple plane waves combine vectorially at the receiver antenna to produce a composite received signal

20

Propagation Modeling-2 The carrier wavelength used in cellular radio is ~30 cm, and hence small changes in the

differential propagation delays due to MS mobility will cause large changes in the phases of the individually arriving plane waves. Thus the plane waves arriving at the BS and MS antennas will experience constructive and destructive addition depending on the location of the MS.

As the MS moves the propagation characteristics will change with time and this introduces a phenomenon called envelope fading ---the rate of fading depends on the MSs velocity.

Radio channels are reciprocal in the sense that if a propagation path exists, then it carries energy in the same manner in either direction.

Interference from other sources and noise will also impact signal behavior: co-channel (mobile users in adjacent cells using same frequency) and adjacent (mobile

users using frequencies adjacent to transmission/reception frequency) channel interference ambient noise from the radio transmitter components or other electronic devices,

21

Antennas are used to radiate and receive EM waves (energy) Antennas consist of one or several radiating elements through which an

electric current circulates Types of antennas:

isotropic: equal radiation in all directions (three dimensional) - only a theoretical reference antenna

omnidirectional directional phased and adaptive antenna arrays

Principal characteristics used to characterize an antenna are: radiation pattern directivity gain: the ratio of the maximum power in the direction of the main

lobe to the power of an isotropic radiator (with the same average power)

Antennas

Directional Antennas

side view (xz-plane)

x

z

top view (xy-plane)

x

y

top view, 3 sector

x

y

top view, 6 sector

x

y

Often used for microwave (directed point to point transmission) or base stations for mobile phones (e.g., radio coverage of a valley or sectors for frequency reuse)

directed antenna

sectorized antenna

We will not emphasize antennas in this course ---except for spatial domain, or smart antenna processing

23

Mobile Radio Propagation Environment Radio signals generally propagate according to four mechanisms

Reflection at large obstacles: plane waves are incident on a surface with dimensions that are very large relative compared to the wavelength.

Scattering at small obstacles: occurs when the plane waves are incident upon an object whose dimensions are on the order of a wavelength or less, and causes energy to be redirected in many directions.

Diffraction at edges: occurs according to Huygens principle when there is an obstruction between the transmitter and receiver antennas, and secondary waves are generated behind the obstructing body. As the frequency gets higher, the rf wave will diffract less and start to behave like light.

Penetration: In addition to diffraction, penetration of objects will allow rf reception when there is an obstruction(s) between the transmitter and receiver.

scattering reflection

diffraction

penetration

24

Mobile Radio Propagation Environment-2 As a result of the above mechanisms, macrocellular radio propagation produces a

statistically varying signal that can be roughly characterized by three nearly independent phenomenon (whose effects are multiplicative)

The measured envelope of the carrier, averaged over a spatial distance of 20 to 30 wavelengths, is called the local mean. The path loss predicts how the local mean will vary with distance. Empirical models exist for path loss [location dependent] which is often modeled as being proportional to the nth power of the distance from the antenna [n =2 in free space, and n~4 for cellular]

The local mean will also experience slow variations, called shadow fading, over 10s of wavelengths due to rf penetration of hills and buildings. Shadow fading will be shown to have a log-normal distribution.

Fast multipath fading: results in rapid variations in the envelope of the received signal and is caused when plane waves arrive from many different directions with random phases and combine vectorially [ie, add as complex numbers] at the receiver antenna. The received envelope can fade and have a Rayleigh distribution that can vary by as much as 30 to 40 dB over a fraction of a wavelength due to constructive and destructive addition. Multipath [see next chart]. also causes time dispersion, since the multiple replicas of the transmitted signal propagate over different transmission paths and reach the receiver with different time delays. Compensation for time dispersion, may require equalization in TDMA and OFDMA systems and RAKE reception in CDMA systems

Shadowing (penetration)

Three-Part Propagation Model: Path Loss, Slow Shadow Fading, and Fast Rayleigh Fading

The effects of path loss, shadow fading and fading are essentially independent and multiplicative 25

26

Mobile Radio Propagation Environment-3

Combining the three phenomena of path loss, shadow fading, and multipath fading, the received power at a distance d from the transmitter is a random variable [ie, statistically varying] and is modeled by the following

where 2 represents the random (Rayleigh) multipath fading, 10x/10 is the

(random) shadow fading, and GT and GR are respectively the gains of the transmitting and receiving antennas, and g(d) represents the inverse variation of power with distance [we will have a lot more to say about g(d) ].

Power ratios are generally expressed in units of decibels [dB]; if a power ratio is p, then P = 10 log10 p dB, and if p is an absolute power level, then the units are dBm ---which is dB above a milliwatt [i.e. 0 dBm = 1 milliwatt]

Pr (d) = 210x

10 g(d)PTGTGR 2.2( )

+50 +40 +30 +20 +10

100 10

1 0.1 0.01 0.001 (1 milliwatt) 0.0001 0.000001 0.00000001

Power [ dBm] Power [ Watts ]

0 10 30 50

27

Mobile Radio Propagation Environment-Free Space Path Loss Path Loss: From (2.1) we see that the intensity of an electromagnetic wave in free

space, decays with the inverse of the radio path length, d. The received power, which is proportional to the squared magnitude of the electric field is given by

where pt is the transmitted power, is the wavelength, gT is the gain of the transmit

antenna, gR is the gain of the receive antenna, and k is a constant of proportionality. This is understandable since the power transmitted is spread uniformly on the surface of a sphere. The received power is often expressed in dBm [0 dBm = 1 milliwatt]. The result (2.3) holds in the far field of the antenna where the far field is defined by d > (largest antenna dimension)2/ ~ 6m [at 900 MHz and with a 1m antenna]

Although it may seem counterintuitive, path loss is essential in a high-capacity cellular system, since the rapid attenuation of signal strength with distance permits a small co-channel [same frequency] reuse distance between cells. The 800-900 MHz band was chosen for cellular systems partly because of the relatively short range radio characteristics. Systems that are low capacity, long range [e.g., non cellular emergency fire and police] use a lower frequency.

Free space propagation does not apply in a mobile radio environment and the propagation loss depends not only on the distance and the wavelength, but also on the antenna heights of the mobile and base stations, as well as on the local terrain characteristics such as buildings and hills. The site specific nature of radio propagation makes theoretical prediction of path loss difficult and there are no easy solutions.

pr (d) = ptk

4d!

"#

$

%&

2gTgR (2.3)

28

Power Budget For Radio Systems For a specific performance requirement [e.g., S/N = 20 dB or Bit Error Rate (BER)

= 0.8 x 10-2 and the carrier frequency, the distance between the transmitter and receiver, we determine

The loss between the transmitter and receiver The transmitting antenna gain (antenna type) The receiver antenna gain (antenna type)

To meet the requirements we calculate The received signal power The received noise (plus interference) power at the receiver Determine the minimum transmitted power we need to meet the requirements

Transmitter Receiver

Analog systems (1G:FDMA): System performance specification is given by S/N > x dB Digital systems (2G: GSM or IS-95),: System performance Specification is given as the Bit Error Rate [BER] < r

29

Power Budget: Free Space

Received power: (recall = c/fc )

pR = pT gT gR 2

4 !!

"

#

$$

%

&

dfcc

(2.4)

Received power (in dBm):

PR = PT + GT + GR +147.56 - 20 log fc - 20 log d (2.5)

Free-space loss: Loss = 20 log d dB

Free-space loss is often referred to as the distance-squared term

d

30

Free Space Path Loss in Watts

For unobstructed propagation in free space the signal falls from a level of one ten thousandth of a milliwatt at 1 mile to a level of one millionth of a milliwatt at 10 miles. The difference is a ratio of one to one hundred (1:100).It is customary to express ratios in terms of a decibel.

31

Mobile Radio Propagation Environment-Two Ray Model Considerable insight can be obtained by considering the two-ray model shown below, to

describe the effect on average power of multiple rays. There are transmit and receive antennas separated by a distance d and at heights ht and hr respectively. In this model only a line of sight, ELOS , and a reflected ray, ER , are received. We will denote the differential distance traveled by these two rays as .

The line-of-sight and reflected waves at the receiver are, where d is the distance traveled by the LOS wave and d is the distance traveled by the reflected ray given by

ELOS

ER

d

ht hr Transmitter Receiver

)] cd(t[

dE(d,t) E)]

cd(t[

dE(d,t)E

'

c'o

Rco

LOS == coscos

Mobile Radio Propagation Environment:Two Ray Model-2

With some algebraic manipulation, it can be shown that the = d-d is given by

Using these relations, the magnitude of the E field is

small assumed is rays arriving twoebetween th difference phase the c

where

22

2sin 2 ||

of magnitude a with components two theof sum theis wavetotal"" theand

c

22

=

=

=

+

=

ddoo

'

c'o

co

TOTALEE)]

cd(tcos[

dE)]

cd(tcos[

dEE

rtrt

rtrt hhddhhdhhdhhdd +>>+++== when 2 )()( 2222'

| ETOTAL (d) |=2E0d

2hthrd

kd 2 , where k is a constant

and the received power, which is proportional to | ETOTAL (d) |2 is given by

Pr = PtGtGrht2hr2d 4 (2.6)

Thus the two ray model shows that the power falls off as the fourth power of the distance from the source --- much faster than in free space

33

Mobile Radio Propagation Environment- The next simplest path loss model (beyond free space) assumes that the

received signal power is

where Pr is the average received signal power (in dBm), Pref is the average

received power [in dBm] at a known reference point ( d0 ) that is in the far field of the transmitting antenna.Typically d0 is 1 km for macrocells, 100m for outdoor microcells, and 1m for indoor picocells. The value of Pref will depend on the frequency, antenna heights and gains, and other factors. The parameter is called the path loss exponent and is a key parameter that affects the spectral efficiency of the cellular system. This parameter is strongly dependent on the cell size and the local terrain characteristics. The path loss exponent ranges from 3 to 4 for a typical urban macrocell and from 2 to 8 for a microcell. The path loss exponent is usually determined by experimental measurement. The parameter Y is a zero-mean Gaussian random variable [when measured in dB] that represents the error between the actual and estimated path loss ---and is a correction factor. This statistical variation in Pr is due to shadowing ----and is generally modeled as a log-normal random variable [we derive this relationship on the next chart].

Pr = Pref (d0 )10 log10 (d / d0 )+Y (dBm) (2.7)

34

Shadow Fading [and the Lognormal distribution]

After a single transmitted carrier, , penetrates several objects the received signal is

The logarithm of the amplitude of the received signal is

and from the Central Limit Theorem, Y has a Gaussian probability distribution. Hence

when expressed in decibels, the received power has a normal distribution ---and R is said to have a lognormal distribution. Y is the random component, the shadow fading, that appears in the path loss equation (2.7)

[note: the Central Limit Theorem says that the sum of a large number of independent

random variables of any probability distribution will have a Gaussian distribution!]

tAts cos)( =

object the throughsmittedpower tranincident of fraction theis

1 where, cos][cos....)( 21

21

th

i

N

iiN

i

atataaatR == =

Y = logR = logaii=1

N

(2.8)

35

Log-normal Distribution

M M

2

p(M)

The pdf of the received signal level

36

Mean Propagation Loss in Different Areas

For the 10 mile range shown in the chart Free space: loss is only 1:100 Rural: typical signal loss is 1:1,000 Suburban: loss is of the order of 1:10,000 Urban: signal loss is about 1:40,000

37

Hata Model for Mean Path Loss

Early studies by Hata [IEEE Trans. On Vehicular Technology, Vol. 29 pp245-251, 1980] yielded empirical path loss models for urban, suburban, and rural (macrocellular) areas that are accurate to with 1dB for distances ranging from 1 to 20 km. More recently the COST231 study [COST231 Working Group2, The Hague September 1991] produced models for urban microcells

Hata and Okumura derived empirical formulas for the median path loss in flat urban areas; he then applied correction factors for other propagation conditions, such as

Antenna height and carrier frequency Suburban, quasi-open and open space, and hilly terrains Diffraction loss due to mountains Sea or lake areas

The parameters used in the Hata equations and their range of validity are: fc = carrier frequency (MHz) 150 < fc < 1,500 MHz d = distance between base station and mobile (km) 1 < d < 20 km hb and hm = base and mobile antenna heights (m) 30 < hb < 200m , 1 < hm < 10m

38

Hata Model for Mean Path Loss 2

Hatas equations for path loss are classified into three models Typical Urban

Typical Suburban (note adding a negative number to the loss means a higher signal level)

Rural

Psuburban = Purban 2 log(fc28)

"

#$

%

&'

(

)*

+

,-

2

-5.4 dB (2.9b)

Prural = Purban 4.78(log fc )2 +18.33log fc 40.94 dB (2.9c)

Purban = 69.55+ 26.16 log fc + (44.9 6.55loghb )logd 13.82 loghb (hm ) (2.9a)where (hm ) = correction factor for mobile antenna heights and is given by Large cities (hm ) = 8.29[log(1.54hm )]2 1.1 fc 200 MHz = 3.2[log(11.75hm )]2 4.97 fc 400 MHzSmall and medium size cities(hm ) = [1.1log( fc ) 0.7]hm [1.56 log( fc ) 0.8]

39

Doppler Shift: The Effect of Terminal Motion Frequency Shift

rf

r; tr

BS vx

The difference in path lengths is x cos, and from (2.2) the carrier phase differential [due to the shorter path is]

= vtx

cos2cos2 = and so the apparent shift in

frequency is the Doppler frequency shift [the differential

phase divided by t ]: v

tfd cos2

1=

=

(2.10)

Transmit: AT cosct

Receive: AR cos (c d)t

.

veff (km/hr.)

Doppler shift (f in Hz)

15 13.11 45 39.34 80 65.57 110 91.80 160 131.1

High Doppler causes channel phase to decorrelate between symbols Leads to an irreducible error floor for differential modulation Increasing power does not reduce errors

Doppler Shift Nomograph

40

Nomograph showing the relationship between maximum Doppler rate (f d),vehicle speed(v), and carrier frequency (fc). Draw a straight line intersecting the appropriate axes at the two known quantities. The unknown is read at the intersection of the line with the axis of the unknown variable.

41

Doppler Shift Spectrum In terrestrial cellular radio systems, the radio signals propagate in three dimensions. We will assume that the transmit signals are vertically polarized and that the distance

between the BS and the MS is sufficiently large, so that the radio propagation environment can be modeled as two dimensional (the horizontal plane)

The figure depicts the x-y plane, where the MS is moving along the x axis with velocity v. Vertical polarization is assumed throughout so that the electric field vector is aligned with the z-axis (not shown) and the nth incoming plane wave arrives at the MS antenna at an angle of incidence . The motion of the mobile introduces a Doppler (or frequency) shift into the incident plane wave and is given by

fD = fm cosn Hz (2.10) where fm = v/ is the maximum Doppler shift that occurs when = 0. Waves arriving from the direction of motion will experience a positive shift, while those arriving from the opposite direction will experience a negative shift.

nth incoming wave

Mobile velocity v

42

Doppler Shift Spectrum-2 Consider N simultaneous arriving waves, and as N gets very large, the incident power

on the receiver antenna, as a function of the angle of incidence approaches a continuous distribution, denoted by p(). The fraction of the total incoming power that arrives between and +d is p() d . If the antenna has a gain of G() at an angle , then the corresponding received power is G() p() d . The power spectral density (psd) of the received signal can be expressed as

From the previous chart, the frequency of the incident plane wave arriving at angle is f = fm cosn + fc where fm = v/ is the maximum Doppler shift, and Using the above, we find that the power spectral density of the signal is

S( f ) df = A( f )[G( )p( )+G( )p( )]d, (2.11a)where A( f ) is the power spectrum of signal in a stationary environment

sin determine toused wastry] trigonome[ie, 1cossin where

)(sin22

22

=+

== dfffdfdf cmm

S( f ) = A( f )fm2 ( f fc )2

[G( )p( )+G( )p( )] (2.11b)

where = cos1( f fcfm)

43

Doppler Shift Spectrum - 3 For isotropic 2-dimensional scattering and isotropic scattering G() p() =1/(2), so

that the power spectrum of the received signal is (limited in range to fm about the carrier frequency)

S( f ) = A4 fm1

1 f fcfm"

#$

%

&'

2 f fc fm (2.12)

= 0 otherwiseS()

c fm c c + fm frequency

44

Doppler Shift Spectrum 4

The Doppler effect, in conjunction with multipath propagation, can produce frequency dispersion [an increase in the bandwidth occupancy] and time-selective fading in the received signal --- fm is the largest of the frequency shifts experienced by the multipath components.

Note that producing signal energy at different frequencies [via a discrete Doppler shift] is the dual of the multipath effect of producing energy at different time instances. The individual components of the Doppler shift increase the bandwidth of the transmitted signal [frequency dispersion]. As the duration of the transmitted signal decreases, its bandwidth becomes larger and as the signal spectrum is modulated by the above shape. This distorts the received signal and is called time-selective fading.

If the baseband signal bandwidth is much greater than the maximum Doppler shift, then the effects of Doppler spread are negligible at the receiver.

To minimize the effect of Doppler, we should use as wide a baseband signal as feasible [e.g. spread spectrum]

45

Multipath And Intersymbol Interference: Delay Spread

Due to the ground, the buildings and other objects between the transmitter and the receiver, the transmitted signal may take multiple paths. The picture shown indicates two paths, the received baseband signal is the (vector) sum with a

multipath delay spread = (longest path length shortest path length)/c [for a 5s symbol duration, a 1s delay spread is a 20% intersymbol overlap]

Depending on the phases of the received signals, the baseband signals could subtract. There will be Intersymbol Interference [ISI] distortion if the original pulse is spread into the next symbol interval. This can cause an error when determining the next bit, even in the absence of noise. Signal processing methods are used to overcome multipath delay spread in TDMA and CDMA systems. If a single receiving antenna is used, then time-only processing works to undo the time distortion of the received signal. Time-only processing takes the form of equalization in TDMA systems, while CDMA systems make use of a RAKE receiver.

46

Signals can take many different paths between sender and receiver due to reflection, scattering, diffraction

Positive effects of multipath: enables communication even when transmitter and receiver are not in LOS

conditions - allows radio waves effectively to go through obstacles by getting around them, thereby increasing the radio coverage area

by proper processing of the multipath signals, with smart or adaptive antennas, you can substantially increase the usable received power [with multiple antennas you capture energy that would otherwise be absorbed by the atmosphere and you can compensate for fades --- since it is highly unlikely that a signal will experience severe fading at more than one antenna]

Multipath Propagation

signal at sender signal at receiver

At receiver antenna: vector sum

47

Multipath Propagation - 2

Negative effects of multipath: Time dispersion or delay spread: signal is dispersed over time due signals coming over different paths of different lengths. This causes interference with neighboring symbols, this is referred to as Inter Symbol Interference (ISI) The signal reaches a receiver directly and phase shifted (due to reflections) as a distorted signal depending on the phases of the different paths; this is referred to as Rayleigh fading, due to the distribution of the fades. Rayleigh fading creates fast fluctuations of the received signal (fast fading). Random frequency modulation due to Doppler frequency shifts on the different paths. Doppler shift is caused by the relative velocity of the receiver to the transmitter, leads to a frequency variation of the received signal. We derive the formulas for Rayleigh fading probability density function and the Doppler shift spectrum in this lecture.

48

Shadow Fading/Rayleigh Fading

.Rayleigh fading accounts for path loss variations about the average over short distances (meters compared to kilometers with Shadow fading). Rayleigh fading occurs when the received signal does not have a direct line-of-sight component and will consist of signals received over several different paths, each with some difference in the total distance traveled.. Shadow fading takes into account the terrain and other obstructions in the radio path and it accounts for the random variation about the average path loss.

49

Frequency Non-Selective (Flat) Multipath Fading Consider the transmission of the bandpass signal

If the channel is comprised of N propagation paths, then the noiseless received bandpass waveform is

where Cn and n are the amplitude and time delay, respectively, associated with the nth propagation path. The received signal has the received complex envelope

is the phase associated with the nth path.

s(t) = Re[ s(t)e j2 fct ] (2.13a)where s(t) is the complex envelope of the transmitted signal, fc is the carrier frequency, and Re[z] denotes the real part of z

r(t) = Re[ Cne j2 [( fc+ fD,n )(t n )]s(t n )]n=1

N

(2.13b)

(2.14b) ])[(2)( where

(2.14a) )(~)(~

,,

1

)(

tffft

tseCtr

nDnnDcn

N

nn

tjn

n

+=

==

50

Frequency Non-Selective (Flat) Multipath Fading -2 The channel can be modeled by a linear time-variant filter having the complex low-pass

impulse response

where g(,t) is the channel response at time t due to an impulse applied at time t- , and ( ) is the Dirac delta function.

Several interesting observations follow from the above: Since the carrier frequency is very large, small changes in the path delays, n, will cause large

changes in the phases n(t) [eg, a path delay of 1 ns corresponds to one full wavelength (or 2 radians phase shift) at 900 MHz.

At any one time instant, the random phases, n(t), may result in the constructive or destructive addition of the N multipath components.

If the differential path delays i - j are small compared to the duration of a modulated symbol, then the n are all approximately equal to 0, and the channel impulse response has the form

The channel transfer function [the Fourier Transform] is G(t,f) = g(t)exp(-j 2f 0) The amplitude response is g(t) ----thus all frequency components are subject to the same

complex gain, g(t), and the received signal is said to exhibit flat fading. Flat fading can be quite problematic, as the entire signal may vanish during the fade.

(2.15) )(),(1

)(=

=N

nn

tjn

neCtg

(2.16) )()()(),( 01

0)( ==

=

tgeCtgN

n

tjn

n

51

Received Envelope Distribution: Rayleigh Fading

What is the probability density function of the faded signal? Consider a single transmitted unmodulated sinusoid s(t) = E cost The multipath produces a received signal, r(t), composed of many time-

scaled, delayed versions of s(t):

.reflection i theof amplitude theis and

],[-over ddistributeuniformly is where

(2.17) ]cos[)](cos[)(

thi

11

i

i

N

iii

N

ii

e

tettetr

== ==

i

N

iii

N

ii

iii

N

ii

eBeB

tBtB

tetetr

sin cos where

,sincos

]sinsincoscos[)(

: termstic trigonome theExpanding

12

11

21

1

==

=

==

+=

+=

52

Rayleigh Fading [continued] When the number of reflections, N, is large, the Central Limit Theorem applies and

B1 and B2 approach independent Gaussian random variables with

The amplitude, or envelope, of r(t) is and is described by

The above are recognized respectively as the Rayleigh probability distribution function and probability density function [pdf], where (2)1/2 is the RMS (root mean square --- that is the square root of the mean-squared value) of the signal voltage.

The mean value of the Rayleigh distribution can be calculated to be (/2)1/2 = 1.25 .

The variance of the Rayleigh distribution is given by 2 , which represents the ac power in the signal envelope

)(21]coscos[)(

0)()(

1

22

2

1 1

21

21

== =

===

==N

iij

N

i

N

jiji BEeeeEBE

BEBE

22

21)()( BBtrtR +=

(2.18) 1 2

1]Pr[2222

221

22

21

2/21

2/][

)(2

rBB

rBB

edBdBerR +

Rayleigh Envelope Fading About The Signal RMS Value

R(t)

Note that there is ~ 0.5 between fades and the average fading rate is ~ v/ fades/sec

54

Rayleigh Fading: Level Crossing Rates and Average Envelope Fade Duration Two important second-order statistics associated with envelope fading are the level

crossing rate (how often the envelope crosses a specified level) and the average fade duration (how long the envelope remains below a specified level).

The Envelope Level Crossing Rate [see Stuber pages 61-65] denoted by LA , is defined as the rate at which the envelope crosses level A and is

It can be reasoned that the average envelope fade duration below the level A is the product of (1) the probability that the envelope will be less than A and (2) the percentage of time that the envelope is below A (which is the inverse of the number of level crossings of A per second). So, the average fade duration is given by,

envelope theof value(RMS) squaremean root theis where and

,at evaluated and of pdfjoint theis ) , of derivative time theis

(2.20) , 2 )

,

,0

2

RMSRMS

RR

mRRA

RR

A

AR RRR(A,pR(t)R

efRdR(A,pRL

=

=

==

(2.21) , 2

121)Pr(

2

2

2

mmA fe

efe

LARt ===

55

Ricean Fading Some types of scattering environments have a specular or LoS component (in

addition to the scattered components) ---typically in microcellular and satellite systems. This dominant path may significantly decrease the depth of fading, and in this case gI(t) and gQ(t) are Gaussian random processes with non-zero means mI(t) and mQ(t). We can assume that these processes are uncorrelated and the random variables gI(t) and gQ(t) have the same variance, , then the received complex envelope has the Ricean distribution

The Rice factor, K, is defined as the ratio of the specular (LoS) power to the scattered power

(2.23) 21)(

by defined is )( kindfirst theoffunction Besselorder zero theand

)()( where

(2.22) 0 )()(

2

0

cos0

0

222

202

)(

22

22

+

=

+=

=

dexI

xItmtms

xxsIexxp

x

QI

sx

r

( ) (2.24) 2paths scattered in thepower

path speculardominant in thepower 2

2

sK ==

56

Ricean Fading -2 When K=0, the channel exhibits Rayleigh fading and for K there is no

fading and the channel is Gaussian. Most channels can be characterized as either Rayleigh, Rician, or Gaussian ---

with Rician being the most general case ---the Rician pdf is shown below.

57

Rician Fading Profiles for a Mobile at 90 Km/Hr 10 0

-10 -20 -30 -40 10 0

-10 -20 -30 -40

10 0

-10 -20

10 0

-10 -20

10 0

-10 -20

Am

plitu

de (d

B)

K = 0, 4, 8, 16, and 32

(a)

(b)

(c)

(d)

(e)

~Rayleigh

~Gaussian

time

58

Spatial Correlations A fundamental question that arises is the antenna separation needed to provide

uncorrelated antenna diversity branches. The figure below shows the normalized envelope correlation versus the normalized distance l/c ---note that the correlation is zero at l = 0.38c and in practice sufficiently uncorrelated diversity branches can be obtained at the mobile by spacing the antenna elements a distance c/2 apart.

Normalized distance l/c

Cor

rela

tion

of th

e en

velo

pe

59

Frequency Selective Multipath Fading

Power delay profile

Delay time 1 2 3

Exponential Decay

The rms delay spread is the square root of the second central moment of the power delay profile

1

2

3 Each pulse arrives with amplitude i and with propagation delay i

To this point we have considered channel models where the inverse signal bandwidth [~ the symbol interval] is much greater than the time spread of the propagation paths. As the differential path delays become large, even closely separated frequencies can experience significantly different phase shifts.

TX RX

60

Power Delay Profile ---Coherence Bandwidth

In order to compare different multipath channels, the time dispersive power profile is treated as an (non-normalized) pdf from which the following are computed

Typical values of rms delay spread are on the order of microseconds in outdoor mobile radio channels [GSM specifies a maximum delay less than 20s] and on the order of nanoseconds in indoor radio channels.

Coherence bandwidth is a statistical measurement of the range of frequencies over which the channel can be considered "flat", or in other words the approximate maximum bandwidth or frequency interval over which two frequencies of a signal are likely to experience comparable or correlated amplitude fading. If the multipath time delay spread equals D seconds, then the coherence bandwidth Wc in hertz is given approximately by the equation: W=1/2D.

The coherence bandwidth varies over cellular or PCS communications paths because the multipath spread D varies from path to path. Frequencies within a coherence bandwidth of one another tend to all fade in a similar or correlated fashion. One reason for designing the CDMA IS-95 waveform with a bandwidth of approximately 1.25 MHz is because in many urban signaling environments the coherence bandwidth Wc is significantly less than 1.25 MHz. Therefore, when fading occurs it occurs only over a relatively small fraction of the total CDMA signal bandwidth. The portion of the signal bandwidth over which fading does not occur typically contains enough signal power to sustain reliable communications.

(2.25) )( :SpreadDelay RMS The

:delay squareMean , :delayMean

22

2

22

22

2

=

==

kk

kkk

kk

kkk

61

Frequency Diversity and Wideband Signals If the rms delay spread, due to differences in multipath delays, is d, and the maximum

spread in frequency due to differences in multipath Doppler is fm, then The coherence bandwidth, Bc, is defined as Bc = 1/(2 d) (2.26) and is a statistical measure of the range of frequencies for which the channel can be considered

flat [i.e. have equal gain]. Frequency components separated by more than Bc will fade independently.

The coherence time, Tc, is the time domain dual of Doppler spread and is the duration over which the channel impulse response is nearly constant and is equal to

Tc = 1/(2 fm), (2.27) where fm = / [ is the relative velocity of the mobile and is the wavelength]

If the transmitter symbol interval exceeds Tc then the channel will change during the symbol interval and must be tracked [or system performance will degrade]. A Rayleigh fading signal may change amplitude significantly in Tc seconds.

If the signal bandwidth B >> Bc , then the signal is called wideband and any fading will be frequency selective. This means that only a portion of the signal bandwidth will fade at any instant of time. If B > Tc , the channel changes or fades rapidly compared to the symbol rate. This case is called fast fading and frequency dispersion occurs, causing distortion. If T

62

Frequency Selective Multipath Fading To this point we have considered channel models where the inverse signal

bandwidth [~ the symbol interval] is much greater than the time spread of the propagation paths.

As the differential path delays become large, even closely separated frequencies can experience significantly different phase shifts.

Multipath fading channels can be modeled as time-varying linear filters with an input output relationship

Approximating the convolution as a discrete sum

allows us to visualize the channel as a transversal filter with tap spacing

.at applied impulsean to at time response channel is ),( and, waveformseoutput tim andinput pass-lowcomplex theare )(~ and )(~ where

(2.28) ~~0

t-ttgtrts

)g(t,)d(ts(t)r

=

(2.29) ~~0

) m )g(t(ts(t)rn

m=

=

W1 =

63

Tapped Delay Line Model For Frequency Selective Fading Channels

1 W

g(t,0 ) g(t, ) g(t,2 ) g (t,L )

The boxes marked by correspond to delays of seconds. In general, the delays can be different in each element. The fading process is generally assumed to a Gaussian process [ie, the gs are uncorrelated zero-mean complex Gaussian random processes and statistically independent]

Ideal Lowpass Filter Bandwidth = W /2

(t)s~

(t)r~

W1 = :Note

64

Frequency Selective Multipath Fading: Two Ray Model

Again consider the two ray model shown below

where a and b are the (random) gains associated with the paths A and B respectively, and is the relative delay between the paths. Note that the same pulse shape is assumed on both paths [a good assumption in practice].

Assuming that the parameters are constant for a period of time, the (short term) transform of the received signal is given by

And depending upon values of a,b, and , the system response will have a frequency selective fade of varying depth and width [see homework problem 2.5]

r(t)

(2.30) )()()( += tbhtahtr

(2.31) ])[()( jbeaHR +=

65

Summary: Fading (based on multipath time delay spread)

Flat Fading 1. BW of signal < BW of channel 2. Delay spread < Symbol period

Fast Fading High Doppler spread Coherence time < symbol

period (time selective fading) Channel variations faster than

baseband signal variations

Frequency Selective Fading 1. BW of signal > BW of channel 2. Delay spread > symbol period

Slow Fading 1. Low Doppler spread 2. Coherence time > Symbol

period 3. Channel variations slower than

baseband signal variations

Summary: Fading (based on Doppler spread)

66

Types of Diversity used for Combating Multipath Fading!

Type

Technique applied

Space

Receiving antennas sufficiently separated for independent fading.

Time Send sequential time samples [interleaving].

Frequency Transmit using different carrier frequencies separated by frequencies greater than the coherence bandwidth for independent fading; or by wideband spread spectrum transmission.

Polarization Transmit using two orthogonal polarizations for independent fading

67

Propagation in Microcells

Microcells are small cells which may be a small segment of a highway, a street along the side of a city block, an office floor, ...

Generally, microcells have a strong specular component [Rice distribution] They are small areas with a high density of teletraffic They handle both vehicular and pedestrian mobile stations The rf radiation must be contained so that the frequency band can be reused

far more frequently than in regular [macro] cells The Base Station antenna is not mounted at a high elevation [regular cellular

antennas are ~100m], but generally at 5 to 12m Radiated power is in the milliwatt range

68

Microcells: Path Loss

Received signal level vs. distance [data taken in London]

The radiated power from the back of the antenna was reduced by 25 dB (compared to the front); so LOS was maintained in the backward direction

An inverse fourth-power propagation law was a good fit The radiation went farther in the forward than in the

backward direction Sharp turns in the road caused diffraction losses

-60

-70

-80

-90

-100

-110

-120

-130 3 2 1 0 1 2 3 4 5 (x 1000) Distance From Base Station (m)

Base Station

Back Loss

Inverse 6th Power Law

Inverse 4th Power Law

Front Loss

M4 Junction 5 M25 Junction 21A M25 Junction 11

Sign

al L

evel

(dB

m)

69

Received Signal and K Factors for Micro and Macro Cells

0 2 4

-50 -60 -70 -80 -90

-100 -110

6 8 10 12 14

Microcell Base Site Location

Macrocell Microcell

(x 100)

0 2 4

32 28

20 16 12 8

0 6 8 10 12 14

Distance (m)

Macrocell

Microcell

(x 100)

Ric

ian

k Fa

ctor

R

ecei

ved

Sign

al L

evel

(d

Bm

)

24

4

Note: Macrocell was overlaid on Microcell

70

Microcellular Experiments

Height of antenna makes little difference An inverse fourth-power propagation law is often a good fit There can be a rapid signal loss as a mobile turns a corner Large vehicles can cause multiple reflections Microcells are not just smaller, they have better propagation characteristics

than large cells

71

Transmitter

Signalsource Signaldestination

Receiverf t c t( )cos f t td c t( )cos( )

+

Problem Effect Solution Signal loss Long term/slow

fading [shadowing]

Reduced S/N Variable S/N over many

wavelengths

Increase power budget Smaller [and more] cells ----

microcells Frequency [Doppler]

shift Increased spectrum width [and

possibly induce amplitude nulls] Use wideband signal to

minimize effects of Doppler shift

Random phase

Phase offset

Phase estimation (for coherent detection) Non-coherent detection

Short term/fast multipath fading [Rayleigh and Rician]

Enormous S/N variation over a few wavelengths (possible nulls in frequency domain)

Delay spread/ISI

Spatial Diversity Interleaving Coding Time-Domain Equalization

Summary: Point-to-Point Propagation for Wireless System

PHY---physical layer (layer 1) Wireless link/channel = AWGN Channel

MAC and Network layers (layers 2 and 3) Wireless link = ON/OFF Channel

Information Theory (Digital Comm) Queuing Theory (later in course)

+ Symbols

Noise

C = W log2(1 + SNR)

Packet Arrivals packets per sec Pr[ON]=p

C = p packets/slot Capacity: Capacity:

Mathematical Models for a Wireless Link (two complementary perspectives)

W = bandwidth SNR = Signal power/Noise power Capacity optimizes bit rate over all coding of symbols. (Foundation: Shannon Theory)

-Slot-by-slot packet transmission . -Metrics: throughput, delay, jitter, .? -Opportunistic scheduling: decide which queue to serve (Foundation: Queuing Theory)

72

Mathematical Models for a Wireless Network

N-user (Gaussian) Broadcast Downlink N-User Downlink (Fading Channels) Information Theory Queuing Theory

bits bits

bits

1 2

ON/OFF

ON/OFF

ON/OFF

-Symbol-by-symbol transmission -(Shannon) Capacity is a REGION of achievable bit rates -Optimizes coding of symbols

-Opportunistic scheduling -Observe ON/OFF channels, decide which queue to serve -Capacity is a REGION of achievable rates ---no ~ Shannon network theory

73

Multipath, Loss, Noise and Reliable Communications

l All physical systems have noise l Electrons always vibrate at non-zero temperature l Motion of electrons induces noise

l Presence of noise limits accuracy of measurement of received signal amplitude

l Errors occur if signal separation is comparable to noise level l Bit Error Rate (BER) increases with decreasing signal-to-noise ratio l Noise places a limit on how many amplitude levels can be used in pulse

transmission

74

l Arbitrarily reliable communications is possible if the transmission rate R < C. l If R > C, then arbitrarily reliable communications is not possible. l Arbitrarily reliable means the BER can be made arbitrarily small through sufficiently

complex coding. l C can be used as a measure of how close a system design is to the best achievable

performance. l The above formula determines the channel capacity, C, for a stationary additive white

Gaussian noise (AWGN) channel with bandwidth Wc and SNR. l Example: Find the Shannon channel capacity for a telephone channel with Wc = 3400 Hz

and SNR = 10,000.

C = 3400 log2 (1 + 10000) = 3400 log10 (10001)/log102 = 45.2 Kbps

Shannon Channel Capacity ---Information Theory

C = Wc log2 (1 + SNR) bps (Claude Shannon 1948)

75

Wireless Channel Capacity (wireless channel is random)

l Assumptions l g[i] : Channel gain --- a random variable (with gain) with stationary statistics l No Estimation Error l No Feedback delay

l C= B log (1+), where is the (random SNR) l So, the capacity is computed by averaging over the SNR:

+=

dpBC )()1log(76

Wireless Communications: Error Control l Objective(s) of error control: to approach channel capacity and provide

reliable communications l Digital transmission systems introduce errors---PHY layer l Applications require certain reliability level

l Data applications require error-free transfer l Voice and video applications tolerate some errors

l Error control used when transmission system does not meet application requirement

l Error control ensures a data stream is transmitted to a certain level of accuracy despite errors

l Two basic approaches: l Error detection and retransmission (ARQ) l Forward error correction (FEC)

77

Error Control---Key Idea l All transmitted data blocks (codewords) satisfy a pattern l If received block doesnt satisfy pattern, it is in error l Redundancy: Only a subset of all possible blocks can be codewords l Blindspot: when channel transforms a codeword into another codeword

( undetected error)

Channel Encoder User information

Pattern checking

All inputs to channel satisfy pattern or condition

Channel output

Deliver user information or set error alarm

78

79

Wireless Communications/Propagation Topics Covered l Speed, Wavelength, Frequency l Types of Waves l Radio Frequency Bands l Propagation Mechanisms l Radio Propagation Effects l Free-Space Propagation l Land Propagation l Path Loss l Fading: Slow Fading / Fast Fading l Delay Spread l Doppler Shift l Co-Channel Interference