EL 675 UHF Propagation for Modern

Wireless Systems

Henry L. Bertoni

Polytechnic University

2003 © 2003 by H.L. Bertoni 2

Context for Discussing Wireless Channel Characteristics

• Frequencies above ~ 300 MHz ( < 1 m)• Radio links in man-made environments

– At least one end is among the buildings

– Link lengths • Macrocells (20 km > R > 1 km)

• Microcells (2 km > R > 100 m)

• Picocells/indoor (R < 100 m)

– Presence of many objects with sizes from 10 cm to 100 m

– Wave interactions described by scattering and shadowing, rather than resonances

2003 © 2003 by H.L. Bertoni 3

Need to Bridge Electromagnetics (EM) and Communications (Com)

• Electromagnetics– Deals with deterministic physical environment - seek

precise solution– Field quantities are prediction output

• Communications – Deals with random processes - seek statistical solutions – Required inputs that are statistical measures of received

signal properties

• Must phrase the electromagnetic solutions in ways that can be used by communication community– Understand and predict channel characteristics

2003 © 2003 by H.L. Bertoni 4

Complimentary View Points

• Electromagnetic view point– Objects cause a rich set of ray paths connecting

transmitter and receiver (multipath)

• Communications view point– Received signal is the sum of delayed versions of the

transmitted signal (multipath)

• Interpreting the ray description of electromagnetic fields provides the channel characteristics– EM propagation governs the channel characteristics,

but signal processing governs what is observed

– Interpret ray results to predict observed statistics

2003 © 2003 by H.L. Bertoni 5

Communication Systems Drive Descriptions of the Radio Channel

• How to characterize channel depends on the radio system and link geometry – All require knowledge of the power level

• Different measures of multipath interference – Narrowband -- pulsed -- multi-frequency systems – Fast fading -- delay spread -- coherence bandwidth– Coherence distance -- angle spread -- ?

• Macrocells, microcells and indoor picocells– Different considerations of multipath interference– Slow fading statistics and range dependence vs. deterministic variations power level

2003 © 2003 by H.L. Bertoni 6

EM Effects That Need to Be Considered

• Propagation of waves through space• Reflection, transmission and diffraction

– Mechanisms by which fields get to locations not visible to the transmitter

• Radiation and reception by antennas• Ray description of radiation

2003 © 2003 by H.L. Bertoni 7

Basic Concepts

• Operation of individual radio systems is dependent on specific channel parameters -- all systems depend on received power and interference.

• Frequency re-use as a basis for increased system capacity

2003 © 2003 by H.L. Bertoni 8

Pre 1980 Vehicular Mobile Telephone System

• Single high base station served entire metropolitan area with Nc frequency channels

• Frequency channels reused in other metropolitan areas

• Because of physical separation, desired signal S much larger than the interfering signal I

IS

~100km~100km

2003 © 2003 by H.L. Bertoni 9

Cellular Mobile Radio:Frequency Re-use Within a Metropolitan Area

• Advanced Mobile Phone System (AMPS) has 395 two-way channels in two 25 MHz bands centered at 850 MHz

• Re-using frequency channels in N sub-regions allows for 395N simultaneous phone calls

395channels395

channels

395channels

MetropolitanRegion

f1

f1

f1

f1

f1

f1

f1

f1

f1

f1f1

2003 © 2003 by H.L. Bertoni 10

Dividing Sub-Regions Into NR Cells Allows Spatial Separation of Cells Using Same Frequency

f1

f7

f4

f5

f2

f3

f6

f4

f6

f5

MTSO

To Telephone Network

CELL SITE

Sub-region

Sub-region

NR = 7 frequency re-use pattern for hexagonal cells in each sub-region

MTSO assigns channelsto mobile and connects totelephone network

2003 © 2003 by H.L. Bertoni 11

Cell Splitting to Increase Capacity

Cell have same number ofchannels (NC / NR) no matterwhat size.

Small cells accommodatehigher subscriber density

2003 © 2003 by H.L. Bertoni 12

Number of Cells Needed in Each Sub Region

Determined by:

I. Propagation characteristics of the environment

Simplest form of propagation dependence

P = PT A / Rn

P = Received power

PT = Transmitted power

A, n= Amplitude and range index dependent on frequency, antenna height, buildings

II. Minimum signal to interference ratio for adequate reception

by radio system.

For AMPS systems P/ I 50 (10log P/ I > 17dB).

R

2003 © 2003 by H.L. Bertoni 13

Example of Linear Cells Along a Highway

NR = 3Reuse

Factor

Signal Power for mobile at the cell boundary from base station of Cell 1, Region 1:

P = PT A / RCn

Interference from base station of Cell 1, Region 2:I = PT A / [( 2NR - 1 ) RC ]

n

f 1 f 2 f 3 f 1 f 2 f 3

Region 1 Region 2

Cell 1 Cell 2 Cell 3 Cell 1 Cell 2 Cell 3

RC

IP

2003 © 2003 by H.L. Bertoni 14

NR for Linear Cells for Different Range Index n

€

PI

⎛ ⎝

⎞ ⎠

min

≤PI

=2NR −1( )RC[ ]

n

RCn = 2NR −1( )

n

or

NR ≥12

1+ (P /I)minn[ ]

For (P /I)min =50

Accounting for interference only from the nearest co-channel cell

Condition n NR

Fre e space 2 4Flat e arth 4 2

2003 © 2003 by H.L. Bertoni 15

Frequency Re-Use Pattern for Covering Area

Symmetric patterns based onhexagonal cells have allco-channel cells located on circles.There are six cells on the smallestcircle of radius D, where

For symmetric reuse patterns

where m1, k1 are any integers.Lowest values are NR= 3, 4, 7, 9, 12, 13, 19, 21, 25, 27,31, 39.

2111

21

.3

kkmmN

NRD

R

RC

++=

=

D

RC

Co-channel cellsin the first tier

2003 © 2003 by H.L. Bertoni 16

Frequency Re-Use for S = A/R n Signal Variation

Signal Power from base stations to mobile at the cell edge

P = PT A /(RC)n

Interference power from co-channel base stations in the first tier

D

D+R

C

RC D+R

C

DRC

DRC

D

I =PTA2

D−RC( )n +

2Dn +

2

D+RC( )n

⎡

⎣ ⎢

⎤

⎦ ⎥

2003 © 2003 by H.L. Bertoni 17

NR for Symmetric Pattern of Hexagonal Cell

€

PI

⎛ ⎝

⎞ ⎠

min

≤PI

⎛ ⎝

⎞ ⎠ =

12

RCD−RC

⎛

⎝ ⎜ ⎞

⎠ ⎟ n

+RCD

⎛ ⎝

⎞ ⎠

n

+RC

D+RC

⎛

⎝ ⎜ ⎞

⎠ ⎟ n

=0.5

1D RC( )−1

⎛

⎝ ⎜ ⎞

⎠ ⎟ n

+1

D RC

⎛

⎝ ⎜ ⎞

⎠ ⎟ n

+1

D RC( )+1

⎛

⎝ ⎜ ⎞

⎠ ⎟ n

If (P /I )min =50, and since D =Rc 3NR , then

50≤0.5

13NR −1

⎛

⎝ ⎜

⎞

⎠ ⎟

n

+1

3NR

⎛

⎝ ⎜

⎞

⎠ ⎟

n

+1

3NR +1

⎛

⎝ ⎜

⎞

⎠ ⎟

n

Condition n NR

Fre e space 2 101Flat e arth 4 7

2003 © 2003 by H.L. Bertoni 18

Interference Limited Cellular Systems

• System design is dependent on the propagation characteristics For signal dependence: S = A/ Rn

Free space propagation:

n = 2 and NR will be large (NR = 101)

Propagation over flat earth:

n = 4 and NR = 7

For Cellular Mobile Radio, NC ~ 400

n Channels / cell Base Station/1,000 Calls

2 ~ 4 ~2504 ~ 60 ~16

2003 © 2003 by H.L. Bertoni 19

Use Sectored Cells to Account forRealistic Propagation Laws

• Range index n is between 3 and 4 for elevated base stationantenna

• Additional random fading of the signal exists• Use sectored cells to achieve P/ I > 50• Three sectors per cell is variation of NR= 21 frequency re-use

pattern.

2 3

1

2 3

1

Patterns for cell sectorization using directive antennas.Single base station serves three sectors.

2003 © 2003 by H.L. Bertoni 20

Effect of Range Index n on Down Link System Capacity for CDMA System

• Same frequency used to communicate to subscribers in all cells.

• Different code used for each subscriber.

• Signals to subscribers in other cells act as interference.

• Subscribers in same cells have orthogonal codes, but multipath

interference results in some interference.

• Subscriber can receive same signal from up to three base stations.

• For adequate reception, I FP, where the value of F > 1 depends processing gain, voice activity factor, etc.

2003 © 2003 by H.L. Bertoni 21

P / I for Subscriber at Junction of 3 Cellsfor A / RC

n Propagation Dependence

€

Power receiveded from 3 nearest base

stations: P =3PTA/RCn

Multipath interference due signals sent

to other subscribers in cells A, B, C:

I0 =3γ NS −1( )PTA/RCn

where 0<γ<1

Interference due to signals sent to

subscribers in cells I, II, III :

Iα =3NSPTA/(2RC)n

Interference due to signals to

subscribers in cells 1, 2, L , 6:

Iβ =6NSPTA/ 7RC( )n NS active subscribers in each cell

CR2

3

1

2

3 4

5

6

A

B

C

I II

III

RC

CR7

RC

2003 © 2003 by H.L. Bertoni 22

Interference Power Received From Base Stations Outside of the Closest 12

€

Smear out base stations over an infinite

disk with a hole of radius R1 to

achieve a transmitted power density

PD = NSPT/(area of a cell).

Area of cell = 3 32

RC2 so that

PD =2

3 3

NSPTRC

2

To find the radius of the hole, set the area

of the hole πRc2 equal to the area of the

12 cells. Thus

R1 =32 3π

RC =3.150RC

CR2

3

1

2

3 4

5

6

A

B

C

I II

III

CR7

RC

R1

2003 © 2003 by H.L. Bertoni 23

Interference Received From Smeared Out Base Stations on the Infinite Disk

€

Interference power = ID = Tx power density( )∫∫ ARn

⎛ ⎝

⎞ ⎠

area element( )

For circular symmetry

ID =2

3 3

NSPTRC

2

⎛

⎝ ⎜ ⎞

⎠ ⎟

R1

∞

∫ ARn

⎛ ⎝

⎞ ⎠

2πRdR( ) =4π

3 3NSPT

ARC

2

dRRn−1

R1

∞

∫

If n≤2, then ID =∞

If n>2, then

ID =4π3 3

NSPTARC

2

1(n−2)R1

n−2 =4π3 3

NSPT(n−2)

A(3.15)(n−2)RC

n

=2.418

(n−2)(3.15)(n−2)NSPTARCn

2003 © 2003 by H.L. Bertoni 24

€

Total interference I =Io +Iα +Iβ +ID . For adequate reception

I ≤F Signal Power( ) =F3PTARCn

For n≤2: ID =∞ so that capacity NS =0

For n>2: I =PTARCn 3γ(NS −1)+3

NS

2n+3

2NS

( 7)n+

2.418(n−2)(3.15)(n−2)Ns

⎡

⎣ ⎢ ⎤

⎦ ⎥

Reception requirement gives

NS γ+12n

+2

( 7)n+

2.4183(n−2)(3.15)(n−2)

⎡

⎣ ⎢ ⎤

⎦ ⎥ ≤F +γ

To see the role of n, recall that F >1 and suppose that γ=0.1

If n=4: NS ≤(F +0.1) 0.224=4.47(F +0.1)

If n=3: NS ≤1.70(F +0.1)

P/I Requirement and Capacity Ns

2003 © 2003 by H.L. Bertoni 25

Conclusions

Modern systems employ frequency re-use to increase capacity

Wireless systems employing frequency re-use are interference limited

It is necessary to balance coverage and interference

Design of Systems to accommodate a given number of subscribers is dependent on the propagation characteristics

Higher values of range index n allow for less base stations to cover a given area

Other channel characteristics will influence system design

Random spatial fading

Doppler spread, time delay spread