Stallings charts modified and added to

1

Antennas, Electromagnetic Propagation, Fading Effects, and Channel Coding

Session 4

Nilesh Jha

General Frequency Ranges Microwave and Millimeter Wave frequency range

Roughly 1 GHz to 20 GHz; 20 GHz to 300 GHz The higher the frequency the higher the beam directionality (antenna gain) for

a given antenna size Used for point to point and satellite communications, but also in lower ranges

for PCS (so far up to 2GHz) and WLAN (so far up to 6 GHz)

Radio frequency range --- VHF and UHF (plus) 30 MHz to 1 GHz Easier to do omni transmission Broadcasting, radio mobile services, cellular

Infrared frequency range --- short range Roughly, 3x1011 to 2x1014 Hz Useful in local point-to-point and to multipoint applications within confined

areas

Fixed Terrestrial Microwave Description of common microwave antenna

Parabolic dish, a few feet or meters in diameter Fixed rigidly and focuses a narrow beam Achieves line-of-sight transmission to receiving antenna Located at substantial heights above ground level

Applications --- Fixed Wireless Long haul telecommunications service Short point-to-point links between buildings Wireless Local Loop --- to Homes or Businesses

Satellite Microwave Description of communication satellite

Microwave relay station Used to link two or more ground-based microwave

transmitter/receivers Receives transmissions on one frequency band (uplink),

amplifies or repeats the signal, and transmits it on another frequency (downlink)

Applications Television distribution Long-distance telephone transmission Private business networks

Broadcast Radio Description of broadcast radio antennas

Omnidirectional Antennas not required to be dish-shaped Antennas need not be rigidly mounted to a precise

alignment Receive antennas often dipoles

Applications Broadcast radio

VHF and part of the UHF band; 30 MHZ to 1GHz Covers FM radio and UHF and VHF television

Cellular, PCS and WLAN Frequencies in the 800 MHz to 1000 MHz range for

cellular --- also called First Generation or 1G PCS and DCS called 2G --- Frequencies around 1800 to

2000 MHz range WLAN around 2400 MHz, also around 5.5 GHz Cell phone antennas are short dipoles, base station

antennas longer dipoles and combinations for some gains Finding more spectrum

Some around 1700 MHz, also down at TV UHF bands Up to around 2700 MHz

Lower frequencies propagate better and penetrate buildings more, but less spectrum

Antennas -- Basic An antenna is an electrical conductor or

system of conductors Transmission - radiates electromagnetic energy

into space Reception - collects electromagnetic energy

from space In two-way communication, the same

antenna can be used for transmission and reception

Radiation Patterns Radiation pattern

Graphical representation of radiation properties of an antenna

Depicted as two-dimensional cross section Beam width (or half-power beam width)

Measure of directivity of antenna Reception pattern

Receiving antenna’s equivalent to radiation pattern

Types of Antennas Isotropic antenna (idealized)

Radiates power equally in all directions Dipole antennas

Half-wave dipole antenna (or Hertz antenna) Quarter-wave vertical antenna (or Marconi

antenna) Parabolic Reflective Antenna

Antenna Gain Antenna gain

Power output, in a particular direction, compared to that produced in any direction by a perfect omnidirectional antenna (isotropic antenna)

Effective area Related to physical size and shape of antenna

Antenna Gain Relationship between antenna gain and effective

area

G = antenna gain Ae = effective area f = carrier frequency c = speed of light (» 3 ´ 108 m/s) = carrier wavelength

2

2

2

44

c

AfAG ee

Propagation Modes Ground-wave propagation Sky-wave propagation Line-of-sight propagation

Ground Wave Propagation

Ground Wave Propagation Follows contour of the earth Can Propagate considerable distances Frequencies up to 2 MHz Example

AM radio

Sky Wave Propagation

Sky Wave Propagation Signal reflected from ionized layer of atmosphere

back down to earth Signal can travel a number of hops, back and forth

between ionosphere and earth’s surface Reflection effect caused by refraction Examples

Amateur radio CB radio

Line-of-Sight Propagation

Line-of-Sight Propagation Transmitting and receiving antennas must be within

line of sight Satellite communication – signal above 30 MHz not reflected

by ionosphere Ground communication – antennas within effective line of

site due to refraction Refraction – bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the density of the medium

When wave changes medium, speed changes Wave bends at the boundary between mediums

Line-of-Sight Equations Optical line of sight

Effective, or radio, line of sight

d = distance between antenna and horizon (km) h = antenna height (m) K = adjustment factor to account for refraction,

rule of thumb K = 4/3

hd 57.3

hd 57.3

Line-of-Sight Equations Maximum distance between two antennas

for LOS propagation:

h1 = height of antenna one

h2 = height of antenna two

2157.3 hh

LOS Wireless Transmission Impairments Attenuation and attenuation distortion Free space loss Noise Atmospheric absorption Multipath Refraction Thermal noise

Attenuation Strength of signal falls off with distance over

transmission medium Attenuation factors for unguided media:

Received signal must have sufficient strength so that circuitry in the receiver can interpret the signal

Signal must maintain a level sufficiently higher than noise to be received without error

Attenuation is greater at higher frequencies, causing distortion

Free Space Loss Free space loss, ideal isotropic antenna

Pt = signal power at transmitting antenna

Pr = signal power at receiving antenna = carrier wavelength d = propagation distance between antennas c = speed of light (= 3x10^ 8 m/s)

where d and are in the same units (e.g., meters)

2

2

2

2 44

c

fdd

P

P

r

t

Free Space Loss Free space loss equation can be recast:

d

P

PL

r

tdB

4log20log10

dB 98.21log20log20 d

dB 56.147log20log204

log20

df

c

fd

Free Space Loss Free space loss accounting for gain of other

antennas

Gt = gain of transmitting antenna

Gr = gain of receiving antenna

At = effective area of transmitting antenna

Ar = effective area of receiving antenna

trtrtrr

t

AAf

cd

AA

d

GG

d

P

P2

22

2

224

Free Space Loss + Antenna Gains Free space loss accounting for gain of other

antennas can be recast as (Note: usually the antenna gains/losses are added separately)

rtdB AAdL log10log20log20

dB54.169log10log20log20 rt AAdf

)G10log(G-dB 56.147

log20log20)log(104

log20

tr

dfGG

c

fdtr

Real Distance Dependence 20xlog(d) comes from 1/d^2 propagation, spherical

propagation of wavefront

In reality propagation is through many multipath channels, with fading effects, scattering around obstacles, etc

Effective distance dependence is 10xnxlog(d)

n is propagation index, environment dependent n is usually 3-5, 4 is not too far off

From Rappaport and Ref. there

Categories of Noise Thermal Noise Intermodulation noise Crosstalk Impulse Noise

Thermal Noise Thermal noise due to agitation of electrons Present in all electronic devices and

transmission media Cannot be eliminated Function of temperature Particularly significant for satellite

communication

Thermal Noise Amount of thermal noise to be found in a

bandwidth of 1Hz in any device or conductor is:

N0 = noise power density in watts per 1 Hz of bandwidth

k = Boltzmann's constant = 1.3803x10-23 J/K T = temperature, in kelvins (absolute temperature)

W/Hz k0 TN

Thermal Noise Noise is assumed to be independent of frequency Thermal noise present in a bandwidth of B Hertz

(in watts):

or, in decibel-milliwatts (dBm)

TBN k

BTN log10 log 10k log10

Blog10(NF) log 10dBm 114

Where T=NFxTsub0, and Tsub0=290 degrees KNF is effective noise figure of device

Noise Terminology Intermodulation noise – occurs if signals with

different frequencies share the same medium Interference caused by a signal produced at a frequency

that is the sum or difference of original frequencies Crosstalk – unwanted coupling between signal

paths Impulse noise – irregular pulses or noise spikes

Short duration and of relatively high amplitude Caused by external electromagnetic disturbances, or

faults and flaws in the communications system

Expression Eb/N0

Ratio of signal energy per bit to noise power density per Hertz

B=bandwidth So SNR and Eb/N0 related through B/R The bit error rate for digital data is a function of Eb/N0

Given a value for Eb/N0 to achieve a desired error rate, parameters of this formula can be selected

As bit rate R increases, transmitted signal power must increase to maintain required Eb/N0

RBSNRRBBN

S

RBN

SB

N

RS

N

Eb /*/*/

0000

Other Impairments and Effects Atmospheric absorption – water vapor and oxygen make it

worse at higher frequencies --- typically some 10-20 GHz, worse higher, some ‘windows’ around 35-40 GHz and 95 GHz

Multipath – obstacles reflect signals so that multiple copies with varying delays are received -- see fig 5.10 next

Particularly important in cellular or any path that does not have a direct line of sight, or where objects near LOS path

Diffraction -- Bending of radio waves around obstacles and corners

Refraction -- Bending by atmosphere (like lenses) due to varying index of refraction at different heights, places

Multipath Propagation

Multipath Propagation Reflection - occurs when signal encounters a

surface that is large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that is large compared to wavelength of radio wave

Scattering – occurs when incoming signal hits an object whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation Multiple copies of a signal may arrive at

different phases If phases add destructively, the signal level

relative to noise declines, making detection more difficult --- Fading

Intersymbol interference (ISI) One or more delayed copies of a pulse may

arrive at the same time as the primary pulse for a subsequent bit

Types of Fading Due to multiple paths arriving at receiver and

adding constructively and destructively in a random basis

Fast fading due to small variations in path lengths as one moves or as

scatterers move -- often modeled as Rayleigh Slow fading -- shadow fading

Slower, as one moves and blockage and objects in between change -- often modeled as a log normal distribution

Figure showing fading, similar to fig. 5.12 in Stallings

Error Control Process--and Error Minimization

Error control process has three components Error minimization Error detection Error correction --- FEC (Forward Error Correction)

Error minimization: modulation/coding techniques to minimize effects of noise/fading, interleaving to scramble bits (fight off effects of error ‘bursts’), equalization vs fading effects, and diversity vs fading effects

Coding done for error detection (eg, CRC) and for error correction (FEC codes: convolutional, block)

Automatic repeat request (ARQ) protocols Block of data with error is discarded, data retransmitted -- not for voice Requires error detection

Wireless Re-transmission ARQ Protocols Often inadequate for wireless applications

Error rate on wireless link can be high, results in a large number of retransmissions

Long propagation delay compared to transmission time --- lots of frames in transit

Not good for voice, possible for data if FEC is used first to have errors less often

Forward Error Correction (FEC) Required to offset channel induced errors Sometimes referred to as ‘channel coding’ Transmitter adds error-correcting code to data block

Code is a function of the data bits Receiver calculates error-correcting code from incoming data

bits If calculated code matches incoming code, no error occurred If error-correcting codes don’t match, receiver attempts to determine

bits in error and correct Codes are in fact able to correct

Channel Coding FEC used to code to offset effects of propagation -- eg

multipath fading Since fading goes in and out, when power down FEC used to

try to offset the lower SNR Involves insertion of additional FEC bits Block Codes -- similar to CRC, but are able to correct 1,

2 or more errors, depending on size of block (number of bits added) and code strength (Hamming distance)

Convolutional Codes -- combines the the bits to be corrected ---- uses Viterbi decoding

Interleaving --- used to mix bits in to minimize the effects of error bursts

Error Detection Probabilities Definitions

Pb : Probability of single bit error (BER)

P1 : Probability that a frame arrives with no bit errors

P2 : While using error detection, the probability that a frame arrives with one or more undetected errors

P3 : While using error detection, the probability that a frame arrives with one or more detected bit errors but no undetected bit errors (ie, all errors detected)

Error Detection Probabilities With no error detection

F = Number of bits per frame

0

1

1

3

12

1

P

PP

PP Fb

Error Detection Process Transmitter

For a given frame, an error-detecting code (check bits) is calculated from data bits

Check bits are appended to data bits Receiver

Separates incoming frame into data bits and check bits Calculates check bits from received data bits Compares calculated check bits against received check

bits Detected error occurs if mismatch

Error Detection Process

Decoder

Parity Check Parity bit appended to a block of data Even parity

Added bit ensures an even number of 1s Odd parity

Added bit ensures an odd number of 1s Example, 7-bit character [1110001]

Even parity [11100010] Odd parity [11100011]

Cyclic Redundancy Check (CRC) Transmitter

For a k-bit block, transmitter generates an (n-k)-bit frame check sequence (FCS)

Resulting frame of n bits is exactly divisible by predetermined number

Receiver Divides incoming frame by predetermined

number If no remainder, assumes no error

CRC using Modulo 2 Arithmetic Exclusive-OR (XOR) operation Parameters:

T = n-bit frame to be transmitted D = k-bit block of data; the first k bits of T F = (n – k)-bit FCS; the last (n – k) bits of T P = pattern of n–k+1 bits; this is the predetermined

divisor Q = Quotient R = Remainder

CRC using Modulo 2 Arithmetic For T/P to have no remainder, start with

Divide 2n-kD by P gives quotient and remainder

Use remainder as FCS

FDT kn 2

P

RQ

P

Dkn

2

RDT kn 2

CRC using Modulo 2 Arithmetic Does R cause T/P have no remainder?

Substituting,

No remainder, so T is exactly divisible by P

P

R

P

D

P

RD

P

T knkn

22

QP

RRQ

P

R

P

RQ

P

T

CRC using Polynomials Widely used versions of P(X)

CRC–12 X12 + X11 + X3 + X2 + X + 1

CRC–16 X16 + X15 + X2 + 1

CRC – CCITT X16 + X12 + X5 + 1

CRC – 32 X32 + X26 + X23 + X22 + X16 + X12 + X11 + X10 + X8 + X7 + X5 + X4

+ X2 + X + 1

Digital Logic CRC

Block Error Correction Codes Transmitter

Forward error correction (FEC) encoder maps each k-bit block into an n-bit block codeword

Codeword is transmitted; analog for wireless transmission

Receiver Incoming signal is demodulated Block passed through an FEC decoder

Forward Error Correction Process

FEC Decoder Outcomes No errors present

Codeword produced by decoder matches original codeword

Decoder detects and corrects bit errors Decoder detects but cannot correct bit

errors; reports uncorrectable error Decoder detects no bit errors, though errors

are present

Block Code Principles Hamming distance – for 2 n-bit binary sequences,

the number of different bits E.g., v1=011011; v2=110001; d(v1, v2)=3

Redundancy – ratio of redundant bits to data bits Code rate – ratio of data bits to total bits Coding gain – the reduction in the required Eb/N0

to achieve a specified BER of an error-correcting coded system

Hamming Code Designed to correct single bit errors Family of (n, k) block error-correcting codes with

parameters: Block length: n = 2m – 1 Number of data bits: k = 2m – m – 1 Number of check bits: n – k = m Minimum distance: dmin = 3

Single-error-correcting (SEC) code SEC double-error-detecting (SEC-DED) code

Cyclic Codes Can be encoded and decoded using linear

feedback shift registers (LFSRs) For cyclic codes, a valid codeword (c0, c1, …, cn-1),

shifted right one bit, is also a valid codeword (cn-1, c0, …, cn-2)

Takes fixed-length input (k) and produces fixed-length check code (n-k) In contrast, CRC error-detecting code accepts arbitrary

length input for fixed-length check code

BCH Codes For positive pair of integers m and t, a (n, k)

BCH code has parameters: Block length: n = 2m – 1, m greater than 2 Number of check bits: n – k mt Minimum distance:dmin 2t + 1

Can correct combinations of t or fewer errors Flexibility in choice of parameters

Block length, code rate

Reed-Solomon Codes Subclass of nonbinary BCH codes Data processed in chunks of m bits, called symbols An (n, k) RS code has parameters:

Symbol length: m bits per symbol Block length: n = 2m – 1 symbols = m(2m – 1) bits Data length: k symbols Size of check code: n – k = 2t symbols = m(2t) bits Minimum distance: dmin = 2t + 1 symbols Can correct t or fewer errors

Convolutional Codes Generates redundant bits continuously Error checking and correcting carried out

continuously (n, k, K) code

Input processes k bits at a time Output produces n bits for every k input bits K = constraint factor k and n generally very small

n-bit output of (n, k, K) code depends on: Current block of k input bits Previous K-1 blocks of k input bits

Convolutional Encoder

Decoding Trellis diagram – expanded encoder diagram Viterbi code – error correction algorithm

Compares received sequence with all possible transmitted sequences

Algorithm chooses path through trellis whose coded sequence differs from received sequence in the fewest number of places

Once a valid path is selected as the correct path, the decoder can recover the input data bits from the output code bits

Some Use of Codes CRC used often to detect uncorrectable errors in a frame, for

an ARQ function on data as last choice Reed-Solomon code used in CDPD Coding gain is determined by change in Eb/Nsub0 that gives

same BER -- few dB eg, 2.77 dB in Fig 8.6 Stallings at ber of 10^-5

IS-95 uses convolutional codes, as do most cellular systems, using Viterbi decoding

Bit error rates : Raw channel BER is about 10^-1 or 10^ -2 Voice needs 10^-2 or 10^-3, so coding needs to do this For data one often needs about 10^-6 --- in 3G a concatenated coding

scheme, with RS block coding and convolutional coding

From Stallings

Block Interleaving -- Time Diversity Data written to and read from memory in different orders Data bits and corresponding check bits are interspersed

with bits from other blocks At receiver, data are deinterleaved to recover original

order A burst error that may occur is spread out over a number

of blocks, making error correction possible Used in 2G and 3G systems --- speech coders produce

important bits in succession, interleaving spreads them out over time, codes can correct them

Block Interleaving

Automatic Repeat Request Mechanism used in data link control and

transport protocols Relies on use of an error detection code

(such as CRC) Flow Control Error Control

Multipath Induced Effects Causes fading (amplitude variations and deep ‘nulls’) and

ISI (copies of symbols come in delayed and overlap next symbol) -- fading is both fast (msec) and slow (seconds)

Fast is rapid variations, slow is shadowing Flat fading is for narrowband channels

BW (signal)<(Coherence) BW of channel, eg, AMPS Fast fading, ‘handled’ somewhat with coding and diversity

Frequency selective fading BW (signal)>(Coherence) BW of channel, eg, TDMA, GSM, CDMA Causes ISI, some fading but not as bad as it averages out some Fast fading ‘handled’ well with coding and diversity

Time diversity in Rake receivers for CDMA (combines multi path energies

ISI handled with equalizers in TDMA/GSM CDMA codes separate multi path returns so no mixing, can combine

Adaptive Equalization for ISI Used to combat intersymbol interference (ISI) caused by multipath Involves gathering dispersed symbol energy back into its original time interval Dispersion determined by maximum time delay spread

Represents the time over which one symbol will affect other symbols Large variation, environment dependent

Outdoors in 5-20 usecs range, maybe to 100 usec Indoors smaller, maybe to .1 to 1 usec At 30kbps one bit is 33 usec long, so if delay spread is 100 usec it causes interference with 3 bits

Even if delay spread is 10 usec it interferes with first third of next bit At 200 kbps one bit is 5 usec long so 10 usec spread interferes with 2 bits

The higher the data rate the worse the ISI effect is -- A BROADBAND EFFECT Channel coherence bandwidth Bc=(approx) 1/5x(RMS delay spread)

For delay spread = 4 usec (say), Bc=50 KHz, so AMPS at 30 KHz (so less) does NOT need equalizer but GSM at 200 KHz DOES

From Rappaport

Equalization Techniques Need to be adaptive since channel is unknown -- at receiver

Digital signal processing algorithms, called equalizers, that estimate the channel transfer function and reverse its effects --- involves an estimate of the channel via a known symbol sequence transmitted which is then compared at receiver with stored replica

Estimate channel: training and tracking Equalizer is a time varying filter whose weights are adapted based on

channel estimate --- often implemented as adaptive transversal (FIR) filter Algorithms: weights to minimize estimated error, eg, least mean squares Linear and nonlinear -- nonlinear needed if deep nulls due to multipath NL: Decision feedback (subtracts detected symbol), maximum likelihood

(tests all possible data sequences and picks best --- lots of computation) Also possible but not as robust: blind algorithms, based on eg, keeping

envelope constant on constant envelope modulations (eg, GSM)

Diversity Techniques Diversity is based on the fact that individual channels experience independent

fading events Space diversity – techniques involving multiple physical transmission paths --

eg, multiple antennas Most base stations have two diversity receive antennas for this reason Rapaport p.327, can go from 90% prob. of not fading to 99% w/2, or 99.99% w/4 diversity

antennas, by selecting the strongest one Smart antennas can collect most of the energy from different multipaths

Frequency diversity – techniques where the signal is spread out over a larger frequency bandwidth or carried on multiple frequency carriers --- CDMA DS spreads energy over a larger BW, affects frequency diversity

Time diversity – techniques aimed at spreading the data out over time --- eg, bit repetition, interleaving, Rake processing (in CDMA)

FEC coding often thought of as a form of time diversity

LINK BUDGETS FOR WIRELESS SYSTEMS

Budget for Link: IS 95 CDMA Forward Traffic Channels

NUMBER CATEGORY BUDGET ITEM LABEL VALUE UNITS OTHER NOTES

1 Transmitter1.1 Power Transmit Power Pt 40.00 dBm 10 W1.2 Antenna Tr. Antenna Gain Gt 17.20 dBi1.3 Loss Polarization Loss Ltp 0.00 dB and Body Losses1.4 Loss Cable Loss Ltc 2.90 dB1.5 Gain Beamforming Gain Gtbf 0.00 dB1.6 Gain Other Gain Gto 0.00 dB1.7 EIRP Transmitter EIRP EIRP 54.30 dBm Effective Radiated Power

1.8 ChannelsNumber Channels per Carrier Ncc 14.00 #

Number channels allocated power at Bit Rate

1.9 Percent PowerChannel Percent Power Allocation Pac 0.64 #

Percent allocated to all channels at Bit Rate -- Traffic channels

1.10 EIRP/Channel EIRP/Channel EIRPc 40.90 dBm

2 Signal Waveform2.1 Bandwidth Carrier Bandwidth Bc 1.25 MHz2.2 Modulation Modulation Type ModT QPSK Text2.3 SNR Required Eb/No Eb/N0 7.50 dB For BER2.4 Frequency Band Frequency Band Fb 1900.00 MHz2.5 Center Frequency Center Frequency Fc 1900.00 MHz

3Propagation Loss Estimate

3.1Reference Distance Reference Distance R0 0.10 Km

3.2 Reference LossPropagation Loss Reference PL(R0) 7.00 dB

At distance R0 (change to 1m for picocells)

3.3 Frequency Factor Frequency Loss Factor PL(f) 65.58 dBFor Frequency Band, 20*log(f^2), f in MHz

3.4 Loss Index Loss Distance Index n 3.50 # For R^n Losses, from Rap.3.5 Cell Size Cell Size R 2.00 Km Planning Purposes3.6 Loss Other Loss Plo 0.00 dB

3.7 LossMean Estimated Propagation Loss Avg PL 118.11 dB Total Mean Estimated Loss

3.8 Loss Loss St. Deviation Sigma 8.00 dB From Rap.

3.9 Margin Fade Margin Mf 5.50 dB

Fade Margin for Approx. 90% Coverage (Rap. P.108)

Samplepg. 1

LINK BUDGETS FOR WIRELESS SYSTEMS

Budget for Link: IS 95 CDMA Forward Traffic Channels

NUMBER CATEGORY BUDGET ITEM LABEL VALUE UNITS OTHER NOTES4.1 Antenna Antenna Gain Gr 0.00 dBi4.2 Antenna Polarization Loss Lrp 2.00 dB and Body Losses if any4.3 Constant kTo kTo -174.00 dBm/Hz4.4 Receiver Noise Figure NF 10.00 dB Rx Design Parameter4.5 Data Rate Channel Data Rate Rc 14400.00 bps Channel Design

4.6 SNR Required Eb/N0 Eb/N0 7.50 dBMod/Demod/Coder Required Eb/N0 for FER

4.7 Error Rate Bit Error Rate BER # For FER below4.8 Error Rate Frame Error Rate FER 0.01 # For good voice quality4.9 Gain Coding Gain Gc 0.00 dB To lower further Eb/N0

4.10 GainDiversity/Beamforming Gain Grdbf 0.00 dB Beyond Gr

4.11 Loss Implementation Loss Lri 1.00 dB4.12 Loss Other Loss Lro 0.00 dB4.13 Voice Activity Voice Activity Factor VAF 0.50 # In multirate systems4.14 Receiver Receiver Sensitivity Sr -117.93 dBm

5 System5.1 Margin Fade Margin Mf 5.50 dB From 3.9

5.2 InterferenceInterference Loading Factor Lilf 1.00 dB Lib.& Rap. 2.8 in reverse

5.3 Gain Handoff Gain Gh 2.00 dB2-3 hard, 3-4 soft, often not taken

5.4 User Facility Loss User Facility Loss Luf 6.00 dB In car. 14 dB in bldg.5.5 Loss Loss Other Lo 0.00 dB5.6 System Losses Total System Losses Ls 10.50 dB

5.7Required Power at Receiver

Required Power at Receiver Req Pr -107.43 dBm Sr+Ls

5.8 Max Prop. LossMaximum Allowed Propagation Loss Max PL 148.33 dB To get Req. Pr

5.9Propagation Margin

Propagation Loss Margin PL Margin 30.22 dB

Can Be Used for More Range

5.10 Range Calc Log(Rmax/R) log(Rmax/R) 0.86 # From Prop. Loss Estimate5.11 Range Max Range Rmax 14.60 Km Possible Cell Size

Or Can Work Inside Building --- Needs 8 dB min.

Samplepg. 2