N, N N
(ae)
b a/F a

Equation (18) says that the number of users per megahertz getting a specified
reliability decreases as the bandwidth of the spread-spectrum system in-
creases.

This result applies only under the listed assumptions. The assumptions
approximate an LMR service with multiple independent networks operating in a
terrestrial area of fixed size. The result says nothing about LMR services
with central control of mobile transmitter power or about geostationary
satellite-to-earth systems (in which all paths are effectively the same
length). In addition, some of the assumptions are over-simplified. For
example, assumption (d) gives a single value for the power received from a
given distance, when in fact, that power has a statistical distribution.
Also, not all transmitters will have the same power. The next section
describes more realistic computer calculations of the spectrum efficiency of

SS LMR systems.

3. COMPUTER CALCULATION OF SPECTRUM EFFICIENCY FOR SS LMR

In this section, we calculate more realistically the performance of a
duplex SS system with all base stations near the center of the service area.
As shown in the previous section, interference will be worse in the mobile-
to-base channel; so we concentrate on it. We include the effects of proba-
bilistic traffic intensity and the statistical distribution of equipment
characteristics and transmission loss. The resulting model is so complicated

that computer evaluation is necessary.

3.1 Analysis of Communications Probability

In a multi-network, spread-spectrum LMR service each network will have
its own assigned code. A user will not be able to hear (decode) trans-
missions from other networks, and so he will transmit whenever he has a
message without waiting for a clear channel. This "instant access" is one
of the appealing features of SS land mobile radio service.

In a city there will be hundreds or thousands of mobile radios; so

there may be several of them transmitting simultaneously at any time, even

14


(2) there are n interferers transmitting simultaneously;

(3) all transmitters have equal radiated power; and

(4) the propagation law is PL = Ka’, where PL is the power
received; K is a constant incorporating common radiated
power, antenna gain, and frequency; d is the transmission

path length; and a is a constant.

Assume a fully loaded spread-spectrum LMR service; that is, the networks
just barely achieve the required signal-to-interference ratio the required
percent of the time, and addition of another network would lower the reliabil-
ity below the standard. Variables for this situation will be subscripted
with a. In situation a, there are Ny interferers at a given time. The
total interference is [using (A-15)]

a

k /E(x,) E(x,) zs
1 vi / 2
Ix. 1+ J} + (N_-k) 5 1 (A~16)
ta la m1 E(x,) a E(x,) 2 Ny 1

and

r -o
Ta 7 8 yo ut : (a-17)

Putting (A-17) into (A-16) and combining constants results in

Qa
> (,-k)

2
Ti, 7 HAD" 90+

, (A-18)
ans) °4

where Q and T are positive numbers independent of No:
We are going to increase the bandwidth of the SS systems and see
whether we get a commensurate increase in the number of users. In situation

b, increase the bandwidth of the spread-spectrum systems so that
B =FB , (A-19)

where F > 1.

Increase the number of users until performance is again at the threshold

of unacceptability. In this case, there are N, simultaneous interferers.

b
The total interference for case b is

a

7 N -k

I = Hoyt)? Q+T b

tb (A-20)

4°

(wt) TM

35



APPENDIX A. THE SPECTRUM EFFICIENCY OF MULTIPLE, INDEPENDENT,
SS LMR NETWORKS

This appendix contains a more rigorous and detailed derivation of the
result given in Section 2.3 of the main body of this report. It is assumed
that the wanted signal is from a mobile to a base station. Interfering
signals come from n other mobiles randomly distributed in the metropolitan
area and transmitting simultaneously. It is understood that the total
number of mobiles in the area is much larger, but proportional to the number

transmitting at any time.

A.1 THE EXPECTED DISTANCES TO THE INTERFERERS

There are n points randomly distributed in a circle with radius r. Then
the distance x from the center of the circle to a point is a random variable

with probability density function (pdf)
f(x) =— x, O£x<kér (a-1)
x = Ye , fxs ,

and probability distribution function

F(x) = x Jer, (A-2)

Order the distances to the n points and label them Xr Kye teen Xe so that

Then the pdf of x,, m= 1, n is (Gumbel, 1958, p. 43)

x2\ m4 x n-m
h(x) = oe (3) (a - =) . (a-3)

(n-m)!(m-1)!r \r

The expected value of Xa!

on! xr 2 m—45 x2\nn
E(x) = (om)! (mel) te Hl »(%) ( - *) dx. (A-3)
Using the transformation U = x /r?,
B(x) = ——e__ { ot (a-uy9TM au (a-4)
mn’ ~ (nem) P(m-1)! 4 .

31



Table B.2.

Frequency
(MHz)

25.01 - 25.33
26.1 - 26.48
27.28 - 27.54
29.7 - 29.8

30.56 - 32
33 - 33.01
33.01 - 33.11
33.11 - 33.41
33.41 - 34
35 - 35.19
35.19 - 35.69
35.69 - 36
37 - 37.01
37.01 - 37.43
37.43 - 37.89
37.89 - 38
39 - 40
42 - 42.95
42.95 - 43.19
43.19 - 43.69
43.69 - 44.61
44.61 - 46.6
47 - 47.43
47.43 - 47.69
47.69 - 49.6
150.8 - 150.98
150.98 - 151.4825
151.4825 - 151.4975
151.4975 - 152
152 - 152.255
152.255 - 152.465
152.465 - 152.495
152.495 - 152.855
152.855 - 153.7325

DP - Domestic Public
I - Industrial

LT - Land Transporta
PS - Public Safety

tion

40

Service Groups Within the LMR Bands

Service Groups

I,LT,PS

LT
PS
I
PS
I
DP,I,PS
I
I
PS

PS

LT
I,PS

DP
LT

DP



The discussion above assumes that an interfering base station is on
nearly all the time. Base stations do transmit a substantial fraction of
the time. If there are several base stations, the probability of none
transmitting at a given time (no interference) is unacceptably small; so the
analysis above still applies.

The conclusion is that if LMR mobile and base stations share the same
spread-spectrum band, no more than a few independently controlled networks
can operate satisfactorily in a city, even though they occupy enough band-
width for hundreds of conventional LMR networks. Therefore, independent SS
LMR systems must have separate frequency bands for base and mobile stations.
From here on, we assume SS LMR systems are duplex and compare them with
conventional duplex FM systems.

Notice that spread-spectrum systems have been represented entirely by
their processing gain. We have ignored implementation losses and gains
achieved with nearly orthogonal codes or filters. Because these two factors
work in opposite directions, they partially cancel each other, and the con-
clusion above is probably valid for both direct sequence and frequency hopping

SS systems.

Figure 2. Geometry for analysis of base station interference to a base-
to-mobile transmission. A mobile at M, is trying to receive

base station T) while base station T, is transmitting.


fails to comprehend because of the noise, he can ask for a repeat of the
critical parts of the message.

Kelly and Ward (1973) suggest that data rates of 2000-2400 words per
minute are a reasonable goal for law enforcement digital communications with
vehicle printers; normal voice is about 150 words per minute. They also
recommend that the digital rates be from 2000-10000 bps to achieve the desired
data rate and to improve the channel utilization. Since the digital data
rates (up to 10 kbps) are less than the digital voice rates (about 30 kbps),
we only need to consider the spread-spectrum system implications when

digitized voice is to be transmitted.

B.3 SPREAD SPECTRUM IN LM RADIO
B.3.1 Spread-Spectrum Concept

In most instances, use of more spectrum than is really necessary to
transmit information is wasteful. For example, voice occupies about 3 kHz of
spectrum and can be transmitted as single sideband amplitude modulation (AM)
in about 3 kHz bandwidth or as double sideband AM in about 6 kHz. An excep-
tion is made to "the transmission bandwidth should equal the information
bandwidth" rule when something is gained by going to wider transmission band-
widths. For example, wideband frequency modulation (WBFM) typically uses
transmission bandwidths which are much wider than that of the voice or in-
formation source bandwidth. In this case, the gain for using the wider
bandwidth is in the signal-to-noise ratio improvement, called the FM improve-
ment. Another benefit is closer frequency re-use distances resulting from
signal-to-interference improvement (captive effect).

Spread spectrum is another exception. In fact, the definition of a
spread-spectrum system is one which meets two criteria (Dixon, 1976):

(1) the transmitted bandwidth is much greater than the bandwidth

of the information being sent, and

(2) some function other than the information being transmitted

is employed to determine the resulting modulated rf band-
width.

Although WBFM meets the first of these criteria, it doesn't meet the
second. The function used by most spread-spectrum systems is a code sequence

that periodically repeats itself.

50



NIAT3y S$33YN9T0 NI OL

*(€L6T ‘LLI) Aouenbezz snszea ssToU eATED9r JO Ss907NOS ‘ped emnbta

ZLYSHVOSAW NI AONANOA YA

<4

48

jo}
nN

je)
m

[o)
T+
a°Ly 3A08v STagioga NI °4

000‘O! Ooo! (ele)}
89 + z 89 » 2 89 + 2
OIxXe
NY (NAS L3INO)
0062 { yv 10S
fo)
= OL
aN | | |_—_—]
Sho 7J N
Olxe —
g | aN S
TS. ya aiaogy
TVOIdAL N dILOVIV9
pOlxe
IN N
Olxe IN
s JN
JaVW-NVW\_ 30VW- NVA
g0IXe nvaun Nvaynans
aN
,OlXe 7 ,
DAN ‘SYNOH OOZ! - 0080 {Y3LNIM
DAN ‘SYNOH OObe - COC? ‘YSWWNS
olxe DINSHdSOWLYV
8

je)
wo

[e)
o



TRANSMITTER
Binary °
Information

to be Transmitted

Spreading

Code Sequence
Spread Signal
Code=I @ C )

Phase of
Transmitted to)
Carrier

RECEIVER
Phase of fe)
Received Signal
After First PSK
Demodulation

=S@c

Information After {e)
Second Demodulation

RECEIVED INTERFERENCE

Phase of CW te)
Interference Before
First PSK Demodulator

Phase of CW ie}
Interference After
First PSK Demodulator

Phase of PSK T

Interferference Before
First PSK Demodulator

Phase of PSK us

Interference After
First PSK Demodulator

Figure B.6. Examples of transmitted SS codes, received SS
and received interference.

54

signals,



preamble. What is the minimum synchronization time for this system? If the
synch recognition rise time is assumed to be 0.35/(30 x 107) = 11.67 us and
if the 4095 bits are searched at 1/2 bit per search, then at least 4095 x 2
x 11.67 x 10° seconds or 0.095 seconds would be required for acquisition.
Without a technique like synchronization preambles, the acquisition time for
the same system could take several seconds.

Passive spread-spectrum devices include Surface Acoustic Wave (SAW) de-
vices and Charge Coupled Devices (CCD). For either device, the code is pro-
grammed by the user who chooses the tap selection, or it is fixed at the time
of the device's fabrication. Because SAW's and CCD's are passive, the SS
receiver doesn't have to search the received code to establish correlation.
The SAW's and CCD's are matched filters only to one code (usually from a
matching SAW or CCD) and whenever that code is transmitted, the receiver is
able immediately to despread the total code with no acquisition time require-
ments or synchronization constraints. These devices have the most promise

for SS LMR applications, but have limited processing gain.

B.3.6 Spread-Spectrum LMR in Multipath

The SS LMR system is a digital system; thus we need to investigate what
happens to the bit error rate or probability of a bit error, Por when the
receiver operates with Rayleigh fading. Figure B.8(a) (from Schwartz et al.,
1966) shows the effects of a nonfading channel and a Rayleigh fading channel
on both PSK and FSK. The probability of a bit error is plotted against the
energy per bit-to-noise power density ratio, E,/N,: The effects of Rayleigh
fading are dramatic; an E/N, of 9 dB in the nonfading channel gives a very
satisfactory bit error probability of 10>, but in the fading channel gives
an unacceptable bit error probability of 5 x 107.

Figures B.8(b) through B.8(h) (developed by Cline, 1973) demonstrate the
improvement of using a PSK spread-spectrum system in multipath. Using Cline's
notation, G represents the SS processing gain, K.

1
tor between the direct and reflected signal paths (e-g., kK = 0 means there

is the power division fac-

is no multipath signal and Ky = 1 means the reflected and direct signals are
equal in power), K, is the multipath time spreading factor relating the
spreading code bit or chip length to the average multipath time spread, and

€ is the correlation coefficient between the direct and reflected signals

58



Signal Level (dB above mean)

15
| ITT TTT]
10 HK Log Normal Distribution
3}— ey,
Standard
Deviation
0 ee, —
-5 — —
-10 -— —
15 | | pt | |
~ S$ SSE 8B
Percent Probability that Received
Signal Level is Less than Ordinate
Figure B.3. Signal level statistics for a log normal distributed

received signal.

46



In an interference-limited environment, such as a fully used SS LMR

service, the mean power radiated by transmitters is not important as long as

it is sufficiently greater than the ambient noise. The variation of power

about the mean is more important. The variation results from transmitters

with different power ratings, installation, maintenance, and antenna character-

istics. The pdf of effective radiated power (ERP) assumed in this study is

shown in Figure 3. The nominal power of 80 percent of the transmitters is

100 W, and most stations ERP is within 3 dB of this value. A few users buy

20 W transmitters, and poor installation and maintenance cause a small

percentage to radiate less than 10 dBW.

0.20

0.15

010

P(ERP)

005

| | | |

Figure 3.

5 10 5 20 5
ERP, dBW

Probability density function for the effective radiated power
of transmitters used in the service calculation. The ordinate
is the probability that a transmitter emits the power shown on
the abcissa.

1g



Assume that the wanted signal has the same value in both cases. Then
the output S/I is the same provided that the input S/I is related by the

ratio of processing gains; that is

B, (S/T, .) = B (S/I,,) ,
or

Tr
Few _ Be
Tea Ba

=F. (A-21)

Substitute (A-18) and (A-20) into (A-21) and simplify:

N,-k
b
a (Q+ tT ——~
NptLy 2 nt) °/4
= . A-22
(2a) Ni-k FP ( )
Q+ttT a/4
(N_+1)
a
Consider
f(x) =Q+7T oN » (&>k>1).
(x+1)
The derivative,
T Q x-k
£ (0) = Q- St)
(et) 0/4 4 x+1
is positive provided
Ge -1
x > — T°: (A-23)
1+ a
But
a.
5 k-1
> gk > Et 4
a a 1 a

for all a > 0 and k > 1; so (A-23) is always true since x >k. Therefore,
£(x) is an increasing function of x, and, because Ny 2 Ny:
N-k Nae
a/4  *

Q+T 2>Q+T
a/4
(w+) (+1)

(A-24)

36



TABLE OF CONTENTS

ABSTRACT © 6 6 ee ee eee ee ee ee ee ee
1. INTRODUCTION. . - - - ee ee ee ee ee ee ee ee ee
2. INTERFERENCE AND SPECTRUM EFFICIENCY OF MULTIPLE INDEPENDENT

NETWORKS IN AN EXCLUSIVE SPREAD-SPECTRUM LAND-MOBILE RADIO
BAND. 2 6 6 6 6 ee ee ee ee

Why Multiple Independent SS Networks Must Be Duplex. . .
Why SS LMR Base Stations Must Be Located Close Together.
Approximate Analysis of Interference When Base Station

Antennas Are Co-located... . . . - - ee ee ee eee
2.3.1 Base-to-Mobile Transmissions. .......-..-.
2.3.2 Mobile-to-Base Transmissions. .......-...

NNN
wWNnR

COMPUTER CALCULATION OF SPECTRUM EFFICIENCY FOR SS LMR. . . .

3.1 Analysis of Communications Probability .........
3.2 Distributions of Input Parameters. .......-+-.--
3.3 Computed Probability of Communications .........
3.4 Spectrum Efficiency of SS Systems. .....-.-.-.2--

OVERLAYING A SPREAD-SPECTRUM SYSTEM ON AN EXISTING SERVICE. .

4.1 SS Interference to FM... . 6 eee ee ee ee ee
4.2 FM Interference to SS. --.-.-.--.- +e ee eee eee

CONCLUSIONS . . - © ee ee ee ee ee ee ee ee ee
ACKNOWLEDGMENTS . . 2. ee ee ee ee ee ee ee ee ee

REFERENCES. « . 6 6 ee ee ee ee ee ee ee ee

APPENDIX A. THE SPECTRUM EFFICIENCY OF MULTIPLE, INDEPENDENT, SS

LMR NETWORKS. . - - ee 6 ee ee ee ee ee ee

1 THE EXPECTED DISTANCES TO THE INTERFERERS. . .....-
-2 THE TOTAL INTERFERENCE POWER... .- + + e+ + eee eee
3 THE SPECTRUM EFFICIENCY AS A FUNCTION OF BANDWIDTH . . -
4 REFERENCES . - 2. 6 ee ee ee ee ee ee ee ee

APPENDIX B. CONVENTIONAL LMR AND SPREAD-SPECTRUM BACKGROUND . . -

B.1 THE LAND-MOBILE RADIO CHANNEL. . .... +. - eee ee
B.1.1 Land-Mobile Radio Frequency Bands ........
B.1.2 Propagation Effects on the Land-Mobile Channel. .-
B.1.3 Noise and Interference in the LMR Channel... -

ll
ll
ll

14
14
16
19
22
24

24
27

27

29

29

31

31
32
34
38

39

39
39
42
47


existing service. The SS service probably could operate satisfactorily with

occasional interuptions from FM transmitters very near the desired receiver.

6. ACKNOWLEDGMENTS

We thank Thijs deHaas of ITS for his critical reading of, and substan-
tive contribution to, Section 4.2. During the study, we had many useful dis-
cussions with John R. Juroshek of ITS and with Phil Gieseler and Roger Madden
of the FCC.

7. REFERENCES

Berry, L. A. (1977a), Probabilistic tradeoffs for efficient spectrum use
with a "CB" example, OT Report 77-117 (National Technical Information
Service, Springfield, VA 22161, PB 266669, $4.50).

Berry, L. A. (1977b), Spectrum metrics and spectrum efficiency: proposed
definitions, IEEE Trans. Electromag. Compat., EMC-19, No. 3, 254-260.

CCIR (1978a), Spread spectrum modulation techniques (Pink Document 1/1007,
Kyoto, Japan).

CCIR (1978b), Definition of spectrum use and efficiency (Kyoto, Japan) .

Cooper, G. R., and R. W. Nettleton (1977), A spread spectrum technique for
high capacity mobile communications, IEEE Vehicular Technology Group
Conference Record (IEEE No. 77CH1176-7VT) .

Costas, J. P. (1959), Poisson, Shannon, and the radio amateur, Proc. IRE,
47, No. 12, pp. 2058-2068.

Crow, E. L. (1972), Effect of variability in received power on probabilities
of communication delay in land mobile radio systems, OT/TRER 40 (National
Telecommunications and Information Administration, Boulder, CO 80302).

Davenport, W. B., Jr. (1970), Probability and Random Processes (McGraw-Hill
Book Company, N.Y.).

Dixon, R. C. (1976), Spread Spectrum Systems (John Wiley & Sons, Inc., N.Y.).

Freeman, E. R. (1972), A minimal data probabilistic model for spectrum manage-
ment, IEEE Trans. Vehicular Tech., VI-21, No. 3, pp. 109-113.

Haakinson, E. J. (1978), Spread spectrum: an annotated bibliography, NTIA
Special Publication 78-1 (National Telecommunications and Information
Administration, Boulder, CO 80303).

Jakes, W. C., dr., Editor (1974), Microwave Mobile Communications (John
Wiley & Sons, N.Y.).

29



if the average individual usage is low. We must calculate the probability
that each user will achieve communications in the presence of interference

from the others.

We assume that communications are satisfactory if
S/(I +N) 2>R ,

where S is the desired signal, I is the total interference, N is the noise,
and R is a specified value.

There can be no communications failure unless someone is trying to com-

municate; so we calculate

P(communications) = P(S/(I +N) >R at least one user is transmitting) ,

where P(A|B) means "the probability of A, given B."

Now (Davenport, 1970),
P(communications) = P(S/(I+N) > R| at least one Ty on)

P([S/(I+N) > R] and [at least one Ty, on])

P (at least one Ty on)

_ P([S/(14+N)>R and 1 on] or [S/(I+N)>R and 2 onlor...or[S(I+N)>R and _m on])
_ P(1 on or 2 on or ... or m on)

(19)
where there are m licensed transmitters in the channel.
Because the event "Ky transmitters are on" and the event "ky transmit-
ters are on" are mutually exclusive when ky F koe
m

Y P([s/(+r) > R] and [k transmitters are on])
k=1

P(communications) =
) 1 - P (no transmitters are on)

P(S/(N+I) > R|k transmitters on) Py

m
=?) , (20)
k=1 1- RP,

15


“ME < WIT OMA ST STYL "T >> iU/,N FeuR SuMSse eTGeR OyR UT SeNTeA

*szeqqTuSsuez} JO ZequMU Te}0} BYR ST
w pue ‘soyNUTWU UT UOTSSTUSUeZ} e JO YRHUST ehersae oy} ST y ‘1999 TUISUeTR TeENPTATPUT
ue Aq znoy zed suotsstusuerz} jo Jequmu eherzeae st N 9zeYyM ‘shueTze w (09/yN) = 0

‘wo € OF T wory sqYyHtey euuseque eTTqow

pue ‘Ww OOP OF OG WoryZ S}YUHTeEYy euusjUe sseq !ZHW OOOT PUS ODOT UuseemM}zeq SeTOUSENbezz
ZoZ ZUSOZed Moz e UTYITM 3OezTOD eq pTNOYS 34nq fu G*T = JUSTey euueque eTTqow
‘w 00% = 24HTey euuejue sseq ‘ZHW OST Jo AOuenbezy otpez 10x pejndwod sem eTqeL |

*@eTOATO 8yy UT peqeooT ATwopuer ere seTTqow
‘uy O€ SNTPer YRTM eTOATO e FO zeqUeD eYA APOU seseq TIW

‘uo ST z0qq9TwWSUez3 suo ATIOeKS JT ouo st uy < I/s 3eUR AATTTGeqozd eyz yey} seumssy :sojON

z80° giz" Bez" o6e* Les" Tb: vos" oge* 0)
8IT* 9Lz° ose’ zsp° zes* 9LL" egs* ove: €-
voT* ze" ltr LIs* 8v9° ots" z06" os6* 9-
Ir’ cz" Lty’ zon" Les* soz’ sve" Tee" 096" 6 - a
st" vez" 960° 19S" s9° 8SL° su8° Lee" 896° zI-
Te" zLe* bls" ovo" LIL" sos* z06" Ts6° 9L6° sT-
62° 9s" zs9° OTL" 9LL" 6s" 926° 196" 786° 8I-
Let ves" €@L" €LL" vis" 988° se" £6" 86" Te-
n° ££9° 98L° 178° T8* 916" 196" 186° 066° ve
ss° TL" ers" ls" 806° Tre" €L6° 186° £66" Le-
19° v8L" 988° ote: Lee" 6s6" 186" 166" S66" oe-
(rd OT S 7 € z T o Se- a
Agysuoquy oTFeIL ‘N

seozy UeqIN UT UOTSSTUSUeTL eSeg-0j-2TTGOW “UO ST TOI TUSUeTL
euO 4seeT }e WEY} USATD ‘SOeTITSUEIUT OTFJeEAL WUeZeTZTIAG A0ZJ YU  I/S FeUR AQTITGeGorad “Ee ETAL


Table 2. Probability that i (Out of Possible m) Transmitters Assigned
to a Channel are Transmitting

(U is the total channel utilization, U = (J2/60) m, where J is number of trans-
missions per hour by a transmitter and & is average transmission length in
minutes.)

U, Channel Utilization
i 0.25 0.5 1 2 3 4 5 10
0 -7788 6065 -3679 -1353 0498 0183 -0067 4.54(10">)
1 1947 +3033 +3679 +2707 1494 +0733 -0337 -0005
2 -0243 -0758 -1839 -2707 2240 -1465 -0842 0023
3 +0020 0126 +0613 -1804 +2240 1954 -1404 -0076
4 -0001 -0016 0153 +0902 -1680 1954 1755 -0189
5 0000 +0002 -0031 0361 -1008 -1563 1755 0378
6 -0000 +0005 0120 -0504 -1042 -1462 0631
7 -0001 -0034 0216 0595 1044 -0901
8 -0000 -0009 0081 0298 0653 -1126
9 0002 0027 -0132 0363 -1251
10 -0000 -0008 0053 -0181 1251
11 +0002 -0019 0082 -1137
12 -0001 -0006 0034 -0948
13 -0000 -0002 +0013 0729
14 -0001 -0005 0521
15 -0000 -0002 0347
16 0000 0217
17 0128
18 (m>15) -0071
19 -0037
20 0019
21 -0009
22 -0004
23 0002
24 -0001
25 0000
(m>30)

17


Kleinrock, L. (1975), Queueing Systems Volume 1: Theory (John Wiley & Sons,
N.Y.).

Lusignan, B. (1978), Single-sideband transmission for land mobile radio, IEEE
Spectrum, 15, No. 7, pp. 33-37.

Okumura, Y., E. Ohmori, T. Kawano, and K. Fukuda (1968), Field strength and
its variability in VHF and UHF land mobile radio service, Review of the
Tokyo Electrical Communication Laboratory, 16, No. 9-10.

Utlaut, W. F. (1978), Spread-spectrum principles and possible application
to spectrum utilization and allocation, ITU Telecommunication Journal,
, No. 1, pp. 1-13.

Wilmotte, R. M., and B. B. Lusignan (1978), Spectrum-efficient technology
for voice communications, UHF Task Force Report (Federal Communications
Commission, Washington, D.C. 20554).

Zehna, P. W. (1970), Probability Distributions and Statistics (Allyn and
Bacon, Inc., Boston).

390



Assume that:

(a) All base stations are located at the center of a circle of
radius a that encloses the metropolitan service area.

(b) All antennas are omnidirectional and are at the same height,
and all transmitters have the same power.

(c) Mobile units of all networks are located randomly in the
circle, so that the probability that an area contains a
mobile is proportional to the size of the area.

(4) The propagation law is P_ = K/aTM, where P| is the received
power in watts, K is a constant, d is the distance from
transmitter to receiver, and ® is a constant. (This is the
power form of equation (2).) For transmission between one
high (base) antenna and one low (mobile) antenna in a
builtup urban area, 4 *3 (Jakes, 1974).

(e) The total interference from n interferers is caused primarily
by the nearest interferer, so that the total interference
can be approximated by a constant times the interference
from the nearest interferer. (See Appendix A for justifi-
cation of this assumption.)

(£) Networks operate independently.

Assumptions (a) and (c) imply that the expected value of the distance
to the nearest of N interferers is o/VN, where Q is a constant (see Appendix
A). Combining this with assumption (d), we find that the interference from
the expected distance to the nearest interferer is

a
2

K Ky . (11)

Ie ——— =
OL

1 em og

Equation (11) and assumption (e) imply that the total interference is just a

constant times this;

Ne

Teotal =vN ' (12)

where V is the combination of all constants.
Now assume that in situation a we have an exclusively spread-spectrum

LMR service that is fully loaded--there are so many users that performance

12



SPECTRAL SHAPE

Information
I

Spreading Code

‘ eeeNFE_e
Spread So NN
s

tp Filter
if\t Bandwidth
vr

|

Demodulated
Signal
(After First Demodulator)

cw
Interference
(Before First Demodulator )

-12— Filter

Demodulated
CW Interference

,
‘
1
1
(After First Demodulator) t
1

|

PSK
Interference
(Before First Demodulator)

aN ON

-y2—Filter
PSK
Interference

7
H
i)
i)
(After First Demodulator) H
i)
+

ST

Figure B.7. Spectral shapes of the information, SS codes, and pro-
cessed SS signals and interference.

56



the radio frequencies are between about 150 MHz and 900 MHz; so our propaga~
tion model is an approximation to that suggested by Okumura et al. (1968)
and quoted by Jakes (1974). The model assumes that the base station antenna
is high (greater than 30 m), and the mobile antenna is low--generally less
than 4 m.

The formula for median received power is

P| (dBW) = ERP (dBW) - [33.2 + 20 log £(MHz) + 20 log d(km) - 6] (1)
- [G + H log d(km)] ,

where ERP is the effective radiated power of the transmitter and G is the
receiving antenna gain.

The quantity in the first brackets is the free space transmission loss
and the term in the second brackets is the "urban loss." The constants G
and H depend on frequency, antenna heights, and path lengths. Table 1 shows

these constants for several values of these parameters.

Table 1. Constants for Urban Propagation Loss Given in Equation 1

(Base station antenna height is 200 m; mobile antenna height is 1.5 m.)

Frequency G H
150 MHz 19 10
d < 30 km 450 MHz 20 10
900 MHz 23 10
150 MHz -25.6 40.3
30 < d < 100 km 450 MHz -31.7 45.35
900 MHz -37.75 50.35

For a fixed pair of antenna heights, fixed antenna gains, and fixed frequency,

note that (1) has the form
P (dBW) =A-Blogd , (2)

where B = 20 + H. For path lengths less than 30 km, which includes most

|
|
|



4.2 FM Interference to SS

Assume FM power is P. and that there is a transmission in an average
channel w fraction of the time. So the time average power in a channel is w
w Pie As before, assume an Ss aystem with 3 MHz bandwidth overlaid on the
FM service. There could be 35 kuz 120 FM channels, and the average inter-
ference power in the 3 MHz bandwidth is 120 w P- If the pdf of path lengths
is the same, and the SS transmitter also has PL watts power, then the mean
signal-to-interference power input to the SS receiver is 1/(120 w). If w

is 1/10, input S/I * -11 dB. If the SS system realizes all 30 4B of its

processing gain, the output S/I of 19 dB is satisfactory. An implementation
loss as high as 9 dB would be acceptable.

As before, there is the possibility that an FM transmitter very near
the desired receiver could interfere with the signal from a remote SS mobile.
It is difficult to analyze the probability of this happening because there
would probably be many more FM mobiles than SS mobiles. The situation would
probably need to be resolved by actual field testing or computer simulation.

The potential seems sufficiently promising to encourage further investigation.

5. CONCLUSIONS

We have analyzed the feasibility and spectrum efficiency of using
spread-spectrum modulation in a land-mobile radio service containing many
independent networks. The cases analyzed are shown in Table 4. In a band
allocated exclusively to spread-spectrum systems, base stations and mobile
stations would have to operate on separate channels so that the total bandwidth
required by the service would be twice that of the SS system. Base stations
all would have to be located near each other. In this configuration, the
worst interference occurs in the mobile-to-base channel.

Analysis of a simplified model of the service and computer calculations
for a more realistic model both show that such a spread-spectrum service
would not be as spectrum-efficient as conventional FM land-mobile radio.

This result is a particular example of the "near-far problem." The calcula-
tions did not include the possibility of central control of all mobiles trans-

mitted power because "central control" is the antithesis of "independence."

However, One or more spread-spectrum systems probably could be overlaid

on an existing FM band without causing unacceptable interference to the

27



FORM OT-29 U.S. DEPARTMENT OF COMMERCE
(s-7a) OFFICE OF TELECOMMUNICATIONS

BIBLIOGRAPHIC DATA SHEET

T, PUBLICATION OR REPORT NO] 2. Gov't Accession No, [3. Recipient's Accession No.

NTIA Report 78-11

4, TITLE AND SUBTITLE 5, Publication Date
November _1978

SPECTRUM EFFICIENCY FOR MULTIPLE INDEPENDENT SPREAD- 6. Performing Organization Code

SPECTRUM LAND MOBILE RADIO SYSTEMS 910.01

7. AUTHOR(S) 9% Project/Task/Work Unit No.

Leslie A. Berry and E. J. Haakinson

8. PERFORMING ORGANIZATION NAME AND ADDRESS
U.S. Department of Commerce 9101112
National Telecommunications & Information Administration | 10. Contract/Grant No.
Institute for Telecommunication Sciences
Boulder, Colorado 80303

11, Sponsoring Organization Name and Address 12, Type of Report and Period Covered
Federal Communications Commission
Office of Plans & Policy

1919 M St., NW 13,
Washington, DC 20554
14, SUPPLEMENTARY NOTES

15, ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant
bibliography ot literature survey, mention it here.)

The use of spread-spectrum modulation in a common type of land-mobile radio ser-
vice is studied. The radio service contains many networks operated independently,
similar to the business land-mobile radio service. Network independence implies
(among other things) that there is no central control of a transmitter's radiated
power. A congested urban environment is assumed.

If a band is allocated exclusively to spread-spectrum modulation for such a ser-
vice, base stations and mobiles must operate on different channels, and all base
station antennas must be located within a relatively small area. In this case, the
worst interference is in the mobile-to-base channel.

An explicit formulation of the "far-near" problem and a powerful computer calcu-
lation both show that in such a service spread-spectrum modulation is less spectrum
efficient than conventional FM modulation. In fact, the spectrum efficiency of the
spread-spectrum systems is inversely proportional to the cube root of the processing

gain. However, overlaying a spread-spectrum system on conventional bands shows
ome promise

16. Key Words (Alphabetical order, separated by semicolons)

Land mobile radio; spectrum efficiency; spread spectrum.

17, AVAILABILITY STATEMENT 18. Security Class (This report) 20. Number of pages
(4 unuimitep. Unclassified 65
19. Security Class (This page) 21, Price:

(J) FOR OFFICIAL DISTRIBUTION.
Unclassified

3EU.S. GOVERNMENT PRINTING OFFICE: 1979-0-677-948/243 USCOMM-DC 20716-P73



less than 0.34 (the value for U = 20) and is probably less than 0.2. Even
if the bandwidth is 30 MHz, the reliability must be much less than 0.64,
which is about the probability of getting on the FM channel immediately.
The reliability is probably less than 0.4.

In each of these examples, the conventional FM systems get comparable
reliability with less total bandwidth than the SS systems or better reli-
ability in the same bandwidth. So FM is more spectrum efficient than SS in
these examples.

Of course, a general rule cannot be proven with examples. But these
examples, using realistic assumptions about the systems and the environment,
agree with the analytical result derived in Section 2.3.2 for a simpler
model. The two results together provide a convincing argument for the
general conclusion: for a land-mobile radio service consisting of many
independent networks, spread-spectrum modulation is less spectrum efficient

than conventional channelized frequency modulation.

4. OVERLAYING A SPREAD-SPECTRUM SYSTEM ON AN EXISTING SERVICE

Because SS systems use low spectral power density and are resistant to
narrowband interference (Dixon, 1976), it has been conjectured that one or
more SS systems could operate in a service band already assigned to conven-
tional LMR without unacceptable interference to any user (Utlaut, 1977).
This section contains a first-order analysis of the probability of intersys-

tem interference for this possibility.

4.1 SS Interference to FM

Assume a single SS system overlaid on an occupied FM LMR service and
assume that the base stations of both systems are near the center of the
city. Assume that both FM and SS transmitters have equal power, Py. Assume
that the bandwidth of the SS system is 3 MHz so that its average spectral
power density is 10° PL/3 W/Hz. The bandwidth of an FM receiver in 25-kHz

channels is about 16 kHz; so it receives

-6 -3
ter192 10 P, = 5t107> PL

L 7 eo we, (26)
a i

where Ly is the transmission loss on the interfering path. Assuming no other

interference and that wanted and interfering paths have the same pdf, the

24


SPECTRUM EFFICIENCY FOR MULTIPLE INDEPENDENT SPREAD-SPECTRUM
LAND MOBILE RADIO SYSTEMS

*
Leslie A. Berry and E. J. Haakinson

The use of spread-spectrum modulation in a common type of
land-mobile radio service is studied. The radio service contains
many networks operated independently, similar to the business
land-mobile radio service. Network independence implies (among
other things) that there is no central control of a transmitter's
radiated power. A congested urban environment is assumed.

If a band is allocated exclusively to spread-spectrum
modulation for such a service, base stations and mobiles must
operate on different channels, and all base station antennas
must be located within a relatively small area. In this case,
the worst interference is in the mobile-to-base channel.

An explicit formulation of the "far-near" problem and a
powerful computer calculation both show that in such a service
spread-spectrum modulation is less spectrum efficient than
conventional FM modulation. In fact, the spectrum efficiency of
the spread-spectrum systems is inversely proportional to the
cube root of the processing gain. However, overlaying a spread-
spectrum system on conventional bands shows some promise.

Key words: Land mobile radio; spectrum efficiency; spread spectrum.

1. INTRODUCTION

With increased demand for land-mobile radio (LMR) services, the Federal
Communications Commission (FCC) has had to increase the communications
capacity of the LMR services. They have split channels and added new spec-
trum bands. (The newest band is the one between 806 and 947 MHz added by
Docket #18262.) The FCC is now investigating the spectrum efficiency of
different technologies and modulation techniques for delivering the service.
An example is the "narrowband technology" described by Lusignan (1978) and
discussed in more detail by Wilmotte and Lusignan (1978) .

Another technique is suggested by Cooper and Nettleton (1977), by
Utlaut (1978), and by the CCIR (1978a). This technique uses spread-spectrum
(SS) modulation--a technique often used to overcome jamming and to hide

covert signals below conventional signals or noise (Dixon, 1976).

* +
The authors are with the U.S. Department of Commerce, National Telecommuni-
cations and Information Administration, Institute for Telecommunication
Sciences, Boulder, Colorado 80303.


TABLE OF CONTENTS (continued)

Page
LAND-MOBILE RADIO SIGNAL CHARACTERISTICS. .......-. 49
B.2.1 Conventional LMR Modulation-FM.......... 49
B.2.2 Digitized Voice. . ... 2... ee eee ee eee 49
B.2.3 Digitized Data. .........-2 445450888 49
SPREAD SPECTRUM IN LM RADIO... .-.-+-+.-+ ++ ee es 50
B.3.1 Spread-Spectrum Concept. . .. 2... ee ee eee 50
B.3.2 Types of SS Techniques and Modulation. ...... 51
B.3.3  Spread-Spectrum Processing Gain. ......... 52
B.3.4 Required Bandwidth for Desired Processing Gain . . 57
B.3.5 Spread-Spectrum System Synchronization Problems. . 57
B.3.6 Spread-Spectrum LMR in Multipath ......... 58
REFERENCES. . - e562 ee ee ee ee ee ee ee 61

vi


is at the threshold of unacceptability. The users achieve the required
input signal-to-interference ratio (S/T) the required percentage of the
time, but no more. In this situation, the SS systems have rf bandwidth Bur
and there are an average of No simultaneous interferers. (The total number
of users is assumed to be proportional to N,-)

We now compute the relative spectrum efficiency of a spread-spectrum

service with greater bandwidth, By: Let

B=FB , (13)
where F > 1, and increase the number of users to the threshold of unaccept-

ability. Because the processing gain of spread-spectrum systems increases

linearly with bandwidth, this will happen when

w

a
(S/T) = By (S/T) = (S/T) /F . (14)

Here I, is the total interference from Ny simultaneous interferers in situa-
tion b. We have assumed that the average signal strength, S, is the same in
both cases, because the coverage area and the transmitter power remain con-

stant. Substituting from (12) into (14) and simplifying yields

1 1
= Oz (15)
N a/2 FN a/2
b a
or 2
Ny a
yi F . (16)
a

Because the service area and time have been kept constant, the relative
spectrum efficiency is given by the relative number of users per unit band-

width. Rewrite (16) as

Met Fa ga e/% a an
(2) BL pl-2/a

B

a

1-2/0

Since F > 1 and a > 2, F > 1. Therefore,

13


2. INTERFERENCE AND SPECTRUM EFFICIENCY OF MULTIPLE INDEPENDENT NETWORKS IN
AN EXCLUSIVE SPREAD-SPECTRUM LAND-MOBILE RADIO BAND

In this section we analyze the mutual interference between independent
LMR networks operating in a band allocated exclusively to similar spread-
spectrum radio systems. The paradigm is the business land-mobile service.
We assume that each network has a base station and several (or many) mobiles
communicating with that base station, and that the networks operate inde-
pendently of each other. The spectrum efficiency of such networks is com-
pared with the spectrum efficiency for similar networks using conventional
FM LMR systems.

The general form of the definition of spectrum efficiency is (Berry,
1977b; CCIR, 1978b)

communications achieved .

spectrum space used

For land-mobile radio, we take this to mean

number of users achieving specified service quality and reliability
bandwidth x area x time denied to other uses .

In actual calculations, we fix the area and time denied to others. In some
comparisons, we also fix the specified service quality and the bandwidth
and compare the number of users achieving the desired service. In this case,
the ratio of the efficiencies of two services is the ratio of the number of
users in the two services. In other comparisons, we fix all variables
except bandwidth and compare the bandwidths necessary to achieve the services.
In this case the ratio of the efficiencies is the ratio of the bandwidths.

First, we derive simple analytical formulas for the interference in
spread-spectrum bands. The implications of the formulas allow us to limit
the number of ways that the service might be configured to duplex systems
with base stations located in close proximity to each other. Then the spec-
trum efficiency of spread-spectrum systems relative to conventional FM
duplex systems is calculated with a computer’ program implementing a proba-
bilistic model of radio system interaction. For all cases evaluated, the FM
systems are more spectrum efficient than the spread-spectrum systems.

We assume that the LMR systems operate in an urban environment because

that is where the greatest need for spectrum efficiency is. We assume that


The mean transmission loss assumed is an empirical fit to the curves

given by Okumura et al. (1968):
Ly = 33.2 + 20 log fun + 20 log, d+G+tHiogd , (25)

where G and H are given in Table 1 of Section 2. For a fixed frequency, and
for paths less than 30 km, (25) reduces to a constant plus 30 log d. It is
the variation with distance that is important.

The transmission loss is assumed to be log normally distributed with a
standard deviation of 9 dB (Okumura et al., 1968). This combines the fast
and slow fading.

Although we are interested in the interference-limited case, ambient
urban noise was added to the interference to provide a natural limit to per-
formance when there are only a few interferers. We assumed urban, man-made
noise is log normally distributed at 150 MHz with the mean noise power equal
to -184 dBW +10 log b, where b is the receiver bandwidth in hertz. The

standard deviation of the noise is 6 dB.

3.3 Computed Probability of Communications

The number of interferers, Noy was varied to compute P(S/(I+N) > RIN,
interferers). (Notice that the number of transmitters on, k = N, + 1.)
Figure 4 shows this probability as a function of Ny every 3 dB from R = -30 dB
to R = 6 dB.

The small and negative input S/I ratios are appropriate for spread-
spectrum systems. Although the probabilities are actually discrete, those
for a given R have been connected with a smooth line to identify them.

Figure 4 and Table 2 [or equations (21) and (23)] provide the data to
evaluate (20)--the probability of communications. Table 3 contains this
probability for the conditions shown. To simplify calculation and use of
Table 3, we assumed that communications were certain if there were no inter-
ferers. Although this is not true, the error in the entries in Table 3 are
correct within a few percent for practical LMR systems.

Notice that the probability of communication gets quite low for
Ny > 10, even for very small S/I ratios. For example, the probability that
S/I > -24 dB is less than 0.5 when there are 20 simultaneous interferers.

19



NTIA-REPORT-78-11

Spectrum Efficiency for Multiple
Independent Spread-Spectrum
Land Mobile Radio Systems

L. A. Berry

E. J. Haakinson

U.S. DEPARTMENT OF COMMERCE
Juanita M. Kreps, Secretary

Henry Geller, Assistant Secretary
for Communications and Information

November 1978



input signal-to-noise ratio. Thus, it is expected that FM channel width will
remain at 25 kHz or greater. As we shall see later, spread-spectrum communi-
cations in land-mobile applications will require bandwidths much greater than
25 kHz.

In the next section, we will consider the effects of propagation on the

LMR channel, and following that we will consider noise and interference.

B.1.2 Propagation Effects on the Land-Mobile Channel

In the typical land-mobile radio application, one end of the communica-
tion system is fixed in location with its antenna high above the average
terrain, on top of a building or hill, with as few obstructions close to the
antenna as are physically controllable. The other end of the system is mobile,
with its antenna usually about 2-3 m (6-10 ft) above the local terrain and
with all sorts of surrounding obstructions such as other vehicles, tall
buildings, and irregular terrain.

Whether the system is to be used in the city or in the country, the sig-
nal path between the mobile and its fixed base station is rarely ever line-
of-sight and usually is a composite of many scatter paths. Thus, as the
mobile unit moves along a particular street or road, the geometry of the
scatter paths from the mobile back to the base station change. The phase and
amplitude of each scatter path signal contribute to the composite signal in
such a way that the received signal amplitude is not constant but instead is
rising or falling continually. This propagation effect is called fading
(Arredondo and Smith, 1977; Hansen and Meno, 1977).

The signal level fading has two definite features: one feature is short-
term or short-distance and is called Rayleigh fading; the other is apparent
over the long-term or long-distance and is log-normal fading. Figure B.1
shows a recorded received mobile signal level which demonstrates both fading
features; the rapid, deep fading occurring over short distances and the slow,
shallow fading over long distances. For each half-wavelength (approximately)
of forward movement of the mobile, the received signal goes through a Rayleigh
fade, which occasionally is as much as 30 to 40 dB. This fading is due to
the many signals, transmitted by the base station, which arrive at the mobile
antenna out of phase with respect to each other, and either enhance or cancel

each other. The amplitude distribution of the received signal level is

42



Now, using (2)

S= A, - By log ays aBw, (3)

I= A, - By log dys dBw . (4)

In general, Ay # Ay because of different ERP of mobile and base stations and
different antenna heights, and possibly By Fal Bor because of different path
characteristics. Let C be the signal-to-interference (S/I) ratio (in deci-
bels) required at the terminals of T,'s receiving antenna in order to produce

the desired output S/I. That is, we require that

s-I>c. (5)

Substituting from (3) and (4) yields

- - >
(Ay A) By log ay + By log a, 2c ,
or
B C+A,-A.
log ad, - = log d, > 21 1 qdBw. (6)
2 By 1 By

Transform from decibels above a watt to watts and rearrange to get

(C+A,-A,) /B.
a,>{a rw 7b 2, (7)

27 1
Equation (7) is an explicit formula for the (deterministic) "near-far problem"
(Dixon, 1976).

The distance a, is the separation required between two independent base
stations if Ty is to be able to hear its mobiles at distance ay in an inter-
ference-limited environment. For conventional LMR systems, this distance is
sometimes called the frequency re-use distance.

Suppose that an SS LMR system requires an output S/I of 10 dB and has
30 dB processing gain. Then C = -20 dB. Assume the bases and the mobile
have equal effective radiated power and equal antenna gains, that the mobile
antenna is 1.5 m above ground, and the base station antennas are 200 m above
ground. Because the antennas of Ty and T, are so high, we can assume free-
space transmission between them; that is, G = H = 0, so A, = ERP + G - 33.2

2
and Bo = 20. Using the constants in Table 1 for a frequency of 450 MHz,


paths of interest in a metropolitan area, B = 30. This form is useful for
approximate analytical analysis.

The distribution of the received power around the median is assumed to
be log normal. Actually, as explained in Appendix B, the short-term fading
has a Rayleigh distribution, and the long-term fading is log normal. To
simplify initial analysis, the distributions are combined and assumed to

have a log normal distribution.

2.1 Why Multiple Independent SS Networks Must Be Duplex

The following derivations apply generally to co-channel operation, but
the specific parameter values assumed to get numerical results are appro-
priate for SS systems in urban areas.

In a half-duplex channel (used for transmitting and receiving by both
mobile and base stations), the worst interference comes from a base station
to another base station trying to receive a transmission from a mobile.
This situation is illustrated in Figure 1, where mobile radio My is trans-
mitting the desired signal, S, to its base station Th which is ay km away.

At the same time, another base station, Tor a, km from T. is transmitting

1
to its network. Transmitter T,'s signal, I, is interference to the My - Ty
link.
Ta
de
e
M, d, T

Figure 1. Geometry for analysis of base-to-base station interference to
a mobile-to-base transmission. A base station at T, is trying
to receive a mobile station at My while a base station at T,

is transmitting.


passing through the first PSK demodulator, the received signal is stripped
of the rapidly changing phase due to the code, and all that remains is the
slowly varying phase due to the information. This signal passes through a
narrowband filter, and the information bit sequence is recovered.

Note, in Figure B.6, the results when cw interference or an unmatched
PSK interference signal is received. The correlator switches the constant
phase of the cw signal at a rate equal to the code sequence. The result is
that the cw interference spreads from an infinitesimally small bandwidth to
a bandwidth equal to the code's bandwidth. Also, the PSK interference has
its phase altered by the correlator, and its resulting bandwidth is either
equal to or greater than the correlator code bandwidth. Thus only the desired
signal becomes narrowband after passing through the receiver correlator.

Figure B.7 shows the spreading and despreading of the signals and inter-
ference. The information, with its relatively slow bit rate, has a narrow
[(sin x) /x]? amplitude. The code has a wide [(sin x)/x]? amplitude spectral
shape due to its fast bit rate. When the information is superimposed on the
code, no noticeable change can be noted in the spectral shape. Then, when
the receiver correlates its code with the signal, the information spectral
shape is recovered. Notice, in Figure B.7, what happens to the spectral
shapes of the cw interference and the PSK interference as they pass through
the receiver correlator.

The spread-spectrum receiver's processing gain is defined by

Bee

info

where Bie is the rf bandwidth of the transmitted spread-spectrum signal and
Bi nfo is the information bandwidth (Dixon, 1976). For the PSK example given,
the signal-to-noise ratio output of the receiver's second PSK demodulator

is

S/Nout * (s/m,,) S '

where S/N, is the signal-to-noise ratio at the input to the receiver's first
PSK demodulator. Suppose the required output S/N is 12 dB and the processing
is 20 dB; then the input S/N can be as low as -8 dB and the system will per-

form as required.

55



The exponent of SS is 1/3 for a = 3. This can be interpreted to mean that
the spectrum efficiency for these kinds of spread-spectrum systems is in-
versely proportional to the cube root of the processing gain.

Recall that it was assumed that the interfering transmitters were ran-
domly located in a circle and had equal power. Therefore, this result says
nothing about geostationary satellite-to-earth systems (in which all paths
are the same length) or about systems in which the base station equalizes the

power from mobiles.

A.4 REFERENCES

Abramowitz, M., and I. A. Stegun, Editors (1964), Handbook of Mathematical
Functions, National Bureau of Standards, Applied Mathematics Series 55
(Superintendent of Documents, U.S. Government Printing Office, Washing-
ton, D.C. 20402).

Gumbel, E. J. (1958), Statistics of Extremes (Columbia University Press,
N.Y.).

38



Substituting q = 0.37 yields

(30)

if both are transmitting.

Assume each SS mobile transmits t fraction of the time; then the prob-
ability of an SS mobile interfering with an FM mobile can be derived as
follows:

We take the conservative view that interference occurs when two trans—
missions overlap totally or partially and aj/a, S 0.37. We further assume
that the average message lengths in both systems are approximately equal and
short compared to the statistical interval--e.g., l-minute message lengths
and l-hour observation intervals. Thus, to a first approximation, if mobile
transmissions in one network occur t fraction of the time, overlap with a
mobile transmission of another network occurs approximately 2t fraction of
the time. For small t's, the probability of overlap x 2t; for larger t's,
the relationship is more complex, and the probability of overlap is less than
2t. Then, an FM mobile transmitting can expect interference with a prob-

ability of

P(interference) = p(ss transmission overlaps and a< 0.37)
w

& (2t) (0.07) 2 0.14t . (31)

For t = 0.25, which might represent a busy hour, the probability of in-
terference is about 34 percent; for t = 0.1, it is about 1% percent. For

large t, the maximum probability of interference is, or course,

a.
P(interference) = of < 0.27) = .07 . (32)
max qo
w
The analysis for several overlaid SS networks is. more complicated. It
seems likely, however, that one SS network (say a digital, semi-secure police

network) could be overlaid on conventional FM services without undue prob-

ability of interference to the FM service.

26


*Z@ATSO9T STTGou e Ze TeAeT TeUbTS ‘T'q eznbTa

I
|
|

a

{e)
m

Al

°oOo000
=~ am +

{o)
N

J whos ® eoyoigia

ZHW G29 = ADNSNOSYS

°°

gp ‘jeAe7 jouBbIis paalaooy

43


mean input S/I is 1/ (51077) = 200, or 23 dB. This is well above the desired

FM threshold of 10 dB; so the FM receiver will not be bothered by the inter-
ference. If S/I is log-normally distributed (normal in decibels) with a
standard deviation of 10 dB, then S/I > 10 dB 99 percent of the time. It is
calculations like this that have led to the suggestion that an overlaid SS
system would not interfere with FM systems.

However, an SS mobile transmitter near an FM base station trying to

receive a remote FM mobile might cause unacceptable interference. If the

. wo _ 3 . .
propagation law is given by P received =K Pi/a , then the input S/I is

[using (26) ]

ay
= (=) 200 , (27)
w

where a, is the distance to the wanted FM mobile and a; is the distance to

the interfering SS mobile. Then S/I is unacceptable (less than 10 dB) if

4, 3
(=) 200 < lo
Ww
or
a3
q < 105° © 0.37 (28)
Ww

provided both transmitters are on.
Assume that both networks have the same number of mobiles randomly

located in a circle of radius r so that the pdf of path lengths is

2 2
fy (ay) =F a; and £4 (a) a) a, -
i a w x

Then the probability that a,/a, < q can be shown to be (Zehna, 1970, p. 213)
2
qe
>
1--4, if q21
2
2q

ifq<l
. (29)

25



Cline, Robert W. (1973), Pseudo random modulation - an effective means of
enhancing PSK signal transmission in a diffuse multipath environment,
South Western IEEE Conference (SWIEECO) Record, Houston, Texas, April.

Cox, Donald C. (1972), Time-and-frequency-domain characterizations of multi-
path propagation at 910 MHz in a suburban mobile-radio environment,
Radio Science, 7, No. 12, December.

Cox, Donald Cc. (1977), Multipath delay spread and path loss correlation for
910-MHz urban mobile radio propagation, IEEE Trans. Vehicular Tech.,
VT-26, No. 4, November.

Dixon, R. C. (1976), Spread Spectrum Systems (John Wiley & Sons, New York).

FCC (1974), Rules and regulations, Vol. VII, Part 21 - Domestic Public Radio
Services, and Volume V, Part 89 - Public Safety Radio Services, Part
91 - Industrial Radio Services, and Part 93 - Land Transportation Radio
Services, Federal Communications Commission.

Hansen, Fleming, and Finn I. Meno (1977), Mobile fading - Rayleigh and log
normal superimposed, IEEE Trans. Vehicular Tech., VT-26, No. 4,
November. ——

ITT (1973), Reference Data for Radio Engineers (Howard W. Sams and Co., Inc.,
New York).

Jakes, William C., Jr. (1974), Microwave Mobile Communication (John Wiley
and Sons, New York).

Kelly, Thomas C., and John E. Ward (1973), Investigation of digital mobile
radio communications, Department of Justice, Law Enforcement Assistance
Administration (NTIS Access. No. PT-231-329).

Longley, A. G., and P. L. Rice (1968), Prediction of tropospheric radio
transmission loss over irregular terrain, a computer method - 1968,
ESSA Tech. Rept. ERL 79-ITS 67 (NTIS Access. No. 676-874).

Longley, A. G. (1978), Radio propagation in urban areas, OT Report 78-144.

Okumura, Y., E. Ohmori, T. Kawano, and K. Fukuda (1968), Field strength and
its variability in VHF and UHF land mobile radio service, Review of the

Toykyo Electrical Communication Laboratory, 16, No. 9-10.

Schwartz, M., W. R. Bennett, and S. Stein (1966), Communication Systems and
Techniques (McGraw-Hill, New York, N.Y.).

62



Appendix B of this report gives a short introduction to spread-spectrum
techniques in the context of land-mobile radio service. Readers unfamiliar
with spread-spectrum techniques should read Appendix B first. More complete
and general discussions are given by Dixon (1976), Utlaut (1978), and the
CCIR (1978a). Haakinson (1978) gives an annotated bibliography on the sub-
ject.

Utlaut quotes Costas (1959) as showing that, under certain assumptions,
wideband systems should be more spectrum efficient than narrowband systems.
One assumption is that each user transmits only a small fraction of the
time--a situation qualitatively similar to some business LMR services. In
principle, each SS user would have instant access to the shared, wideband
channel without disabling interference.

This exciting possibility was investigated in the study reported here.
The study is limited to services containing multiple independent networks in
an urban environment. Network independence implies that there is no dynamic
central control of any transmitter's radiated power and that the transmission
times of different networks are independent. We assume that the processing
gain of a spread-spectrum system is a reasonable upper bound for the actual
performance gain. This is equivalent to assuming that potential gains from
nearly orthogonal codes or (for frequency hoppers) good filters are approxi-
mately balanced by implementation losses. To the extent that this assumption
is valid, the conclusions apply to all spread-spectrum systems, but the
validity is easier to demonstrate for direct sequence systems. A probabilis-
tic analysis of an LMR service using SS modulation exclusively was reinforced
by a more realistic computer calculation. This analysis is shown in Sections
2 and 3. For these conditions, we conclude that spread-spectrum modulation
would not allow as many users with a specified reliability as conventional
FM modulation in the same total bandwidth.

Another possible use of spread-spectrum systems, suggested by their
resistance to jamming and the low power density of their emissions, is to
overlay them on conventional service bands (Utlaut, 1978). This possibility

is investigated in Section 4. There is some potential for this application.


where Py = P(k transmitters are on).

Let U = Jm%/60, where J is the average number of transmissions per hour
by each transmitter, m is the total number of transmitters assigned to the
channel, and % is the average length of a transmission in minutes. Then U

is the total number of message hours per hour and (Kleinrock, 1975, p. 105)
m uk -1

Po ~ he, | ‘ ”

we, igo ymmyyi << 1. (22)

Notice the U must be less than or equal to m.

For k > 0,

. (23)

These formulas are based on the usual assumption that the distribution
of transmitter turn-ons is exponential, and the distribution of message
lengths is poisson (Kleinrock, 1975). Table 2 shows Py as a function of k
for various N.

Berry (1977a) describes a computer program that calculates the other
factor in (20), P(S/(N+I) > R|k transmitters are on), when given the statis-
tical distributions of system parameters, path lengths, and propagation

loss. This program was used with the input described in the next section.

3.2 Distributions of Input Parameters

As a result of the analysis in Section 2.2, we assume that all base
station antennas are located in close proximity near the center of a metro-
politan area. Mobile stations are located randomly inside a circle with
radius 30 km, which is large enough to enclose most metropolitan areas.
Other calculations show that the results are not very sensitive to the size
of the circle; as long as it encloses most stations of interest (Berry,
1977a). The probability density function (pdf) of the distance from the

base station to a random mobile is then

fi@=e—“ a. (24)

a (30)?

This distribution applies to both wanted and interfering signal paths.

16


. *uoT}eTNpou
butfex-33TYS-eseyd souenbes joortp Sbutsn weisAs umazjoeds-peeazds eTdwexe uy -Gg‘q eanbTy

b=O ‘L=I $l (4m) soo y=(“+ uw 44m) sooy )
b=9 ‘O=I gH! (4+ O+4M) sory | _ _
O=9 ‘b=I dH! (0+ 4 414) sooy [7 TOO=S |
O=9 ‘O=I }! (4m) $09 y |
b=I HH (244m) sory
| = (4) 145
O=I H (4m) soo y |
ny (4 << a
aouanbas aj0Y 418) (429}Dy 419)
Asoulg wn uly
Buipoaads aouanbas aouanbag
' JO} fWUSUDIL Aaouig Aaoulg
(4) 'S OL JO DdIday Buipoaids UOl}OWJOJUT
Payojow 49DxXQ asion
JODiNpowag :
ASd OL HOLIMS HOLIAS Ly HOLINS |,
d = T |
(yis 4S ? foubig poasds WSd wes WSd 1M S007
souasapajuT payojnpoy

(HSd) pakay
4}14S @sdYq


G=13dB, K,=0.5, Kg=L0 (all Curves) G=13dB, K,=0.5, p=0.5(all Curves)

=1 —'
10 rs ee es Se <
19°?
103
R
104
15
108 ! 1 it |
0 2 4 6 8 0 12 14 0 2 4 6 8 0 i 14
E_/No (dB) (e) Eb/Ny (dB) ¢£)
4 G=13 dB, K=1.0, p=0.5 (all Curves) 4 K,=0.5, Ko=1.0, p=0.5 (all Curves)
10 TT TTT 10 TT
102} oe
103 103}
Re R
10-4 10-4 4
1G = OdB
26 = 1348
105 wt. 3 = 2008 |
08 wei 1 1 1 yy
0 0 2 4 6 8 0 k 14
Ep/No (dB) = (9) Eb/No (dB) (h)

Figure B.8. (continued) Comparison of FSK, PSK, and SS system
performance in Rayleigh fading.

60



constant that depends on frequency and the transmitter power.

transmitters have the same power.

We assume all

In the LMR bands, for paths less than 30

km, & * 3 for transmission from a high base station to a mobile in an urban

environment; 0 x 4 for transmission over smooth land between two low antennas.

Assume that the total interfering power is the sum of the powers from all

interferers:

n
K

K

i
I 1+
1 } m=2

m1 [EG )]*  [EG) y~

f-

iE }}
E(x)

Recursive application of (A-10) shows that E(x)) /E (x, ) is independent of
m

a
eh
m=2 E (x)

(A-12)

r and of n. Table A-1 shows values of E(x,) /E(x,) and the factor in brackets
in (A-12) for m = 1--10 and a

Table A.1

= 3 and 4.

. Ratios of the Expected Values of Ordered Distances

from Random Points to the Center of a Circle

OS x, Sx, 5%, 8 eee 2x, < see
E(x) fs (x. )\? mfztx,)\? E(x.)\4 mfe(x,)\ 4

= amy G2) Ges) GS) i¢ =)

m m 1 1 m 1 1
1 1.0000 1.0000 1.0000 1.0000 1.0000
2 0.6667 0.2963 1.2963 0.1975 1.1975
3 0.5333 0.1517 1.4480 0.0809 1.2784
4 0.4571 0.0955 1.5435 0.0437 1.3221
5 0.4063 0.0671 1.6106 0.0273 1.3494
6 0.3694 0.0504 1.6610 0.0186 1.3688
7 0.3410 0.0396 1.7007 0.0135 1.3815
8 0.3183 0.0322 1.7329 0.0103 1.3918
9 0.2995 0.0269 1.7598 0.0081 1.3998
10 0.2838 0.0229 1.7827 0.0065 1.4063

33



The first three or four interferers contribute most of the interference.
For a = 3, interference from the expected location of the second closest
interferer is 5 dB below that from the nearest interferer, the third inter-
ferer is 8 dB down, and the fourth is 10 dB down. The approximation,

Ty w2° qr is accurate enough for crude analyses like that in Section 2.3.2
of this report.

However, a more rigorous and accurate derivation of (17) in the main
report is possible. First, an accurate approximation to (A-12) is derived.
The idea is to approximate the‘sum of higher-order terms in (A-12) by multi-
plying the average value of the terms by the number of terms. Table A-1
shows that E(x,)/E (x) is a slowly varying function of m for m > 5. Also,
combination of equations (A-7) and (A-9) yields an approximation for

E (x) /E (x) :

1
E(x,)/E(x)) aa nL . (A-13)
Trial shows that the geometric mean,
E(x,) E(x,) *
Ea) ER) , (A-14)
Kk n

is a better approximation to the average of terms with index higher than k

than the arithmetic mean. So

a a
k /E(x,) E(x,) >
1 vii fa \2
Ie 1, gl + } im,) + (n-k) Tm) 5 fami (A-15)

m=2

for k <n. The sum of the first k terms and E(x,)/E(x,) can be found in
Table 1. For a = 3, n = 10, and k = 6, the error in (A-15) is only two
units in the fourth significant digit. For k = 3, (A-15) is correct to two

digits.
A.3 THE SPECTRUM EFFICIENCY AS A FUNCTION OF BANDWIDTH

Now, follow the outline of the analysis in Section 2.3.2 of the report.
The assumptions are as follows:
(1) interferers are randomly located in a circle with radius r

around the base station;

34



B.2 LAND-MOBILE RADIO SIGNAL CHARACTERISTICS

B.2.1 Conventional LMR Modulation-FM

In the past, land-mobile radio has been used primarily for the trans-
mission of analog voice, which has a bandwidth of about 3 kHz at baseband.
The FCC rules for nongovernment land mobile allow F3 (FM) modulation to be
used with 5 kHz frequency deviation in the 25 kHz authorized channels and
15 kHz deviation in the 50 kHz channels (FCC, 1974). Frequency modulation is
preferred because of the FM improvement factor, but A3 (telephony) modulation
also is allowed.

For either F3 or A3, analog voice is the signal that modulates the car-
rier. However, for spread-spectrum systems, digital signals are preferred
over analog as the source signal; thus digitized voice and digitized data

signal characteristics are discussed next.

B.2.2 Digitized Voice

To digitize voice, the voice signal must be sampled at a sufficient
sampling rate, and a sufficient number of quantization bits must be used so
that the message is understandable when the digital signal is converted back
to analog voice. However, listener intelligibility or tolerance allows quite
a large range in data rates. Rates from 10000 bps to 64000 bps have been sug-
gested, with a rate of about 30000 bps giving acceptable performance (assuming

8 bits of quantization per sample and 6000 samples per second).

B.2.3 Digitized Data

For some applications of LMR such as in the land transportation (taxis)
and public safety (police and fire protection) services, the use of hard-copy
terminals is desired. This allows the user to have a permanent copy of the
message, but it also requires that digital data be transmitted. Although
information can be transmitted faster as digital data than as analog voice,
the digital data must be coded carefully to detect and correct errors which
result when the digital signal fades into the noise. A listener can adapt
his comprehension of a voice message as the voice signal fades; i.e., as the
signal fades, the listener usually can guess what was lost in the message

because of the message context on either side of the fade. Or if the listener

49



3.4 Spectrum Efficiency of SS Systems

Table 3 can be used as a trade-off table to compare the efficiency of
spread-spectrum LMR systems to conventional FM LMR systems. The approach is
to assume both kinds of systems operate in the same metropolitan area and
handle the same amount and type of traffic. If we require that they do so
with the same reliability, the relative spectrum efficiency will be the
ratio of the total radio bandwidth required to provide the service. Alterna-
tively, we can give both systems the same bandwidth and compare their com-
munications reliability.

In all cases, we assume a voice signal with 3 kHz bandwidth. We assume
that FM channels are 25 kHz wide, and the systems have sufficient power so
that reliability is nearly perfect in the absence of interference. This is
the same assumption made in constructing Table 3. We do not count transmis-
sions from mobiles in the same network as interference because we assume
circuit discipline is maintained by the base station. We assume that both
systems require an output S/I of 10 dB.

We also assume that the performance gain of spread-spectrum systems is
equal to the processing gain, (total bandwidth)/(3 kHz). This is equivalent
to assuming that the implementation loss is balanced by the gain realized
from use of nearly orthogonal codes or (in frequency hopping systems) good
filters. It turns out that the difference in efficiency of SS and conventional
systems is very large; so a more accurate assumption is probably not required.

Relative spectrum efficiency will now be computed for several examples.
We begin with an example with very small total utilization because Costas
(1959) concluded that wideband systems would be more efficient in this case.

Example 1: Assume 10 networks, each with a base station and 6 mobiles.
Each mobile transmits 1 minute per hour. Each FM network could be given an
exclusive channel, and hence "perfect" reliability under the assumptions, in
a total of 25 kHz <x 10 = 250 kHz total bandwidth.

On the other hand, Table 3 shows that the SS system gets comparable
reliability (0.98) if R = -30. (For this traffic, U = (60°1)/60 = 1.) This
requires a processing gain of 40 dB--or a system bandwidth of 104 (3 kHz) =
30 MHz! Comparing another way, if the SS bandwidth is 250 kHz, the processing
gain is 19 dB; so the required input S/I is R= -9. The reliability is only
0.845 for this case.



of the frequencies try to exit from the filter at the same instant. The
collapsed signal is like an impulse at the filter's output.

Frequency synthesizers with the range and speed required are probably
too expensive to compete in the business LMR market. So in our discussions
for land-mobile applications, we will concentrate on the direct sequence

methods and, in particular, the PSK and FSK forms of modulation.

B.3.3  Spread-Spectrum Processing Gain

A direct sequence spread-spectrum system transmits and receives a code
whose sequence is known to both the transmitter and receiver. Because the
receiver does not initially know exactly where in the code sequence the
transmitter will start and because of the time lags in propagation and com-
ponent transit, the receiver must first acquire, synchronize, and track the
transmitted code. Once the receiver is "locked" to the transmitter, it can
decode the information.

The code occupies a wide bandwidth relative to the information's band-
width. For each information bit, there will be 100 to 1000 (or more) code
bits or chips that are transmitted and received. The system can achieve a
processing gain if the information is superimposed on the code. Because of
this superposition, the narrow information bandwidth is spread out to the
wide code bandwidth. The receiver correlates the received signal with its
own replica of the code. If the receiver code is locked to the transmitter
code, then the output from the receiver correlator is the narrow bandwidth
information. This signal passes through a narrowband filter which is a
matched filter to the information. It is the correlating and filtering pro-
cesses which give the receiver its processing gain to interference.

As an example, consider a spread-spectrum system where both the informa-
tion and code are used to PSK (phase-shift-key) modulate the carrier (see
Figure B.5). The information is a binary sequence of 1's and 0's at a bit
rate of r bits per second. The code is also a binary sequence, but at a
much higher bit rate of R chips per second. The information bit stream phase
modulates the carrier at the first PSK modulator, and the code bit sequence
further modulates the carrier at the second modulator. An example of the bit
sequences and the output carrier phase sequences is shown in Figure B.6.

Note the long period of the information bit relative to the code bit. After

52



(for p = 1 the reflected signal is specular, whereas when 0 = 0 it is dif-
fuse) .

Compare Figures B.8(a) and (b). Note that the curve labeled 1 in Figure
B.8(b) is identical to the curve in Figure B.8(a) labeled ideal PSK in a non-
fading channel. Curves 2, 3, and 4 are to be compared with the ideal PSK in
a Rayleigh fading channel curve. Curves 2, 3, and 4 consider static rela-
tionships between the direct and reflected signal whereas the fading PSK
curve of Figure B.8(a) is dynamic (see Figure B.2).

Figure B.8(c) shows the dramatic improvement available with PSK spread
spectrum using a processing gain of 13 dB. Increasing the gain offers little
improvement as shown in Figure B.8(d).

Figures B.8(e) through B.8(h) show the effects of multipath when it
isn't entirely diffuse. Figure B.8(e) considers the case when the multipath
energy is within the SS receiver's correlation filter window (i.e., the
direct signal and the multipath signal are separated by less than one chip's
time length). Note that as the multipath gets more diffuse, the spread-
spectrum system's multipath rejection improves. Figure B.8(f) shows that as
more of the multipath energy is outside of the correlation window (i.e., K,
approaches 0), the SS system's multipath rejection again improves. Finally,
Figures B.8(g) and (h) demonstrate how the SS system behaves with nondiffuse
multipath that is within the correlation filter window as a function of Kj
and G.

Cox (1972 and 1977) shows measurements of the average multipath time de-
lay spreads in urban and suburban environments.

In all cases, spread-spectrum system performance is markedly better than
nonspread-spectrum system performance. Of course, this improvement has been

bought with the additional bandwidth.
B.4 REFERENCES
Arredondo, Gaston A., and John I. Smith (1977), Voice and data transmission
in a mobile radio channel at 850 MHz, IEEE Trans. Vehicular Tech., VT-26,

No. 1, February.

Brennan, D. G. (1959), Linear diversity combining techniques, IRE Proc.,
June.

61





Table B.2

(151.4975
152
152.255
152.465
152.495

152.855 —-

153.7325
154.46
154.6375
157.45
157.725
157.755
158.115
158.475
158.715
159.48
161.625
173.2

450
451
454
455
456
459
460
462.5375
462.7375
465.0125
467.5375
467.7375

806
821
825
845
851
866
870
890
928

Service Groups Within the LMR Bands

(continued)

- 152

- 152.255
- 152.465
- 152.495
- 152.855
153.7325
- 154.46

- 154.6375
- 156.25

- 157.725
- 157.755
- 158.115
- 158.475
- 158.715

- 159.48

- 161.575
- 161.775
- 173.4

- 451
- 454
- 455
- 456
- 459
- 460
- 462.5375
- 462.7375
- 465.0125
- 467.5375
- 467.7375
- 470

- 821
- 825
- 845
- 851
- 866
- 870
- 890
- 902
- 947

41

PS,I,LT
DP
PS,I,LT
DP
PS,I,LT
PS,I,LT
PS,I,LT

PS,1I,LT


APPENDIX B. CONVENTIONAL LMR AND SPREAD-SPECTRUM BACKGROUND

B.1 THE LAND-MOBILE RADIO CHANNEL
B.1.1 Land-Mobile Radio Frequency Bands

Land-mobile radio (LMR) serves both nongovernment and federal government
users; however, the LMR frequency bands have been divided to allocate separate
spectrum space to nongovernment needs and government requirements. The LMR

bands are given in Table B.1.

Table B.1. LMR Frequency Bands

Government. Non-Government
30-50 MHz 25-50 MHz
162-174 MHz 150-174 MHz
406-420 MHz 450-470 MHz

470-512 MHz (some cities only)
806-947 MHz

The Federal Communications Commission (FCC) has divided each nongovernment
band into smaller groups called Services such as Public Safety, Industrial,
etc. The nongovernment bands, as they are divided into the various services,
are shown in Table B.2.

Specific channel assignments within each band are made for both non-
government and government LMR. The channel widths are normally from 25 kHz
to 50 kHz, depending upon the band and the service, with allowed emission
bandwidths less than the channel widths. Attempts have been made to reduce
the channel widths to 12.5 kHz, which would double the number of available
channels in the already congested LMR bands. However, since frequency modu-
lation (FM) is the most widely used form of modulation in LMR, the 12.5 kHz
channel width would lead to less allowable frequency deviation for the FM
systems. This results in a lower FM improvement which, in turn, means that
the performance of the communication system is reduced; i.e., the LMR user

would have to tolerate more noise and more interference for a given level of

39





2.2 Why SS LMR Base Stations Must Be Located Close Together

Consider a wanted, base-to-mobile transmission in a duplex system. In-
terference comes from other bases sharing the same channel, as illustrated

in Figure 2, where the two base stations, T, and Toe are r km apart. The

1
wanted signal from Ty to M) has power
S=A,-Bloga, . daBw
The interference is
T= A, - B log a, . dBW

As before, assume that at the antenna terminals of My we require that

S-1I>c. Then

A, ~ A, - Blog d) + B logd, 2c
or

d (C + A, - A,)/B

=> 10 a eR. (9)
4,

Tf R=1, a,/4, = 1 is the perpendicular bisector of T,T,- Performance is

unacceptable (S - I < C) to the right of this locus. As Freeman (1972)

shows, if R#1, 4,/4a, = R defines a circle with radius
2
xr ir/(R* - a]. (10)

If Tv!) and Ty are on the x-axis of an (x,y) coordinate system with T) at the

origin, the center of the circle is at (r/(l - R’) , O). TE R? <1, as it
usually is for SS systems, the circle contains Tr and the region of unaccept-
able interference (S - I < C) is inside the circle. If R? > 1, the circle
contains Ty) and S - I < C outside the circle. This is the conventional LMR
case in an interference-limited environment (I >> N).

Assume identical base stations so that A, = Ay: For paths less than

1
30 km, B = 30 (from Table 1). If the processing gain is 30 dB and the

required output S/I is 10 dB, then C = -20 dB and R = 1072/3 = 0.2154. Then
the radius of the denied circle is 0.226 r. If T, is 10 km from Ty then

mobile stations cannot receive messages from T, inside a circle containing

1


The desired properties of spread-spectrum systems listed by Dixon (1976)
include the following:

(1) selective addressing,

(2) code division multiplexing,

(3) low power spectral densities,

(4) message privacy,

(5) high resolution ranging, and

(6) interference rejection.

Items (1), (2), and (6) are the primary advantages to be gained by using
spread-spectrum techniques in land-mobile radio, along with instant access to

the channel.

B.3.2 Types of SS Techniques and Modulation

The types of techniques used in spread spectrum are as follows:
(1) direct sequence,

(2) frequency hopping,

(3) chirp, and

(4) hybrid of the above methods.

The direct sequence technique usually uses PSK (phase-shift-key) or FSK

(frequency-shift-key) modulation of the carrier. Other spectrum conserving

modulation methods such as MSK (minimum-shift-key) also are used and, in fact,

are sometimes preferred.

The frequency hopping technique has available m discrete carrier fre-
quencies, each separated by the width of the information bandwidth. Thus,
the total bandwidth is m times the information bandwidth. The transmitter's
carrier frequency jumps from one of the m frequencies to another in a pre-
scribed manner known to both the transmitter and the receiver.

Chirp spread-spectrum systems have primarily radar and navigation
applications. Chirp signals are generated by sweeping the carrier from a
low frequency to a high frequency, delta F, in a certain time period, T.

The resultant signal is spread over the bandwidth of delta F, or more, for
the time duration T. In the receiver, the chirp signal is processed by a
filter with the characteristic that the lower frequencies in the chirp signal

are time delayed longer than the higher frequencies. The result is that all

51



B.3.4 Required Bandwidth for Desired Processing Gain

For land-mobile spread-spectrum systems, the processing gain should be
at least 20 dB, or a 100 to 1 code rate to information rate ratio. Pre-
viously, we suggested that digitized voice required from 10000 bps to
64000 bps. Assuming this is the range of the information rate, the required
rf bandwidth would have to be from 1 to 6.4 MHz.

For illustration, we choose a digitizing rate of 30 kbps. Although this
is not strictly a part of the spread-spectrum process, by digitizing the
voice we have spread its spectrum from 3 kHz to 30 kHz. In demodulating and
converting the digital 30 kHz signal back to the analog 3 kHz signal, we
have an available processing gain of 10 dB. This can be added to Sor less

any realization losses.

B.3.5 Spread-Spectrum System Synchronization Problems

Code synchronization has to be accomplished before any information can
be received, and synchronization is probably the most difficult function that
any SS system has to perform. In addition, code acquisition and synchroniza-
tion problems are compounded when interference is present. Conceptually,
the receiver must slide its replica of the code along with the incoming code
until they are matched in time or correlated. The shorter the code, the
faster the correlation can be made. Here then is the trade-off. Shorter
codes result in shorter acquisition and synchronization times, but longer
codes result in much better cross-correlation characteristics. We would
expect that acquisition times longer than 1 sec would be unacceptable in LMR.
The SS LMR receiver must be synchronized within 1 sec after the user at the
transmitter end has pushed his microphone button to talk.

Two possible solutions to the synchronization problem are suggested.

The first is a synchronization preamble; the second is the use of passive
spread-spectrum devices.

Synchronization preambles are described by Dixon (1976) as an effective
technique for establishing synchronization between push-to-talk systems. At
the beginning of each transmission, a well-chosen code sequence (preamble)
is transmitted. The receiver's acquisition time depends upon the preamble's
length. Consider the following example. A spread-spectrum system has 3 MHz

rf bandwidth, a 30 kHz information bandwidth, and a 4095 bit synchronization

57



2.3 Approximate Analysis of Interference When Base Station Antennas
Are Co-located

2.3.1 Base-to-Mobile Transmissions

Fading of a signal received at a mobile from a high base-station antenna
is due primarily to scattering from objects near the mobile (Jakes, 1974). If
the antenna for the wanted transmitter is sufficiently near the antenna(s)
for the interfering transmitter(s), the signal and interference will fade
together. If all transmitters have the same power and radiate from the same
height, and if there are N interferers, then the signal-to-interference
ratio is 1/N, or -10 10535 N dB.

If a spread-spectrum system has 30 dB processing gain and requires 10 dB
output S/I, then the minimum input S/I = -20 dB. This implies that 100 base
stations could be transmitting simultaneously from the same location without
causing unacceptable interference at a mobile. Because each base station
would be silent part of the time (when listening to a mobile), an even
greater number of networks could operate satisfactorily.

By comparison, the 3 MHz of bandwidth necessary (at least) for a pro-
cessing gain of 30 dB would hold 120 25-kHz FM channels. For this situation,
the number of networks is roughly comparable. A more refined analysis that
accounts for the channel usage statistics would be necessary to. compute
which modulation is more spectrally efficient. This analysis will not be
pursued because mobile-to-base transmissions limit the number of SS networks

that can operate.

2.3.2 Mobile-to-Base Transmissions

In duplex systems, a mobile-to-base transmission is interfered with by
simultaneous transmissions from other mobiles. If all base stations are co-
located or proximate, then it is likely that some of the interfering mobiles
will be closer than the wanted mobile to the base stations. Interferers
close to the receiver have a disproportionate effect on signal quality be-
cause of the rapid attenuation of signal strength with distance. This is
called the "near-far problem" (Dixon, 1976). An approximate analysis of how
this interference affects the spectrum efficiency of spread-spectrum systems

follows.

ll


PREFACE

This study was supported by the UHF Task Force of the Federal Communica-

tions Commission.

iii


Section 6.2 of Abramovitz and Stegun (1964) ‘shows that

_ nix T(m+s) T (n-m+1)
Oc.) = Gon) rani)! 3 : (5)
T(n + 5)
2
Because k! = I'(k+1l),
B(x.) = x LOH Tow tas)

Pin + 3 Tom

The expected values can be calculated recursively beginning with the largest

by noting that for m=n, (A-6) reduces to

E(x.) = ay ri, (A-7)

and that

E(x) = form<n . (A-8)

E(x 1)
my Pa)

If n is large (say, 10 or more), E(x,) can be approximated with the first

term of (6.1.36) from Abramowitz and Stegun (1964):

x ofa
E(x,) =IOVE . (A-9)

tt
12 n°
When n >> 1, E(x,) is inversely proportional to yn as assumed in the

The relative error is of the order of

main report. The expected distance to the other points in order is

= me
E(x,4)) =" EG),m>1 . (A-10)

A.2 THE TOTAL INTERFERENCE POWER

The analysis of the relative efficiency of spread-spectrum LMR systems
in the main body of this report requires expressing the total interference
that arrives at a point in terms of the interference from the nearest inter-
ferer. Assume that the power from the m‘ nearest interferer is inversely
proportional to some power of the expected distance to the nth interferer;
that is,

1 =—K_ , w, (A-11)

m a.
(E(x) ]
* . « th . .
where Th is the interfering power from the mTM nearest interferer and K is a

32



*yx0] ey} UT UeATH esoyZ ere JuSUUOTTAUS

*szeTeJASUT sNosuejz[NuTS Jo equmu syz Jo uoTIOuns e se
‘py eanbta

pue szojeuwezed weqshs ouL
03-TeubTs aya yeuR AITITGeGord euL

4q ‘anqtea petTytToeds e speeoxe oT}Jer sdUueTezASAUT—

IN ‘saasapiayu] SnoauDyjnwig yo Jaquiny,
4 02
ol a S Ving

ro)
8
Ss

d

20

(sios9y,94u) !N | YZI/S)

x
S





Rayleigh distributed, hence the name Rayleigh fading. Figure B.2 shows the
expected received signal strength versus percent of time for a Rayleigh dis-
tribution. What the conventional FM LMR user actually hears in a multipath
environment has been described aptly by Arrendo and Smith (1977) for land-
mobile operations at 900 MHz:
"As a vehicle moves through the fading signal pattern, inter-

ruptions of the voice modulation can be heard, noise capturing the

FM receiver during the interruptions. These interruptions have a

different subjective effect as a function of the vehicle speed.

At low speeds, less than 5 mi/h, the rate of speech interruptions

is not as important as their duration. The effect is much like

the swishing sound heard when driving slowly with the window open

close to parked cars or closely spaced trees. At higher speeds,

up to 20 mi/h, the interruptions are heard as a series of 'pops'

or 'clicks', much like the sound made running down the street

hitting a picket fence with a stick. At speeds higher than 20 mi/h,

the interruptions blend into a low-pitched noise, the pitch in-
creasing with speed."

The long-term fading, which is apparent over a distance of 100 wavelengths
or more, is due to natural or man-made obstacles. The log of the received
signal amplitude has a normal distribution; hence the fading is called log-
normal fading. Figure B.3 shows an example received signal level with log-
normal fading. The mean and the standard deviation of the received signal
level depend upon frequency; antenna heights; terrain irregularity; and size,
construction, and density of buildings. There are methods to predict the
log-normal fading due to irregular terrain (Longley and Rice, 1968) or the
amount of urbanization (Jakes, 1974; Okumura et al., 1968; Longley, 1978).
Okumura's measurements (1968) show that the signal mean is about 5 dB (at
150 MHz) to 10 dB (at 900 MHz) higher in a suburban environment (mostly one
and two story buildings) as compared to an urban area (mostly multiple story
buildings) for the same antenna heights and separation distances. The log
normal signal's standard deviation is about 5-6 dB in urban locations and
7-8 dB in suburban areas.

Remedies exist to lessen the effects of Rayleigh fading; for example,
space or frequency diversity (Jakes, 1974; Brennan, 1959). However, we will
show later that spread-spectrum techniques also can help to lessen Rayleigh
fading effects.

44



Table 4. Configurations of Spread-Spectrum LMR Networks Considered
in This Report and Conclusions Reached

Assumptions: A service band is allocated exclusively to land-mobile
radio networks that use only spread-spectrum modulation. There are
many networks in the service band, and they operate without dynamic
central control of transmitter power or transmission time.

1. Bases and Mobiles on Same Channel

Conclusion: Base stations cause unacceptable interfer-
ence to mobile-to-base signals.

2. Bases on One Channel; Mobiles on Another
A. Arbitrary location of base stations, base-to-mobile
channel.

Conclusion: A mobile receives unacceptable inter-
ference in the vicinity of a base station of another
network. Thus, the areas around the base stations
of all other networks are denied to it, and the total
denied area is unacceptably large.

B. All base stations located close together.
(i) Base-to-mobile channel

Conclusions: Spectrum efficiency of SS systems
comparable to that of conventional FM systems.

(ii) Mobile-to-base channel

Conclusions: Interference from mobiles near
the bases to signals from mobiles further away
limits the number of networks achieving a spe-
cified reliability. This number is less than
the number of conventional FM LMR networks that
could achieve comparable reliability.

28



Comparing (A-24) with (A-22) shows that

a
2
+
Nit Fy
Ni+1] —
a

+
Ny +1

<P (a-25)

No+1
a

Both situations involve the same geographic area and the same time; so
the spectrum efficiency is proportional to the number of users per unit
bandwidth. Multiplying both sides of (A-25) by BL/B, and rearranging does

not change the inequality:

A)
B B 2/0
bl. a 2/0 _F = pe/o-l .

woyse FP => <1 (A-26)
a b
G )
a
provided that a > 2.
Finally,
Nit1 N+
< ; (A-27)
By Ba

that is, there are fewer successful users per unit bandwidth in situation b
than there are in situation a. Increasing the bandwidth of the spread-
spectrum systems decreased the spectrum efficiency.

To further appreciate the information in (A-26), assume that BL is the
bandwidth of the information to be sent. (Then the system in case a is not
strictly a spread-spectrum system; it is the limiting case of a spread-
spectrum system with the processing gain, G, = 1.) Then F = G_ for situation

b, and (A-26) can be written as follows:

+
Nyt

—b_ ~« i _
+ = =
Nit1 g 12/0
B P

. (A-28)

37



It should be pointed out that intermodulation and adjacent channel in-
terference prevent assignment of all FM channels in a practical LMR environ-
ment. Suppose that only one-half of all FM channels could be assigned because
of these problems. Then if each FM network is assigned one channel, the
total required bandwidth would be 500 kHz--one-sixtieth of that required for
SS networks with comparable reliability.

Example 2: There are 120 networks with an average of 10 mobiles per
network; each mobile transmits an average of 1 min/hr. Thus, U = 20.

(a) If the processing gain of an SS system is 40 dB and the

required output S/I is 10 dB, then the required input S/I
is -30 dB. The table shows that the probability of getting
this S/I is 0.64. For 3 kHz voice, this system would
require at least 30 MHz bandwidth.

(b) If the processing gain is only 30 dB so that the required
input S/I is -20 dB, the probability of success is only
0.34. This system would require at least 3 MHz bandwidth.

(c) On the other hand, assume 25-kHz FM channels. Each network
can have its own channel, with "perfect" reliability in 3 MHz
of bandwidth. Compare this with the reliability of 0.34 in
(b), which requires the same bandwidth, or the reliability
of 0.64 in (a), which requires ten times as much bandwidth.

As in Example 1, the total bandwidth required for the FM networks may
need to be increased to prevent intermodulation and adjacent channel inter-
ference. However, even if the bandwidth is doubled, SS still requires more
for comparable reliability.

Example 3: Assume 120 25-kHz FM channels in a 3 MHz band. Assign 600
networks, each with 5 mobiles that transmit 1 min/hr. This example represents
a well-loaded urban LMR band. Then for the FM networks on each channel, the
average channel utilization is 25/60 = 0.417, and the probability of finding
the channel free is only 0.61 (Kleinrock, 1975). The average waiting time
is about 0.71 %. After waiting (if necessary), the user transmits with nearly
perfect reliability.

For an SS system, the utilization factor U = 50. This isn't in the
table, but we can make estimates. If we confine the SS system to the same

3 MHz of bandwidth, so R = -20, the probability of communicating is certainly

23



AY = ERP + G. - 33.2 + 20, and Ay - Ay = 20. Also, By = 20 + 10 = 30. Sub-

stituting these values into (7) yields

3
v . 19 (720+20) /20 = a, . (8)

If T wants to receive messages from its mobile when the mobile is 10 km

away, then T, must be 31.6 km away. In most metropolitan areas, this would

mean that net even two base stations could operate simultaneously. But 30 dB
of processing gain for a 3 kHz voice signal takes at least 3 MHz bandwidth.
One LMR net that requires 3 MHz of exclusive bandwidth in a city is certainly
not spectrum efficient!

So increase the bandwidth to 30 MHz and assume the processing gain is

40 dB. Then
3

d,2d - 10 = .32 4,7 .

rw

If we set ay = 10 km, then a, > 10km. For this case, there could pos-
sibly be several base stations (LMR networks) in the same metropolitan area.
But there could be 20,900, = 1200 conventional LMR networks (with 25 kHz
channel spacing); each with an exclusive channel. If intermodulation and
adjacent channel interference allowed only half of these channels to be used,
there could still be 600 FM networks. The spread-spectrum half-duplex sys-
tems clearly would be very inefficient spectrum users.

Consider the effect of different assumptions. It is likely that the
transmitter power plus antenna gain of base stations will be greater than
that of mobiles. This would increase AZ AY and hence would increase the
required separation a,- On the other hand, it is possible that base-to-base
transmission is not quite as good as free space. As a limiting condition,
assume that base-to-base signals attenuate as much with distance as mobile-
to-base signals do; that is, that By = 30.

Then, for 30 dB processing gain,

If ay = 10 km, only a few SS networks could operate simultaneously in a city

compared to 120 conventional LMR networks; each with an exclusive channel.


0-2 ON \ 1073
\ \
Pe \ \ Pe
yo
-. \ -
10-3-— \ \ Nonfading to4 1K)= 0
\ Channels 2K,= Ot
\ ‘Noncoherent FSK 3 x _ Os
‘ s
Ideal PSK | "
194} — “ 4 5 4k, =
‘ ‘
109 | | | jf ! 106 ! |
0 4 8 2 1 20 24 2 2 4 #6 8 10 12 14
Ey /No (dB) E,/No (dB)
' (a) 1 (b)
0 TTT 0 T TTT
1
10-2 4 102 4
Pe Re
3 G=13 dB 2 K)=0.5, p=0
103}- (all Curves) 103 (all Curves), |
3
4} -4 4
° 1K,= Of 0 16 = OdB
2K) = 03 26 = 13dB
3K,= 1.0 3G = 20dB
175} 175 7
wei | 1 4 welt | | | |
0 2 4 6 8 0 2 0 2 4 6 8 1 12 14
Eb/No (dB) E,/No (dB)
fc) (a)
Figure B.8. Comparison of FSK, PSK, and SS system performance in

TT T T

Coherent FSK
OPSK
Ideal PSK

Noncoherent

Fading

Channels

2 G= 048 (all Curves

Rayleigh fading.

59



Signal Level (dB above mean)

PFE TTT TIT) Tle
0 = —_f
-|0 R— —
-20 -— Dist eater a
-30 --— —_
“ort | ti tt i tit | dio
B8 $53 828328 328

Percent Probability that Received
Signal Level is Less than Ordinate

Figure B.2. Signal level statistics for a Rayleigh distributed

received signal.

45

99.99


B.1.3 Noise and Interference in the LMR Channel

The noise experienced by a land-mobile receiver comes from sources which
are both internal to the receiver and external. However, the dominance of
one noise source over the other depends upon the receiver's operating fre-
quency. Figure B.4 shows this dependence of the received noise power on
frequency. At frequencies above 2 GHz, the receiver's own internal noise
usually dominates. Below 2 GHz in the urban environment and below 500 MHz
in the suburban environment, man-made impulsive noise dominates; and below
500 MHz in the quiet rural areas, atmospheric and galactic noise sources are
predominant.

Cline (1973) shows that spread-spectrum systems provide no noise power
reduction when only wideband Gaussian noise is present; i.e., the noise power
at the input to the receiver's IF filter is the same regardless of whether
or not spread-spectrum modulation is used ahead of the filter. We shall
show later that spread-spectrum systems do show an improvement when the
noise is narrower than the spread signal bandwidth. Thus, in most cases,
the spread-spectrum systems offer no improvement with impulsive noise present
since impulsive noise, both man-made and atmospheric noise, is very wide
bandwidth. For example, automotive ignition sparks are about 4 ns in dura-
tion, which relates to a 3 dB bandwidth of about 500 MHz. This is certainly
wider than conceivable land-mobile spread-spectrum bandwidths.

In many cases, land-mobile radio systems are not noise limited, but they
are interference limited. In large metropolitan areas, there may be thousands
of users all trying to share the same few multiple-user LMR channels. As a
result, channel discipline is tossed aside and it becomes "everyone for him-
self." In this environment, the user learns to tolerate the "party-line"
type of co-channel interference and to recognize those messages directed
toward him. There are methods to reduce the interference to which the user
has to listen, such as tone-coded squelch; however, if two co-channel users
attempt to transmit simultaneously, the receiver will detect both signals
with a possible result of a garbled message. On the other hand, spread-
spectrum systems result in signal-to-interference ratio improvements, if the

interference is narrowband.

47


T) with radius 2.26 km. Station T, denies a significant area in the city to
T,'s mobiles.
An exclusive spread-spectrum LMR band would have many networks and many

base stations sharing the band, each one denying an area to T. If these

1°
bases are scattered randomly over the city, the total area denied to the Ty
network is clearly unacceptable.

However, suppose that r = 0.1 km. Then the radius of the denied area

is only 23 m--a small spot very near T If all the base station antennas

are located on the same tall building or tower, then all the denied areas
would overlap the area in proximity to the tower. This situation might be
acceptable. We evaluate this possibility in Section 3.

Under the same conditions, but with a processing gain of 40 dB, the
radius of the denied circle is only 0.0226 r and the denied area is 5.11
(10°) x? km?. This might be acceptable even for r = 10 km.

However, there must be many networks assigned to the band to use this
much bandwidth (> 30 MHz) efficiently. A large number of stations like T,
randomly distributed over the area causes these effects:

(a) Interference from many sources at the mobile receiver

increases the denied area and distorts its shape.

(b) Some of the denied areas overlap and should not be counted

twice in a calculation of total denied area.

These two effects work in opposite directions; so for a crude estimate
of total denied area, assume that they cancel each other. Then the denied
area is about K * 5.11 (1074) r” km’, where K is the number of interfering
stations and r is the average separation of the stations. As shown in the
previous section, K > 1000 for efficient use of 30 MHz of bandwidth. For
points randomly distributed in a circle with radius 20 km, Y = 18 km (Crow,
1972), and the denied area is about 166 km? or 13 percent of the area of the
circle. This is probably unacceptable.

However, if all base station antennas are confined to a small area, r
is much smaller, and the denied areas effectively coincide. The conclusion
is that in an exclusive SS LMR band with multiple independent networks, base

station antennas must be effectively co-located.

10