NTIA Report 99-370

An Evaluation of the Proposed

Railroad VHF Band Channel Plan

J.M. Vanderau

E.J. Haakinson

U.S. DEPARTMENT OF COMMERCE

William M. Daley, Secretary

Larry Irving, Assistant Secretary

for Communications and Information

September 1999
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iii

CONTENTS

ABSTRACT........................................................................................................................ 1

1 INTRODUCTION .......................................................................................................... 1

2 SYSTEM DESIGN ISSUES........................................................................................... 2

3 RAILROAD VHF BAND PLAN ................................................................................... 3

4 EQUIPMENT STANDARD........................................................................................... 4

4.1 Receiver Sensitivity.................................................................................................. 5

4.2 Cochannel and Adjacent-Channel Rejection ............................................................ 6

5 CO-SITE ANALYSIS .................................................................................................... 8

5.1 Transmitter Combining Techniques ......................................................................... 8

5.2 Receiver Multicouplers........................................................................................... 11

5.3 Duplexers................................................................................................................ 12

5.4 Separate Antennas for Transmit and Receive......................................................... 14

5.5 Intermodulation Interference................................................................................... 15

6 SIGNAL COVERAGE ANALYSIS ............................................................................ 23

6.1 Land Mobile Communications Propagation Models.............................................. 24

6.2 Variability about the Median Propagation Loss ..................................................... 25

6.3 Excess System Link Margin ................................................................................... 30

6.4 Cellular Topologies ................................................................................................ 32

6.5 Adjacent-Channel Rejection, Cochannel Rejection, and Frequency Reuse Ratio

(Cell Cluster Size)................................................................................................... 35

7 TRUNKING AND TRAFFIC LOAD CAPACITY...................................................... 37

8 EQUIPMENT COSTS.................................................................................................. 39

9 AN ALTERNATIVE BAND PLAN ............................................................................ 40

9.1 Description.............................................................................................................. 40

9.2 Multichannel Passband and Guardband Requirements .......................................... 42

9.3 Intermodulation Interference................................................................................... 43

9.4 Trunking and Traffic Load Capacity ...................................................................... 44

9.5 Cellular Topologies ................................................................................................ 44

9.6 Comparison of the ITS and WCTF Band Plans...................................................... 45

10 SUMMARY, ISSUES, AND OBSERVATIONS ........................................................ 45

11 REFERENCES ............................................................................................................. 48
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1

AN EVALUATION OF THE PROPOSED RAILROAD

VHF BAND CHANNEL PLAN

John M. Vanderau and Eldon J. Haakinson*

ABSTRACT

As a result of the Federal Communications Commission’s radio spectrum

realignment initiative, land mobile radio manufacturers are being

encouraged to incorporate narrowband and trunking technologies into their

designs in order to efficiently utilize the radio spectrum. As new

equipment designs become available in the marketplace, users must infuse

these new systems into their existing land mobile radio infrastructures.

The railroad industry is developing a strategy to accomplish this migration.

This strategy includes defining a band plan for the efficient use of the

railroad VHF spectrum. In this report, the authors evaluate the railroad

industry’s rechannelization strategy, offer an alternate approach, and

conclude with comments regarding the efficacy of both railroad VHF band

plans.

Keywords: Band plan, channel plan, land mobile radio, WCTF, Project 25, railroad,

spectrum realignment, TIA-102, VHF

1 INTRODUCTION

The Federal Communications Commission (FCC) has encouraged land mobile radio

(LMR) manufacturers to incorporate narrowband (12.5-kHz bandwidth or smaller) and

trunking technologies into their designs to more efficiently utilize the radio spectrum,

particularly in the crowded very high frequency (VHF) bands [1]. Failure to comply with

this directive could result in the denial of FCC equipment type acceptance. Whereas this

directive does not affect current equipment designs, as the state-of-the-art in radio

technology continues to advance, new radio designs will incorporate digital narrowband

 

*

 The authors are with the Institute for Telecommunication Sciences, National Telecommunications and

Information Administration, U.S. Department of Commerce, Boulder, CO 80303.
2

technologies. Users should begin planning now to deal with migration and compatibility

issues when they introduce new equipment and systems into their existing LMR

infrastructures.

To address this issue within the railroad community, the railroads, radio equipment

manufacturers, and Government formed the Wireless Communications Task Force

(WCTF), an ad-hoc committee dedicated to solving radio communications issues unique

to the North American railroad industry. WCTF is currently considering how to best

migrate the railroad industry's existing 160-MHz wideband (15-kHz bandwidth) analog

LMR equipment to more modern, spectrally-efficient narrowband digital equipment.

In order to utilize the railroad VHF spectrum more efficiently, WCTF has proposed a

channel assignment scheme that accommodates trunking technology solutions and uses

the narrower channel spacings of the realigned railroad VHF spectrum. WCTF has

adopted radio equipment conforming to the Telecommunications Industry Association

(TIA) land-mobile radio standard TIA-102 [2], also known as Project 25.

The Federal Railroad Administration (FRA) wants to ensure that if the railroads adopt

this VHF band plan and the TIA-102 standard, railroad communications will not be

degraded. The Institute for Telecommunication Sciences (ITS) was tasked by the FRA to

determine whether the proposed rechannelization plan will provide the radio coverage

and system capacity needed to achieve these objectives.

2 SYSTEM DESIGN ISSUES

In order to assess the viability of the proposed band plan, several issues must be

investigated. These issues are:

• Performance of new equipment — within the constraints of the given channel

assignments, will the new equipment perform adequately? Is it backward-compatible

with legacy analog FM systems now in service? Is the new equipment a proprietary

design, or does it conform to recognized industry standards, thereby ensuring

interoperability between different vendors’ equipment?

• Channel assignments — are there enough radio channels to support all the business

processes of the railroad industry? Is the voice traffic loading equally distributed

across the available channels? Are there any techniques that can be employed to

increase the traffic capacity?

• Interference issues — will the proposed new equipment cause interference to the older

existing equipment? Will the older systems cause interference to the new systems? If

repeaters and base stations will be collocated (such as would be the case for trunked

systems), what is the likelihood that intermodulation interference will be present? If

present, can it be adequately suppressed? Are receivers likely to be subject to

desensitization? Will cochannel and adjacent-channel interference be a problem?
3

• Coverage — For a given level of speech intelligibility or effective data throughput,

will the proposed radio system provide adequate geographic coverage?

The authors explore these topics, evaluate options, and provide procedural guidelines that

LMR systems planners can follow when designing a new system. The proposed railroad

band plan is described in Chapter 3. In Chapters 4 through 8, the impact of equipment

selection, collocation of repeaters and intermodulation interference, VHF propagation,

adjacent-channel and cochannel interference, cellular topologies, and trunking on the

proposed band plan is described. Chapter 9 presents an alternate plan and compares it to

the railroad’s plan.

3 RAILROAD VHF BAND PLAN

The existing railroad VHF band plan consists of 181 frequencies, spaced every 7.5 kHz,

from 160.215 to 161.565 MHz [3]. The band plan proposed by WCTF is shown in

Figure 1. The two blocks of spectrum from 160.215 to 160.8075 MHz and 160.935 to

161.5275 MHz comprise 80 trunked duplex voice channel-pairs. The two blocks of

spectrum comprised of 5 channels apiece (from 160.815 to 160.845 MHz and 161.535 to

161.565 MHz) are non-trunked duplex channel-pairs. The remaining block of spectrum

consists of 11 simplex channels (from 160.8525 to 160.9275 MHz).

1

6

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(80) (5) (11) (80) (5)

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Figure 1. Railroad VHF band and WCTF’s band plan.

Trunking permits many users to share a finite number of radio channels, similar to how a

finite number of telephone lines interconnecting telephone central office switches can be

shared by a large number of individual telephone subscribers. These eighty duplex

channel-pairs are apportioned among ten trunk groups. Each trunk group has eight

channel-pairs; each channel-pair uses one frequency (channel) for transmitting and a

different frequency (channel) for receiving. At each radio base station site, collocated

transmitters and receivers are assigned operating frequencies from a given trunk group.

Frequency assignments at an individual site are not commingled with frequencies from

other trunk groups. The trunk groups are interstitially placed in the frequency domain, as

depicted in Figure 2.
4

duplex channel

T–R split 720 kHz

duplex channel

T–R split 720 kHz

duplex channel

T–R split 720 kHz

(96 x 7.5)

trunk group

channel spacing

75 kHz

adjacent

channel

spacing

7.5 kHz

trunk group

channel spacing

75 kHz

trunk group

channel spacing

75 kHz

freq

Figure 2. WCTF-proposed channel spacing. Trunk groups

are interstitially placed in the frequency domain.

All frequencies belonging to a particular trunk group are depicted with the same color

(and same vertical line length). Different trunk groups are differentiated by different

colors (and different line lengths). Within a given trunk group, adjacent channels are

spaced 75 kHz apart, and the frequency split between transmit and receive frequencies of

any particular channel-pair is 720 kHz. The 75-kHz channel spacing within any particular

trunk group allows all ten trunk groups to be “interlaced” in the frequency domain at

7.5-kHz channel spacings.

4 EQUIPMENT STANDARD

WCTF adopted TIA-102 as the radio standard for railroad radio systems in

February 1996. ITS agrees that adoption of this standard has merit because:

• TIA-102 provides a migration path by allowing existing legacy analog FM radio

equipment to interoperate with the newer, dual-mode narrowband, trunkingcapable equipment,

• adoption of the TIA-102 standard promotes interoperability between different user

communities, which could provide significant benefit in mutual aid situations

between the railroads, public safety, and other critical infrastructure services, and

• TIA-102-compliant equipment is capable of voice-only, data-only, or voice-plusdata operation, thereby eliminating logistics requirements for separate radios to

carry out these desired functions.

First-generation TIA-102 radios have a 12.5-kHz bandwidth, use digital modulation, and

are backward-compatible with analog frequency-modulated (FM) equipment, supporting

both 25- and 12.5-kHz bandwidths. Minimum performance parameters are cited in
5

various TIA documents [2, 4]. Second-generation TIA-102 radios will utilize 6.25-kHz

bandwidths, but presently the characteristics for these radios are not well established.

4.1 Receiver Sensitivity

ITS measured the digital and narrowband analog receiver sensitivity of a typical TIA-102

radio [5] by following TIA’s land mobile radio and digital transceiver performance

measurements documents [6, 7]. This data is presented in Figure 3. Measured sensitivities

were better than the manufacturer-advertised typical sensitivities for this radio in both

modulation formats.

Receiver Sensitivity 

-10

0

10

20

30

40

-140 -120 -100 -80

Power (dBm)

SINAD

(dBS)

0.1

1.0

10.0

100.0

BER

(%)

SINAD (dBS)

BER (%)

Figure 3. Measured receiver sensitivity of a typical

TIA-102 radio.*

Delivered audio quality (DAQ) is a figure of merit that indicates the intelligibility of a

speech signal,†

 and ranges in value from “1” to “5” [4]. ITS estimated the DAQs of

demodulated speech signals by using an automated computer technique that computed the

 

*

 Sensitivity for analog FM modulation format was measured using 2.5-kHz frequency deviation. For

wider bandwidths, sensitivity can improve by as much as 20 log(∆fwb / ∆fnb), where ∆fwb and ∆fnb are the

wideband and narrowband (2.5-kHz) frequency deviations.

† Delivered Audio Quality Metrics:

DAQ 1 Unusable. Speech present but not understandable.

DAQ 2 Speech understandable with considerable effort. Requires frequent repetition due to

 noise/distortion.

DAQ 3 Speech understandable with slight effort. Requires occasional repetition due to

 noise/distortion.

DAQ 3.4 Speech understandable without repetition. Some noise/distortion present.

DAQ 4 Speech easily understood. Occasional noise/distortion present.

DAQ 5 Speech easily understood.
6

auditory distance*

 between the received speech signal and its originally transmitted

(reference) speech signal [8]. This was done at a number of SINAD and BER reference

sensitivities. Auditory distance was then mapped to a DAQ score by using a previously

determined empirical relation. Figure 4 shows the DAQ values of speech signals, as

determined by ITS, at power levels corresponding to various BERs and SINAD ratios.

Also shown in the figure are TIA’s reference DAQ values.

Delivered Audio Quality 

0

1

2

3

4

5

-10 0 10 20 30 40 SINAD (dBS)

DAQ

(dimensionless)

100 BER (%) 10 1 0.1

SINAD (dBS)

TIA reference SINAD (dBS)

BER (%)

TIA reference BER (%)

Figure 4. DAQ vs. SINAD and BER.

A threshold effect is apparent in the ITS digital DAQ plot, above which DAQ values

remain relatively constant versus BER. This indicates an upper limit on the audio quality

from analog-to-digital conversion. It also demonstrates the error-correcting capability of

the TIA-102 vocoder. At operating points below this threshold (greater BER), the DAQ

begins to deteriorate rapidly. But even in this region, the perceived speech quality of the

digital signal still exceeds that of an analog signal.

This information can be used when determining the geographic coverage. The greater the

minimum level of speech intelligibility required, the smaller the geographic coverage area

will be for “acceptable” speech quality. Chapter 6 provides example computations to

determine the radio coverage area.

4.2 Cochannel and Adjacent-Channel Rejection

TIA-102 performance specifications [2] assume a channel spacing of 12.5 kHz or more.

However, since the railroad VHF band’s channel spacing is only 7.5 kHz, spectrum

 

*

 Auditory distance measures the perceived difference between two speech signals. When one speech

signal is a “perfect” reference signal, and the other speech signal is a distorted signal (e.g., radio

output), auditory distance corresponds to the perceived quality of that distorted signal relative to the

reference signal. When two speech signals are identical, the auditory distance between them is zero. As

the perceived differences between the two signals increase, the auditory distance increases.
7

overlap will occur between signals on adjacent channels. Therefore, adjacent-channel

rejection performance in 7.5-kHz channel-spacing environments is of interest.

Under varying conditions of adjacent-channel and cochannel interference, ITS measured

the DAQs of a typical TIA-102 radio’s demodulated speech signals [5], in a manner like

that discussed in Section 4.1. Results are presented in Figure 5.

Delivered Audio Quality with 15-kHz .

Adjacent-Channel Interference .

1

2

3

4

5

30 50 70 90

Interference Rejection Ratio, -C/I (dB) 

DAQ

(dimensionless)

d/D/15

a5/D/15

a5/A5/15

d/A5/15

Delivered Audio Quality of

Digital Signal with 7.5-kHz

Adjacent Channel Interference

1.0

2.0

3.0

4.0

5.0

0.0 20.0 40.0 60.0 80.0

Interference Rejection Ratio, -C/I (dB)

DAQ 

(dimensionless)

d/d/7.5

a5/D/7.5

Delivered Audio Quality with 

Cochannel Interference 

1

2

3

4

5

-20 -15 -10 -5 0

Interference Rejection Ratio, -C/I (dB) 

DAQ

(dimensionless)

a5/A5/0

d/D/0

Figure 5. Delivered audio quality of demodulated speech

signals under various interference conditions.

The interference modes depicted in the plots are:

(1) a digital signal interfering with a desired digital channel (d/D),

(2) a wideband*

 analog signal interfering with a desired digital channel (a5/D),

(3) a digital signal interfering with a desired wideband*

 analog channel (d/A5), and

(4) a wideband* analog signal interfering with a desired wideband* analog

channel (a5/A5).

 

*

 5-kHz peak frequency deviation.
8

Adjacent-channel and cochannel rejection performance impacts the physical separation

distance requirements between a receiver and undesired transmitters. The greater the level

of speech intelligibility required, the greater the distance between the receiver and

unwanted transmitters must be. This, in turn, influences base station siting and frequency

reuse planning parameters. In Chapter 6, a sample procedure is presented that delineates

the necessary steps to determine the required geographical separation between a receiver

and interfering adjacent-channel and cochannel transmitters.

5 CO-SITE ANALYSIS

This chapter reviews some of the methods used that allow multiple transmitters and/or

multiple receivers to share a common antenna at a fixed repeater or base station site.

Following that, example procedures are given to:

• identify possible receiver intermodulation frequencies,

• estimate power levels of intermodulation interference, and

• determine the degradation in noise figure and intermodulation rejection

performance.

5.1 Transmitter Combining Techniques

There are several methods to combine multiple transmitters so they can share a common

transmitting antenna. Typically, hybrid ferrite combiners or cavity combiners are

employed. These devices can combine RF signals at moderate power levels.

5.1.1 Hybrid Ferrite Combiners

Hybrid ferrite combiners, commonly referred to as hybrids, are useful in cases where

frequency separation between the combined transmitters is very small. They provide very

good isolation between transmitters closely spaced in frequency, are compact, and are

easily expandable to accommodate additional transmitters.

Hybrids are, however, more lossy than the bandpass-isolator type of combiners. A hybrid

combines two signals into one composite signal. Its insertion loss is approximately 3.2 dB

per hybrid; that is, a hybrid will reduce the output power of each signal presented to it by

about 3.2 dB. Figure 6 illustrates how hybrids can be used to combine up to four RF

signals.

Losses would be about 6.4 dB per channel (because there are two “tiers,” or “layers,” of

hybrid assemblies, the insertion loss is 2 × 3.2 = 6.4 dB). Extending this approach to

combine up to eight channels would require three “tiers” of hybrids and isolators, yielding

a per-channel insertion loss of about 9.6 dB. The limitations of using hybrids to combine

multiple transmitters quickly becomes apparent, with each factor-of-two increase in the

total number of combined transmitters adding 3.2 dB of attenuation to each channel.
9

TX 2 TX 3 TX 4

 to antenna

TX 1

 

 Load 

Hybrid

Lowpass

Filter Lowpass

Filter









 Isolator





 Isolator 







 Load 

Hybrid

Lowpass

Filter Lowpass

Filter

 





 Isolator





 Isolator

   

 Load 

Hybrid

Lowpass

Filter Lowpass

Filter









 Isolator





 Isolator





Figure 6. Four-channel transmitter hybrid-ferrite combiner.

5.1.2 Bandpass-Isolator Combiner

Bandpass-isolator combiners are constructed with ferrite isolators and band-pass cavities.

One such design is shown in Figure 7. Adjacent-channel rejection and spurious signal

suppression can be improved by cascading additional cavities in each transmitter’s signal

path. A cavity’s insertion loss is about 0.5 to 3 dB at its resonant frequency. The

insertion loss depends on the cavity’s selectivity (bandwidth and “steepness,” or “roll-off”

of the passband edges). Adjustable coupling loops determine a cavity’s selectivity.

Insertion loss increases as the coupling loops are adjusted to provide more selectivity.
10

Combined 

Transmitter 

Output 

Bandpass Cavity Filters

Bandpass Cavity Filters

































          

  

 



  

  

               

                  

  

    

 

      

Bandpass Cavity Filters

Open Circuit 

Tuning Stub

Coaxial

Junction

             TX 2

TX 3

TX 1































 

































































Isolator

    

 







 



 



 













 





 





 











 





 



Isolator







































 





























 



 







 



 



 

Isolator

Figure 7. Bandpass-isolator combiner.

Channel spacings cannot be as close in frequency as they can with hybrid ferrite

combiners. Most manufacturer product sheets recommend channel spacings on the order

of 200 kHz or so, but closer channel spacings are possible. Closer spacing requires

cavities to be tuned for the narrowest passband response (highest insertion loss), or a

greater number of cavities (each having less overall insertion loss, but wider frequency

passband) to be cascaded in series (greater physical volume and cost), or both.

5.1.3 Combination of Hybrid- and Cavity-Combining Solutions

Figure 8 illustrates a composite approach that utilizes both hybrids and cavities to

overcome the drawbacks of using only hybrids (high insertion loss for eight channels) or

only cavities (limited selectivity for close channel spacings).

In this scheme, “odd” channels, spaced every 150 kHz, are combined using cavities.

“Even” channels, also spaced every 150 kHz, are combined in a similar fashion. Finally,

these two “even” and “odd” channel banks are interstitially combined using a hybrid

coupler. The two channel banks are offset in frequency from one another by 75 kHz.
11

Bandpass Cavity Filters

Open Circuit

Tuning Stub

    







    

 







   

 

  

 

  

TX 8

TX 2

•

•

•

•

Bandpass Cavity Filters

150 kHz

Bandpass Cavity Filters

Open Circuit

Tuning Stub     

     

TX 7

TX 1

Hybrid

•

•

•

•

Bandpass Cavity Filters

150 kHz

75 kHz

to antenna

other “oddnumbered”

channels

other “evennumbered”

channels

Coaxial

 Junction















  

             

 

   

  

  

  

      



    

                

    

                 

            

 





























































Load

Coaxial

Junction

  

















  



  



  

  

 

       

  

 



  

 

     

  



  

                 

        





      





























   









































































Isolator

      









































































































Isolator



































 

































































































Isolator































 

 







 



 



 







 



 



 



 







 



 



 





Isolator

Figure 8. Composite cavity/hybrid combiner.

5.2 Receiver Multicouplers

To combine multiple independent radio receivers to a common receiving antenna system,

multicouplers are employed. Receiver multicouplers divide a multichannel signal into

several discrete receiver channels. This division reduces the strength of each signal

delivered to each individual receiver.
12

Preceding the multicoupler’s RF splitter with a preamplifier will offset these losses. If the

gain of the preamplifier is too great, though, the preamplifier will cause unacceptable

levels of intermodulation interference to the receivers that follow. Similarly, if the gain is

too low, receiver sensitivity will be worse than for an isolated receiver with no

multicoupler. Section 5.5 gives mathematical formulas to determine the effects of

multicoupler preamplifier gain on system noise figure, system sensitivity, and

intermodulation distortion.

5.3 Duplexers

Duplexers permit simultaneous operation of transmitters and receivers with a single

antenna. They are constructed from parallel sets of bandpass/band-reject filters. They

route RF energy flow from a transmitter to an antenna at one frequency, and from an

antenna to a receiver at a different frequency, while preventing the flow of RF energy

directly between transmitter and receiver. Figure 9 shows a block diagram of a cavitytype duplexer.

Bandpass Cavity Filters 

(at frequency F1)

Bandpass Cavity Filters 

(at frequency F2)

Band-Reject 

Cavity Filters 

(at frequency F2)

Band-Reject 

Cavity Filters 

(at frequency F1)

 

to / from 

T antenna 

r

a

n

s

m

i

t

t

e

r

(s)

R

e

c

e

i

v

e

r

(s)

Figure 9. A duplexer constructed from parallel cavity

filters.

Figure 10 shows a typical frequency response of a duplexer that has a 600-kHz separation

between transmit and receive frequencies.*

 For wider frequency splits (such as 720 kHz),

the curves are shaped somewhat differently, but the same general behavioral

characteristics will hold. These characteristics include a sharp “notch” (large amount of

attenuation) around some desired rejection frequency, minimum attenuation around some

 

*

 The data shown here are representative of manufacturers’ product sheets for a 600-kHz frequency split

at VHF. Of the publicly available product data reviewed, this frequency split was the closest

approximation to the proposed band plan’s 720-kHz frequency split.
13

desired pass frequency, and “moderate” attenuation of signals at frequencies more

distantly removed from the resonant pass and notch frequencies.

Typical Bandpass/Band-Reject Duplexer . 

Response Curve at VHF

0

10

20

30

40

50

60

70

80

90

-4 -3 -2 -1 0 1 2 3 4

Frequency Offset (MHz)

Insertion

Loss (dB)

Ant-RX

TX-Ant

TX-RX

Figure 10. A typical frequency response for a duplexer.

“Ant-RX” is the insertion loss between the

antenna and receiver. “TX-Ant” is the insertion

loss between the transmitter and antenna.

“TX-RX” is the isolation between transmitter

and receiver.

Figure 10 reveals a limitation of using duplexers (and, hence, a single antenna) at a

multichannel site. The useful passband and notchband are relatively narrow, and only in

cases where a multichannel site has just a few channels will a duplexer (and single

antenna) be a viable alternative.

Figure 11 shows the aggregate transmission bandwidth of a multichannel RF signal

utilizing WCTF’s band plan, along with the corresponding “guardband” between the most

closely-spaced transmit and receive frequencies. For example, an individual site

complying with the proposed WCTF band plan*

 but only using six of the possible eight

channels, would require a transmission bandwidth of (6 - 1) × 75 + 12.5 = 387.5 kHz. The

separation between the lowest-frequency transmit channel and the highest-frequency

receive channel would be 720 - 387.5 = 332.5 kHz.

 

*

 720-kHz TX-RX frequency split, 75-kHz channel spacing.
14

WCTF Channel Plan .

Multichannel Passband/ .

Guardband Requirements .

87.5

162.5

632.5

557.5

482.5

237.5

537.5

462.5

312.5

387.5

12.5

257.5

182.5

332.5

407.5

707.5

0

100

200

300

400

500

600

700

800

12345678

N = Number of Channels

Frequency

Passband/

Guardband 

(kHz)

Aggregate RF

Transmission

Bandwidth (kHz)

Frequency

Guardband

Separation

TX1 – RXN (kHz)

Figure 11. Passband and guardband constraints required of

a duplexer versus the number of channels, using

the WCTF band plan.

In summary, a duplexer approach, which would permit collocated repeaters and (duplex)

base station transceivers to share a single antenna, is suitable only for sites having just a

few channels. A greater number of collocated channels requires a different solution.

5.4 Separate Antennas for Transmit and Receive

Separate antennas, one dedicated for transmit and the second dedicated for receive, offer

distinct advantages over a single antenna/duplexer approach. Figure 12 shows the amount

of isolation between two vertically-polarized, vertically-collinear, dipole antennas versus

the vertical separation distance between them. Additional isolation between transmitters

and receivers can be obtained by using passband filters and taking advantage of their

frequency selectivity.
15

Spatial Isolation Between Vertically- .

Polarized, Vertically-Collinear .

Dipole Antennas at 160 MHz .

10

30

50

70

1 10 100

Vertical Separation (meters)

Spatial

Isolation

(dB)

Figure 12. Spatial isolation between two verticallypolarized, vertically-collinear dipole antennas.

Disadvantages to using separate antennas for transmit and receive include:

• antenna tower heights must be much taller to accommodate the second antenna,

• taller towers may be prohibited by local zoning ordinances,

• an additional antenna may be impractical on shared antenna tower facilities

because

- there may be no place on the tower to affix it such that there is adequate

isolation between it and other services’ antennas,

- the impact of additional antennas on the antenna tower’s wind/ice-loading

design margins may be a concern, and

• greater cost.

5.5 Intermodulation Interference

The preceding sections have presented several approaches to allow multiple transmitters

and/or receivers to share a common antenna. However, collocated transmitters and

receivers might be subject to intermodulation interference.

5.5.1 Determining Intermodulation Frequencies

Intermodulation interference arises from the unintentional mixing of two or more RF

signals in a transmitter or receiver. Consider a hypothetical multichannel site with
16

channel assignments belonging to one of the trunk groups*

 of the proposed WCTF band

plan. If channels 2, 3, 4, 7, and 8 are simultaneously transmitting, one possible

intermodulation frequency is

fIM = fE2(tx) + fE3(tx) + fE4(tx) – fE7(tx) – fE8(tx) (1)

 = 161.0400 + 161.1150 + 161.1900 – 161.4150 – 161.4900

 = 160.4400 = 160.4700 – 0.03 = fE4(rx) – 0.03

In this example, an unwanted intermodulation frequency is 30 kHz away from the

assigned frequency of the channel 4 receiver. Performing this calculation using any other

trunk group gives a similar result. That is, when channels 2, 3, 4, 7, and 8 at any

collocated site are simultaneously transmitting, one of the possible intermodulation

frequencies will be 30 kHz less than the tuned frequency of that site’s channel 4 receiver.

That is because the channel spacing within the trunk group and the transmit-receive

frequency split of each channel-pair are the same from one trunk group to the next.

This example would seem to imply that since the intermodulation product is more than

two receiver bandwidths away (30 ÷ 12.5) from the assigned frequency of the “channel 4”

receiver, the “channel 4” receiver would not be subjected to intermodulation interference.

However, the finite bandwidths of each channel, due to the modulation of each of the

contributing carrier frequencies, have not been considered.

Holbeche [9] has modeled a modulated carrier as a “cluster” of many unmodulated

sinusoids. The cluster occupies a finite bandwidth. Computing the intermodulation

interference components arising from different combinations of these individual

sinusoidal components, Holbeche showed that the bandwidth of the resulting cluster of

interference components equals the sum of the bandwidths of each contributing signal. So

if several signals each occupy a bandwidth of 12.5 kHz, the bandwidth of a 3rd-order

intermodulation product is 3 × 12.5 kHz. Similarly, the bandwidth of a 5th-order

intermodulation product is 5 × 12.5 kHz. It is therefore conceivable that modulated

carriers could cause interference to a receiver while unmodulated carriers would not.

 

*

 Recall that within the railroad VHF spectrum, WCTF’s proposed band plan has ten interstitially-placed

trunk groups. These trunk groups are identified as trunk groups “A” through “J” and the important

features of these interstitial trunk groups were depicted in Figure 2. Although any one of these ten trunk

groups could be chosen to explain the concepts presented in the subsequent discussion, the frequency

assignments corresponding to trunk group “E” frequencies (160.965/160.245, 161.040/160.320,

161.115/160.395, ... , 161.490/160.770 MHz) have been arbitrarily selected to explain these concepts.
17

fIM

k BW

rx f

BW

frequency fIM

k BW

rx f

BW

frequency

(a) (b)

Figure 13. Bandwidth of intermodulation products:

(a) ƒrx > ƒIM, (b) ƒIM > ƒrx. If the spectrum of the

intermodulation product overlaps into the

passband of a receiver, there is a potential for

intermodulation interference.

Figure 13 shows two cases where the frequency of an intermodulation product is nearly

the same as a receiver’s frequency. A “k

th-order” intermodulation product possesses a

bandwidth “k” times greater than the fundamental bandwidth and is identified by the term

“k BW.” To avoid intermodulation interference, the difference between an intermodulation

product’s center frequency and the receiver’s tuned frequency should be greater than the

sum of half the intermodulation product’s bandwidth and half the receiver’s passband,

i.e.,

|fIM – frx| > kBt /2 + Br /2 (2)

where k is the order of the intermodulation product, Bt is the transmitter bandwidth, and

Br is the receiver bandwidth.

Reconsider, then, Equation (1). But now, assume that “significant” spectral components

exist ±5.1 kHz away from each of the assigned transmitter channel frequencies.

Following Holbeche’s model, a possible intermodulation frequency arising from the

spectral components of these modulated carriers could now occur at

 fIM = (161.04 + .0051) + (161.115 + .0051) + (161.19 + .0051)

- (161.415 - .0051) - (161.49 - .0051)

= 160.4655 = 160.47 - .0045 = fE4(rx) - .0045

This says that there is a possibility of fifth-order intermodulation interference, arising

from the unintentional mixing of channels 2, 3, 4, 7, and 8, occurring only 4.5 kHz away

from the assigned frequency of the “channel 4” receiver. This intermodulation

interference would fall within a TIA-102 receiver’s ±6.25-kHz passband.

The above example gives just one of many possible conditions for generating

intermodulation interference. In a more general context, intermodulation frequencies are

caused by nonlinearities in transmitter or receiver components. These nonlinearities
18

distort the intended signal y = A1x, and can be represented mathematically by including

additional power series expansion terms, i.e.,

y = A0 + A1x + A2x

2

 + A3x

3

 + ... + Anx

n (3)

where y represents the output response of a radio to an input signal x and the terms An are

integer coefficients. When x is a sum of sinusoidal signals, trigonometric expansions of

the power terms of x (x

2

, x

3

, etc.) show that new signals are formed at new frequencies not

present in the first-order x term. These new frequencies occur at values given by different

combinations of sums and differences of the original fundamental frequencies in x, and

their harmonics. So, in general, intermodulation frequencies are given by

fIM = ±k1f1 ± k2f2 ± k3f3 ± ... ± kNfN 

= ±k1f1 ± k2(f1+∂ f ) ± k3(f1+2∂ f) ± ... ± kN(f1+(N-1)∂ f) (4)

where each kj is an integer coefficient designating the “k

th” harmonic of frequency fj, and

∂ f is the channel spacing between the collocated radio repeater channels.

For the condition where the sum of the harmonic coefficients Σ(±kj) = 1, the expression

for fIM becomes

fIM = f1 ± k2 ∂ f ± k3 2∂ f ± ... ± kN(N-1) ∂ f (5)

Equation (5) indicates that for equal channel spacings, a fixed transmit/receive frequency

split, and a particular set of channel harmonic coefficients [k], the frequency of the

intermodulation interference signal maintains a fixed arithmetic offset from the base

channel frequency f1. Whether the intermodulation interference actually occurs or not

depends on many other factors such as:

• individual transmitter power spectral densities,

• ambient receiver noise level,

• intermodulation rejection specification of the receiver,

• amount of attenuation that transmitter signals experience as they propagate

through the various hybrids, cavities, postselectors, and preselectors in the

transmitter-to-receiver path, and

• the probability that the offending transmitters are simultaneously transmitting.

5.5.2 Amplitudes of Intermodulation Distortion Products

To estimate the absolute power levels of intermodulation interference, the equations

shown in Figure 14 are used. In this figure, the ordinate is “output power minus amplifier

gain,” and the abscissa is input power. The two heavy, intersecting sloped lines are the

first-order (fundamental) “output power minus amplifier gain” vs. input power

(1:1 log-log slope) and the third-order intermodulation distortion “output power minus

amplifier gain” vs. input power (3:1 log-log slope).
19

Noise Floor FkTB

3X = IP3 - MDS

 IMR

"Relative" IMR = 2 (IP3 - Ci)

X

DR = (2/3) (IP3 – MDS)

C/N (ref sens)





arbitrary Ci = (1/3) (2V1 + V2)





IP3

Pin (logarithmic scale)

IML = Ci – "Relative" 

IMR= Ci – 2(IP3 – Ci)

= 3Ci – 2IP3

IMR

= DR – C/N(ref sens)

= (2/3) (IP3 – MDS) – C/N(ref sens)

= (2/3) [IP3 – (Pin(ref sens)) – C/N(ref sens)] – C/N(ref sens)

= (2/3) (IP3 – (Pin(ref sens)) – (1/3) C/N(ref sens)

IMR

Pout – Gain

(logarithmic

scale)

MDS

Pin(ref sens)

Figure 14. Amplifier intermodulation performance diagram.

The amplitudes of these intermodulation interference signals are determined by

expanding the power series in Equation (3) term by term. Doing this, one can show that

for every 1-dB increase in the amplitude of the first-order power terms, the third-order

distortion terms increase by 3 dB. That is why the first- and third-order responses in

Figure 14 have 1:1 and 3:1 log-log slopes, respectively.

In practice, the amplifier’s first- and third-order responses will saturate (the two lines will

flatten out to horizontal, indicating constant power output with continued increases in

input power) before the lines intersect. However, for analysis purposes, the responses are

linearly extrapolated to the point where they do intersect. This intersection point is known

as the third-order intercept point, and is denoted by IP3 (or IIP3 to emphasize third-order

input intercept point).

Pin(ref sens) is the input power required to achieve some measure of radio receiver

sensitivity, such as 5% BER or 12-dB SINAD. C/N(ref sens) is the corresponding input

carrier-to-noise ratio when the specified reference sensitivity criteria has been achieved.

The intermodulation rejection (IMR) ratio is the ratio between the power level of an offchannel interferer to the power level of the desired channel Pin(ref sens), when two equalpower off-channel interferers introduce a distortion product whose power is equal to the
20

level of the noise threshold. Other quantities, graphically depicted in Figure 14, include

dynamic range DR, and minimum discernable signal MDS.

When two RF carriers, at power levels Ci that are “X” dB less than the receiver’s IP3,

create intermodulation interference, the third-order intermodulation level (IML) is

“3X” dB below the receiver’s IIP3, at a power level of

IML(2-signal) = 3Ci – 2IIP3 (6)

In general, similar plots can be drawn for any “nth-order” intermodulation process, with

the nth-order intermodulation response curve possessing an n:1 log-log slope, and with an

IML “n × X” dB below the nth-order intercept point, at “nCi – (n-1)IIP3” dBm. Usually,

third-order intermodulation products have the greatest IMLs and are the most

troublesome. Therefore, the focus of the following analysis is directed to the third-order

intermodulation interference problem.

Expanding the third-order term A3x

3

 in Equation (3), when x is the sum of two sinusoids

at frequencies f1 and f2, gives rise to several terms, one of which is

(3/4) A3 (V1

2

V2) cos(2π (2f1 – f2)t) (7)

The value of coefficient A3 can be inferred from an IMR ratio measurement. The standard

measurement procedures [6, 7] use two equal-amplitude adjacent-channel signals to

create intermodulation interference. When the power of the intermodulation distortion

product IML just equals the value of the noise, the voltage amplitude Vi of each

interfering signal will exceed the reference sensitivity level by an amount equal to the

IMR ratio. That is, when

IML = (2V1 + V2) + 20 log ((3/4)A3) = N = (Prefsens – C/Nrefsens) ( dBm) (8)

then

V1 = V2 = Prefsens + IMR ( dBm) (9)

When the two interfering signals have unequal amplitudes, the “equivalent” interfering

carrier power is

Ci = (1/3)(2V1 + V2) ( dBm) (10)

because the resulting intermodulation distortion power IML, due to unequal amplitudes

V1 and V2 on the adjacent and alternate channels, is the same as if V1 and V2 were both

equal to Ci.

Receiver performance IMR specifications are measured under laboratory conditions using

two (adjacent and alternate channel) equal-amplitude signals. However, third-order

intermodulation interference can also arise from three signals. When x in Equation (3) is a
21

sum of three sinusoids, the cubic A3x

3

 gives rise to new terms not present in the cubic

expansion of a sum of two sinusoids. One of these new terms is

(3/2)A3(V1V2V3)cos(2π (f1 + f2 – f3)t) (11)

The intermodulation product component described by Equation (11) arises from the

“triple beat” of three signals at frequencies f1, f2, and f3. Its leading coefficient term,

(3/2)A3, is 6 dB greater than equation (7)’s coefficient (3/4)A3, because

20 log ((3/2) A3) – 20 log ((3/4) A3) = 6 dB

When the amplitudes of these three (adjacent, alternate, and tertiary) signals are the same

as the values of the adjacent and alternate channel amplitudes used in the usual “2V1 - V2”

IMR test, the resulting intermodulation distortion term at frequency (f1 + f2 - f3) is 6 dB

greater than the intermodulation distortion term at frequency (2f1 - f2). Thus, the power

level of the intermodulation distortion, due to three signals, is

IML(3-signal) = IML(2-signal) + 6 = 3 Ci – 2 IIP3sys + 6 (dBm) (12)

When the three interfering signals have unequal amplitudes, the “equivalent” interfering

carrier power is

Ci = (1/3)(V1 + V2 + V3) ( dBm) (13)

because the resulting intermodulation distortion power

IML(3-signal) = IML(2-signal) + 6 = (Pref sens – C/Nref sens) + 6 (dBm) (14)

due to unequal amplitudes V1, V2, and V3, is the same as if V1, V2, and V3 were each set

equal to Ci.

As an example, assume an adjacent channel power of -32 dBm, an alternate channel

power of -37 dBm, and a tertiary power level of -48 dBm, incident upon a receiver

whose third-order input intercept point is +4 dBm.

The equivalent interfering carrier power

Ci = (1/3) ((-32) + (-37) + (-48)) = -39 dBm

The resulting interference at one of the “triple-beat” frequencies is

IML(3-signal) = 3 × (-39) - 2 × 4 + 6 = -119 dBm

This level of intermodulation interference is roughly the same as the value of the ambient

noise level that might be expected at the receiver output.
22

The procedure culminating in Equations (3) – (14) could be extended to account for

quartic- and higher-order products, A4x

4

, A5x

5

, etc., although the algebraic and

trigonometric manipulations become unwieldy in short order.

5.5.3 Composite Receiver System Noise Figure and Intercept Point

The above discussion has investigated intermodulation interference created within a

receiver. It did not consider the effects of preceding a receiver with a multicoupler.

Collocated repeaters sharing a common receive antenna will have an amplifier preceding

the RF splitter to compensate for the losses introduced by splitting the multichannel

signal into several distinct receiver paths. A multicoupler will degrade the composite IIP3

and noise figure of the system, and if the preamplifier gain is set too high, the

multicoupler will amplify the interfering carriers to such a high level that intermodulation

interference is unavoidable. If its gain is set too low, the composite system noise figure

will be larger than desired, degrading the system’s overall sensitivity.

System noise figure Fsys is given by

Fsys = 10 log (ƒ1 + (ƒ2 – 1)/g1 + (ƒ3 – 1)/g1g2 + ...) (15)

where Fsys, the composite system noise figure, is expressed in decibels, and fi and gi

correspond to the noise factor* and gain of the individual stages comprising the cascaded

chain, which are expressed linearly rather than in decibels.

Sagers [10] derived the third-order input intercept point of a cascaded network as

1/(IIP3)sys = 1/(IIP3)1 + g1/(IIP3)2 + g1g2/(IIP3)3 + ... (16)

where the intercept points IIP3i and gains gi are expressed linearly (in milliwatts and as a

dimensionless multiplicative factor, respectively).

Consider the following example: Each receiver at a multichannel site has a noise figure of

9 dB and third-order intercept point of +4 dBm. The receivers share a common antenna,

so a multicoupler precedes them. The multicoupler’s distribution preamplifier has a noise

figure of 4 dB, a gain of 25 dB, and a third-order input intercept point of 9 dBm. The

multicoupler’s RF splitter has an insertion loss†

 of 17 dB. From Equation (15), the

composite system noise figure is

Fsys = 10 log (

10

17

10

25

10

9

10

25

10

17

10

4

10 10

10 1

10

10 1 10 −

⋅

− + − + ) = 5.8 dB

 

*

 Noise figure F is related to noise factor f by F = 10 log f.

†

 The noise figure of a passive, linear, and isotropic device is equal to its amount of attenuation.
23

This is a 3.2-dB improvement over the noise figure of a single receiver. But from

Equation (16), the composite third-order intercept point is found to be

IIP3sys = -10log (

10

4

10

17

10

25

10

25

10

9

10

10 10

10

10

10

1 −

+∞

⋅ + + ) = -4.2 dBm *

This is 8.2 dB worse than the intercept point of the receiver alone. From Equation (12),

the level of the intermodulation interference at the final receiver is therefore

IML = 3 × (-39) - 2 × (-4.2) + 6 = -102.6 dBm

The net effect is that the multicoupler has amplified the interference to unacceptably high

levels, from -119 dBm to -102.6 dBm. Either the multicoupler’s gain must be reduced,

or the levels of interference present at the receiver site must somehow be suppressed.

5.5.4 Conclusion

Will intermodulation interference be a problem with multichannel sites assigned

frequencies according to the proposed WCTF band plan? If the local environment is such

that high-power interference signals are likely to be present, intermodulation interference

will be unavoidable unless the system’s sensitivity is significantly degraded. This, of

course, means that weak signals may not be detected. On the other hand, if lower

transmitter power levels can still provide adequate geographical coverage, or if local

ambient noise levels and received interference signal strengths are not excessive, then a

system design can utilize the proposed band plan. Candidate sites will have to be

evaluated on a case-by-case basis.

6 SIGNAL COVERAGE ANALYSIS

The radio coverage area, for a given level of speech intelligibility and service reliability,

depends on the effective isotropic radiated power (EIRP) of the transmitter, signal fading

and shadowing margins, receive antenna gain, and receiver sensitivity. EIRP is equal to

the transmitter output power plus the transmitter antenna gain minus the miscellaneous

transmitter system losses (losses through combiners, duplexers, coaxial cable, etc.). A

typical mobile antenna will exhibit a gain on the order of 3 dBi, and a typical twoelement dipole array will exhibit a gain of 7 dBi. Typical receiver sensitivities for various

levels of speech intelligibility were presented in Section 4.1. The remaining parameters,

signal fading and shadowing, are considered in the following discussion.

 

*

 The third-order intercept point of a passive, linear, and reciprocal device is, by definition, infinite, since

such a device can generate no intermodulation products. Therefore the denominator of the second term

inside the parentheses is 10+∞

.
24

6.1 Land Mobile Communications Propagation Models

The Hata-Okumura propagation model is commonly used by the LMR community to

predict radio coverage [11]. This model is based upon the measurements and empirical

prediction curves of Okumura, et al. [12], and is easily implemented using a personal

computer spreadsheet program. Hata’s model is limited to path distances of 20 km,

although Okumura’s prediction curves were provided out to 100 km. Others have

extended the model to paths up to about 100 km, as in the Hata-Davidson model [4]. The

Hata model and Okumura curves considered several different operating environments:

(1) urban, (2) medium/small city, (3) suburban, (4) quasi-open, and (5) open. The model

assumes that the base station antenna is well above the heights of surrounding buildings

for the given environments. Stueber [13] observed that U.S. suburban environments are

more like the quasi-open environments defined by Okumura. For railroad operations in

cities, the suburban and quasi-open environments are probably the best choices of the

Hata model selections.

Other more sophisticated modeling tools are available to communications systems

designers. ITS’ Communications System Performance Model*

 (CSPM) incorporates the

Longley-Rice Irregular Terrain Model (ITM) algorithm and utilizes digital terrain

elevation data to define the terrain profile along the signal propagation path. CSPM

produces maps showing signal strength contours within a user-defined geographic area.

Alternatively, data can be output in a tabular textual format. Many antenna system

manufacturers and engineering consultants have similar computer programs to design

their customers’ LMR systems, and commercial implementations of the ITM algorithm

can be obtained from various sources.

6.1.1 Median Propagation Loss from the Hata-Davidson Model

Figure 15 shows the predicted median propagation loss within the five environments

described above for the situation where the base station antenna height is 33 meters, the

mobile unit antenna height is 5 meters, and the frequency is 161 MHz. For this given

situation of frequency and antenna heights, the Hata-Davidson Model predicts virtually

identical attenuations for the urban and medium/small city environments; the curves

overlay very closely and cannot be readily resolved.

Two additional curves are also shown on the plot, where the path loss with distance is

10 n log10(distance) and n is the path loss exponent. The first additional curve is for freespace loss where the path loss term n = 2 and the second additional curve is for a path

loss term where n = 3.6.

A third additional curve is also shown on the plot. This curve shows the loss predicted by

ITM over a particular path in the central United States. At distances exceeding about

 

*

 More detailed information regarding internet access to the CSPM program can be obtained from the

Institute for Telecommunication Sciences, telephone (303) 497-5301.
25

20 km, variations and undulations in the predicted propagation loss are seen. This

behavior is not unexpected since the terrain profile is irregular.

Hata-Davidson Propagation Loss .

70

90

110

130

150

170

190

210

1 10 100

Range (km)

Attenuation 

(dB)

Large city

Med/small city

Suburban

Quasi-Open

Open

Loss exponent n=3.6

Free space n=2

ITM Median Loss

Figure 15. Hata-Davidson, exponential power loss, and

ITM models of propagation loss for mobile

communications at 161 MHz. Base station

antenna height is 33 meters and mobile unit

antenna height is 5 meters.

For the purposes of this discussion, the important feature of the ITM prediction is that its

propagation path loss behavior obeys the same general trend as the more generic HataDavidson model. In addition, the Hata-Davidson curves have a common slope that

indicates a path loss exponent of approximately 3.6. Lee [14] has provided examples of

measurements where n varies over 3.05 (an urban area in Japan), 3.68 (an urban area in

Philadelphia), 4.31 (an urban area in Newark), 3.84 (in suburban areas), and 4.35 (in an

open area). Thus, the Hata model should be a reasonable estimator with its path loss

exponent set to about 3.6.

6.2 Variability about the Median Propagation Loss

The Hata-Davidson model provides a prediction of the median loss versus distance for a

given frequency and base station and mobile unit antenna heights. Due to blockage of the

signal caused by buildings or terrain plus the reflection of the signal by other buildings

and terrain features, the signal as measured at a particular distance is not constant [15].

Multipath conditions experienced by mobile units in motion can also cause Rayleigh

fading of the radio signal [15].
26

6.2.1 Lognormal Shadowing

If the received signal strength were measured at discrete locations along a constant radius

surrounding a particular transmitting site, the signal level would be found to vary in a

lognormal manner. Figure 16 shows the probability that the actual received signal would

vary from the median level by a given amount, for three different values of standard

deviation. From the statistics of a lognormal distribution, 68% of all the actual received

signals will be no more than one standard deviation from the median signal level.

Lognormal Probability Density Function 

.

0

0.01

0.02

0.03

0.04

0.05

0.06

-30 -20 -10 0 10 20 30

X (Received signal level - median signal level) (dB)

Probability

Density(X)

Std Dev = 8 dB

Std Dev = 10 dB

••••••• Std Dev = 12 dB

Figure 16. Probability distribution of the difference between the

actual received signal level and the median signal level,

for three standard deviations of the lognormal signal.

Figure 17 shows the cumulative probability of the actual received signal minus the

median signal level for three different standard deviations. The system design needs to be

based upon the standard deviation of the signal variability where the system is to be used.

Typical values of standard deviation for mobile communications at VHF are about

5 - 12 dB in a variety of urban, suburban, and open environments [14]. A reasonable

value, then, for lognormal standard deviation is probably about 8 dB or so for railroad

environments.

Assuming an 8-dB standard deviation in signal strength, suppose that the system design

specification requires an adequate communications link be available for at least 90% of

the times and at 90% of the locations that the mobile user depresses the push-to-talk

switch. For a lognormal distribution, the required margin above the median signal level

can be found from

Prob(X ≥ Kσ ) = 1 - 1/

2 erfc ( K/

√ 2 ) (17)
27

where erfc(∙) is the complementary error function and is given by

1/

2 erfc(υ ) = ∫υ

+∞ e - ξ 2

 dξ (18)

Lognormal Cumulative .

Distribution Function .

0

0.2

0.4

0.6

0.8

1

-30 -20 -10 0 10 20 30

X (Received signal level - median signal level) (dB)

Probability 

(rcv'd signal

≤ median)

Std Dev = 8 dB

Std Dev = 10 dB

•••••••Std Dev = 12 dB

Figure 17. Cumulative probability that the actual received

signal level will differ from the median signal

level by at least a specific amount, for three

standard deviations of the lognormal signal.

The erfc(∙) arises from integrating the lognormal probability density function of a

Gaussian-distributed random variable ξ . X is the difference between the received signal

level and the median signal level and σ is the standard deviation of X. For the required

Prob(X ≥ Kσ ) = 90%, K is found to be 1.28 so X, the margin, would need to be about

10.25 dB (1.28 × 8 dB). Suppose instead the system reliability was specified to be 95%,

then K would be 1.65 and X would need to be 13.2 dB (1.65 × 8 dB).

To see how this margin is used in the design of the system, assume the Hata-Davidson

model predicts a propagation loss of 150 dB at a distance of 24 km. If the available

excess system link margin equals the median propagation loss, then an adequate signal

level will exist 50% of the time at 50% of the locations along a circular contour 24 km

away from the transmitter. By subtracting 10.25 dB from the available excess system link

margin, the design will assure that 90% of these locations will have an adequate signal

level. Subtracting 13.2 dB from the available excess system link margin would assure

that 95% of these locations will have an adequate signal level.
28

6.2.2 Rayleigh Fading

Rayleigh fading describes the phenomenon of signal fluctuations caused by multipath

effects while a mobile unit is in motion. The probability density function of a signal

whose envelope (voltage) r obeys Rayleigh fading statistics is

pr(r) = γ

γ

2

r 2

e

r −

(19)

where γ is the mean power of the signal. Equation (19) is graphed in Figure 18.

Rayleigh Probability Density Function

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

01234

r

p(r)

/γ

γ ×

Figure 18. Normalized probability distribution of the

magnitude of a Rayleigh-faded signal.

The probability density function of this same Rayleigh-faded signal can be expressed in

terms of the signal power s by equating incremental areas under the probability density

curves ps(s)ds to pr(r)dr, i.e., 

dr

ds

p (r ) p (s) r

s = , yielding the exponential probability density

function

 ps(s) = γ

γ

2

s

e

2

1 −

(20)

This function is graphed in Figure 19.
29

Exponential Density Function of a 

Rayleigh-faded Signal

0

0.1

0.2

0.3

0.4

0.5

0 4 8 12 16

s

p(s)

/γ

γ x 

Figure 19. Normalized probability distribution of the power

of a Rayleigh-faded signal.

Hess [15] and Parsons [16] further developed Equation (20) to express the probability

density function in terms of decibels* rather than watts. The result is

pS (S) = e ) 2

S 1 (

S

e

2

1 κ

κ γ

κ γ

−

(21)

where S = 10 log(s) = ln( 10 )

10

 ln(s) = κ ln(s), and the mean signal power γ is expressed

linearly as before. The authors [15,16] also showed that the mean of the received power

in a Rayleigh-fading environment is about 2.51 dB less than for the static case, at a value

of κ ln(γ) - κC dB,† with a standard deviation σr equal to 6

κ π dB, or about 5.57 dB, with

σr being independent of the value of mean power.

6.2.3 Suzuki Distribution

The superposition of Rayleigh fading onto lognormal shadowing yields a probability

density function known as the Suzuki Distribution [16]. When determining the statistics of a

Suzuki-distributed signal, Equations (20) and (21) must be written in a slightly different

form. In the land-mobile radio environment, the mean power γ

‡

 of a Rayleigh-faded

signal is itself a random variable, exhibiting the lognormal-shadowing behavior described

 

* S = 10 log s

†

 Euler’s constant C ≈ 0.577215665

‡

 or Γ = 10 log γ (dB)
30

previously. Therefore, Equations (20) and (21) are rewritten as conditional probabilities

ps|γ(s|γ) and pS|Γ

(S|Γ). The composite probability density function fs(s) becomes

∫−

+

∞

∞ ps|γ(s|γ)ps(s)dγ, where the second term describes the lognormal behavior and the

integration corresponds to averaging the first (Rayleigh) term weighted by the lognormal

distribution. Hess [15] gives the Suzuki probability density function of power as

f

s (s) = γ

π σ

σ

γ γ

κ

γ κ

γ

e d

2

1 ) 2

( ) ( se

2

2

2

∫

+∞

−∞

− − − −

(22)

where γ is the mean value of the non-Rayleigh-faded received power γ , σ is the

standard deviation of the lognormal shadowing distribution, and κ is the proportionality

constant defined previously.

This probability density function and its resulting cumulative distribution function

FS(S < Sr(dB)) = ∫-∞

Sr

 fs(S)dS present significant computational difficulties. Parsons [16]

reports that other theoreticians have suggested that subject to certain limitations,* the

Suzuki Distribution can be approximated by a lognormal distribution with a mean power

level S Suzuki = ( S lognormal - κC) and standard deviation σSuzuki = 

6

2 2

2

log normal

κ π

σ + , both

given in decibels.

6.3 Excess System Link Margin

Based upon the above discussions, the excess system link margins and maximum signal

coverage distances can be determined, for both digital and analog modulation formats of

a TIA-102 radio system. The excess system link margin indicates how much path loss a

radio channel can withstand while providing some specified minimum reliability of

service and delivered audio quality out to some distance. The maximum available excess

system link margin is given by

Available margin = EIRPTX + GRX – Lsystem – Pref sens – κC - KσSuzuki (23)

Table 1 shows two sets of example calculations, using Equation (23), to determine the

available excess system link margins for analog and digital modulation formats. The

available excess system link margin is a function of several transmitter and radio channel

parameters.†

 For this example, a DAQ of 3.4 is assumed, which, according to TIA [4],

 

*

 For example, σlognormal > 6 dB and reliability percentiles bounded within 5% and 95% values.

†

 These parameters are: (1) the transmitter’s effective isotropic radiated power (EIRP), (2) the mobile

receiver’s antenna gain (GRX), (3) miscellaneous losses within the local RF infrastructure (Lsystem),

(4) the receiver noise level (FkTB), (5) the carrier-to-noise ratio (CNR) required for a specified grade of

service, and (6) the contour reliability (which determines Kσ). The constant term κC, discussed earlier,

accounts for the reduction in the mean power of the received signal due to Rayleigh fading.
31

requires a CNR of 17.7 dB. Similar calculations can be done for base-to-portable and

mobile/portable-to-repeater scenarios.*

Notice that the TIA-102 digital modulation gives about an 7 dB performance advantage

over analog FM. Thus, given the same conditions for both options, the digital modulation

should have superior performance to that expected of the analog modulation option. From

another viewpoint, for a given level of speech intelligibility, digital modulation should

provide coverage out to a further range than analog modulation.

Table 1.Excess System Link Margin Calculations for Analog

and Digital Modulation Formats — Base-to-Mobile

Transmitter EIRP = Pt - Lsystem + Gantenna (dBm)

Receiver antenna gain (dBi)

Rx cable losses (dB)

Rx equiv noise bandwidth (kHz) (TIA TSB-88 Jan98 p.90) 5.7 10.1

Noise level = kTB (dBm) -136.4 -133.9

Rx DAQ2/5%BER/12dBS reference sensitivity (dBm) -113.0 -113.0

CNR for DAQ 2.0 (dB) (TIA TSB-88 Jan 98 p.93) 7.6 5.0

Receiver noise figure (dB) 15.8 15.9

CNR for DAQ 3.4 (dB) (TIA TSB-88 Jan 98 p.93) 17.7 22.0

Rayleigh fading mean value correction κC (dB)

Rayleigh fading standard deviation κπ/√6(dB)

Lognormal shadowing standard deviation (dB)

Contour reliability P(X≥Kσ)=1-(1/2)erfc(K/√2) (%)

Suzuki fading margin Kσ (dB)

Available Excess System margin (dB) 136.4 129.5

IMBE vocoder 

transceiver

Analog voice 

transceiver

8.0

12.5

5.6

3.0

1.0

2.5

Available Excess System Margin

46.5

90.0

Figure 20 shows the excess system link margin versus distance of the base-to-mobile

channel for the two modulation options in two different environments, by subtracting

Figure 15’s median path loss from Table 1’s available excess system link margin. The

points where each line crosses the abscissa (i.e., where the excess margin equals zero)

define the maximum estimated ranges that signal coverage can be expected to provide the

specified quality and reliability. The figure shows that the digital system should provide

signal coverage out to about 17 km in suburban environments, and out to about 31 km in

quasi-open environments. This is approximately 1.4 times the coverage distance that an

analog system can provide, for the same level of speech intelligibility.

 

*

 For mobile/portable-to-repeater, substitute the value of the mobile/portable transmitter power for the

transmitter EIRP, and for portables (inbound or outbound), substitute the value of the portable’s

antenna gain (nominally about –10 dBi at VHF).
32

Excess System Link Margin .

0

10

20

30

40

50

60

1 10 100

Range (km)

Margin

(dB)

Digital system margin -

quasi-open losses

Analog system margin -

quasi-open losses

Digital system margin -

suburban losses

Analog system margin -

suburban losses

Figure 20. Typical excess system link margin for digital

and analog modulation formats in two different

terrain environments.

6.4 Cellular Topologies

In regions where many rail lines converge and rail yard activity increases the amount of

traffic, cellular topologies can be used to provide the required signal coverage. Typically,

a hexagonal shape is used to describe the most basic coverage area. From this shape,

several patterns are defined that provide different separations between base station

transmitters using the same frequency. The common patterns are found by moving i cells

in one direction away from the current cell, turning 60 degrees, then moving j cells to

arrive at a new cell. This new cell uses the same frequency as the starting cell. The

formula for the frequency reuse factor N, which is equal to the number of cells per cluster,

is related to the allowed moves i and j by

N = i2

 + ij + j2 (24)

Figure 21 shows several examples of cellular clusters for several different frequency

reuse values N.
33

1

2 3

2 3

1

1

2 3

2 3

1

1 2

3

1

3 3

2 1

4

1

4 4

2

1 2

4 3

5

6 7

1 2

4 3

5

1 2 6 7

4 3

6

1 2

4 3

5

6 7

7

1 3

456

7 8 9

1 2 3

5 6

7 9

1 2

4 56

7 9

2 3 1

6 4 5

7

8

9

2

4

8

1 2

4 3

5

6

9

10 11 1 2

4 3

5

6 7

8

9

10

7

2

4 3

5 8

9

10

1

11

6

8

7 12

N = 3 N = 4 N = 7

N = 9 N = 12

Figure 21. Example cellular cluster designs for several

different values of frequency reuse factors N.

The quantity Q is the ratio of the distance D between the centers of cochannel cells and

the radius R of a hexagonal cell. It is related to the frequency reuse factor N by

Q = D/R = 3N (25)

Generalizing Rappaport’s approximation for the cochannel carrier-to-interference

ratio [17] to account for any path loss exponent n gives

} Q

1

(Q )

(Q ) (Q )

(Q 1)

2(Q 1) (Q 1) 10 log{ IC n n

4

2 1

n

2

n 1

2

1

2 n

n n

cochannel

+ −

+ + − + −

+ + − = −

(26)

Equation (26) describes the situation where a mobile unit is at the boundary of its cell and

the base stations all have equal characteristics. Table 2 gives the expected C/Icochannel,

computed using Equation (26), for several different values of path loss coefficient n for

the most common cellular patterns such as those depicted in Figure 21.
34

Table 2. Cellular Cluster Size N and Cochannel Carrierto-Interference Ratio

2 3 3.6 4

1 0 1 1.73 -7.04 -7.76 -8.35 -8.79

1 1 3 3.00 0.38 4.09 6.22 7.61

2 0 4 3.46 1.94 6.51 9.18 10.93

2 1 7 4.58 4.76 10.86 14.48 16.87

3 0 9 5.20 5.97 12.72 16.73 19.39

2 2 12 6.00 7.33 14.79 19.24 22.19

3 1 13 6.24 7.70 15.36 19.92 22.95

3 2 19 7.55 9.45 18.01 23.12 26.53

3 3 27 9.00 11.05 20.42 26.03 29.77

p a t h l o s s c o e f f I c I e n t n

C / I ( d B )

i j N = 

i

2 + ij +j 2

Q = D/R 

= √ 3N

Cellular patterns incorporating variable-sized cells may be warranted. Reducing cell size

(thus increasing the total number of cells encompassing a geographic area) is one way to

increase the traffic capacity of radio systems.* Figure 22 shows a possible frequency

group reuse plan using variable-size cells. The smaller sized cells would be used where

the greatest need for channel capacity exists, i.e., rail centers. Larger-sized cells would be

used in areas with reduced channel capacity.

1 2

4 3

5

6 7 5

4

6

5

4 3

3

2

2

7

6 7

8 9

10

8

8

10

10

9

9

4

4

11

11

12

13

13

1 2 4

6 75 1

2 4 3

5 1 2

6 5 7

Figure 22. Example variable cell cluster size for a

frequency reuse factor N = 7, using 13

frequency groups to control interference in

“cell-size transition regions.”

 

*

 The ability to dynamically control transmit power level is desirable in order to accommodate smaller

cell sizes. Too much transmitter power in small-sized cell configurations causes interference to radios

in cochannel or neighboring adjacent-channel cells. Currently, P25 radios do not have the capability to

automatically control the transmit power of mobile and portable units from the repeater or base station.

However, some measure of protection can be had by controlling antenna heights, beam downtilt, gain,

and radiation pattern at the repeater/base station. ITS has suggested automatic power control be

incorporated into the Project 25 standards (private verbal communications, TIA-102 standards

committee).
35

6.5 Adjacent-Channel Rejection, Cochannel Rejection, and Frequency Reuse Ratio

(Cell Cluster Size)

Typical measured adjacent-channel and cochannel rejection performance of analogmodulated and digitally-modulated radios was presented in Section 4.2. In that section,

typical delivered audio qualities of demodulated speech signals were given for a variety

of adjacent-channel and cochannel environments. The following subsections discuss how

cellular topology and narrow channel spacings affect the intelligibility of the received

speech signal.

6.5.1 Adjacent-Channel Rejection

The worst-case situation for determining the effects of adjacent-channel interference on

DAQ occurs in the portable-to-base direction, when a lower-powered portable transmitter

must compete against higher-powered interference sources. Refer to Figure 23. Two

adjacent-channel mobiles, located in neighboring cells at the cell boundaries, are depicted

interfering with the reception of a desired signal from a lower-powered portable located

within the cell of interest.

Figure 23. Portable-to-repeater situation: Two adjacentchannel mobiles near the boundaries of

neighboring cells interfere with the reception of

a desired signal from a lower-powered portable

located within the target cell.

When ITS measured the DAQ performance of a TIA-102 radio in the presence of 7.5-kHz

offset adjacent-channel interference (Section 4.2), the desired transmitter’s power level

was first adjusted to invoke a 0.25% BER at the receiver. This provided a signal whose

DAQ was superior to 3.4. Interference signals were then introduced to degrade the desired

signal’s DAQ. When the adjacent-channel interference power was about 9 dB greater

than the on-channel signal, the DAQ of the desired speech signal was degraded to a score

of 3.4 (Figure 5). This implies that two independent interference signals, one on the lower

adjacent channel and the other on the upper adjacent channel, could each be about 6 dB

stronger than the intended signal at the receiver, since 10 log(10

6

10 + 10

6

10 ) = 9 dB.
36

An analysis*

 such as that performed in Section 6.3 predicts a maximum distance (where

the excess system link margin is 0 dB) between portable and base station of about 2 km

in suburban environments for a 0.25% BER. Performing a similar analysis for interfering

mobiles†

 to find where the excess system link margin is 6 dB,‡ shows that the interfering

mobiles should be no closer than 37 km to the receiving base station. Since, for the

assumed conditions of this example, the cell radius is 17 km (Section 6.3), two interfering

adjacent-channel mobiles in neighboring cells, offset ±7.5 kHz in frequency from the onchannel portable, might degrade the desired signal’s DAQ to something less than

DAQ 3.4. However, the railroads may decide that a DAQ less than 3.4 still gives

acceptable speech quality, or that this situation occurs infrequently enough that it is not an

issue.

6.5.2 Cochannel Rejection

Table 3 gives the cochannel carrier-to-interference (C/I) ratios measured by ITS and

relates these values to the corresponding minimum cell cluster sizes N from Table 2, for

the interference modes and channel spacings specified in Section 4.2.

Table 3. Representative Values of C/I and N for Different

Radio Interference Environments

C / I (dB) N

Frequency Reuse Ratio (Cell Cluster Size) 

N for Path Loss Exponent n = 3.6 and 

Delivered Audio Quality DAQ = 3.4

Interference Mode Cochannel

unwanted digital signal interfering with 

desired digital signal 9.2 7

unwanted digital signal interfering with 

desired analog signal

not 

measured

unwanted analog signal interfering with 

desired digital signal 18 12

unwanted analog signal interfering with 

desired analog signal 25 19

The table shows that the number of cells comprising a cluster§ can be less for an alldigital environment than for all-analog or mixed-mode environments. This means that

 

*

 Portable: 0.5-watt transmitter EIRP, 1.0-meter antenna height. Base station: 33-meter antenna height,

5-dBd antenna gain. Estimated CNR for 0.25% BER: 31 dB.

†

 45-watt transmitter EIRP, 5.0-meter antenna height. Contour coverage reliability: 50%.

‡

 From the previous paragraph, two simultaneously occurring adjacent-channel interfering signals can

each be 6 dB stronger than the desired signal.

§

 Each shaded group of cells in each of the cellular topologies depicted in Figure 21 is a cluster.
37

more channel-pairs can be assigned to each cell. If “C ” channel-pairs are available for

use throughout a cluster of cells, then “C/N ” channel-pairs can be assigned to each cell.

For eighty channel-pairs and N = 7, eleven to twelve channel-pairs can be assigned to

each cell.

7 TRUNKING AND TRAFFIC LOAD CAPACITY

Collocated repeaters can be configured to significantly increase the amount of

supportable communications traffic. Utilizing a concept known as trunking, many more

users can be served by sharing a finite number of radio channels, similar to how a finite

number of telephone trunk lines connecting telephone central office switches can be

shared by a large number of individual telephone customers. This is possible because of

the statistics related to any particular user needing access to a telephone circuit, or, in this

case, a radio channel. These statistics have been well documented and are known as

Erlang traffic queueing theory. A family of curves has been developed that illustrates the

gains possible in system capacity by incorporating trunking strategies, and is presented in

Figure 24.

Erlang-C Model .

Blocked Calls Delayed .

0.1

1

10

0.1 1 10

Offered Traffic Load (Erlangs)

Probability 

of Delay (%) 1

2

3

4

5

6

7

8

Number of 

channels

Figure 24. Erlang-C traffic queueing theory relating the

traffic load offered to the network to the number

of trunking channels.

The unit of measure of traffic intensity is known as the Erlang. The Erlang-C (blocked

calls delayed) model is presented here. The model assumes that channel requests arrive

randomly and that there is an infinite population of users. A blocked user will be queued

up to some predetermined time pending a channel grant. If the user is not assigned to a

traffic channel within this period of time, the request is dropped, the user gets a “system

busy” indication, and the user is returned to the population pool. If returned to the

population pool, the model further assumes that the user is no more likely to initiate a
38

follow-on request for an available channel than any other user in the population pool is to

generate a channel request.

To use Figure 24, a maximum acceptable probability of being denied immediate

assignment to a traffic channel must be known. For example, assume that a 2%

probability of a call not being immediately granted a traffic channel is acceptable. Then,

on average, 2% of the time that a user initiates a channel request by depressing the radio’s

PTT switch, the system would queue the call request because all trunk channels were

busy. Find the 2% blocking point on the “Probability of Delay” axis of the graph and

move horizontally across to where it intersects the appropriate “No. of Channels” curve.

Then move vertically down from this point to the “Offered Traffic Load” axis.

Consider a trunked system with eight channels at each site. One of these channels will be

reserved exclusively for control channel functions and the remaining seven channels will

be available for message traffic. If a 2% probability of blocking is desired, the total

offered load that this trunking system could support would be about 2.6 E.

Sixteen non-trunked simplex channels,*

 with the same 2% probability of blocking, would

support an offered load of 16 × 0.02, or 0.32 E.†

 For these assumed conditions, trunking

yields about an eight-fold increase in the amount of offered load, versus an equivalent

number of non-trunked radio channels.

To equate the offered traffic load to the number of talk groups that can be carried by a

trunking system, the average duration of a conversation, known as circuit holding time H,

the average call request rate μ, and the maximum permissible queuing time tq must be

known. The product of the first two terms gives the offered traffic load per talk group, Au.

The total number of talk groups U is the quotient of the total offered traffic load A (from

Figure 24) and the offered traffic load per talk group Au. That is,

Au = μ H

U = A / Au (27)

Figure 24 gives the probability that a channel request will be delayed. Multiplying this

probability by the factor e

−

(C− A)tq

H gives the probability that a channel request will be

delayed longer than time tq, where C is the number of traffic channels and the other

variables are as previously defined. After time tq, the delayed call is dropped.

 

*

 The comparison of seven trunked duplex channels to sixteen non-trunked simplex channels is made

because: (1) repeaters require one channel for transmit and a second channel for receive, while pointto-point simplex uses the same channel for both transmit and receive, and (2) a trunked system will

dedicate one channel-pair to the control channel so it will not be available as a traffic channel.

†

 The offered radio traffic load, in Erlangs, of a single non-trunked radio channel is equal to the

probability, in percent, that a user will not gain immediate access to a traffic channel, divided by 100.
39

8 EQUIPMENT COSTS

A market survey of TIA-102 radios yielded six* major suppliers. Their product offerings

are summarized below in Table 4. More products, from these and new manufacturers not

listed here, are expected to enter the marketplace soon, but as of this writing, they are still

awaiting FCC type acceptance certification.

Table 4. Project 25 Radio Prices

Cost

Radio Portable Mobile Base/Rptr

Manufacturer "A" 2075 150 500 125 400 405 3655

Manufacturer "B" 1710 495 135 150 611 3101

Manufacturer "C" 1850 495 135 150 113 2743

Manufacturer "C" 8606 495 170 225 9496

Manufacturer "D" 1439 1061 92 973 3565

Manufacturer "D" 1507 1021 86 711 3325

Manufacturer "D" 4887 898 132 1200 1958 9075

Manufacturer "E" 2180 297 148 220 2845

Manufacturer "E" 15157 297 148 370 15972

Req'd Misc. 

Accessories Subtotal Fact/Vendor Training

Voice + Data O&M manuals Pgm/Maint 

Software

Project 25 

Trunking

DES-OFB 

Encryption 

Collocated repeaters at base station sites require RF combining equipment as was

discussed in Chapter 5. Representative equipment prices are given in Table 5.†

Table 5. RF Combiner Prices

T8/R8 w/2 Antennas Cavity 7.0 8.0 $64K $8.0K

Manufacturer #1 T8/R8 w/1 Antenna Cavity 8.0 8.0 $75K $9.4K

T5/R5 w/2 Antennas Cavity 4.5 4.5 $33K $6.6K

T5/R5 w/1 Antenna Cavity 6.0 6.0 $47K $9.5K

T4/R4 w/2 Ant (Var 1) Cavity 4.0 4.5 $19K $4.7K

T4/R4 w/2 Ant (Var 2) Cavity 5.5 7.0 $28K $7.0K

T4/R4 w/1 Ant (Var 2) Cavity 7.0 7.0 $38K $9.5K

Manufacturer #2 T8/R8 w/2 Antennas Hybrid 12.5 1.0 $17K $2.1K

T8/R8 w/1 Antenna Hybrid 13.5 1.0 $20K $2.5K

T5/R5 w/2 Antennas Hybrid 9.0 1.0 $12K $2.3K

T5/R5 w/1 Antenna Hybrid 10.0 1.0 $15K $3.0K

T4/R4 w/2 Ant (Var 1) Hybrid/Cavity 8.0 1.0 $9K $2.3K

T4/R4 w/2 Ant (Var 2) Hybrid 8.0 1.0 $9K $2.3K

T4/R4 w/1 Ant (Var 2) Hybrid 9.0 1.0 $12K $3.0K

Manufacturer #3 T8/R8 w/2 Antennas Cavity 3.8 1.0 $16K $2.0K

T8/R8 w/1 Antenna Cavity 6.0 1.0 $19K $2.5K

T5/R5 w/2 Antennas Cavity 3.5 1.0 $10K $1.2K

T5/R5 w/1 Antenna Cavity 5.2 1.0 $13K $1.6K

T4/R4 w/2 Ant (Var 1) Cavity 3.9 1.0 $10K $1.2K

T4/R4 w/2 Ant (Var 2) Cavity 3.9 1.0 $10K $1.3K

T4/R4 w/1 Ant (Var 2) Cavity 5.2 1.0 $12K $1.5K

Manufacturer #4 T8/R8 w/2 Antennas Cavity 4.9 4.1 $18K $2.3K

T5/R5 w/2 Antennas Cavity 4.3 3.5 $11K $2.3K

T4/R4 w/2 Ant (Var 1) Cavity 4.1 3.3 $9K $2.3K

T4/R4 w/2 Ant (Var 2) Cavity 4.5 3.7 $9K $2.3K

Manufacturer #5 T8/R8 w/2 Antennas Hybrid/Cavity 6.0 3.0 $14K $1.8K

T8/R8 w/1 Antenna Hybrid/Cavity 10.0 7.0 $20K $2.5K

T5/R5 w/2 Antennas Cavity 3.3 3.0 $9K $1.8K

T5/R5 w/1 Antenna Cavity 7.3 7.0 $15K $3.1K

T4/R4 w/2 Ant (Var 1) Cavity 2.8 2.3 $8K $1.9K

T4/R4 w/2 Ant (Var 2) Hybrid/Cavity 6.0 2.5 $9K $2.1K

T4/R4 w/1 Ant (Var 2) Hybrid/Cavity 10.0 6.5 $15K $3.7K

Rx 

System 

Loss (dB)

System 

Cost

Cost per 

Channel

Combiner 

Manufacturer Configuration Design

Tx 

System 

Loss (dB)

 

*

 One of the suppliers manufactures base station equipment for resale under license by other

portable/mobile equipment manufacturers and therefore is not explicitly identified in Table 4.

†

 Private communication, Motorola (Salak), 1998. By way of example, in “Configuration,” “T5/R5 w/1

Ant” means a 5-channel repeater duplexed onto a single antenna, while “w/2 antennas” means separate

antennas for transmit and receive. “(Var 1)” and (Var 2)” refer to proposed variations in the 4-channel

combining schemes.
40

Antenna costs, both mobile and base, are neglected here. Likewise, costs for towers,

communications huts, coaxial cable, etc., are not considered here because it is assumed

that existing antennas and facilities will be reutilized to the maximum extent possible as

the present analog FM systems are replaced.

9 AN ALTERNATIVE BAND PLAN

An alternative to the WCTF band plan is discussed in this chapter. This alternative plan,

hereinafter referred to as the “ITS band plan,” occupies the same block of railroad VHF

spectrum as does the WCTF band plan. That is, both plans are composed of 181 channels

spaced every 7.5 kHz, from 160.215 MHz to 161.565 MHz.

9.1 Description

A graphic presentation of the ITS band plan is shown in Figure 25. Compare this band

plan to the WCTF band plan shown in Figure 1. The structure of the two band plans is

very similar. The ITS version has two blocks of spectrum, from 160.215 to

160.7925 MHz and 160.950 to 161.5275 MHz, that comprise 78 trunked duplex voice

channel-pairs. The two blocks of spectrum comprised of 5 channels apiece (from 160.800

to 160.830 MHz and 161.535 to 161.565 MHz) are non-trunked duplex channel-pairs.

The remaining block of spectrum consists of 15 simplex channels (from 160.8375 to

160.9245 MHz).

1

6

0

.

2

1

5

1

6

0

.

7

9

2

5

1

6

0

.

8

0

0

1

6

0

.

8

3

0

1

6

0

.

8

3

7

5

1

6

0

.

9

4

2

5

1

6

0

.

9

5

0

1

6

1

.

5

2

7

5

1

6

1

.

5

3

5

1

6

1

.

5

6

5

(78) (5) (15) (78) (5)

Figure 25. Railroad VHF band and the alternative ITS band

plan.

The 78 duplex channel-pairs are apportioned among thirteen trunk groups of six channelpairs each. This is in contrast to WCTF’s ten trunk groups of eight channel-pairs each.

The trunk groups of the ITS band plan are interstitially placed in the frequency domain, as

depicted in Figure 26. Compare this figure to Figure 2.
41

trunk group

channel spacing

97.5 kHz

adjacent

channel

spacing

7.5 kHz

freq

duplex channel

T–R split 735 kHz

trunk group

channel spacing

97.5 kHz

trunk group

channel spacing

97.5 kHz

duplex channel

T–R split 735 kHz

duplex channel

T–R split 735 kHz

(98 x 7.5)

Figure 26. ITS band plan’s channel spacing.

The channel spacing at each site, and the transmit-receive frequency split differ between

the two plans, but both versions will easily support legacy analog FM systems, as the

frequency splits of both plans are multiples of 15 kHz.*

During the migration period from legacy analog FM to TIA-102 digital, the arrangement

of interstitial channels is somewhat different between the two band plans, but they are

essentially equivalent. For the WCTF plan, legacy systems that cannot be programmed to

the new interstitial channels (i.e., at odd multiples of 7.5 kHz, such as 160.7925 MHz)

are constrained to operate only on half of the available trunk groups. The frequencies of

these trunk groups are divisible by 15 kHz. Under the ITS band plan, older legacy analog

FM radios that cannot be channeled to these interstitial frequencies are constrained to

operate on half of the frequencies in each one of the trunk groups.†

 

*

 Transmit-receive frequency splits — WCTF: 720 kHz. ITS: 735 kHz.

† For example, frequency assignments of two adjacent trunk groups for both the WCTF and ITS band

plans are:

RX TX RX TX RX TX RX TX

160.2150 160.9350 160.2225 160.9425 160.2150 160.9500 160.2225 160.9575

160.2900 161.0100 160.2975 161.0175 160.3125 161.0475 160.3200 161.0550

160.3650 161.0850 160.3725 161.0925 160.4100 161.1450 160.4175 161.1525

160.4400 161.1600 160.4475 161.1675 160.5075 161.2425 160.5150 161.2500

160.5150 161.2350 160.5225 161.2425 160.6050 161.3400 160.6125 161.3475

160.5900 161.3100 160.5975 161.3175 160.7025 161.4375 160.7100 161.4450

160.6650 161.3850 160.6725 161.3925 ----

160.7400 161.4600 160.7475 161.4675 ----

W C T F B a n d P l a n

T r u n k G r o u p B

I T S B a n d P l a n

T r u n k G r o u p A T r u n k G r o u p A T r u n k G r o u p B

For the WCTF band plan, all frequencies from Trunk Group B (and similarly for Trunk Groups

D, F, ...) are from the new interstitial frequencies. For the ITS band plan, half of the frequency-pairs in

each trunk group are from the new interstitial frequencies.
42

The non-trunked channels could be configured as a single 5-channel-wide duplex data

channel and as a single 15-channel-wide simplex data channel, or as a single asymmetric

duplex data channel.*

9.2 Multichannel Passband and Guardband Requirements

Figure 27 shows the aggregate transmission bandwidth of a multichannel RF signal

utilizing ITS’s band plan, along with the corresponding “guardband” between the most

closely-spaced transmit and receive frequencies. Also shown in the figure, as dashed

lines, are the WCTF passband/guardband data from Figure 11. An individual site

complying with the ITS band plan†

 and using all six possible channels would require a

transmission bandwidth of (6 - 1) × 97.5 + 12.5 = 500 kHz. With a transmit-receive

frequency split of 735 kHz on a single channel, the separation between the lowestfrequency transmit channel and the highest-frequency receive channel is

735 - 500 = 235 kHz.

ITS Channel Plan .

Multichannel Passband/ .

Guardband Requirements .

0

200

400

600

800

12345678

N = Number of Channels

Frequency 

Passband/ 

Guardband 

(kHz)

WCTF Transmission

Bandwidth (kHz)

WCTF Guardband

TX1 – RXN (kHz)

ITS Transmission

Bandwidth (kHz)

ITS Guardband

TX1 – RXN (kHz)

12.5

110.0

207.5

305.0

402.5

500.0

722.5

625.0

527.5

430.0

332.5

235.0

Figure 27. ITS band plan passband and guardband

constraints.

Figure 27 can be somewhat misleading in that it appears that the WCTF band plan offers

a narrower transmission bandwidth and a larger transmit-receive guardband for the same

number of channels. This is true, but one must not forget that if a WCTF-configured site

 

*

 Wider bandwidth channels permit faster data throughput. Duplex channels improve the efficiency of

data transfer by reducing channel contention. Asymmetric channels permit a higher data throughput

(using a larger bandwidth) in one direction than in the other direction.

†

 735-kHz TX-RX frequency split, 97.5-kHz channel spacing.
43

is only using six or fewer duplex channels, then there are two or more channels at that site

that are never used. This is a waste of radio spectrum resources. An alternative

comparison between the two plans contrasts the passbands and guardbands of fullyutilized sites (i.e., the maximum number of channels used at each site), or of equalpercentage utilization (i.e., 50% = 3 channels for the ITS plan and 50% = 4 channels for

the WCTF plan). Viewed in this light, the ITS band plan provides a narrower aggregate

multichannel transmission bandwidth and larger guardband protection between the

transmit and receive frequencies.

9.3 Intermodulation Interference

The method used by ITS to determine potential intermodulation frequencies was

described in Section 5.5. To briefly recap, the bandwidth of a “k

th-order” harmonic or of a

“k

th-order” intermodulation product frequency is “k” times the bandwidth of the original

signals. Therefore, if the difference between the frequency of an intermodulation

interference signal and the center frequency of a receiver is less than the sum of half the

receiver bandwidth and “k” times half the transmitter bandwidth, that situation is

“flagged” as an intermodulation “hit” (refer to Figure 13 and Equation (2)).

Using this methodology, an intermodulation analysis was conducted on both the WCTF

and ITS band plans. Neither plan had any third-order hits. However, the WCTF plan

showed potential for fifth-order intermodulation interference, whereas the ITS plan

showed no intermodulation potential until the seventh-order.*

Section 5.5 noted that while the above approach identifies the potential for

intermodulation interference to occur, whether it actually does or not depends on many

other factors such as:

• individual transmitter power spectral densities,

• ambient receiver noise level,

• intermodulation rejection specification of the receiver,

• amount of attenuation that transmitter signals experience as they propagate

through the various hybrids, cavities, postselectors, and preselectors in the

transmitter-to-receiver path, and

• the probability that the offending transmitters are simultaneously transmitting.

Nevertheless, the ITS band plan indicates less potential for the occurrence of

intermodulation interference than does the WCTF band plan, since seventh-order IMLs

will be at lower power levels than fifth-order IMLs.

 

*

 Data output analysis files are available in electronic format from the author.
44

9.4 Trunking and Traffic Load Capacity

Erlang traffic theory was discussed in Chapter 7. Figure 24 showed that WCTF’s eightchannel trunked design is clearly superior to ITS’ six-channel design insofar as traffic

handling capacity is concerned. For a 2% probability of channel requests being queued,

the WCTF plan has about 67% greater traffic capacity than the ITS plan. However, the

WCTF band plan is more limited in its possible cellular topologies.

9.5 Cellular Topologies

Section 4.2 notes that TIA-102 radios have a bandwidth of 12.5 kHz, but the railroad

spectrum is channeled every 7.5 kHz. This means adjacent-channel transmissions from

neighboring cells might interfere with intended reception of on-channel signals. One way

to circumvent this problem is to assign the frequencies of the neighboring cell sites such

that each site is at least two channels offset from all its neighbors. In a 7-cell topology,

however, the WCTF band plan cannot achieve a 2-channel offset between all neighboring

cells, whereas the ITS band plan can. These situations are depicted in Figure 28. Notice

that after several iterations of swapping trunk groups around, the WCTF plan still has

neighboring cells whose channel assignments are only offset by one channel (here, cells 3

and 4, and 6 and 7). With thirteen trunk groups available, the ITS plan can maintain a

2-channel offset between any one cell and all its neighbors. Until 6.25-kHz bandwidth

equipment is available, the ITS plan provides the advantage in adapting to different

cellular topologies.

1

3

7

4 6

7

8

4

4 6

7

6 10

3

8 10 3

8 10

1

5 3

7

9 11

7

13

9

9 11

7

5

3

13 5 3

13

11

(a) WCTF (b) ITS

Figure 28. Implementing a 7-cell topology with

neighboring cells offset in frequency by two

channels (15 kHz).
45

Section 9.1 noted that some older analog FM systems cannot operate on the new

interstitial channels. This would limit the WCTF band plan to half of the ten trunk groups

during the migration period. In this situation, a 7-cell topology cannot be implemented.

With the ITS band plan, the new interstitial frequencies are commingled with the

“legacy” frequencies in each and every trunk group, as the footnote on page 41 explains.

What this means is that while the ITS band plan can accommodate 7-, 9-, 12-, and 13-cell

topologies, each cell has only 2, vice 5, traffic channels available. Using the example

scenario described in Chapter 7 (2% probability of a channel request being queued),

Figure 24 indicates that a trunked 3-channel ITS-configured cell site can only carry

0.21 E of radio traffic. In contrast, a 6-channel site can carry 1.5 E. This is still an

improvement, however, over the 0.06 E that a non-trunked 3-channel duplex site could

carry, and is comparable to the 0.32 E that sixteen non-trunked simplex channels could

carry.

9.6 Comparison of the ITS and WCTF Band Plans

Both the WCTF and ITS band plans have their own advantages and disadvantages.

Table 6 summarizes the salient features of both plans. Reviewing these features in the

context of all the previous discussions should enable the railroads to select a band plan

best suited to their needs.

Table 6. Features of the ITS and WCTF Band Plans

P a r a m e t e r W C T F I T S

Spectrum 160.215-161.565 160.215-161.565

Total no. of Channels 181 181

No. of Trunked Duplex Channels 80 78

No. of Trunk Groups 10 13

No. of Control Channels per Trunk 1 1

No. of Traffic Channels per Trunk 7 5

Traffic Cap'y @ 2% Blocking 2.6 E 1.5 E

No. of Non-Trunked Duplex Channels 5 5

No. of Simplex Channels 11 15

Transmitter Site Channel Spacing 75 kHz 97.5 kHz

Repeater Frequency Split 720 kHz 735 kHz

Support 7-Cell Topology with 15-kHz Channel Spacings? No Yes

Lowest Order of Intermodulation Interference that could 

occur within frx ± 6.25 kHz 5th-order 7th-order

10 SUMMARY, ISSUES, AND OBSERVATIONS

The Federal Communications Commission (FCC) has encouraged LMR manufacturers to

design new equipment that incorporates narrowband and trunking technologies in order to

increase radio system capacity and improve spectrum utilization, particularly in the

crowded very high frequency (VHF) bands [1]. New equipment designs that do not use

narrowband techniques will likely be denied FCC equipment type acceptance. This

directive does not affect existing equipment or newly manufactured equipment designed
46

in accordance with existing type acceptances. However, as the state-of-the-art in radio

technology continues to advance, newly introduced radio systems and equipment will, by

necessity, be narrowband. Users should begin planning now to deal with migration and

compatibility issues when they introduce new equipment and systems into their existing

LMR infrastructures.

The railroads have responded to the FCC’s directive by forming an ad-hoc industry

working group, the WCTF, to address the challenge and opportunities offered by the

FCC’s realignment initiative. WCTF has proposed a channel plan and is developing an

equipment migration strategy.

As the railroad industry has proceeded with this initiative, several issues have been

identified. An assessment of each is proffered by the Institute for Telecommunication

Sciences.

ISSUE: Performance of new equipment — within the constraints of the given channel

assignments, will the new equipment perform adequately? Is it backward-compatible with

the older equipment now in service? Is the new equipment a proprietary design, or does it

conform to recognized industry standards, ensuring interoperability between different

vendors’ equipment?

ASSESSMENT: New TIA-102 “Project 25” digital equipment is backward-compatible

with 15-kHz analog FM equipment. Project 25 is an open standard architecture, so

manufacturers building equipment complying to the specification can interoperate with

other Project 25 equipment. Project 25 is not a proprietary design. WCTF has

recommended Project 25 as the railroad’s standard VHF LMR platform.

ISSUE: Channel assignments — are there enough radio channels to support all the

business processes of the railroad industry? Is the voice traffic loading equally distributed

across the available channels? Are there any techniques that can be employed to increase

the traffic capacity?

ASSESSMENT: A collection of radio channels, each dedicated solely to a specific class

of users, does not lend itself well to distributing the offered message traffic load

efficiently among the available spectrum. While some channels might be lightly loaded,

other radio channels, such as dispatch, may be very heavily loaded, giving the impression

of not enough spectrum being available to adequately support the railroads’ business

needs and processes.

Trunking increases the traffic capacity of finite communications resources by distributing

the offered message traffic load equally among the available radio channels, so one radio

channel is not heavily loaded while others remain virtually unused. The ability to assign

system access priorities to talk groups helps ensure that critical functions can always gain

access to the radio system by pre-empting routine (i.e., non-safety-critical) radio

communications, should all available radio channels be occupied. Of the two band plans

presented here, the WCTF plan provides about 67% greater trunked-traffic capacity than
47

the ITS band plan; however, there could be situations where adjacent-channel interference

could limit the usefulness of the WCTF band plan.

ISSUE: Interference — will the proposed new equipment cause interference to the older

existing equipment? Will the older systems cause interference to the new systems? If

repeaters and base stations will be collocated (such as would be the case for trunked

systems), what is the likelihood that intermodulation interference will be present? If

present, can it be adequately suppressed? Will cochannel and adjacent-channel

interference be a problem?

ASSESSMENT: Two of the more troublesome issues that must be considered are

adjacent-channel interference, and intermodulation interference arising from the

collocation of multiple channels and their frequency assignments.

Current Project 25 radios are designed with a 12.5-kHz bandwidth, but railroad VHF

radio channels are spaced every 7.5 kHz. This means adjacent-channel transmissions will

encroach on desired signals. One approach to alleviate this situation is to ensure that

transmitters in neighboring regions are offset in frequency by at least two channels

(15 kHz). The WCTF plan presents more difficulties in implementing a typical 7-cell

topology than does the ITS plan.

Using the methodology described in Section 5.5, the ITS band plan is more resistant to

co-site intermodulation interference than is the WCTF band plan.

ISSUE: Coverage — For a given level of speech intelligibility or effective data

throughput, will the proposed radio system provide adequate geographic coverage?

ASSESSMENT: Measurements performed on a “typical” Project 25 radio indicate that

for a given level of speech intelligibility, the Project 25 digital modulation format is

superior to the traditional analog FM format, providing greater geographic coverage.
48

11 REFERENCES

[1] Federal Communications Commission, “Replacement of Part 90 by Part 88 to

revise the private land mobile radio services and modify the policies governing

them,” PR Docket 92-235, Federal Communications Commission, Washington

DC, 1992.

[2] Telecommunications Industry Association, Project 25, the TIA-published

102-series documents, Jun. 1998.

[3] Title 47 Code of Federal Regulations Part 90, paragraph 91 (47 CFR 90.91), US

Government Printing Office, 1997.

[4] Telecommunications Industry Association, “Wireless communications

systems - performance in noise and interference limited situations - recommended

methods for technology-independent modeling, simulation and verification,”

Technical Service Bulletin TSB-88, Jan. 1998.

[5] J. Vanderau, “Delivered audio quality measurements on Project 25 land mobile

radios,” NTIA Report 99-358, Nov. 1998.

[6] Telecommunications Industry Association, “Land mobile FM or PM

communications equipment measurement and performance standards,”

TIA/EIA-603, Feb. 1993.

[7] Telecommunications Industry Association, “Digital C4FM/CQPSK transceiver

measurement methods,” TIA/EIA TSB-102.CAAA, May 1997.

[8] S. Voran, “Objective estimation of perceived speech quality using measuring

normalizing blocks,” NTIA Report 98-347, Apr. 1998.

[9] R. Holbeche, Land Mobile Radio Systems, London: Peter Peregrinus Press, 1985.

[10] R. Sagers, “Intercept point and undesired responses,” 32nd IEEE Vehicular

Technology Conference, May 23-26 1982, pp. 219-230.

[11] M. Hata, “Empirical formula for propagation loss in land mobile radio services,”

IEEE Trans. Veh. Technol., Vol. VT-29, No. 3, pp. 317-325, Aug. 1980.

[12] Y. Okumura, et al., “Field strength and its variability in VHF and UHF landmobile radio service,” Rev. of Elec. Comm. Lab., Vol. 16, Nos. 9-10, pp. 825-873,

Sep.-Oct. 1968.
49

[13] G. Stueber, Mobile Communications, Norwell MA: Kluwer Acaemic Publishers,

1996.

[14] W. Lee, Mobile Communications Design Fundamentals, New York: John Wiley

& Sons, 1993.

[15] G. Hess, Land-Mobile Radio System Engineering, Boston: Artech House, 1993.

[16] J. Parsons, The Mobile Radio Channel, New York: John Wiley & Sons, 1992.

[17] T. Rappaport, Wireless Communications, Principles and Practice, New Jersey:

Prentice-Hall, 1996.