NTIA Report 08-451

ASSESSMENT OF ALTERNATIVE FUTURE 

FEDERAL LAND MOBILE RADIO SYSTEMS

 

technical report

U.S. DEPARTMENT OF COMMERCE National Telecommunications and Information Administration
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NTIA Report 08-451

ASSESSMENT OF ALTERNATIVE FUTURE 

FEDERAL LAND MOBILE RADIO SYSTEMS 

Kim Cai

Bernard Joiner

Robert Matheson

Edward Drocella

Gary Patrick

David Anderson

U.S. Department of Commerce

Carlos M. Gutierrez, Secretary 

Meredith A. Baker, Acting Assistant Secretary

for Communications and Information

December 2007
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i

EXECUTIVE SUMMARY

In May 2003, President Bush established the Spectrum Policy Initiative to promote the development 

and implementation of a United States spectrum policy for the 21st century. In response to the 

Spectrum Policy Initiative, the Secretary of Commerce established a Federal Government Spectrum 

Task Force and initiated a series of public meetings to address policies affecting spectrum use by the 

federal government, state, and local governments, and the private sector. In June 2004, the Secretary 

of Commerce released two reports that included the recommendations resulting from these activities. 

In November 2004, the President directed the federal agencies to develop a plan to implement the

recommendations contained in the reports. One of the recommendations called for the National 

Telecommunications and Information Administration (NTIA) to develop analytic approaches, 

software tools, and engineering techniques for evaluating and improving the efficiency and 

effectiveness of federal spectrum use. 

To evaluate the efficiency of federal spectrum use, NTIA performed a study that compares the 

spectrum resources used by several alternative land mobile radio (LMR) system architectures 

employing trunked radio technology to the spectrum resources used by the current conventional 

LMR systems. This study considered the 162-174 MHz federal LMR band in the Washington, D.C. 

area. NTIA selected the Washington, D.C. area because it represents a spectrally congested 

environment and the 162-174 MHz band because it represents the most heavily used federal land 

mobile frequency band.

LMR systems operate using conventional and/or trunking methods. Conventional LMR systems 

dedicate a single channel (radio frequency channel) to a specific group of users who share it. Since 

radios on conventional LMR systems transmit and receive on a single channel, the user must wait if 

the channel is occupied by another user. Trunking is a proven technology that permits a large 

number of users to share a relatively small number of channels. Unlike conventional LMR 

technology, trunking allows for the automatic sharing of multiple channels. The trunked system 

dynamically allocates the mobile user’s access to the available channels. Currently, most of the 

federal agencies are using conventional LMR systems in the 162-174 MHz band. However, several 

agencies are deploying trunked LMR systems.

The NTIA study presents three alternative trunked LMR system architectures. The distinguishing 

characteristic of these three system architectures is the size of the service area associated with the 

trunked system base stations. The service area represents the area over which the base station 

supports radio communications with mobile users. NTIA considered three system architectures. 

The first system architecture uses large service areas for the entire coverage area (Large-ServiceArea-Only). The second system architecture uses a combination of medium service areas where 

there is a high concentration of users and large service areas where there are a medium or low 

concentration of users (Large-Medium-Service-Area-Mixed). The third system architecture is a 

combination of overlapping large and small service areas with the small service areas used for high 

concentrations of users (Large-Small-Service-Area-Overlapping). NTIA also considered three 

potential levels of federal agency participation: 30 percent agency participation representing partial 

participation by the current federal users of the conventional LMR systems; 100 percent agency 

participation representing full participation by the current federal users of the conventional LMR 

systems; and 300 percent agency participation representing future expanded use by the federal users. 

The three system architectures combined with the three levels of agency participation provides nine 

unique trunking scenarios. NTIA studied each trunking scenario within a 100-mile radius coverage 
ii

area centered in Washington, D.C. The frequency assignment data from the GMF and channel 

occupancy measurements performed by the NTIA Institute for Telecommunication Sciences (ITS) 

enabled NTIA to derive traffic levels expressed in Erlangs for the service area of each base station. 

The traffic levels provided a basis to determine the number of channels required (spectrum 

requirements) for the different trunking scenarios. NTIA developed spectrum requirements for each 

trunking scenario based on 12.5 kHz channel spacing in the 162-174 MHz band, and a 70-mile (113 

kilometer) frequency reuse distance criterion used by the Federal Communications Commission 

(FCC) for LMR systems. The table below summarizes the number of frequency assignments 

required for each of the nine trunking scenarios considered in this study. 

Number of Required Frequency Assignments in the 162-174 MHz Band 

for Different Trunking Scenarios

Trunked LMR System 

Architecture

Number of Required Frequency Assignments in the 162 – 174 MHz Banda

(100 Mile Radius Coverage Centered in Washington D.C.)

30% Agency 

Participationb

(partial participation, 

the remaining 70% 

continue with 

conventional systems)

100% Agency 

Participation

(current level – total 

participation, all 

conventional system 

users participate in the 

trunking system)

300% Agency 

Participation (trunking 

system supporting three 

times the current 

number of users)

Large-Service-Area-Only 

Systemc

124d166 264

Large-Medium-Service-AreaMixed System146 194 296

Large-Small-Service-AreaOverlapping System158 200 302

a. Based on 12.5 kHz channel spacing, the 162-174 MHz band consists of 960 channels.

b. The required number of frequencies shown for 30% level of agency participation represents only the 

frequencies required for the trunked system. In addition, the 70% of users that remain employing conventional 

LMR systems would require approximately 367 frequency assignments. 

c. Service area is the area over which the base station supports radio communications with mobile users.

d. This report assumes access to the entire 162-174MHz band. However, a single agency does not have access to 

the entire band, but is limited to a subset of frequencies (e.g., allotments). In many instances, it may not be 

possible to select enough interference free frequencies (inter-modulation and adjacent channel interference) to 

satisfy the requirements for a large number of channels at a single base station.

As of November 2002, the GMF had 524 frequency assignments associated with base stations at 

specific locations in the 162-174 MHz band within a 100-mile radius of Washington D.C. The 524 

frequency assignments do not include area frequency assignments (e.g., base stations are not 

constrained to a specific location) or other non-LMR frequency assignments (e.g., weather 

channels). As shown in the table above, frequency requirements for the nine trunking scenarios fall 

far below the 524 frequency assignments currently used by conventional LMR systems with base 

stations at specific locations. The frequency requirements for the trunking scenarios contained in 

this study also considered additional channel usage to support emergencies and future growth as 

shown for the 300 percent level of agency participation.

For the 100 percent level of agency participation, approximately 32 percent or 166 of the 524

frequencies in the GMF are needed for the Large-Service-Area-Only System, approximately 37 
iii

percent or 194 are needed for the Large-Medium-Service-Area-Mixed System, and approximately 38 

percent or 200 are needed for the Large-Small-Service-Area-Overlapping System. Since the 30 

percent and 300 percent levels of agency participation do not directly correspond to the existing 

users, NTIA could not determine the actual number of frequencies required for conventional LMR 

systems from the GMF, and could not perform a direct comparison of the frequency requirements for 

the trunked LMR system at these two levels. However, fewer frequencies are required for all three 

trunked system architectures for the 30 percent and 300 percent levels of agency participation as 

compared to the number of frequencies required for the existing conventional LMR systems. 

The report concludes that the trunked LMR systems use less spectrum resources than conventional 

LMR systems. In addition, trunked LMR systems servicing a large number of users are more 

spectrum efficient than trunked LMR systems servicing a small number of users due to more 

efficient sharing of the available channels. In this study, the number of users per frequency 

increased by a factor of 2.5 for the 100 percent level of agency participation and by a factor of 4.7

for the 300 percent level of agency participation as compared to the number of frequencies used for 

the 30 percent level of agency participation. 

The report also concludes that a proper design of base station frequency use in the areas where there 

is a high concentration of users is a key consideration in obtaining a high frequency reuse. Such

reuse reduces the necessary spectrum resources. If a shared trunked LMR system is implemented in 

the Washington D.C. area, NTIA believes there will be sufficient frequencies in the 162-174 MHz 

band to support more users with the appropriate frequency reuse scheme. For example, the 300 

percent level of agency participation (3 times the current number of users) requires approximately 30 

percent of the 960 assignable 12.5 kHz channels in the band. Trunked LMR systems shared by 

federal agencies would be an effective approach to more efficient use of the 162-174 MHz band.

As shown in the report, shared trunked LMR systems can be designed to use less spectrum resources 

as compared to individual conventional LMR systems, while still achieving the same grade of

service requirements (probability of a call being blocked and call waiting time). Therefore, spectrum 

efficiency can be improved while maintaining the same level of operational effectiveness. 

This report presents a study of hypothetical LMR system designs, and does not provide detailed 

design specifications. Instead, it provides a comparison of spectrum resources used by the 

alternative trunked LMR system designs and conventional LMR systems. Although this study 

addressed only the 162-174 MHz LMR band in the Washington D.C. area, NTIA believes the 

methodology presented in this report could be applied to other LMR bands in spectrally congested 

areas.
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TABLE OF CONTENTS

EXECUTIVE SUMMARY i

TABLE OF CONTENTS v

LIST OF TABLES vi

LIST OF FIGURES vi

GLOSSARY AND TERMS vii

SECTION 1 INTRODUCTION 1-1

1.1 Background 1-1

1.2 Objective 1-2

1.3 Approach 1-2

SECTION 2 DESIGN APPROACH FOR ALTERNATIVE FUTURE LMR SYSTEMS 2-1

2.1 Fundamentals of Trunking Technology 2-1

2.2 Rationale for Using Trunked Radio Systems 2-1

2.2.1 Spectrum Efficiency in Trunked Radio Systems 2-2

2.2.2 Features of Trunked Radio Systems 2-3

2.3 Erlang Formulas and System Design Assumptions 2-4

2.4 Design Methodology for the Alternative Trunked LMR Systems 2-5

2.4.1 Average Signal Capacity Maps 2-6

2.4.2 Design Channel Occupancy 2-7

2.4.3 Service Area Definitions 2-7

2.4.4 Channel Requirement Methodology 2-8

SECTION 3 ALTERNATIVE FUTURE LMR SYSTEM DESIGNS 3-1

3.1 System Architecture Selection 3-1

3.1.1 Large-Service-Area-Only System Architecture 3-1

3.1.2 Large-Medium-Service-Area-Mixed System Architecture 3-6

3.1.3 Large-Small-Service-Area-Overlapping System Architectures 3-9

3.2 Initial Frequency Requirements 3-13

3.3 Design Summary and Analysis 3-17

3.3.1 Summary Table 3-17

3.3.2 Comparison of Frequency Requirement 3-19

SECTION 4 CONCLUSION 4-1

APPENDIX A TRUNKING EFFICIENCY AND HYBRID SYSTEMS A-1
vi

LIST OF TABLES

Table 2-1. Sample Trunked LMR System Dimensioning Calculation......................................... 2-10

Table 3-1. Network Dimensioning for the Alternative Trunked LMR System with a Large-ServiceArea-Only System Architecture............................................................................................. 3-4

Table 3-2. Network Dimensioning for the Alternative Trunked LMR System with a Large-MediumService-Area-Mixed System Architecture ............................................................................. 3-8

Table 3-3. Network Dimensioning for the Alternative Trunked LMR System with a Large-SmallService-Area-Overlapping System Architecture .................................................................. 3-12

Table 3-4. Example of Frequency Reuse Scheme ....................................................................... 3-14

Table 3-5. Example of Channel Assignments (Large-Service-Area-Only System Architecture with 

30% Agency Participation).................................................................................................. 3-15

Table 3-6. Summary of Frequency Requirements for Different Trunking Scenarios................... 3-18

Table 3-7. Frequency Usage Comparison for LMR Systems ...................................................... 3-19

Table 3-8. Example of Frequency Requirements Versus Level of Agency Participation (Large 

Service-Area-Only System Architecture)............................................................................. 3-20

Table 3-9. Example of Relative Frequency Efficiency Versus Level of Agency Participation (Large 

Service-Area-Only System Architecture)............................................................................. 3-20

Table A-1. Statistical Numbers for Average Call Attempts and Average Holding Time for the Busy 

Hour..................................................................................................................................... A-1

Table A-2. Trunked Radio Network Dimensioning (Busy Hour)................................................. A-4

LIST OF FIGURES

Figure 2-1. Typical Configuration of a Trunked Radio System..................................................... 2-2

Figure 2-2. Busiest Day of the Week for Each Channel in the 162-174 MHz Band....................... 2-3

Figure 2-3. Example of ASC Map with Hexagon Service Areas Overlaid .................................. 2-10

Figure 3-1. Large-Service-Area-Only System Architecture Map .................................................. 3-3

Figure 3-2. Large-Medium-Service-Area-Mixed System Architecture Map.................................. 3-7

Figure 3-3. Large-Small-Service-Area-Overlapping System Architecture Map .......................... 3-11

Figure A-1. Trunked Radio Network Dimensioning.................................................................... A-5
vii

GLOSSARY AND TERMS

ASC Average Signal Capacity

BS Base Station

CCH Control Channel

C/I Carrier-to-Interference Ratio

DCO Design Channel Occupancy

dB Decibels

dBi Decibels of gain of an antenna referenced to the zero dB gain of a freespace isotropic radiator

dBm Decibels above one milliwatt 

dBV/m Electric field strength in decibels referenced to 1 V/m

FCC Federal Communications Commission

GMF Government Master File

Gn Network Grade of Service

GoS Grade of Service

ITS Institute for Telecommunication Sciences

kHz Kilohertz

km Kilometer

LMR Land Mobile Radio

MHz Megahertz

NMS Network Management System

NOC Network Operation Center

NOAA National Oceanic and Atmospheric Administration

NTIA National Telecommunications and Information Administration

P25 Association of Public Safety Communications Officials International 

Project 25

PCS Personal Communications Service

PSTN Public Switched Telephone Network

PSWAC Public Safety Wireless Advisory Committee

PSWN Public Safety Wireless Network

PTT Push to Talk

RCPC Reverse Channel Power Control

RSMS Radio Spectrum Measurement System 

RX Receive

SC Signal Capacity

SCAP Signal Capacity Analysis Program

TCH Traffic Channel

TX Transmit

VHF Very High Frequency (30 to 300 MHz)

V/m Microvolt per meter
viii

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SECTION 1 

INTRODUCTION

1.1 Background

The National Telecommunications and Information Administration (NTIA) is the Executive Branch 

agency principally responsible for developing and articulating domestic and international 

telecommunications policy. NTIA acts as the principal advisor to the President on 

telecommunications policies pertaining to the Nation’s economic and technological advancement 

and to the regulation of the telecommunications industry. Accordingly, NTIA conducts studies,

makes recommendations regarding telecommunications policies and presents executive branch 

views on telecommunications matters to the Congress, the Federal Communications Commission 

(FCC), and the public. Furthermore, NTIA manages federal use of the radio frequency spectrum.

In May 2003, President Bush established the Spectrum Policy Initiative to promote the development 

and implementation of a United States spectrum policy for the 21st Century. In response to the 

Spectrum Policy Initiative, the Secretary of Commerce established a Federal Government Spectrum 

Task Force and initiated a series of public meetings to address policies affecting spectrum use by the 

federal government, state, and local governments, and the private sector. The recommendations 

resulting from these activities were included in two reports released by the Secretary of Commerce 

in June 2004.1 In November 2004, the President directed the federal agencies to develop a plan to, 

implement the recommendations contained in the reports.2 One of the recommendations called for

the NTIA to develop analytic approaches, software tools, and engineering techniques for evaluating 

and improving the efficiency and effectiveness of federal spectrum use.

As discussed in the Spectrum Policy Initiative reports, the radio frequency spectrum is a critical 

resource used by the federal government to perform congressionally mandated missions. Efficient 

use of the spectrum is one of the cornerstones for obtaining maximum usage of the available 

spectrum. NTIA and the federal agencies realize that the primary way to satisfy the growing 

demands for spectrum in the land mobile radio (LMR) frequency bands is to employ more spectrum 

efficient technologies. For example, in response to Congressional legislation, NTIA developed a 

plan that selected a 12.5 kHz channel width for re-channeling the 162-174 MHz and 406.1-420 MHz 

federal LMR frequency bands, effectively doubling the number of available channels. 3 In addition 

to transmitter performance standards, NTIA has adopted receiver performance standards for LMR 

 

1. National Telecommunications and Information Administration, U.S. Department of Commerce, Spectrum Policy for 

the 21st Century – The President’s Spectrum Policy Initiative: Report 1 (June 2004), available at 

http://www.ntia.doc.gov/reports/specpolini/presspecpolini_report1_06242004.htm; 

Spectrum Policy for the 21st Century – The President’s Spectrum Policy Initiative: Report 2 (June 2004), available at 

http://www.ntia.doc.gov/reports/specpolini/presspecpolini_report2_06242004.htm. 

2. White House Executive Memorandum, Subject: Improving Spectrum Management for the 21st Century (November 

23, 2004). The latest released document for this subject is: National Telecommunications and Information 

Administration, U.S. Department of Commerce, Spectrum Management for the 21st Century – Plan to Implement 

Recommendations of the President’s Spectrum Policy Initiative (March 2006), available at 

http://www.ntia.doc.gov/osmhome/reports/ImplementationPlan2006.htm. 

3. Telecommunications Authorization Act of 1992, Pub. L. 102-538, 106 Stat. 3533 (1992).
1-2

systems in an effort to increase spectrum efficiency.4 This report assesses the use of trunked radio 

technology to increase spectrum efficiency in the federal LMR bands. 

1.2 Objective

The objective of this report is to compare the spectrum resources used by several alternative LMR 

system designs employing trunked radio technology to the spectrum resources currently used by 

conventional LMR systems to determine methods of improving spectrum efficiency for federal 

government operations. 

1.3 Approach

The study presented in this report uses the results of two previous NTIA studies. The first study 

created a database of frequency assignments from the Government Master File (GMF) in the 162-

174 MHz band, within a 100-mile radius of Washington D.C.5 NTIA selected the Washington D.C.

metropolitan area because it represents a spectrally congested environment and the 162-174 MHz 

band because it represents the most heavily used federal land mobile frequency band. As part of the 

first study, NTIA developed a metric referred to as average signal capacity (ASC) to assess the 

geographical coverage capabilities of base stations operating in the 162-174 MHz band. A second 

study used field measurements to characterize the federal LMR channel usage in the 162-174 MHz 

band.6 The study in this report uses the results of the two previous studies to derive the geographical 

coverage and traffic level specifications in terms of Erlangs needed to design alternative shared 

trunked LMR systems that would provide the same level of performance and coverage as the current 

conventional LMR systems but in a more spectrally efficient manner.7 

To evaluate and improve the efficiency of federal spectrum use, the study in this report assesses

several alternative LMR system designs in 162-174 MHz band employing trunked radio technology. 

It examines, based on frequency assignment data contained in the GMF and channel occupancy 

measurements, top-level LMR system designs that will accommodate the same amount of traffic that 

is being carried today. The study does not provide detailed design specifications or a complete set of 

specific frequencies for the alternative trunked systems. Instead, the study provides a comparison of 

 

4. Both transmitter and receiver performance characteristics must be considered for maximum spectrum efficiency. See 

National Telecommunications and Information Administration, U.S. Department of Commerce, Receiver Spectrum 

Standards, Phase 1 – Summary of Research into Existing Standards, NTIA Report 03-404 (November 2003).

5. National Telecommunications and Information Administration, U.S. Department of Commerce, Federal Land Mobile 

Operations in the 162-174 MHz Band in the Washington D.C. Area, Phase 1: Study of Agency Operations, NTIA Report 

06-440 (August 2006) (Federal Land Mobile Operations Report). English units were used to define the study area (100-

mile radius) for the calculations in the Phase 1 report. For consistency, the study in this report will continue to use 

English units.

6. National Telecommunications and Information Administration, U.S. Department of Commerce, Institute for 

Telecommunication Sciences, Measurements to Characterize Land Mobile Channel Occupancy for Federal Bands 162-

174 MHz and 406-420 MHz in the Washington, D.C. Area, NTIA Report TR-07-448 (July 2007) (Channel Occupancy 

Measurement Report). 

7. An Erlang is a traffic equivalent to full time occupancy of a channel for an hour. For example, one channel used 

continuously for 60 minutes, or two channels with a combined usage of 60 minutes.
1-3

spectrum resources used by the alternative trunked LMR system designs and conventional LMR 

systems. The alternative LMR system designs are used to determine whether a more efficient use of 

the LMR spectrum can be accomplished with a trunked LMR system. The methodology developed

in this report is general in nature, and thus can be applied to other LMR bands in other geographic 

areas.

This report presents three alternative trunked LMR system architectures for the 162-174 MHz band. 

The distinguishing characteristic of these three system architectures is the size of the service area 

associated with the trunked system base stations. The service area is the area over which the base 

station supports radio communications with mobile users. Three potential levels of federal agency 

participation were also considered in the alternative trunked LMR systems: 30 percent agency 

participation representing partial participation by the current federal users of the conventional LMR 

systems; 100 percent agency participation representing full participation by the current federal users 

of the conventional LMR systems; and 300 percent agency participation representing future 

expanded use by the federal users. The three system architectures combined with the three levels of 

agency participation resulted in nine unique trunking scenarios.

The alternative LMR system designs studied all employ proven trunked radio technologies widely in 

use today. The trunked radio network size (channel requirements) were calculated using the ErlangC model for various traffic levels along with the grade of service specification for each architecture 

in order to address the sharing of spectrum resources.8 The system spectrum requirements for each 

trunking scenario were computed based on frequency plans developed using the 70-mile (113 

kilometer) frequency reuse distance criteria specified by the FCC for LMR systems.

9

 

 

8. The Erlang model is a widely adopted network traffic analysis model that can be used to determine the channel 

requirements of a trunked radio system. 

9. 47 C.F.R. § 90.187.
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2-1

SECTION 2 

DESIGN APPROACH FOR ALTERNATIVE FUTURE LMR SYSTEMS 

The design approach for the alternative future LMR systems uses existing trunking technology. 

Trunking permits a large number of users to share a relatively small number of channels. The user’s 

access to the base station is dynamically allocated to the available channels. A brief description of 

trunking technology is provided in this section along with the design approach for the alternative 

LMR systems. Appendix A provides a more detailed description of trunked radio technology.

2.1 Fundamentals of Trunking Technology

“Trunking” gets its name from the telephone industry. A trunk is simply a telephone line between 

two central office locations that multiple users share. Often, there are many trunks between the same 

two locations. When a user wants to make a telephone call, that user receives one of these trunked 

lines to use for the duration of their call. When the call is over, that user gives up the telephone line 

and someone else can use it. 

For a trunked radio system, there is not a fixed assignment of channels to users but the assignment is 

dynamic. A radio sends a transmission to the control channel of a base station to request 

communication with a specific talk-group. An unused channel will be assigned automatically to that

radio, while the trunking central controller (computerized switch) will alert the other radios in the 

same talkgroup what channel to use to receive the message. At the completion of the call, all radios 

return to monitor the control channel for additional transmissions, and the channel is released and is 

available for other users. In a trunked system, a radio channel is assigned to a user only when the 

user is ready to communicate. This scheme minimizes the idle time of the available radio channels 

since users only access the channels when needed. When the channel is not used, the channel is 

released and returned to a common pool so it can be assigned to other users. Trunked radio 

technology takes advantage of the probability that in any number of users, not everyone will need to 

access a channel at the same time. Therefore, with a given number of users, fewer discrete channels 

are required.

2.2 Rationale for Using Trunked Radio Systems

Trunked radio systems provide the ability to send and receive voice and low data rate information in 

a highly efficient and cost effective manner. Trunked radio systems utilize technologies similar to 

the computer-controlled telephone networks to logically organize a large number of users into an 

orderly communications network. A computerized central switch, referred to as a central controller, 

makes channel selections and other decisions previously made by the user. Channel assignment is 

automatic and completely transparent to the individual users. Figure 2-1 illustrates a typical trunked 

radio system configuration. 
2-2

 

Figure 2-1. Typical Configuration of a Trunked Radio System

2.2.1 Spectrum Efficiency in Trunked Radio Systems

Trunking provides great improvements in spectrum efficiency by allowing all channels to be shared 

by all users, thus reducing congestion and requiring fewer channels and radio frequencies. By 

dynamically assigning channels between users on an “as required” basis, considerably fewer 

channels are required to satisfy the same number of users as compared to a conventional system 

using dedicated channels that are reserved even while carrying no traffic. Instead of requiring that 

traffic on a channel be kept very low in order to be immediately available to others, the trunked radio 

system ensures high channel availability by switching the new user to any channel that is not 

currently being used. This technique simultaneously permits high average traffic on channels and

high availability whenever a channel is needed. This technique is especially effective in increasing 

the amount of traffic that can be carried when users require very high channel availability. 

The improvement in spectrum efficiency will occur even if a trunked system is used by one agency 

or multiple agencies with common and/or same mission requirements, where all users have the same 

busy hour. When systems are shared by different agencies with different duties and missions, and 

the busy hours are different, the improvement from sharing is even greater (e.g., the low usage 

period for one agency could be a busy time for another agency). This allows one agency to 

accommodate its busiest-hour requirements using channels that are not needed by other agencies

experiencing low usage at that time. In the extreme case of a major emergency for one or more 

agencies, priorities could be enabled that would shift channel availability from lower-priority 

missions to the highest-priority missions, having the effect of shifting more channels to the highBackbone Network

BS

Dispatch 

Consoles

System Monitoring 

and NMS

Telephone Interconnect

BS: Base Station

NMS: Network Management System

NOC: Network Operation Center

PSTN: Public Switched Telephone Network

PSTN

BS BS BS

Central Controller

Mobile Radio 

User

Portable 

Radio User

NOC/Master Site
2-3

priority mission than would ever have been available on a non-shared, single-agency conventional 

LMR system.

The peak channel activity measured in the Washington D.C. area during an eight-day measurement 

period is shown in Figure 2-2.

10

 The figure shows the busiest hour of the entire week for each 

measured frequency in the 162-174 MHz band. The figure shows that the channel activity for each 

frequency is different throughout the week and occurs on a fairly random basis. Figure 2-2 also 

shows that there are general patterns of being more busy during the weekdays and less busy on 

weekends. The measurements indicate that the peak usage is not occurring within one specific 

period and can occur during different days of the week. The channel usage measurements indicate 

that sharing a common trunked radio system would be especially effective since the channel activity

for the different agencies is dispersed.

Figure 2-2. Busiest Hour of the Week for Each Channel in the 162-174 MHz Band

2.2.2 Features of Trunked Radio Systems

Systems employing trunked radio technology offer many benefits besides spectrum efficiency, 

which include:

 Larger coverage areas where all users on the system have coverage over the entire area, not 

just in the relatively small areas around each base station that agencies deem crucial for 

communications, which is a typical coverage area for single-agency systems;

 Interoperability with other agencies and users on the system completely defined by talkgroup management, as needed to handle special events or emergencies;

 

10. See supra note 6, the Channel Occupancy Measurements Report, NTIA Report TR-07-448, Figure 27.
2-4

 Faster system access since there is no need to monitor the channels prior to use;

 More user privacy because users in the same talk-groups are given exclusive access to a 

voice channel for the duration of a conversation;

 Flexible expansion because talk-groups can be added or modified without necessarily 

requiring additional channels or modifying existing radios;

 Dynamic regrouping which allows the system to reassign units so users can talk between 

departments for special events; and

 Protection of lost or stolen radios since any radio can be disabled remotely by the central 

controller.

These benefits allow federal users to create their own functional talkgroups for each department and 

operation group within departments, and to include specific agency requirements (e.g., multi-level 

priority, dynamic regrouping, inter-agency or multi-agency interoperability) so there should be no 

decrease in the effectiveness of an agency performing its missions. 

The ability to combine multiple departments or agencies under one system while maintaining 

independent operations is the cornerstone of the trunking advantage. The advanced features listed

above will also help ensure that each user has reliable, quick access to a channel during emergencies.

2.3 Erlang Formulas and System Design Assumptions

Erlang is a basic unit of telecommunications traffic intensity. One Erlang is equivalent to the 

amount of traffic carried in a continuously occupied channel in one hour, or 3600 seconds. The 

Erlang model is a widely adopted network traffic analysis model that is used to determine the 

channel requirements for wireline and trunked LMR systems. The Erlang-C formula is designed 

around the queuing or waiting type theory that a random call request arrives and is held in a queue 

for a specified period until the call request is satisfied.

Trunked radio systems are queuing or waiting type radio systems. Therefore, the Erlang-C model 

can be used in the network dimension computations in the study. Dimensioning or sizing a trunked 

radio system is the process of calculating the number of traffic channels required to provide an 

adequate GoS with an acceptable waiting time for the mobile users in the system. In addition to the 

number of traffic channels calculated, a control channel must be added to each base station. Each 

channel requires two frequencies for a paired transmitter and receiver (TX/RX) allowing for fullduplex operation. 

GoS is defined as the probability that a call will be blocked or delayed. For a trunked radio system, 

the GoS is a function of the probability that a call request has to wait to be served (delayed) and the 

probability that the waiting time (in the queue) exceeds the reference waiting time W0 in seconds:11

The probability that a call waiting or delay exceeds the waiting time, W0, is computed using 

Equation 2-1:

GoS = 

[ ( ) / ]

0

0

( )

N A W H

D P W W P e

 

 

(2-1)

 

11. Jose M Hernando and F. Perez-Fontan, Introduction to Mobile Communications Engineering, Artech House (1999); 

Roger L. Freeman, Reference Manual For Telecommunications Engineering, Volume 1, Third Edition, Chapter 1-5, A 

Wiley-Interscience Publication, John Wiley & Sons, Inc. (2002).
2-5

Where the probability that a call has to wait (PD) is given by the Erlang-C formula in Equation 2-2:

 





 

 







1

0

! !

!

( , )

N

K

K N

N

D

N A

N

N

A

K

A

N A

N

N

A

P A N

(2-2)

Where

PD: Probability that a call has to wait;

A: Call traffic in Erlangs;

N: Number of traffic channels;

W0: Reference waiting time in queue in seconds; and

H: Average busy hour holding time in seconds.

The average busy hour holding time H is defined as the average call duration in a busy hour that

includes radio push-to-talk (PTT) switch time, message length and channel hang time.12

When A is known, an iterative process can be performed to compute the network size in terms of the 

number of traffic channels required (N). The iterative process then increases N until the resulting 

GoS requirement is satisfied.

Typical federal public safety systems use the following parameters in the Erlang-C statistical model 

design:13

 GoS: 1 percent probability of a call having to wait longer than the allowable waiting time;

 W0: 1 second allowable waiting time; and 

 H: 4 second average busy hour holding time.

The above parameters mean that a user requesting service will obtain a channel within 1 second for 

99 percent of all requests, and calls occupy the channel 4 seconds on average. This means that if a 

channel is not immediately available (e.g. because all of the channels are in use), the request will be 

placed in a queue with other requests, and the waiting time for a channel will exceed 1 second in 

only 1 percent of the cases. 

2.4 Design Methodology for the Alternative Trunked LMR Systems

The alternative trunked LMR system designs considered in this report are based on the analysis of 

GMF frequency assignments and channel occupancy measurements in the 162-174 MHz band within 

 

12. When the PTT is released, the assigned channel remains on until the pre-programmed delay is expired. During the 

delay period, the users can return to the same channel, which refers to message trunking. If an assigned channel 

becomes available immediately upon PTT release, this is referred to as transmission trunking.

13. The design parameters used in this study were recommended by the public safety industry and radio manufacturers. 

The GoS of 1 percent is also recommended in the Public Safety Wireless Advisory Committee (PSWAC) Report, 

Spectrum Requirements Subcommittee (SRSC) Final Report, Appendix D, Public Safety Wireless Communications User 

Traffic Profiles and Grade-Of-Service Recommendations (September 1996) at 76 (676).
2-6

the Washington D.C. metropolitan area. A brief description of the GMF analysis and channel 

occupancy measurements is given below.14 

2.4.1 Average Signal Capacity Maps 

In the Federal Land Mobile Operations Report, NTIA Report 06-440, NTIA derived the ASC maps 

by processing the frequency assignment data contained in the GMF for all federal radio users. The 

ASC is a metric developed by NTIA to assess the geographic coverage of existing conventional 

radio systems and therefore provides the coverage requirements for each service area of alternative 

trunked LMR systems operating in the 162-174 MHz band. The ASC maps show the number of 

independent receivable radio signals per square mile from each base station in the GMF.

To develop the ASC map, a 100-mile radius area centered on Washington, D.C. was divided into one 

square mile subsections. The coverage areas for each base station associated with a specific location 

were determined by the Signal Capacity Analysis Program (SCAP) using a terrain dependent 

propagation model.15 The SCAP assigned each square mile subsection with a received signal level 

of at least 100 μV/m (-80 dBm) as being in the base station coverage area.16 The following 

paragraphs provide an overview of the ASC calculations.

For each base station (one frequency assignment in the GMF), the coverage area (all subsections 

with received signal strength of at least 100 μV/m or -80 dBm) was calculated by the SCAP. The 

total coverage area K in square miles was divided into one, 1/K, to determine a density function for 

that base station. If, for example, the coverage area is 200 square miles, the density function will be 

0.005/square mile. This value was then assigned to each one square mile subsection within the base 

station coverage area. Then the next base station and assigned frequency were selected and this 

procedure was repeated until all the base stations within the 100-mile study radius were taken into 

account. The ACS calculations only considered base stations with fixed locations in the GMF. 

There are also frequency assignments in the GMF that are not constrained to a specific location 

referred to as area assignments.17 Since area frequency assignments would not be used to support 

any local radio infrastructure they were not considered in the ASC calculations. 

For each one square mile subsection, the density function entries for each base station were 

combined to yield the ASC for that subsection. If the summation for each one square mile 

 

14. A detailed discussion of the GMF analysis is provided in the Federal Land Mobile Operations Report, NTIA Report 

06-440, and a detailed description of the channel occupancy measurements is provided in the Channel Occupancy 

Measurement Report, NTIA Report TR-07-448.

15. The terrain dependent propagation loss values in the SCAP were computed using the Irregular Terrain Model (ITM) 

in the point-to-point mode. The software model is available on the website: http://flattop.its.bldrdoc.gov/itm.html. 

16. The ASC maps produced in the Federal Land Mobile Operations Report, NTIA Report 06-440 assumed that the base 

station coverage areas were defined by all areas where the transmitter provided a received signal strength of at least 10

μV/m (-100 dBm). However, it was determined that the 10 μV/m receive signal strength was too low because the 10

μV/m resulting coverage areas were too spread out to be realistic, while the 100 μV/m resulted in more realistic coverage 

areas with greater concentration where actual users were expected to be, e.g., downtown urban areas and highway rather 

than mountain and rural areas.

17. Examples of area assignments include: US&P (United States and Possessions), US (the 50 states and the District of 

Columbia), and USA (the 48 contiguous states and the District of Columbia).
2-7

subsection is 0.25, this means that an average of 25 percent of one channel (one independent signal) 

is available to a randomly deployed user in that subsection. The ASC maps can then be used to 

determine the number of independent receivable radio signals per square mile. In this study, the 

ASC maps are used to provide an assessment of the geographic coverage capabilities of each base 

station for the existing conventional LMR systems. 

2.4.2 Design Channel Occupancy

The trunked LMR system design must provide adequate service at peak traffic hours as well as 

handle emergency incidents. Thus, another important factor used in the analysis to determine the 

number of channels needed for the different trunked LMR system architectures is the busy hour 

channel occupancy or usage for each channel.

The ITS Radio Spectrum Measurement System (RSMS) channel occupancy measurement effort 

provided data to compute Hourly Channel Percent Occupancy for the current LMR systems. The 

data was measured for all LMR channels, for each hour and for each day of the measurement period. 

This Hourly Channel Percent Occupancy data was then averaged across all the channels in the band 

for each hour of the day. These average values for each hour of the day were then averaged with the 

corresponding hours of the day across all days of the measurement period to compute the Band 

Occupancy by Time-of-Day. As discussed earlier, the ASC calculations did not consider area 

frequency assignments. The channel occupancy measurements on the other hand will include both 

frequency assignments with fixed base station locations and area frequency assignments. As shown

in the measurement report, if area assignments are not considered, the Band Occupancy by Time-ofDay for the LMR frequency assignments for base stations at specific locations was 2.1 percent which 

is higher than the 1.6 percent overall maximum value of Band Occupancy by Time-of-Day.18 In 

addition to accommodating routine channel usage, a future trunked LMR system should be designed 

to handle increased channel usage associated with disasters or emergencies. There should also be 

provisions for channel usage to support future growth. Therefore, for this study, NTIA decided to 

design the alternative future trunked LMR system to handle 5 percent channel occupancy across the 

band. In this study, the 5 percent is referred to as the Design Channel Occupancy (DCO). 

2.4.3 Service Area Definitions

The ASC values within the coverage area of a given base station thus were summed to determine the 

traffic level for this given base station that would need to be provided by the trunked system to 

replicate the number of users served by the existing conventional LMR systems. The coverage area 

of this given base station was defined conceptually by a hexagon service area in the study.

19

 Each 

service area was assumed to be associated with one base station. As discussed in the Section 3, 

several cases required more than one base station for a service area. The summation of the ASC 

values within the boundaries of each service area are referred to as ∑ASC. 

 

18. Figure 30 in the Channel Occupancy Measurement Report, NTIA Report TR-07-448. The details of the RSMS 

measurements and the channel usage calculations are provided in the report as well.

19. In this study, base stations are shown at the center of each service area, whereas in the real system, they would be 

located to take advantage of terrain and existing facilities.
2-8

To perform the alternative LMR trunked system design, the size of the service areas and traffic 

levels were defined. The size of the hexagon service areas were categorized as follows:

 The large service areas provide an approximate 20-mile-radius geographic coverage, and

represent the most common base station coverage and are used commonly in large 

geographic areas with a low-concentration of users. 

 The medium service areas provide an approximate 12-mile-radius geographic coverage, and

are used in the areas with a high- and medium- concentration of users. 

 The small service areas provide an approximate 7-mile-radius geographic coverage, and are 

typically used in the areas with a very high-concentration of users. 

An example of an ASC map with hexagon service areas overlaid is shown in Figure 2-3. The 

service areas for the base stations were not selected in accordance with the traffic volume or 

geographic features, but were superimposed on a map to cover the entire 100-mile radius geographic 

area considered in this study. Therefore, the service areas with a low-concentration of users can 

have a small number of users (e.g., light color areas shown in Figure 2-3) while the service areas 

with a high-concentration of users can have many users (e.g., dark green areas shown in Figure 2-3). 

Each hexagon on the map is assigned an identification (ID) number, which is used to identify the 

service area in the study. 

2.4.4 Channel Requirement Methodology

The design methodology used in this study contains several approximations and assumptions. If 

such a trunked radio system were actually built in the future, a more detailed analysis would be 

necessary to provide more accurate traffic levels for each base station. Nevertheless, the 

methodology used in this study provides a rational starting point for evaluating and comparing future 

LMR system designs.

The type of information used in designing a LMR system is usually expressed in terms of the 

number of users that could be served by a radio system. The ASC calculation determines the 

number of independent users that would need to be accommodated in a specific service area. The 

independent user refers to the independent receivable radio signals (a voice channel). The 

independent user could be a talk-group or talk-groups with multiple users, or could actually be a 

single user since many users could be simultaneously listening to a common signal (communicate 

over one channel with each other). The details of ASC calculations are described in Appendix A of 

the Federal Land Mobile Operations Report, NTIA Report 06-440.

The major steps in determining the channel requirements for the alternative trunked radio systems 

are summarized below and discussed in more detail in the preceding paragraphs. 

1. The ASC calculations were performed based on 100 μV/m received signal threshold level 

and displayed on a map, which provides the number of independent users per square mile.

2. The map defining service areas for the base stations of the trunked LMR systems

(represented by hexagons) was overlaid on the ASC map.

3. The ASC values in each square mile were summed within each hexagon service area to give 

total number of independent users to be accommodated by this service area (∑ASC).
2-9

4. The calculated ∑ASC values for each service area were multiplied by the DCO (5%) to give 

the traffic level in Erlangs required for each service area.

5. Using the Erlangs of each service area (A) and other defined parameters (GoS, H, W0), the 

number of channels required (N) for each base station was calculated using Equations 2-1 

and 2-2.

An example of such an ASC map is shown in Figure 2-3. The map legend, which appears in the 

lower right corner of Figure 2-3 shows the ASC value range and its corresponding color - the 

number in the parenthesis on the right side of the range is the count of the number of one square mile 

subsections with the ASC value in this particular range. 

The resulting ∑ASC values represent the total number of independent users that are to be serviced 

by each service area. A channel that is used 5 percent of the time, represented by the DCO in this 

study, is equivalent to saying that 0.05 Erlangs of traffic is generated by each channel. Using 

Equation 2-3, the ∑ASC value for each service area is multiplied by the DCO of 0.05 Erlangs to 

compute the amount of traffic in Erlangs that the service areas in various alternative trunked LMR 

systems should be designed to carry:

Erlangs per Service Area = ∑ASC x DCO (2-3)

The base station is assumed to be located at the center of each hexagon service area in performing 

the LMR system design analysis. Such regular hexagons approximate a realistic coverage model for 

base stations. Table 2-1 provides a sample calculation showing how the number of channels for the 

alternative trunked LMR systems is computed. 
2-10

Figure 2-3. Example of ASC Map with Hexagon Service Areas Overlaid

Table 2-1. Sample Trunked LMR System Dimensioning Calculation

Service 

Area 

ID

∑ASC per Service Area

Design 

Channel 

Occupancy

(DCO)

Grade of 

Service 

(GoS)

100% Agency Participation

Erlangs per 

Service Area = 

∑ASC x DCO

Number of 

Channels 

Required 

1 202.53 5% 1% 10.13 17

2 26.79 5% 1% 1.34 5

3 46.21 5% 1% 2.31 7

4 20.29 5% 1% 1.01 5

5 8.62 5% 1% 0.43 3
3-1

SECTION 3

ALTERNATIVE FUTURE LMR SYSTEM DESIGNS

3.1 System Architecture Selection

This section presents different designs used to determine the spectrum requirements for three 

trunked LMR system architectures. The methods used to perform the design and analysis for each of 

the trunked system architectures are described. The channel and frequency requirements for each

trunking scenario are determined and compared to those of the existing conventional LMR systems 

to develop a measure of relative spectrum efficiency. The trunked system architectures designs 

considered combinations of the following features: 

 Larger service areas to provide coverage for large geographic areas;

 Smaller service areas to provide improved coverage in areas with a high-concentration of 

users, while using larger service areas to provide coverage in areas with a medium- or lowconcentration of users; and

 Overlapping architecture, with large and small service areas overlapped in areas with a highconcentration of users, which combines the above two features while taking advantage of 

redundant service (over the large service area and the small service area) and creating higher 

channel availability during localized emergencies.

Three different trunked radio system architectures were analyzed: Large-Service-Area-Only, LargeMedium-Service-Area-Mixed, and Large-Small-Service-Area-Overlapping. The first two system 

architectures represent common characteristics and techniques employed in public safety system 

designs. The third system architecture is a design approach employing some new features for 

trunked LMR systems.20 

3.1.1 Large-Service-Area-Only System Architecture

This system architecture uses all large hexagon service areas for the entire coverage area (100-mile 

radius). Using a large service area to provide coverage over a large geographical area is a common 

design practice for public safety LMR systems. Figure 3-1 shows the service areas overlaid on the 

ASC map. The calculations used to determine the channel requirements for this system architecture 

are shown in Table 3-1. 

The first column in Table 3-1 contains the service area ID shown in the middle of each hexagonal 

service area on the map. The second column contains ∑ASC within that hexagonal service area 

derived from the 100 μV/m ASC map. The DCO in the third column indicates each independent 

user was assumed to use a channel 5 percent of the time. The fourth column provides the required 

GoS level (1%) for each service area. The number of Erlangs required for each service area to 

support the 100 percent level of agency participation (e.g., total participation in the trunked LMR 

system by federal users) was computed using Equation (2-3). The number of Erlangs for each 

service area at the 30 percent and 300 percent levels of agency participation were then computed by 

 

20. The overlapping design is a new concept where some technical requirements may not be supported by current 

trunked radio equipment such as overlapping service.
3-2

multiplying the number of Erlangs for the 100 percent level by factors of 0.3 and 3 respectively. The 

actual number of Erlangs required for each service area are shown in the first column under each 

agency participation level heading and are used to determine the number of trunking channels 

required for each service area. 

The results in Table 3-1 show that for the 30, 100 and 300 percent levels of agency participation, the 

increase of the total number of channels required for each service area is not equal to the agency 

participation level multiplier of 0.3 and 3, but is actually much less. The number of channels 

required in the service areas with a high-concentration of users (e.g., Service Area #1, #2, #3,etc.) is 

increased by a larger percentage than the number of channels in the service areas with a lowconcentration of users (e.g., Service Area #13, #14, #15, etc.). This is because the channels in the 

areas with a high-concentration of users were already carrying traffic close to the maximum number 

of Erlangs for that number of channels, and the increased traffic could be accommodated only by 

adding more channels. However, in the areas with a low-concentration of users, less traffic is 

carried on each channel, and the increased traffic could be accommodated by increasing the number 

of Erlangs on each channel.21

While interpreting the results, it should be noted that the ASC calculations were based on the 

analysis of the GMF database. The GMF does not contain data describing detailed user geographic 

locations or their true operational range. Therefore, several assumptions were made during different 

stages of the analysis. The area showing a large quantity of receivable signals on the ASC map may 

have only few users in reality. For example, Service Areas #8 and #19, west of the Washington D.C.

area, include a tall mountain ridge. Due to this geographic feature, the SCAP model predicted that 

those areas received many signals. Since it was assumed that a user can be uniformly located over 

the area where a signal can be received, a large number of users (e.g., high ASC values) are shown 

on the ASC map in these areas. However, in reality, the mountain area may have only a few users, 

and could be served by a single base station on the ridge with an antenna high enough to provide 

coverage beyond the 20-mile hexagon radius. 

Due to hardware limitations such as site inter-modulation, maximum total transmit power, noise, and 

receiver filtering, there is typically a maximum limit of 32 channels including the traffic channels 

and control channels at each base station.22 A large service area can be served by more than one 

base station. Based on the Erlang calculation, 40 channels are required for the 300 percent level of 

agency participation for Service Area #1 which is located in an area of heavy usage. The required 

number of channels is greater than can be accommodated by one base station for a practical 

engineering design. One solution for this problem is discussed in the next subsection. 

As shown in Table 3-1, the Large-Service-Area-Only System architecture requires 35 service areas 

to provide coverage to the Washington D.C. area. The total number of Erlangs (from ASC map) for 

 

21. Referring to Table A-2 in Appendix A, for example, 0.5386 Erlangs is the maximum capacity for three channels 

while 1.0103 Erlangs is the maximum capacity for 4 channels. Any increase of number of Erlangs within the range of 

0.5386 to 1.0103 can be accommodated by four channels. When the number of Erlangs exceeds the 1.0103, an extra 

channel must be added to the service area to accommodate the new users. 

22. The study in this report was based on access to the entire 162-174 MHz band. However, a single agency does not 

have access to the entire band, but instead is limited to a subset of frequencies (e.g., allotments). In many instances, it 

may not be possible to select enough interference free frequencies (inter-modulation and adjacent channel interference) 

to satisfy the requirement for a large number of channels at single base station. Therefore, the number of channels for a 

base station is restricted and much fewer than the 32 maximum channels. 
3-3

the 35 service areas is 8.33 Erlangs for 30 percent agency participation, 27.7 Erlangs for 100 percent

agency participation, and 83.3 Erlangs for 300 percent agency participation while the number of 

trunking channels required for each level of agency participation is 85, 125 and 213 respectively. 

The required channel calculations include only the traffic channels (TCH), and do no include control 

channels (CCH) that are required for a trunked LMR system. The total number of channels (TCHs + 

CCHs) required for each trunked system architecture is determined in Subsection 3.3. 

Figure 3-1. Large-Service-Area-Only System Architecture Map
3-4

Table 3-1. Network Dimensioning for the Alternative Trunked LMR System with a Large-Service-Area-Only System Architecture

Service 

Area 

ID

∑ASC per 

Service Area

Design 

Channel 

Occupancy 

(DCO)

Grade of 

Service 

(GOS)

30% Agency Participation 100% Agency Participation 300% Agency Participation

Erlangs per 

Service Area 

= 0.3 x ∑ASC 

x DCO

Number of 

Channels 

Required

Erlangs per 

Service Area 

= ∑ASC x 

DCO 

Number of 

Channels 

Required

Erlangs per 

Service Area = 

3 x ∑ASC x 

DCO 

Number of 

Channels 

Required

1 202.53 5% 1% 3.04 8 10.13 17 30.38 40

2 26.79 5% 1% 0.40 3 1.34 5 4.02 9

3 46.21 5% 1% 0.69 4 2.31 7 6.93 13

4 20.29 5% 1% 0.30 3 1.01 5 3.04 8

5 8.62 5% 1% 0.13 2 0.43 3 1.29 5

6 39.66 5% 1% 0.59 4 1.98 6 5.95 12

7 25.81 5% 1% 0.39 3 1.29 5 3.87 9

8 16.73 5% 1% 0.25 3 0.84 4 2.51 7

9 14.84 5% 1% 0.22 3 0.74 4 2.23 7

10 6.32 5% 1% 0.09 2 0.32 3 0.95 4

11 7.73 5% 1% 0.12 2 0.39 3 1.16 5

12 17.44 5% 1% 0.26 3 0.87 4 2.62 7

13 1.96 5% 1% 0.03 2 0.10 2 0.29 3

14 0.80 5% 1% 0.01 1 0.04 2 0.12 2

15 1.02 5% 1% 0.02 2 0.05 2 0.15 2

16 6.13 5% 1% 0.09 2 0.31 3 0.92 4

17 5.07 5% 1% 0.08 2 0.25 3 0.76 4

18 5.81 5% 1% 0.09 2 0.29 3 0.87 4

19 9.20 5% 1% 0.14 2 0.46 3 1.38 5

20 1.46 5% 1% 0.02 2 0.07 2 0.22 3

21 2.19 5% 1% 0.03 2 0.11 2 0.33 3

22 1.39 5% 1% 0.02 2 0.07 2 0.21 3

23 11.73 5% 1% 0.18 2 0.59 4 1.76 6

24 19.20 5% 1% 0.29 3 0.96 4 2.88 8

25 3.32 5% 1% 0.05 2 0.17 2 0.50 3

26 11.54 5% 1% 0.17 2 0.58 4 1.73 6
3-5

Continued from Table 3-1 above:

Service 

Area 

ID

∑ASC per 

Service Area

Design 

Channel 

Occupancy 

(DCO)

Grade of 

Service 

(GoS)

30% Agency Participation 100% Agency Participation 300% Agency Participation

Erlangs per 

Service Area 

= 0.3 x ∑ASC 

x DCO

Number of 

Channels 

Required 

Erlangs per 

Service Area 

= ∑ASC x 

DCO

Number of 

Channels 

Required

Erlangs per 

Service Area 

= 3 x ∑ASC x 

DCO 

Number of 

Channels 

Required

27 8.57 5% 1% 0.13 2 0.43 3 1.29 5

28 4.03 5% 1% 0.06 2 0.20 3 0.60 4

29 1.81 5% 1% 0.03 2 0.09 2 0.27 3

30 0.03 5% 1% 0.0004 1 0.0013 1 0.0039 1

31 0.36 5% 1% 0.01 1 0.02 2 0.05 2

32 19.94 5% 1% 0.30 3 1.00 4 2.99 8

33 1.23 5% 1% 0.02 2 0.06 2 0.19 2

34 2.05 5% 1% 0.03 2 0.10 2 0.31 3

35 3.59 5% 1% 0.05 2 0.18 2 0.54 3

Total Number of Traffic Channels 85 125 213

Total Number of Erlangs 8.33 27.7 83.3

Note 1: The total number of channels above does not include the control channels.

Note 2: The total number of service areas for this system architecture is 35. 
3-6

3.1.2 Large-Medium-Service-Area-Mixed System Architecture

The Large-Service-Area-Only System architecture works well for the 30 percent and 100 percent

levels of agency participation. However, as shown in Table 3-1, Service Area #1 for the 300 percent

level of agency participation requires 40 channels. This is greater than the maximum number of 

channels that the hardware for a single base station can support. For a base station supporting higher 

traffic levels, one solution is to split the traffic of one service area between several base stations, 

each with fewer channels. 

It is a typical design technique to use different coverage sizes for the base stations in the same 

network. In fact, it is often advantageous to use several base stations each with a smaller coverage 

area to provide better service in areas with a high-concentration of users and base stations with larger 

coverage areas in areas with a medium- and low-concentration of users. Using this concept, the 

Large-Medium-Service-Area-Mixed System architecture is examined where four base stations each 

with a medium service area are used to cover the Service Area #1 instead of a single base station 

with a large service area.

To simplify the design and calculation of the required number of channels, the four medium service 

area hexagons were superimposed on the Service Area #1 of the Large-Service-Area-Only System 

architecture without changing the hexagon layout. The medium service area has a radius of 12 

miles. The new Service Area IDs are #1M, #36M, #37M and #38M. The new hexagon layout is 

shown in Figure 3-2. 

There were some overlapping coverage areas created by the four medium service areas and the 

surrounding large service areas as shown in Figure 3-2. For example, Service Area #1M has some 

overlapping service areas with Service Area #7 and Service Area #36M has some overlapping 

service areas with Service Area #2 and #3. The ASC values for overlapping service areas were not 

included in determining the medium service area channel requirements. This means that the 

overlapping areas were only counted once. In practice, service areas should be defined more 

precisely in the actual system design to eliminate large coverage overlaps, although it is an 

acceptable design practice to have some coverage overlap at the border of two base stations in order 

to facilitate un-interruptible communications. The overlapping service area design will be discussed 

in more detail in the next subsection.

The results of the analysis are shown in Table 3-2. Since the required number of channels for 

Service Area #2 to #35 remained unchanged, Table 3-2 only provides the number of required 

channels for the four new medium service areas as well as the number of required channels for the 

entire system architecture. 

As shown in Table 3-2, splitting a large service area and assigning a portion of the traffic (Erlangs)

to several smaller service areas will decrease the channel requirements for the base stations of each 

service area. However, distributing the traffic equally or unequally from one service area to several 

service areas increases the total number of channels required for the same level of service (GoS, 

reference waiting time, and average hold time). For example, the four medium service areas require 

17, 9, 18 and 10 channels respectively for a 300 percent level of agency participation. This results in

a total of 54 channels compared to the original 40 channels required for Service Area #1.
3-7

Figure 3-2. Large-Medium-Service-Area-Mixed System Architecture Map 
3-8

Table 3-2. Network Dimensioning for the Alternative Trunked LMR System 

with a Large-Medium-Service-Area-Mixed System Architecture

Service 

Area 

ID

∑ASC per 

Service Area

Design 

Channel 

Occupancy 

(DCO)

Grade of 

Service 

(GoS)

30% Agency Participation 100% Agency Participation 300% Agency Participation

Erlangs per 

Service Area 

= 0.3 x ∑ASC 

x DCO 

Number of 

Channels 

Required 

Erlangs per 

Service Area 

= ∑ASC x 

DCO 

Number of 

Channels 

Required 

Erlangs per 

Service Area 

= 3 x ∑ASC x 

DCO 

Number of 

Channels 

Required 

1M 68.13 5% 1% 1.02 5 3.41 8 10.22 17

36M 27.83 5% 1% 0.42 3 1.39 5 4.17 9

37M 74.77 5% 1% 1.12 5 3.74 9 11.22 18

38M 31.80 5% 1% 0.48 3 1.59 6 4.77 10

Sub-Total Number of Traffic Channels 16 28 54

Including Service Area #2 to #35

Total Number of Traffic Channels 93 136 227

Note 1: The total number of channels above does not include the control channels.

Note 2: The results are for medium service areas only. The results for Service Area #2 to #35 are shown in Table 3-1.

Note 3: The total number of service areas for this system architecture is 38.
3-9

3.1.3 Large-Small-Service-Area-Overlapping System Architectures

The first two system architectures, Large-Service-Area-Only System and Large-Medium-ServiceArea-Mixed System, were analyzed as possible future shared trunked LMR systems. A third system 

architecture, which is a combination of overlapping large and small service areas is analyzed with 

the smaller service areas placed in the locations where there is a high-concentration of users. 

Large service areas are used to provide coverage to users that are distributed over a large geographic 

area, while smaller service areas are used to provide coverage for users that are concentrated in 

smaller areas. Using small service areas, especially in locations where there is a high-concentration 

of users (e.g., downtown Washington D.C.), is a well-known technique in the cellular 

communications industry to provide better coverage to users as well as coverage inside buildings, 

basement parking lots, inside tunnels, etc. The base stations of the small service areas are also closer 

to the users of mobile and portable radios with low transmitter power. This facilitates the 

transmission of higher data rates over shorter distances without increasing transmitter power. 

Furthermore, using the design of a large service area overlapping several smaller service areas, the 

large service area can supplement its channels to the small service area channels. This will create a 

total communications capability that is well beyond the capabilities of the small service areas alone, 

that could be used to handle localized emergencies. In addition, base stations with smaller service 

areas employing lower transmit power will reduce the interference areas and increase frequency 

reuse.

The architecture analyzed for Large-Small-Service-Area-Overlapping uses large hexagonal service 

areas identical to the Large-Service-Area-Only System, in conjunction with a group of seven small

hexagonal service areas superimposed in the Washington, D.C. urban area. The small service areas 

have a 7-mile radius as shown in Figure 3-3, with a service area approximately 1/9 as large as the 

large service area. Since federal user location data is not available in the GMF, the traffic within the 

overlapping areas has been divided equally in the Erlang calculation between the large service area 

and each of the small service areas. The small service areas were overlaid on the ASC map and a 

∑ASC value was determined for each individual small service area (#36-#42). The ∑ASC value for 

each small service area was divided in half with half of the corresponding ∑ASC allocated to the 

small service area. The ∑ASC value for large service area #1 for this system architecture was 

determined by subtracting the ∑ASC values associated with the seven small service areas from the 

∑ASC value for the service area #1 determined for the Large-Service-Area-Only System 

architecture (Table 3-1). The resulting seven ∑ASC values, listed in Table 3-3, were used to develop 

the channel requirements for the trunked system employing the seven overlapping service areas. 

The results of the channel requirements analysis are shown in the Table 3-3.

A user in overlapping service areas can receive service from either the base station associated with 

the large service area or one of the base stations associated with the small service areas since they 

provide service to the same geographical areas. Those base stations share the traffic with an overall 

GoS level of 1 percent and a 1-second call waiting time. Thus, the GoS level in the overlapping 

large and small service areas must be adjusted. In this analysis, the term Gn is defined as the 

network GoS considering the overlap of the large and small service areas. The term G is the 

designed individual base station GoS. A user that has access to two base stations has an equal 

probability (G) of not being served by either base station. Therefore, the probability of not being 

served by both base stations is determined by Gn = G x G, or G = (Gn)1/2. It should be noted that 
3-10

many other base station GoS combinations could be chosen to satisfy the desired network GoS (Gn)

depending on the actual system requirements. The calculation for overlapping designed GoS could 

become very complicated when overlapping coverage is created by more than one base station. To 

simplify the study, the overlap of the large service area and each of the small service areas is

considered as 100 percent. Since the Gn is 1 percent, the GoS for large service area (Service Area 

#1) and small service areas (Service Area #36 to Service Area #42) is adjusted to 10 percent as 

shown in Table 3-3. The GoS of 1 percent for Service Area #2 to Service Area #35 remains 

unchanged.

Table 3-3 shows the results of channel requirement calculations for the large service area and the 

seven small service areas. The results of Service Area #2 to Service Area #35 are identical to those 

shown in Table 3-1, where large service areas provide coverage in areas with a medium- or lowconcentration of users. The total number of service areas for this system architecture is 42. The 

number of traffic channels required is 95 (30% agency participation), 135 (100% agency 

participation), and 226 (300% agency participation).

Although the use of small service areas could have some considerable advantages as discussed 

above, there are also some problems. The first problem is that many federal LMR users (as well as 

many non-federal public safety users) are organized as large, geographically dispersed talkgroups. 

This means that as service areas are reduced in size, the talkgroups may be spread across multiple 

service areas. Since the entire talkgroup must be able to hear all of the talkgroup communications,

channels will need to be used in all of the service areas containing talkgroup members. In the worst 

case, one could imagine talkgroup members spread across all of the service areas, resulting in no net 

gain of communications capacity. The geographic location of talkgroup members is therefore an 

important (but currently unknown) factor in determining whether small service areas will actually 

result in improving spectrum efficiency.

The relative advantages of the small service areas in allowing higher frequency reuse as well as 

permitting the use of lower power transmitters needs to be balanced against the requirements where 

large service areas are necessary to serve users operating over a large geographic area and small 

service areas are needed to serve large concentrations of users. 
3-11

Figure 3-3. Large-Small-Service-Area-Overlapping System Architecture Map
3-12

Table 3-3. Network Dimensioning for the Alternative Trunked LMR System 

with a Large-Small-Service-Area-Overlapping System Architecture

Service 

Area 

ID

∑ASC per 

Service Area

Design 

Channel 

Occupancy 

(DCO)

Grade of 

Service 

(GoS)

30% Agency Participation 100% Agency Participation 300% Agency Participation

Erlangs per 

Service Area 

= 0.3 x ∑ASC 

x DCO 

Number of 

Channels 

Required 

Erlangs per 

Service Area 

= ∑ASC x 

DCO 

Number of 

Channels 

Required 

Erlangs per 

Service Area 

= 3 x ∑ASC x 

DCO 

Number of 

Channels 

Required 

1 112.90 5% 10% 1.69 4 5.65 9 16.94 21

36 19.72 5% 10% 0.30 2 0.99 3 2.96 6

37 9.00 5% 10% 0.14 2 0.45 2 1.35 4

38 11.33 5% 10% 0.17 2 0.57 2 1.70 4

39 13.26 5% 10% 0.20 2 0.66 3 1.99 5

40 13.22 5% 10% 0.20 2 0.66 3 1.98 5

41 12.50 5% 10% 0.19 2 0.62 3 1.87 4

42 10.60 5% 10% 0.16 2 0.53 2 1.59 4

Sub-Total Number of Traffic Channels 18 27 53

Including Service Area #2 to #35

Total Number of Traffic Channels 95 135 226

Note 1: The total number of channels above does not include the control channels.

Note 2: The results for Service Area #2 to #35 are shown in Table 3-1.

Note 3: The total number of service areas for this system architecture is 42. 
3-13

3.2 Initial Frequency Requirements

In order to determine if the alternative trunked LMR systems can satisfy the design goals and use 

less spectrum than conventional LMR systems, the frequency requirements for each of the 

trunking scenarios must be determined. 

Based on the hexagon service area layout maps (Figure 3-1, Figure 3-2 and Figure 3-3), the 

frequencies were assigned starting from the central downtown area, Service Area #1, and 

proceeding to outlying areas on a service area-by-service area basis. As in any large network 

design, a frequency reuse scheme was used. The assumptions and guidelines that were used to 

develop the frequency plan for each of the trunking scenarios are described in the following 

paragraphs. 

Many factors affect the frequency assignment process such as terrain shielding, building 

blockage, adjacent site distance, antenna height, transmit power, receive signal level, and carrierto-interference ratio (C/I) requirement. Since many of these factors were unknown, a simplified 

approach based on a minimum frequency reuse distance was used to develop the frequency plan 

for the different LMR trunking scenarios. In this study, a distance separation criterion of 70 

miles between co-channel base stations (center to center) was used as the frequency reuse 

distance. A frequency reuse distance of 70 miles will provide a minimum C/I ratio of 

approximately 18 dB for co-channel base stations with the same size service areas, i.e. 20-mile 

radius. 

The frequency reuse determination will be described using the Large-Service-Area-Only System 

architecture (see Figure 3-1). Because of the 70-mile reuse distance criterion, the separation 

distance between service areas such as Service Area #1 and #13 or Service Area #1 and #14 is 

not sufficient. To satisfy the reuse distance criterion there must be at least two service areas

between service areas that reuse the same frequency. For example, frequency reuse is possible 

between Service Area #1 and Service Areas #20 through #35. Frequency reuse is also possible 

between Service Area #2 and Service Areas #13 through #17 or Service Areas #25 through #35. 

Furthermore, a subset of the frequencies from Service Area #2 can be reused in Service Area #13 

and then again in Service Area #16 or #17. However, none of the frequencies associated with 

Service Area #2 can be reused in each of the Service Areas #18 through #12 (clockwise) because 

of the reuse distance criterion. 

The 70-mile reuse distance criterion dictated that Service Areas #1 through #7 (designated as the 

primary service areas in this analysis) must each have a unique set of frequencies. Because of 

the traffic requirements of Service Areas #1 through #7, they will generally require more 

frequencies than the other service areas. Taking the factors discussed above into consideration, 

the frequency reuse scheme summarized in Table 3-4 was developed.

Table 3-4 shows which service areas were considered for reuse of the frequencies associated 

with each primary service area. This frequency reuse scheme is not unique. Other arrangements 

for Service Areas #8 through #35 are possible. However, Table 3-4 was used in this analysis to 

guide the frequency reuse evaluation. The frequency reuse evaluation for the trunking scenario
3-14

of Large-Service-Area-Only System architecture with 30 percent agency participation is used to 

further describe the procedures used in this analysis. The reuse evaluation was carried out using 

channels instead of frequency assignments (e.g., there are two frequencies for each channel). 

Since full duplex operation is necessary, each channel requires two unique frequencies.

Table 3-4. Example of Frequency Reuse Scheme

Primary Service Areas Reuse Service Areas

#1 #20 through #35a

#2 #13 through #17aand #25

#3 #15 through #19aand #22

#4 #17 through #9aand #30

#5 #19 through #11aand #33

#6 #9 through #13a

#7 #11 through #15a

a: The subset of frequencies from the primary service area and reused in these service areas are also 

constrained by the 70-mile reuse distance criterion within the reuse service area grouping. 

The channel requirements for the Large-Service-Area-Only System architecture were

summarized in Table 3-1 under the column heading for 30 percent agency participation. The 

process first requires that Service Areas #1 through #7 be assigned a total of 27 unique channels 

(which is 54 frequency assignments). These channels will be referred to in terms of a numeric (1 

through 7) denoting the service area and a letter designating each channel associated with the 

service area. For example, channels 1-A through 1-H are the eight channels associated with 

Service Area #1. Similarly, channels 2-A through 2-C are the three channels associated with 

Service Area #2.

The process began with the reuse of channels in Service Areas #2 through #7. Service Area #1 

channels are used in the outer ring of the service areas and were considered last. Service Area #8 

requires three channels and channels from Service Areas #4 and #5 (see Table 3-4) can be used. 

Service Area #8 was assigned channels 4-A through 4-C. Service Area #9 requires three 

channels and was assigned channels 6-A through 6-C. This process was continued through all of 

the service areas resulting in the channel assignments shown in Table 3-5.

As shown in Table 3-5, the channel requirements for Service Areas #8 through #35 can be 

accommodated by the reuse of channels assigned to Service Areas #1 through #7. Therefore, 

only the original 27 unique channels are required for this trunking scenario. This procedure was 

carried out for the other Large-Service-Area-Only trunking scenarios with similar results. The 

channel assignments for Service Areas #1 through #7 could be reused in the other service areas. 

For the trunking scenarios of Large-Medium-Service-Area-Mixed System architecture, the 

Service Areas #1M, #36M, #37M, and #38M along with Service Areas #2 through #7 each 

required a unique set of channel assignments. The reuse analysis, as previously explained, was 

then followed. The result was the unique channel assignments were adequate for the trunking 

scenarios. 

The trunking scenarios of Large-Small-Service-Area-Overlapping System architecture were 

evaluated using the same procedure and the initial unique channel assignments were adequate.
3-15

Table 3-5. Example of Channel Assignments 

(Large-Service-Area-Only System Architecture with 30% Agency Participation)

Service Area Assigned Channels

#8 4-A through C

#9 6-A through C

#10 5-A and B

#11 7-A and B

#12 6-A through C

#13 2-A and B

#14 2-C

#15 3-A and B

#16 3-C and D

#17 2-A and B

#18 3-A and B

#19 3-C and D

#20 1-C and D

#21 1-A and B

#22 3-A and B

#23 1-F and G

#24 1-C through E

#25 2-A and B

#26 1-A and B

#27 1-F and G

#28 1-D and E

#29 1-B and C

#30 4-A

#31 1-A

#32 1-E through G

#33 5-A and B

#34 1-C and D

#35 1-A and B

Using the procedure described in the preceding paragraphs, the frequency requirements for 

traffic channels (TCHs) were developed for each of the trunking scenarios and the results are 

summarized in Table 3-6.

To determine the frequency requirements for each trunking scenario, the frequency plan must 

include frequency assignments for control channels (CCHs).

23

 Each base station for a centralized 

trunked system has one dedicated CCH. Sometimes, there is a redundant CCH, which carries 

traffic during normal operation. Since the CCH transmits continuously and serves the entire base 

station all the time, the CCH frequency planning for the entire network is very conservative and 

more complicated in actual design to eliminate any type of interference. For the purpose of this 

 

23. The alternative approach used on decentralized trunked systems is to have no dedicated CCHs but to send 

control information over idle voice channels. This requires the mobiles to scan free voice channels carrying control 

information. For very small systems, this has the advantage of making all channels available for voice calls, and is 

more spectrally efficient than a trunked system with dedicated CCHs since no additional frequencies are required for 

CCHs. However, because any voice channel can potentially become the control channel at any time, calls can be 

missed during the relatively long scanning time.
3-16

study, unique frequencies were assigned to all CCHs although the frequency reuse criterion used 

for determining the TCHs can also be used for the CCHs. Since one base station can handle the 

traffic for most service areas, the number of CCHs required for most trunking scenarios in this 

study was equal to the total number of service areas. The only exception was in a few cases 

when the service area had a large number of channels to accommodate a higher number of users

(e.g., 40 channels at 300 percent agency participation in the Large-Service-Area-Only System). 

In this case, the service areas were broken down to multiple base stations each with a smaller 

number of channels to meet the limitations on the maximum number of channels for a base 

station (32 channels). To address this case, a few extra CCHs were added to the total number of 

channels to determine the frequency requirements for those trunking scenarios.
3-17

3.3 Design Summary and Analysis

3.3.1 Summary Table

The total number of channels required and associated number of frequencies for each of the three 

system architectures for each of the trunking scenarios are summarized in Table 3-6.

24

 These 

results are based on the hypothetical design and the assumptions made during different stages of 

the analysis and calculations. 

The Large-Service-Area-Only system architecture with 100 percent agency participation is used 

to explain how the frequency requirements are determined using the TCH and CCH

requirements. The Large-Service-Area-Only system architecture for 100 percent agency 

participation, the total number of frequencies required is 166. This number was first calculated 

by adding the number of channels required for areas with a high-concentration of users (17) to 

the number of channels required for areas with a medium- and low-concentration of users (108) 

for a total number of 125 TCHs (Table 3-1). The number of control channels required was equal 

to the number of service areas (35) in this case. Therefore, the total number of channels required 

for the system was the number of channels required for the traffic and control channels added 

together, or 160 (125 + 35). However, by using the frequency reuse scheme, the actual 

frequency requirement derived from the frequency plan for the traffic channels was 48 unique 

frequency pairs to support full duplex operation, which is much less than 125 channels. Unique 

frequencies were assigned to all control channels, which is 35 pairs. Therefore, with two 

frequency assignments required for each channel, the 166 total number of frequency assignments 

was calculated by adding 48 and 35 together, or 83, and then multiplying the summation by a 

factor of 2. The values of the total number of frequency assignments for other trunking scenarios 

were calculated in the same manner.

The frequency requirements shown in the Table 3-6 indicates that although the majority of the 

frequencies are used in the areas with a high-concentration of users, many of these frequencies 

can be reused in any areas with a medium- and low-concentration of users as long as 70-mile 

reuse distance criterion is satisfied. For example, 17 frequency pairs or 34 frequency 

assignments are required for Service Area #1 at 100 percent agency participation for the LargeService-Area-Only System architecture, which is approximately 35 percent of 48 frequency pairs 

for TCHs in this scenario. The total number of frequencies required was determined by the 

frequency use in the areas with a high and concentration of users (e.g., Service Area #1 to 

Service Area #7).

25

 Therefore, the proper design of channel requirements in areas where there is 

expected to be a high concentration of users is a key to obtain greater frequency reuse, thus 

reducing the necessary frequency resources. 

 

24. More base stations with fewer traffic channels may be required to provide the same level of service in the service 

areas as described in the study, especially in the areas of high concentration of users. Therefore, the total number of 

channels and the total number of frequencies required could be higher than the results presented in this report.

25. Within the areas with a high and medium concentration of users, frequency reuse was not possible because of 

the 70-mile reuse distance established for this study.
3-18

Table 3-6. Summary of Frequency Requirements for Different Trunking Scenarios

Trunked 

LMR 

System 

Architecture

Parameters Frequency Requirements

30% 

Agency 

Participation

100% 

Agency 

Participation

300% 

Agency 

Participation

LargeService-AreaOnly

(Coverage 

Radius: 

Large = 20 

miles)

(Total 35 

Service 

Areas)

Number of Channels Required for Service Area #1(Areas 

of High-Concentration of Users) 8 17 40

Number of Channels Required for Service Areas #2-#35 

(Areas of Medium- and Low-Concentration of Users) 77 108 173

Total Number of Traffic Channels (TCHs) 85 125 213

Total Number of Control Channels (CCHs) 35 35 36

Total Number of Channels Required for the System 

(TCHs + CCHs) 120 160 249

Total Number of Frequency Pairs Required for TCHs 

(TX/RX pair) 27 48 96

Total Number of Frequency Pairs Required for CCHs 

(TX/RX pair) 35 35 36

Total Number of Frequency Assignments Required for 

the System (TX+RX) 124 166 264

LargeMediumService-AreaMixed 

(Coverage 

Radius: 

Large = 20 

miles, 

Medium = 12 

miles)

(Total 38 

Service 

Areas)

Number of Channels Required for Four (4) Medium 

Service Areas (Areas of High-Concentration of Users) 16 28 54

Number of Channels Required for Service Areas #2-#35 

(Areas of Medium- and Low-Concentration of Users) 77 108 173

Total Number of Traffic Channels (TCHs) 93 136 227

Total Number of Control Channels (CCHs) 38 38 38

Total Number of Channels Required for the System 

(TCHs + CCHs) 131 174 265

Total Number of Frequency Pairs Required for TCHs 

(TX/RX pair) 35 59 110

Total Number of Frequency Pairs Required for CCHs 

(TX/RX pair) 38 38 38

Total Number of Frequency Assignments Required for 

the System (TX+RX) 146 194 296

Large-SmallService-AreaOverlapping 

(Coverage 

Radius: 

Large = 20 

miles, 

Small = 7 

miles)

(Total 42 

Service 

Areas)

Number of Channels Required for Service Areas #1 and 

#36-#42 (Areas of High-Concentration of Users) 18 27 53

Number of Channels Required for Service Areas #2-#35 

(Areas of Medium- and Low-Concentration of Users) 77 108 173

Total Number of Traffic Channels (TCHs) 95 135 226

Total Number of Control Channels (CCHs) 42 42 42

Total Number of Channels Required for the System 

(TCHs + CCHs) 137 177 268

Total Number of Frequency Pairs Required for TCHs 

(TX/RX pair) 37 58 109

Total Number of Frequency Pairs Required for CCHs 

(TX/RX pair) 42 42 42

Total Number of Frequency Assignments Required for 

the System (TX+RX) 158 200 302
3-19

3.3.2 Comparison of Frequency Requirement

Comparison of the total number of frequencies required for the alternative trunked LMR systems 

with current frequency usage in the GMF for conventional LMR systems provides a measure of 

relative spectrum efficiency. The level of federal users obtained from the GMF represents the 

100 percent agency participation considered in this analysis. There were 524 frequency 

assignments associated with base stations at specific locations in the GMF for the 162-174 MHz 

band within 100-mile radius of Washington D.C.

26

 Table 3-7 shows the frequency usage 

comparison between the 524 frequency assignments used in the GMF and the three alternative 

trunked LMR system architectures at the 100 percent level of agency participation.

Table 3-7. Frequency Usage Comparison for LMR Systems

LMR System Total Number of 

Frequencies Used at 100% 

Level of Agency 

Participation

Percent Frequency Usage of 

Trunked System Relative to 

Conventional System

Conventional 524 ----

Large-Service-Area-Only Trunked 166 32%

Large-Medium-Service-Area-Mix Trunked 194 37%

Large-Small-Area-Overlapping Trunked 200 38%

As shown in Table 3-7, only 166 frequencies are required for the Large-Service-Area-Only 

System, which is approximately 32 percent of the frequencies used for conventional LMR 

systems. For the Large-Medium-Service-Area-Mixed System only 194 frequencies are required, 

which is approximately 37 percent of the frequencies used for conventional LMR systems. For 

the Large-Small-Service-Area-Overlapping System, only 200 frequencies are required, which is 

approximate 38 percent of frequencies used for conventional LMR systems. The number of 

frequencies that would be required for conventional LMR systems at the 30 percent level of 

agency participation and the 300 percent level of agency participation cannot be determined from 

GMF, thus, a direct comparison of the frequency usage cannot be made. The comparison of 

frequency usage in Table 3-7 clearly shows that the trunking system architectures use 

frequencies more efficiently than individual conventional LMR systems. 

An example of the frequency requirements as a function of the level of agency participation for 

the Large-Service-Area-Only trunked LMR system architecture is provided in Table 3-8. 

Comparing the 30 percent and 100 percent levels of agency participation, only 42 additional 

frequencies are required to support three times the number of users. Similarly, comparing the 30 

percent and 300 percent levels of agency participation, only 140 more frequencies are required to 

support ten times the number of users. As shown in Table 3-8, frequency requirements do not 

increase at the same rate as the level of agency participation. 

 

26. The 524 frequencies were derived from GMF in the 162-174 MHz band. The frequency assignment records 

considered are within a 100-mile radius of Washington D.C. for LMR systems with specific locations, excluding all 

area assignments. The frequencies used by National Oceanic and Atmospheric Administration (NOAA) for weather 

broadcasts, wildlife tracking and other non-LMR systems in the band were also excluded from consideration. The 

frequency assignment results from the GMF were compared to the channel occupancy measurement data to obtain 

the channel usage for each frequency. 
3-20

Table 3-8. Example of Frequency Requirements Versus Level of Agency Participation 

(Large Service-Area-Only System Architecture)

Trunked 

LMR System 

Architecture

Parameters 30% 

Agency 

Participation 

100% 

Agency 

Participation

300%

Agency 

Participation

LargeService-AreaOnly

Total Number of Erlangs Carried 

by System from Table 3-1

8.3 27.7 83.3

Total Number of Frequencies 

Required (Traffic and Control 

Channels) from Table 3-6

124 166 264

An example of the relative frequency efficiency versus level of agency participation for the 

Large-Service-Area-Only trunked LMR system architecture is shown in Table 3-9.

Table 3-9. Example of Relative Frequency Efficiency Versus Level of Agency Participation 

(Large Service-Area-Only System Architecture)

Trunked 

LMR System 

Architecture

Comparisons 30% 

Agency 

Participation

100% 

Agency 

Participation

300%

Agency 

Participation

LargeService-AreaOnly

Number of Erlangs per Frequency (8.3/124)

0.067

(27.2/166)

0.167

(83.3/264)

0.316

Ratio of Required Frequencies Relative 

to 30% Level of Agency Participation

(124/124)

1.0

(166/124)

1.3

(264/124)

2.1

Ratio of Number of Erlangs per 

Frequency Relative to 30% Level of 

Agency Participation

(0.067/0.067)

1.0

(0.167/0.067)

2.5

(0.316/0.067)

4.7

As shown in Table 3-9, the larger the system in terms of Erlangs carried, the more efficient it 

becomes in terms of the amount of traffic that can be carried per amount of spectrum (number of 

frequencies used). Table 3-8 and Table 3-9 show that for the 30 percent level of agency 

participation, 124 frequencies are required and the system was designed to carry a total of 8.3 

Erlangs of traffic, 0.067 Erlangs per frequency. For the 100 percent level of agency 

participation, the system was designed to carry 27.7 Erlangs of traffic and requires 166 

frequencies, 0.167 Erlangs per frequency. For the level of 300 percent agency participation, the 

system was designed to carry 83.3 Erlangs of traffic and requires 264 frequencies, 0.316 Erlangs 

per frequency. Therefore, the system designed for 100 percent level of agency participation is 

2.5 times as efficient compared to the system designed for 30 percent agency participation. The 

system designed for an agency participation of 300 percent is 4.7 times as efficient as the system 

designed for a 30 percent level of agency participation. The number of users per frequency is a 

more common parameter to use than the number of Erlangs per frequency where the relative 

comparison ratios based on either one of them are the same (see Erlang formulas in Appendix 

A). Furthermore, as shown in Table 3-9, the number of users per frequency increased by a factor 

of 2.5 for the 100 percent level of agency participation and by a factor of 4.7 for the 300 percent

level of agency participation as compared to the frequency usage at an agency participation level 

of 30 percent.
3-21

The results for the Large-Medium-Service-Area-Mixed and Large-Small-Service-AreaOverlapping system architectures will be similar to those shown in Table 3-8 and Table 3-9.

The frequency usage comparison with current GMF data shows that the trunking system 

architectures use frequencies more efficiently than conventional LMR systems. Moreover, the 

analysis based on the level of agency participation shows that larger capacity trunked systems 

offer much higher frequency efficiency than the smaller capacity systems.
3-22

This Page Intentionally Left Blank
4-1

SECTION 4 

CONCLUSION

Trunking is a proven technology that permits a large number of users to share a relatively small 

number of channels. Unlike conventional LMR systems, where the user must wait if the channel 

is occupied by another user, trunking allows for the automatic sharing of multiple channels. 

Access to the trunked system is dynamically allocated to the available channels. Because 

trunked LMR systems shared channels, they can offer more efficient use of the radio spectrum 

than conventional LMR systems.

This study presented three different alternative trunked LMR system architectures in the 162-174 

MHz band: a Large-Service-Area-Only System, a Large-Medium-Service-Area-Mixed System, 

and a Large-Small-Service-Area-Overlapping System. Three potential levels of federal agency 

participation were considered: 30 percent agency participation representing partial participation 

by the current federal users of conventional LMR systems; 100 percent agency participation

representing full participation by the current federal users of conventional LMR systems; and 

300 percent agency participation representing future expanded use by the federal users. The 

three system architectures combined with the three levels of agency participation resulted in nine 

unique trunking scenarios. Each trunking scenario was studied within a 100-mile radius 

coverage area centered in Washington, D.C. The frequency assignment data from the GMF and 

channel occupancy measurements were utilized to derive traffic levels expressed in Erlangs for 

the service area of each base station. The traffic levels were used to determine the number of 

channels required for the different trunking scenarios. The spectrum requirements for each 

trunking scenario were developed based on 12.5 kHz channel spacing in the 162-174 MHz band, 

and the 70-mile frequency reuse distance criterion. 

For the 100 percent level of agency participation, approximately 32 percent or 166 of the 524 

frequencies in the GMF are needed for the Large-Service-Area-Only System. For the LargeMedium-Service-Area-Mixed System, approximately 37 percent or 194 of the 524 frequencies in 

the GMF are needed. The Large-Small-Service-Area-Overlapping System requires 

approximately 38 percent or 200 of the 524 frequencies in the GMF. The study in this report 

clearly shows that fewer frequencies are required for the trunked system architectures as 

compared to the total number of frequencies required for the existing conventional LMR 

systems. 

This study quantifies how the number of users per frequency increases for trunked LMR systems 

servicing a large number of users as compared to trunked LMR systems servicing a small 

number of users. The number of users per frequency increased by a factor of 2.5 for the 100 

percent level of agency participation and by a factor of 4.7 for the 300 percent level of agency 

participation as compared to the frequency usage for the 30 percent level of agency participation. 

By combining spectrum resources in a shared system, agencies can implement trunking systems 

with improved trunking capacity, total coverage area, multi-agency interoperability and 

advanced control, monitoring and system management capabilities.

The results of frequency planning for each of the trunking scenarios show that, although the 

majority of the frequencies are used by service areas where there is a high-concentration of users, 
4-2

many of these frequencies can be reused in service areas where there are medium- and lowconcentration of users for assignments that satisfy the 70-mile frequency reuse criterion. For a 

trunked LMR system in a metropolitan area, the total number of frequencies required is primarily 

dominated by frequency usage of service areas where there is a high concentration of users. The 

proper design of the base station capacity in the high usage areas is a key to obtain high 

frequency reuse, reducing the necessary spectrum resources for better spectrum management. 

This study shows that if a shared trunked LMR system is implemented in the Washington D.C.

area, there will be sufficient frequencies in the 162-174 MHz band to support future federal LMR 

spectrum requirements. For example, the 300 percent level of agency participation (3 times the 

current number of users) requires approximately 30 percent of the 960 assignable 12.5 kHz 

channels in the 162-174 MHz band. Thus, trunked LMR systems that are shared by federal 

agencies are an effective approach to more efficient use of the federal LMR frequency bands.

This study also shows that the use of overlapping small cells does not save frequencies, 

compared to the use of Large-Service-Area-Only though all of the analyzed architectures use 

frequencies more efficiently than the present case of independent conventional systems. The 

apparent lack of frequency savings with the small cells is probably due to the use of the 70-mile 

frequency reuse criteria. More detailed frequency reuse models based on appropriate C/I criteria 

should show a frequency reuse improvement for the overlapped cells. 

This study is based on hypothetical LMR system designs, and does not provide detailed design 

specifications. Instead, this study provides a comparison of spectrum resources used by the 

alternative trunked LMR system designs and conventional LMR systems. Although this study 

only addressed the 162-174 MHz LMR band in the Washington D.C. area, application of the 

method presented in this report to other LMR bands in spectrally congested areas, should 

produce similar results.
A-1

APPENDIX A

TRUNKING EFFICIENCY AND HYBRID SYSTEMS

A.1 Trunking Efficiency

Trunking allows a large number of users to share a relatively small number of channels for a 

base station. Trunking efficiency is a measure of the number of users (radio terminals) that can 

be served at particular grade of service (GoS) with a particular configuration. Equation A-1

below is used to calculate the traffic level in Erlangs for a base station:

1

A = (M x L x H) / 3600 (A-1)

Where

A: Call traffic level in Erlangs

M: Total number of users per base station

L: Average busy hour call attempts per user

H: Average busy hour holding time in seconds

The number of users (M) for a base station can be calculated using Equation A-2:

M = A x 3600 / (L x H) (A-2)

Table A-1 provides some statistical numbers for average call attempts and average holding time 

for the busy hour.

2

Table A-1. Statistical Numbers for Average Call Attempts and Average Holding Time for 

the Busy Hour

Call Type Busy Hour Call Attempts 

per User

Average Busy Hour Holding 

Time

Group Call 6.5 4 seconds

Individual Call 0.2 4.2 seconds

Telephone Interconnect 0.01 60 seconds

Using values in Table A-1, a typical public safety traffic level per user per call in Erlangs in a 

busy hour is:

(6.5 x 4+0.2 x 4.2+0.01 x 60) / 3600 = 0.0076 Erlangs/user

 

1. Jose M Hernando and F. Perez-Fontan, Introduction to Mobile Communications Engineering, 1999 Artech 

House.

2. Data referenced to tutorial paper Traffic Analysis from radio manufacturer M/A-Com presented in 2004. Four 

seconds holding time for a group call is used in this analysis.
A-2

Since one Erlang is 3600 seconds of calls, the 0.0076 Erlangs is equivalent to 27.36 seconds per 

call per user. Therefore, the total number of users for a base station in Equation A-2 can also be 

calculated using Equation A-3:

M = (Total Erlangs per Base Station) / (Traffic Load per user per call in Erlangs) (A-3)

The total average holding time (H) is calculated as:

(6.5 x 4 + 0.2 x 4.2 + 0.01 x 60) / (4 + 4.2 + 60) = 4 seconds

 

Trunked radio systems are queuing or waiting type radio systems. The Erlang-C model is used 

in the network dimension or size computations. Dimensioning or sizing a trunked radio system 

means calculating the number of traffic channels required to provide an adequate GoS with an 

acceptable queuing time or waiting time for the mobile users in the system. In addition to the 

number of traffic channels calculated, a control channel must be added to each base station. 

Each channel requires two frequencies for a paired transmitter and receiver (TX/RX) allowing 

for full-duplex operation. 

GoS is defined as the probability that a call will be blocked or delayed. For a trunked radio 

system, the GoS is a function of the probability that a call request has to wait to be served 

(delayed) and the probability that the waiting time (in the queue) exceeds the reference waiting 

time W0 in seconds.3

The probability that a call waiting or delay exceeds the waiting time W0 is computed using 

Equation A-4:

GoS = 

[ ( ) / ]

0

0

( )

N A W H

D P W W P e

 

 

(A-4)

Where the probability that a call has to wait (PD) is given by the Erlang-C formula in Equation 

A-5.





 

 







1

0

! !

!

( , )

N

K

K N

N

D

N A

N

N

A

K

A

N A

N

N

A

P A N

(A-5)

Where:

PD: Probability that a call has to wait;

A: Call traffic level in Erlangs;

N: Number of traffic channels;

W0: Reference waiting time in queue in seconds; and

H: Average busy hour holding time in seconds

 

3. Jose M Hernando and F. Perez-Fontan, Introduction to Mobile Communications Engineering, Artech House 

(1999); Roger L. Freeman, Reference Manual For Telecommunications Engineering, Volume 1, Third Edition, 

Chapter 1-5, A Wiley-Inter-science Publication, John Wiley & Sons, Inc. (2002).
A-3

For a GoS = 1%, H = 4 seconds, W0 = 1 second and traffic load 0.0076 Erlangs per user, the 

number of channels per base station (N) vs. Erlang values (A), the number of users per base 

station (M) and the number of users per channel (M/N) at the busy hour were calculated using

Equations A-3, A-4 and A-5 and are shown in Table A-2. Figure A-1 shows the number of 

channels as a function of the number of users. The Erlang values shown in Table A-2 are for the 

maximum number of users associated with that number of channels per base station, thus the 

number of users is the maximum that this number of channels can handle at the busy hour. This 

only represents the busy hour. Therefore, the system should be able to serve many more users 

during other times because the traffic load beyond the busy hour will be less (e.g., half or third of 

the busy hour load). The total number of channels shown in Table A-2 does not include control 

channels.

As shown in Table A-2, a base station with one channel handles only two users when the traffic 

load is 0.0076 Erlangs/user. However, the number of users that the base station can serve 

increases much faster than the number of channels. This demonstrates that a trunking system can 

increase spectrum efficiency tremendously. However, the spectrum efficiency of a trunking 

system may not be fully realized when the traffic level is very small. For example, when there is 

partial agency participation in the trunked system most of base stations have very low traffic 

levels (small Erlang values). However, the same number of channels required for partial agency 

participation in the trunked system can accommodate many more users when there is greater 

agency participation in the trunked system. Trunking technology is very efficient for land 

mobile radio systems because a larger number of users can be served much more efficiently with 

a smaller number of channels as compared to conventional land mobile radio systems. 

Moreover, trunked systems with a large number of users offer much higher frequency efficiency 

than trunked systems servicing a small number of users. 

The rate of increase for trunking efficiency decreases when the number of channels gets too high. 

This is demonstrated by the fact that the number of users does not increase linearly with the 

number of channels (for a low number of channels) as shown in Figure A-1. As the number of 

channels increases beyond a point, the change in users approaches a fixed increment with the 

change in the number of channels. The trend of the number of users to increase will continue to 

be a constant number beyond 20 channels.
A-4

Table A-2. Trunked Radio Network Dimensioning (Busy Hour)

Number of 

Channels / Base 

Station

(N)

Traffic in Erlangs

(A)

Number of Users / 

Base Station 

(M)

Number of Users / 

Channel 

(M/N)

1 0.0127 2 2

2 0.1854 24 12

3 0.5386 71 24

4 1.0103 133 33

5 1.5625 206 41

6 2.1729 286 48

7 2.8276 372 53

8 3.5172 463 58

9 4.2352 557 62

10 4.9766 655 65

11 5.7378 755 69

12 6.516 857 71

13 7.3089 962 74

14 8.1147 1068 76

15 8.932 1175 78

16 9.7594 1284 80

17 10.596 1394 82

18 11.4407 1505 84

19 12.293 1618 85

20 13.1521 1731 87

21 14.0173 1844 88

22 14.8883 1959 89

23 15.7643 2074 90

24 16.6453 2190 91

25 17.5313 2307 92

26 18.4213 2424 93

27 19.3153 2541 94

28 20.2123 2660 95

29 21.1143 2778 96

30 22.0183 2897 97

31 22.9253 3016 97

32 23.8363 3136 98

33 24.7483 3256 99

34 25.6643 3377 99

35 26.5823 3498 100

36 27.5023 3619 101

37 28.4253 3740 101

38 29.3493 3862 102

39 30.2763 3984 102

40 31.2043 4106 103

Note: All calculations above were based on the following parameters: GoS = 1%, H = 4 

seconds, W0 = 1 second and traffic load 0.0076 Erlangs/user (or 27.36 seconds per call 

per user).
A-5

Trunked Radio Network Dimensioning (busy hour):

 Number of Channels vs. Number of Users

(Calculations were based on following parameters: 

GoS=1%, H=4s, W0=1s, Traffic Load=0.0076 Erlangs/user)

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Number of Channels

Number of Users

Figure A-1. Trunked Radio Network Dimensioning
A-6

A.2 Hybrid LMR Systems

Trunking technology provides major advancements for two-way radio communications. Since 

its development, public safety agencies at all levels of government as well as critical 

infrastructure entities and enterprise corporations are increasingly implementing trunked LMR 

systems to meet their advanced communications requirements. However, a trunked site in very 

low-traffic areas may not be the most efficient system because of low channel usage when the 

talk-group is geographically spread over different base stations. It is possible to combine 

different technologies in one system to take advantage of all of them. 

A.2.1 Combining Conventional and Trunked LMR Systems

The trunked radio systems are designed to best meet the communications needs of having high

communications traffic volume, requiring multiple channel communications and inter-agency or 

multi-agency interoperability. In contrast, conventional systems are typically used for wide-area 

coverage with small number of radio users and low communications traffic volume. These are 

usually the requirements of public safety agencies in large rural areas. Therefore, there are tradeoffs to be considered in the decision between a trunking and conventional system.

Implementing a hybrid system, combining conventional and trunked systems within a single 

system, may be an effective way for agencies to obtain the benefits of trunking where they need 

it most such as in large metropolitan areas, having high user density and interoperability 

requirements. Radios designated to operate in both the conventional mode and the trunked mode 

can be programmed to operate in either mode. Users are required to select either the 

conventional mode or trunked mode on their radio prior to making a call. When operating in a 

conventional site area, users would then monitor the conventional channel and wait until it is 

available, similar to a conventional system. When operating in a trunked site area, they just 

press the Push-to-Talk (PTT) button to make a call, similar to trunked operation.

A.2.2 Using Simulcast Technology 

For talk-groups that are widely dispersed, channels may have to be provided at several sites to 

provide the required coverage. The transmission of the same information on different channels 

is not the optimum way to use spectrum. For example, if a particular multi-site system uses a 

12:1 frequency reuse pattern, a given frequency might be usable only every twelfth site. Full 

coverage across all sits could require as many as 12 different frequencies. For an occasional 

requirement, the use of multiple separate channels at different sites may not cause a significant 

waste of spectrum; but for heavy use of widely dispersed talk-group requirements, the use of 

simulcasting on a few channels maybe a better way. Simulcast technology uses the same 

frequency on each site, allowing coverage across many sites with only a single frequency.

Simulcast systems use several geographically separated base stations/repeaters that transmit on 

exactly the same frequencies simultaneously. These networks require a timing system to 

synchronize each transmitter on the network to assure that transmissions on the same frequency 
A-7

are in phase to reduce the heterodyne interference. Should a traffic analysis show that there are 

geographically dispersed talk-groups that would regularly require channels across multiple sites, 

it may be advantageous to provide trunking systems that simulcast on one or more channels at 

some or all sites. In another words, simulcast technology can be used on a few channels as 

required as part of the overall trunking system. Whenever a large geographically dispersed talkgroup required service, this service would be provided through the use of a simulcast channel. If 

all simulcast channels were already in use, the service could be provided with multiple trunked 

channels. 

For a large, wide-coverage, and multi-agency trunking system the total simulcast trunking 

system (all channels in the system are simulcast channels) is not recommended, pending a more 

thorough understanding of the proportion of such geographically dispersed talk-groups. Unless 

there are a very large number of widely dispersed talk-groups, it is likely that the disadvantages 

of total simulcast architecture would outweigh the advantages. It prevents the frequency reuse in 

the entire network because the same frequencies are required at low-traffic area sites with fewer 

users as are required at high-traffic volume sites.

Only with a detailed traffic analysis can the advantages of simulcast for a particular system be 

determined. A major unknown in such analysis is the location of users belonging to talk-groups 

that would be serviced by such a system.