• No results found

Standard APCO25 Physical Layer of the Radio Transmission Chain

N/A
N/A
Protected

Academic year: 2021

Share "Standard APCO25 Physical Layer of the Radio Transmission Chain"

Copied!
77
0
0

Loading.... (view fulltext now)

Full text

(1)

Standard APCO25 Physical Layer of the Radio Transmission Chain

MATHIEU SIMON

Master’s Degree Project

Stockholm, Sweden

(2)
(3)

Master Thesis

Supervised by Christophe M.

Examined by Lars Kildehøj Rasmussen

January 25, 2014

The reproduction, distribution and use of this document as well as the communication of its contents to others without explicit authorization is prohibited. Offenders will be held liable for the payment of damages. All

rights reserved in the event of the grant of a patent, utility model or

design.

(4)
(5)

Acknowledgments

Firstly, I would like to thank Philippe M. manager of the DSP SW department at Cassidian, for having proposed this internship, in accordance to my field of studies as well as particularly challenging and therefore, very interesting.

Special thank to my supervisor at Cassidian, Christophe M. for his insightful guidance, constant help and encouragement that helped me conduct this project during those six months. Thank to Laurent M. for his numerous and crystal clear explanations along with his patience. Thanks to my colleagues Mickael M. and Jimmy S. for their professional insights and daily uplifting humor. Big thanks to all the other members of the DSP Software team, Olivier, Lynda and Valentin for having kindly integrated me within their team.

I would also like to thank all the teachers and classmates that helped me understand the different aspects of digital communications, through courses or fruitful discussions.

Special thank to Lars Rasmussen for having accepted to examine my thesis and for his course at KTH, particularly helpful during my thesis.

Finally, I would like to warmly thank my parents and sister, to whom I dedicate this thesis, for their constant support in my studies.

(6)

CONTENTS CONTENTS

Contents

1 Abstract XI

2 Sammanfattning XII

3 Company presentation 1

3.1 Airbus Group - EADS . . . 1

3.2 Airbus Defence and Space - Cassidian . . . 1

3.3 DSP SW team . . . 1

4 Introduction 2 4.1 Professional Mobile Radio - PMR . . . 2

4.2 Specificity of PMR networks . . . 2

4.3 Project P25 . . . 3

4.4 Thesis objective . . . 4

5 P25 Phase 1 frames format 5 5.1 Header frame . . . 5

5.2 Voice frame . . . 5

5.3 Link Data Unit . . . 6

5.4 Superframe . . . 6

6 P25 Phase 2 frames format 8 6.1 Time slot . . . 8

6.2 Superframe . . . 9

7 Modulation - Demodulation 10 7.1 Phase 1 modulation . . . 10

7.1.1 C4FM modulator . . . 10

7.1.2 CQPSK modulator . . . 16

7.2 Phase 2 modulation . . . 18

7.2.1 DQPSK modulator . . . 18

7.2.2 D8PSK modulator . . . 20

7.2.3 HCPM modulator . . . 22

7.3 Phase 1 demodulation . . . 24

7.4 Phase 2 demodulation . . . 25

8 Encoders - Decoders 27 8.1 Hamming . . . 27

8.2 Shortened cyclic code . . . 28

8.3 Golay . . . 30

8.4 Reed-Solomon . . . 31

8.5 BCH code . . . 34

(7)

CONTENTS CONTENTS

9 Synchronization 36

9.1 Rough temporal synchronization . . . 36

9.2 Fine-tuning . . . 36

10 Performances 38 10.1 Definitions . . . 38

10.2 Modem - Phase 1 . . . 39

10.2.1 Static Reference Sensitivity . . . 39

10.2.2 Faded Reference Sensitivity . . . 39

10.2.3 Adjacent Channel Rejection . . . 42

10.2.4 Co-channel Rejection . . . 42

10.2.5 Delay spread resistance . . . 43

10.3 Modem - Phase 2 . . . 44

10.3.1 Static Reference Sensitivity . . . 44

10.3.2 Faded Reference Sensitivity . . . 44

10.3.3 Adjacent Channel Rejection . . . 46

10.3.4 Co-channel Rejection . . . 47

10.3.5 Delay spread resistance . . . 47

10.4 Encoders/Decoders tests . . . 48

10.5 Graphical user interface . . . 49

11 Integration on a USRP device 52 11.1 Introduction . . . 52

11.2 Matlab Spectrum Analyzer . . . 52

11.3 Intermediate frequency . . . 54

11.4 Detection of synchronization frames . . . 55

12 Conclusion 57

13 Further studies 57

Appendices 58

A Propagation models 58

B Theta’s pdf derivation 61

(8)

LIST OF FIGURES LIST OF FIGURES

List of Figures

4-1 Working principle of a P25 network . . . 3

4-2 Cassidian mobile terminal . . . 4

4-3 Cassidian TETRA base station . . . 4

5-1 Diagram of Header Code Word Construction . . . 6

5-2 Diagram of Voice Code Word Construction . . . 7

5-3 Logical Data Unit 1 . . . 7

5-4 Phase 1 superframe . . . 7

6-1 Phase 2 TDMA Slot . . . 8

6-2 Phase 2 superframe . . . 9

7-1 C4FM modulator . . . 10

7-2 C4FM constellation . . . 11

7-3 C4FM eye-diagram . . . 11

7-4 C4FM transmission filter impulse response . . . 12

7-5 PSD of C4FM transmitted baseband signal . . . 12

7-6 Θ1 and Θ2 joint probability density function . . . 15

7-7 F req probability density function . . . 16

7-8 Theoretical BER as a function of NEb 0 . . . 17

7-9 CQPSK modulator . . . 17

7-10 CQPSK constellation . . . 18

7-11 CQPSK eye-diagram . . . 18

7-12 CQPSK transmission filter impulse response . . . 18

7-13 PSD of CQPSK transmitted baseband signal . . . 18

7-14 DQPSK constellation . . . 19

7-15 DQPSK eye-diagram . . . 19

7-16 DQPSK transmission filter impulse response . . . 20

7-17 PSD of DQPSK transmitted baseband signal . . . 20

7-18 D8PSK constellation . . . 21

7-19 D8PSK eye-diagram . . . 21

7-20 D8PSK transmission filter impulse response . . . 21

7-21 PSD of D8PSK transmitted baseband signal . . . 21

7-22 HCPM constellation . . . 23

7-23 HCPM eye-diagram . . . 23

7-24 HCPM transmission filter impulse response . . . 23

7-25 PSD of HCPM transmitted baseband signal . . . 23

7-26 C4FM and CQPSK demodulator . . . 24

7-27 H-CPM non-coherent demodulator . . . 25

7-28 Performances of H-CPM non-coherent demodulation depending on equalizers . . 26

8-1 Syndrome decoding . . . 29

10-1 Static Reference Sensitivity - Phase 1 . . . 39

10-2 TU 8 sensitivity - Phase 1 . . . 40

10-3 TU 100 sensitivity - Phase 1 . . . 40

(9)

LIST OF FIGURES LIST OF FIGURES

10-7 Delay spread resistance - Phase 1 . . . 43

10-8 Static Reference Sensitivity - Phase 2 . . . 44

10-9 TU 8 sensitivity - Phase 2 . . . 45

10-10TU 100 sensitivity - Phase 2 . . . 45

10-11HT 100 sensitivity - Phase 2 . . . 46

10-12Adjacent Channel Rejection - Phase 2 . . . 46

10-13Co-channel Rejection - Phase 2 . . . 47

10-14Delay spread resistance - Phase 2 . . . 47

10-15Results Visualization GUI . . . 49

11-1 USRP R E100 . . . 52

11-2 USRP R N210 . . . 52

11-3 Matlab GUI used to get ”real-time” information about the signal . . . 53

11-4 Motorola terminal XTS 5000 . . . 53

11-5 Correction of the frequency shift, observed with a waterfall . . . 54

11-6 Constellation obtained without any intermediate frequency . . . 54

11-7 Constellation obtained with an intermediate frequency . . . 54

11-8 Visualization of the demodulated signal on a spectrum analyzer . . . 55

11-9 Inter-correlation between received signal and reference . . . 56

11-10Reconstructed sound signal after transmission over the air . . . 56

A-1 Propagation models . . . 58

A-2 TU channel impulse response . . . 59

A-3 HT channel impulse response . . . 60

B-1 Problem diagram . . . 61

B-2 Θ probability density function . . . 62

(10)

LIST OF TABLES LIST OF TABLES

List of Tables

1 C4FM mapping table . . . 10

2 Theoretical sensitivity . . . 16

3 CQPSK mapping table . . . 16

4 D8PSK mapping table . . . 21

5 Logarithm table in GF(26) . . . 32

6 Exponential table in GF(26) . . . 32

7 States Transitions for Trellis code 1/2 . . . 34

8 States Transitions for Trellis code 3/4 . . . 35

9 Simulation time gains . . . 35

10 Results summary and comparison to standard requirements - Phase 1 . . . 43

11 Results summary and comparison to standard requirements - Phase 2 . . . 48

12 TU propagation . . . 58

13 HT propagation . . . 59

(11)

LIST OF TABLES LIST OF TABLES

Acronyms

ALGID Algorithm ID

APCO25 Association of Public Safety Communications Officials’ Project 25 AWGN Additive White Gaussian Noise

BER Bit Error Rate

C4FM Continuous Four Level Frequency Modulation CASA Construcciones Aeron´auticas Sociedad An´onima CPM Continuous Phase Modulation

CQPSK Compatible Quadrature Phase Shift Keying D8PSK π/8 Differential Shift Keyed Modulation DASA Daimler Chrysler Aerospace AG

DFE-MSE Decision Feedback Minimum Square Error Equalizer DFE-ZF Decision Feedback Zero-Forcing equalizer

EADS European Aeronautic Defence and Space FDMA Frequency Division Multiple Access FIR Finite Impulse Response

GF Galois Field

H-CPM Harmonized Continuous Phase Modulation

H-DQPSK Harmonized Differential Quadrature Phase Shift Keyed Modulation

HT Hilly Terrain

ISI InterSymbol Interference KID Key IDentifier

LSB Least Significant Bit LTE Long Term Evolution

L-MSE Linear Minimum Square Error Equalizer L-ZF Linear Zero-Forcing equalizer

MFID Manufacturer’s IDentifier MI Message Indicator

MLSE Maximum Likelihood Sequence Equalizer MSB Most Significant Bit

P25 Project 25

pdf probability density function PMR Private/Professional Mobile Radio PSD Power Spectral Density

RS Reed-Solomon

SNR Signal to Noise Ratio

TDMA Time Division Multiple Access TETRA TErrestrial Trunked RAdio TGID Talk-group ID

TIA Telecommunications Industry Association Tos Sampling time

Ts Symbol time

TU Typical Urban

UDP User Datagram Protocol

USRP Universal Software Radio Peripheral

(12)

1 ABSTRACT

1 Abstract

Professional Mobile Radio (PMR) also known as Private Mobile Radio or Land Mobile Radio (LMR) are radio systems conceived for public safety or professional event organizers. They are designed to provide a reliable and robust communication system independent from conventional public networks.

In France, for instance, the national police is equipped with a PMR network, namely ACROPOL, that blankets the entire country and allows both voice and low data rate services.

The object of this thesis is the North-American standard Project P25. It is a standard defined by the Telecommunications Industry Association (TIA) and is currently used by many radio communication systems in North-America.

This report presents the results of a Matlab/C simulation designed to provide performances information on P25 physical layer. This knowledge is exploited to verify that the standard requirements are met. The final purpose of this thesis is the integration of Project 25 Layer 1 on a real radio platform. Thus, this report gauges the performances of all the modulators defined in the TIA standard for both Project 25 phase 1 and phase 2. Several tests are presented, they were realized in different conditions, that is with different channel models, propagation models as well as with or without any fading, in static and dynamic conditions.

From this simulation, the Bit Error Rates vs NEb

0 results have been extracted and are presented.

The complete Forward Error Correction part has also been implemented and the correction capability of all the encoders and decoders has been verified, yielding the BER vs NEb

0 plots. The resistance to an interferer has been evaluated, in several cases, with an interferer in the same channel or in an adjacent channel.

The second part of this report presents the integration of the physical layer on a radio device.

This was done to validate that both physical and MAC layers were compliant to the standard.

This has been realized by interfacing the radio platform with Matlab via an Ethernet link and using UDP protocol. Furthermore, at the end of the thesis some conclusions are drawn and future possible studies are detailed.

(13)

2 SAMMANFATTNING

2 Sammanfattning

Privat mobil radio (PMR) ¨ar ett radiosystem som anv¨ands f¨or offentlig s¨akerhet eller av pro- fessionella arrang¨orer. PMR ¨ar utformad att ge en robust och p˚alitlig tr˚adl¨os kommunikation- ssystem som ¨ar oberoende av offentliga n¨atverk.

I Frankrike till exempel ¨ar polisen utrustad med ett PMR-n¨atverk som kallas ACROPOL.

N¨atverket t¨acker hela landet och m¨ojligg¨or b˚ade r¨ost- och datakommunikationer.

¨amnet i detta exjobb ¨ar det Nordamerikanska standard projektet P25 vilket etablerades av Telecommunication Industry Association (TIA). De flesta radiosystem d¨ar denna standard an- v¨ands finns f¨or n¨arvarande i Nordamerika. Denna rapport visar resultatet av en Matlab och C-simulering utformad att ge prestandainformation av P25:s fysiska skikt. Informationen som f˚as av simuleringen anv¨ands f¨or att kontrollera att standardkraven uppfylls. Det prim¨ara syftet av denna tes ¨ar integrationen av P25 i en radioplattform. Rapporten uppskattar alla modulators beteenden som specificeras i TIA-standarden i fas ett och tv˚a.

Testerna som redovisas har genomf¨orts p˚a olika s¨att, antingen med olika kanalmodeller eller med olika spridningsmodeller i statistiska och dynamiska f¨orh˚allanden.

Felr¨attande koder har implementeras i simuleringen och ¨aven korrektionsf¨orm˚agan har kon- trollerats f¨or alla kodare och avkodare.

Den andra delen av denna rapport handlar om integreringen av systemet i en radioapparat f¨or att kontrollera att b˚ade det fysiska skiktet och datal¨anken fungerar felfritt. Radioapparaten var ansluten till Matlab f¨or att simuleringen skulle kunna anv¨andas och testet genomf¨ordes med en Motorola-apparat som redan sl¨appts ut p˚a marknaden. I slutet av rapporten dras slutsatser kring resultaten och m¨ojliga framtida studier diskuteras.

(14)

3 COMPANY PRESENTATION

3 Company presentation

3.1 Airbus Group - EADS

The European Aeronautic Defence and Space Company (EADS) is an aerospace and defense company. EADS was created in July 2000 as the merger of three European aeronautic and defense companies: the french company Aerospatiale-Matra SA, the German Daimler Chrysler Aerospace AG (DASA) and the Spanish Construcciones Aeron´auticas Sociedad An´onima (CASA).

EADS is therefore a global leader in aerospace and defense, and provides civil and military air- craft, space rockets, satellites, missiles and communication systems with revenues of 43 billion euros and counts 133 000 employees (2012). Its CEO is currently Thomas Enders.

In 2013, it was announced that EADS was planning to change its name to Airbus Group in January 2014.

3.2 Airbus Defence and Space - Cassidian

Cassidian is the main division of EADS defense security services. It counts around 28,000 employees and is present in more than 80 countries throughout the world. Its field of activities encompasses radio communication systems, unmanned aerial systems and radar technology.

Along with EADS change of name to Airbus Group, Cassidian will merge with Astrium and Airbus Military to form Airbus Defence and Space in 2014.

3.3 DSP SW team

My internship took place in the DSP Software Engineering Department. The team I worked in focuses on :

• DSP Software functions development (signal processing and real-time processing) for LTE, TETRA, TETRAPOL, and APCO25

• System architecture studies:

– New PMR standards performances and implementation costs, LTE for instance – Antenna processing

– Digital communications, signal processing and audio analysis

The team counts around twenty people composed of engineers, service providers and trainees.

The department is divided between France and Finland. The team is focused on the development of PMR standards TETRA and particularly of the future LTE standard. The work is carried out in cooperation with other teams in Elancourt, especially with hardware engineers who develop the radio boards. Some projects are also led together with research laboratories, for instance

(15)

4 INTRODUCTION

4 Introduction

4.1 Professional Mobile Radio - PMR

The first analog PMRs were developed in the 20s in the USA. PMRs are commonly narrow band systems using a Frequency Modulation or an Amplitude Modulation. Frequency Modulation is widely exploited for the constant envelope signal it creates, which does not require a linear Power Amplifier before being transmitted over the air.

PMRs are radio communication systems dedicated to public safety professional or events orga- nizers such as firemen, policemen or Olympic Games organizers for instance. Their robustness and reliability is crucial since they should keep working even in case of a natural catastrophe, such as a hurricane, a flood... They shall work even when the conventional networks are out of order.

PMRs usually provide voice and low data rate services, such as text messages. Nevertheless, the development of broadband LTE may pave the way to Private Mobile Network able to convey large data such as images or even videos.

This feature would be particularly helpful to firemen or policemen, who could have access to maps or get visual information about an ongoing event.

4.2 Specificity of PMR networks

• Trunking

It is a technique allowing the network resources to be shared, a channel is allocated for the duration of a voice or data transmission. At the end, it is released and available for other terminals. A user does not have a dedicated channel, instead a channel among a pool will be allocated by the site controller.

• Conventional mode/Direct Mode

If some terminals are out of the coverage area of the network, they can communicate with one another without control channel. They communicate on a dedicated channel hard-coded into the terminal. They can also communicate through a simple repeater that re-transmits the signal at higher power to cover a longer distance.

• Group call

Several users may be registered in a common talk-group. If the Group ID contained in the signal corresponds to their talk-group, they listen to this signal.

• End-to-end encryption

PMRs allow end-to-end encryption, that is an uninterrupted encryption of data from an emitter to a receiver. It ensures confidentiality of the communication as well as its integrity.

• Air interface encryption

Unlike the end-to-end encryption, this mode encrypts and decrypts the data at each extremity of a communication link. Solely the transmission over the air is encrypted, and third parties may have access to plain data.

(16)

4.3 Project P25 4 INTRODUCTION

• Simulcast

It is the broadcasting of the same information by several sites. It can consequently improve the network coverage. The synchronization of the different sites is a crucial condition.

Simulcast performances of Project 25 are further discussed in this report.

4.3 Project P25

Project 25 (P25) is the standard for the design and manufacture of interoperable digital two- way wireless communications products. Developed in North America with state, local and fed- eral representatives and Telecommunications Industry Association governance, P25 has gained worldwide acceptance for public safety, security, public service, and commercial applications.

The published P25 standards suite is administered by the Telecommunications Industry As- sociation. Radio equipment that demonstrates compliance with P25 is able to meet a set of minimum requirements to fit the needs of public safety. The P25 standard was created by, and is intended for, public safety professionals.[3]

(17)

4.4 Thesis objective 4 INTRODUCTION

In a normal mode, where all the resources are available, a communication is done using the trunked mode. If a user with Terminal 1 wants to call the user with Terminal 2; Terminal 1 sends a request to the base station on a dedicated signaling channel. The request is transmitted to the site controller which allocates a channel for the upcoming communication. The base sta- tion sends this information to terminals 1 and 2 which can start communicating on this channel through the base station.

If a failover happens and the trunked radio system can no longer communicate with the site controller, the system is put in a failsoft mode. In this case, all the base stations work in the conventional mode, that is, they act as simple repeaters. The users must then switch to con- ventional mode to support the failsoft mode. The terminal is programmed to use a dedicated channel hard-coded in its memory. Users can then communicate directly to another user or through a base station which acts as a bare repeater.

In both cases, the communications are half-duplex, this means that users talk in turn and not simultaneously. A push-to-talk button is used to start communicating and released to free the resource for the other user.

Details about Project 25 can be found on the official website [3].

Figure 4-2: Cassidian mobile terminal Figure 4-3: Cassidian TETRA base station Figs.4-2 and 4-3 show two products developed by Cassidian, a TETRA mobile terminal and a TETRA base station. Cassidian also proposes some products concerning the APCO25 standard, but solely for the core network and not for the access network.

4.4 Thesis objective

The thesis objective is to implement the entire Physical Layer of this standard, as well as a part of the Media Access Layer. Some choices have to be made to reach the best performances that can be achieved for this standard. The final purpose is the validation of the implementation by exploiting a radio platform to communicate with a terminal that is known to be compliant to the standard.

(18)

5 P25 PHASE 1 FRAMES FORMAT

5 P25 Phase 1 frames format

Note: Part of the following information is directly extracted from TIA Recommended Common Air Interface [11].

P25 Phase 1 uses a FDMA access method, it works in a 12.5 kHz bandwidth at rate 4800 baud, with two bits per symbol, it can operate in both an analog or digital mode, however this study treats only of the digital mode.

In Phase 1 :

• 45 % of the bits are used to encode the voice information

• 30 % are required for Forward Error Correction

• 25 % are exploited for signaling 5.1 Header frame

The header word includes the following information fields :

• Message Indicator (MI) 72 bits

This is the initialization vector for the choice of an encryption algorithm.

• Manufacturer’s ID (MFID)8 bits

This is asserted when non-standard features are included in the voice message by the manufacturer. This field has a standard value when all of the other information fields conform to the definitions of the Common Air Interface. It is a minimum requirement for a standard radio to be able to transmit or receive messages using the standard field definitions of the Common Air Interface, with the standard value for the MFID field. The minimum requirement for standard receivers is to ignore messages which do not contain the standard value for the MFID field.

• Algorithm ID (ALGID) 8 bits

This identifies the encryption algorithm in systems with multiple algorithms.

• Key ID (KID) 16 bits

This identifies the encryption key for systems with multiple encryption keys.

• Talk-group ID (TGID) 16 bits

This identifies the talk-group for the message. These information fields are concatenated together into 120 bits. They are then separated into 20 symbols of 6 bits each. Each symbol is called a hex bit. These are encoded with a (36,20,17) Reed-Solomon code to yield 36 hex bits. These 36 hex bits are then in turn encoded.

5.2 Voice frame

(19)

5.3 Link Data Unit 5 P25 PHASE 1 FRAMES FORMAT

Figure 5-1: Diagram of Header Code Word Construction

codewords are used to protect the four first vectors (u0 7→ u3), adding 44 bits to the 48 bits of information.

The next 3 information vectors (u4 7→ u6) are protected using a (15,11,3) Hamming code, adding 12 parity bits to the 33 information bits.

The last 7 least significant bits are not protected.

A pseudo-noise sequence (PN sequence) is constructed from u0 and is XOR-ed to the remaining protected vectors. This sequence is defined as follows:

p0 = 16u0

pn= [173pn−1+ 13849] mod 65536 ∀n ∈ [1, 114].

Let pn[15] denote the 15th bit of pn, then the PN sequence is (pn[15])n∈[1,114]

Finally, the vectors are concatenated as described in Fig.5-2 and interleaved. This yields a code word more robust with respect to burst errors, that is more resistant to fading. The interleaving table is provided in [11]. A voice frame is transmitted in about 20ms.

5.3 Link Data Unit

Before being transmitted over the channel, the voice frames are concatenated into a data unit, either called Logical Link Data Unit 1 or Link Data Unit 2. A LDU1 is described in Fig.5-3 and consists of 9 voice frames. A LDU2 has a similar structure, the position of the voice frames is similar, but the other frames differ from a LDU1 frame.

5.4 Superframe

A superframe consists of a LDU1 followed by a LDU2. At the beginning of a voice communi- cation, a header is sent over the channel followed by several superframes, the communication is terminated with a Terminator Data Unit not described here. A superframe constitutes the basic block of a voice communication in phase 1.

(20)

5.4 Superframe 5 P25 PHASE 1 FRAMES FORMAT

Figure 5-2: Diagram of Voice Code Word Construction

Figure 5-3: Logical Data Unit 1

This superframe is depicted Fig. 5-4.

Figure 5-4: Phase 1 superframe

(21)

6 P25 PHASE 2 FRAMES FORMAT

6 P25 Phase 2 frames format

It has been decided that P25 phase 2 would use a two-slot TDMA access scheme, that is one 12.5 kHz channel can convey two individual voice calls. This allows a re-use of P25 Phase 1 technologies and does not involve any changes in the licensing requirements.

The data transmission speed is increased compared to Phase 1, two different schemes are used to transmit the 12 kbit/s data stream.

H-CPM is used for uplink, that is in the mobile terminals so that non-linear power amplifiers can be used. H-DQPSK is used for downlink, that is in the base stations, since many were already equipped with linear power amplifiers, and this modulator increases the simulcast performances.

In Phase 2 :

• 40 % of the bits are used to encode the voice information

• 20 % are required for Forward Error Correction

• 40 % are exploited for signaling 6.1 Time slot

Figure 6-1: Phase 2 TDMA Slot

Since a TDMA scheme is used, 6 symbols are used at the beginning and at the end of a frame to smoothly increase and decrease the power and consequently prevent inter-frame interference.

Four pilot symbols are available at the beginning and anew four at the end of a frame to estimate the channel.

Those symbols are particularly interesting when a H-CPM modulation scheme is used as it is described section 7.4. In a voice communication, every TDMA slot conveys up to 4 voice frames.

(22)

6.2 Superframe 6 P25 PHASE 2 FRAMES FORMAT

6.2 Superframe

By analogy to phase 1, there also exists a superframe in the second phase of the standard. This frame also lasts 360 ms with 6 slots reserved for the inbound channel (downlink) and 6 reserved for the outbound channel (uplink). The repartition of these slots is given by Fig.6-2.

Figure 6-2: Phase 2 superframe

Further details about the Media Access Layer for phase 2 can be read in [13].

(23)

7 MODULATION - DEMODULATION

7 Modulation - Demodulation

7.1 Phase 1 modulation

In Project P25 phase 1, two kinds of modulators are defined and according to the standard, both should be demodulated using the same receiving chain. A non-coherent approach was chosen for its low complexity and the good results it provides. This section describes C4FM and CQPSK modulators. Some theoretical results have been derived in order to provide a reference for the demodulator performances. Since all modulation schemes carry the information in their phase or frequency, the derivation intends to show the impact of an additive white noise on the signal phase and on its derivative.

7.1.1 C4FM modulator

The C4FM is a constant envelope frequency modulation.

The modulation sends 4800 symbols/s with each symbol conveying 2 bits of information. The information bit stream is first mapped to symbols as defined in Table 1.

The signal is then over-sampled to form a Dirac comb weighted by those symbols. It is shaped with a Raised-cosine filter defined in eq.(2) to obtain a signal without intersymbol interference.

This filter is cascaded with a shaping filter defined in eq.(1). The resulting signal is then integrated and sent over the channel as the phase of a complex exponential.

A summary of the transmission chain is shown on Fig.7-1.

Information Bits Symbols Deviation

01 +3 +1800Hz

00 +1 +600Hz

10 −1 −600Hz

11 −3 −1800Hz

Table 1: C4FM mapping table

Figure 7-1: C4FM modulator





|P (f)| = magnitude of the Tx Shaping Filter

|P (f)| =

πf 4800

sin(4800πf ) for|f| < 2880Hz

|P (f)| = 0 for|f| > 2880Hz

(1)









|H(f)| = magnitude of the Raised Cosine Filter

|H(f)| = T2Toss for|f| < 1920Hz

|H(f)| = T2Toss

1 2



1 + cos

2πf 1920



for 1920Hz <|f| < 2880Hz

|H(f)| = 0 for|f| > 2880Hz

(2)

(24)

7.1 Phase 1 modulation 7 MODULATION - DEMODULATION

where :

• Tos : Sample time

• Ts : Symbol time, Ts' 208µs

The time expression of H can be found in [4].

The baseband signal, s, can be written as:

s(t) = exp(iφ(t)) (3)

With :

 φ(t) = 2πhP akq(t− kTs) q(t) = Rt

−∞p(u)du (4)

1. p is the convolution of the Raised-Cosine defined in eq.(2) with the shaping filter defined in eq.(1).

2. h is the modulation index equals to 14 for a C4FM modulation scheme.

3. (ak) are the symbols, with values in set{−3, −1, 3, 1}.

This signal has a continuous phase, its frequency varies roughly in the range [−1800Hz, 1800Hz].

−1.4 −1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

−1

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

Inphase

Quadrature

Figure 7-2: C4FM constellation

−120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120

−8

−6

−4

−2 0 2 4 6 8

Time (µs)

Figure 7-3: C4FM eye-diagram

Figures 7-2 to 7-5 show different representations of the modulated baseband signal. The con- stellation shows a perfect circle since the modulation has a constant envelope. The transmission filter described previously is also plotted in Fig.7-4, although it is a FIR, it lasts 24 symbols to improve its spectral efficiency. The signal PSD is shown Fig.7-5, its wide shape is characteristic of a CPM modulation.

(25)

7.1 Phase 1 modulation 7 MODULATION - DEMODULATION

−2,500 −2,000 −1,500 −1,000 −500 0 500 1,000 1,500 2,000 2,500

−2

−1 0 1 2 3 4 5 6·10−2

Time (µs)

Amplitude

Transmission filter impulse response

Figure 7-4: C4FM transmission filter im- pulse response

−25 −20 −15 −10 −5 0 5 10 15 20 25

−140

−120

−100

−80

−60

−40

−20 0

Frequency (kHz)

PowerSpectralDensity(dB)

Figure 7-5: PSD of C4FM transmitted baseband signal

Theoretical derivation

Project P25 defines a standard static sensitivity, as the level of ENb

0 reached when standard BER is achieved (standard BER being 5%). This measure is done when the signal is sent over an AWGN channel without any fading. The theoretical sensitivity of the C4FM modulation scheme is determined as follows :

Let s(t) = exp(jφ(t)) be the baseband signal sent over the channel.

Let N (t) be the additive complex white Gaussian noise with variance N0.

The signal received after transmission over the channel and filtered by the Low-pass filter is denoted y.

After being received, y is sampled at rate T1

os.

Let t = t0 = k0Tos be a sample time. To simplify the calculation, φ(t0) will be considered as equal to zero without loss of generality, the result for any other angle can be found by a simple shift.

From this point, all the calculations are done using discrete time signals.

The random variables are written with capital letters unlike the deterministic signals.

The energy per sample is arbitrarily unitary, thus given a level of NEb

0 in decibels, the noise variance can be deduced as :

N0 = 10

Eb

N0+10 log10(2)−10 log10(TosTs)

10 (5)

The frequency response of the Low-pass filter is defined as :

 H(ν) = 1 for |ν| < fcTos= ν0

H(ν) = 0 otherwise (6)

where ν represents the reduced frequency, that is ν = f Tos. The corresponding time filter is thus :

h[k] = 2ν0sinc(2ν0k) (7)

(26)

7.1 Phase 1 modulation 7 MODULATION - DEMODULATION

The received signal Y [k] is :

Y [k] = A[k] exp(jΘ[k]) = (s[k] + N [k]) ? h[k] (8) where ? represents the convolution of two discrete time signals.

Let Θ1 denote the random variable Θ(t0) and Θ2 be the random variable Θ(t0+ Tos).

The Low-pass filter h is unitary, and wider than the useful signal bandwidth, therefore s can be considered as non-altered by h.

Hence,

Y [k] = A[k] exp(jΘ[k]) = s[k] + (N [k] ? h[k]) = s[k] + W [k] (9)

W [k] = Wx[k] + iWy[k] (10)

This equation can be re-written at sampling time as :

Y [k0] = A[k0] exp(jΘ[k0]) = 1 + W [k0] (11) W is still Gaussian (as a linear combination of Gaussians), however it has been colored by the filtering.

Let rh be the auto-correlation function of h, and rw be the auto-correlation function of W : rW[k] = rh[k]N0

rWx[k] = rh[k]N0 2 rWy[k] = rh[k]N0

2

(12)

Let ρ denote the Pearson product-moment correlation coefficient of Wx[k0] and Wx[k0 + 1]

(Wy[k0] and Wy[k0+ 1])

ρ = rh[1]

rh[0] (13)

In addition,

var[Wx[k0]] = var[Wx[k0]] = var[Wx[k0]] = var[Wx[k0]] = rh[0]N0

2 (14)

Where var denote the variance of a random variable.

The joint probability density function of Wx[k0] and Wx[k0+ 1] can be deduced : fWx0,Wx1(x1, x2) = 1

πN0p1 − ρ2exp



− 1

N0(1− ρ2) x12− 2ρx1x2+ x22



(15) The joint probability density function of Wy[k0] and Wy[k0+ 1] is the same. Furthermore, the

(27)

7.1 Phase 1 modulation 7 MODULATION - DEMODULATION

fWx0,Wx1,Wy0,Wy1(x1, x2, y1, y2) = 1

π2N02(1− ρ2)exp



− 1

N0(1− ρ2) x21+ y12− 2ρ(x1x2+ y1y2) + x22+ y22



(16) From this expression, a polar coordinate change can be used to express the joint pdf of Θ1 and Θ2 defined above.

This pdf is :

fΘ121, θ2) = Z +∞

0

Z +∞

0

1

π2N02(1− ρ2)exp



−g(r1, r2, θ1, θ2) N0(1− ρ2)



r1r2dr1dr2

(17)

with :

g(r1, r2, θ1, θ2) =

(r1cos θ1− 1)2+ (r1sin θ1)2− 2ρ((r1cos θ1− 1)(r2cos θ2) + (r1sin θ1)(r2sin θ2)) + r22

(18)

Since this integral is not easily evaluated, a Matlab script was written to get a numerical solution.

An example is given Fig.7-6.

The parameters used for this example are:

• Modulation rate : 4800 baud.

• Sampling frequency : 14400 Hz

• low-pass filter cut-off frequency : 9600 Hz

ENb0 = 0 dB.

Note on Fig.7-6 that the maximum is obtained for θ1 = θ2 = 0 which is logical. Furthermore, Θ1 and Θ2 are correlated, since the highest probabilities are obtained along the diagonal, that is when θ1= θ2.

Since the information is not carried by the phase but by the signal frequency at the sampling time, this frequency is derived as the derivative of the phase divided by 2π. The signal being discrete, the frequency f req(t) is derived as :

f req(t) = θ(t + Tos)− θ(t) 2πTos

(19) Hence, the pdf of F req, a random variable defined by F req = Θ2πT2−Θ1

os can be deduced from Θ1 and Θ2’s joint pdf. The pdf of Θ1 is not sufficient to give a conclusion because Θ1 and Θ2 are correlated. They are even more correlated as the oversampling increases. F req’s pdf, fF req(f ), can be calculated as the ”inner” autocorrelation of the joint pdf, that is :

(28)

7.1 Phase 1 modulation 7 MODULATION - DEMODULATION

−4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 4

−4

−3

−2

−1 0 1 2 3 4

θ1(rad) θ2(rad)

Logarithm of Θ1and Θ2joint pdf

−8

−7

−6

−5

−4

−3

−2

−1 0

Figure 7-6: Θ1 and Θ2 joint probability density function

fF req(f ) = Z +∞

−∞

fΘ12(θ− 2πfTos, θ)dθ (20) The probability density function fF req is shown in Fig.7-7.

From this distribution, the error probability can be derived, assuming that no more than one bit is erroneous when a symbol is erroneous. This assumption holds at relatively high SNR, that is at SNR around the static sensitivity, since a Gray coding is used in this modulation scheme.

It follows that the bit error probability is roughly half the symbol error probability.

The symbol error probability is finally deduced as :

Pesymb = 2Pebit = 1

2P (F req∈ [−600Hz, 600Hz]) + 1

4P (F req∈ [−∞, 600Hz])+

1

4P (F req∈ [−600Hz, +∞])

(21)

A Matlab script was written to plot the theoretical BER as a function of NEb

0, which is shown in Fig.7-8.

The horizontal line represents the standard BER, that is 5% of error. The interested reader can find a derivation of Θ’s exact pdf in Annex B.

One can notice that the BERs plotted on Fig.7-8 give a sensitivity lower, and even much lower than the one obtained with the simulation. Table 2 summarizes those values. This can be

(29)

7.1 Phase 1 modulation 7 MODULATION - DEMODULATION

−4,000 −3,000 −2,000 −1,000 0 1,000 2,000 3,000 4,000

−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

·10−3

Frequency (Hz) Frequency pdf

Figure 7-7: F req probability density function

trade-off between noise rejection and signal deterioration that gives the best sensitivity, but this trade-off problem is non-trivial.

fc 7200 Hz 8000 Hz 8800 Hz

Sensitivity (BER = 5%) 1.6 dB 2.7 dB 4 dB Table 2: Theoretical sensitivity

7.1.2 CQPSK modulator

The CQPSK modulation is an Inphase and Quadrature modulation. The modulation sends 4800 symbols/sec with each symbol conveying 2 bits of information. The information bit stream is first mapped to symbols Ik as defined in Table 3. The transmission chain is summarized in Fig.7-9.

Information Bits Symbols (Ik) Phase change (rad)

01 +3 +4

00 +1 +π4

10 −1 −π4

11 −3 −4

Table 3: CQPSK mapping table

The baseband formula for a CQPSK signal is:

(30)

7.1 Phase 1 modulation 7 MODULATION - DEMODULATION

−4 −2 0 2 4 6 8 10 12 14

10−5 10−4 10−3 10−2 10−1 100

Eb/N0(dB)

BER

Comparison of BER plots with different channels low-pass filters

fc= 7200 Hz fc= 8000 Hz fc= 8800 Hz

Figure 7-8: Theoretical BER as a function of NEb

0

s(t) =

Z r Es Ts

exp(jφ(u, I))h(t− u)du (22)

φ(t, I) = π 4

XIk (23)

where :

• Es : Energy per symbol

• Ts : Symbol time, Ts' 208µs

h(t) defines a filter applied to the Inphase and Quadrature signals, thus it constraints the spectral spread of the baseband modulated signal s(t). It is defined as a Raised-Cosine with a roll-off coefficient α = 0.2 and a bandwidth of (1+α)T

s = 5760Hz.

Figure 7-9: CQPSK modulator

(31)

7.2 Phase 2 modulation 7 MODULATION - DEMODULATION

−2 −1.8−1.6−1.4−1.2 −1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

−1.2

−1

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1 1.2

Inphase

Quadrature

Figure 7-10: CQPSK constellation

−120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120

−8

−6

−4

−2 0 2 4 6 8

Time (µs)

Figure 7-11: CQPSK eye-diagram

−1,000 −800 −600 −400 −200 0 200 400 600 800 1,000

−0.2 0 0.2 0.4 0.6 0.8 1 1.2

Time (µs)

Amplitude

Transmission filter impulse response

Figure 7-12: CQPSK transmission filter impulse response

−50 −40 −30 −20 −10 0 10 20 30 40 50

−100

−90

−80

−70

−60

−50

−40

−30

−20

−10 0

Frequency (kHz)

PowerSpectralDensity(dB)

Figure 7-13: PSD of CQPSK transmitted baseband signal

The CQPSK eye-diagram Fig.7-11 is much wider than for a C4FM modulation scheme, therefore it should be more resistant to multipath. However, as it can be observed in Fig.7-10, the signal can get close to zero. If the noise variance is high enough, the inphase and quadrature components can quickly change their sign. In a non-coherent demodulation, this creates a considerable amount of errors. The PSD in Fig.7-13 shows a narrow signal, typical of an amplitude modulation scheme. The finite impulse response Fig.7-12 is shorter than the C4FM one, but is sufficiently long to give an excellent spectral efficiency. As it is seen section 7.3, both modulators can be demodulated using the same receiving chain in a non-coherent approach.

7.2 Phase 2 modulation 7.2.1 DQPSK modulator

DQPSK or H-DQPSK stands for Harmonized differential quadrature phase shift keyed. The baseband formula for a DQPSK signal is:

s(t) =

Z r Es

Ts exp(jφ(u, I))h(t− u)du (24)

where :

(32)

7.2 Phase 2 modulation 7 MODULATION - DEMODULATION

φ(t, I) = π 4

XIk (25)

where :

• Es : Energy per symbol

• Ts : Symbol time, Ts' 167µs

h(t) defines a filter applied to the Inphase and Quadrature signals, thus it constraints the spectral spread of the baseband modulated signal s(t). It is defined as a Raised-Cosine with a roll-off coefficient α = 1 and a bandwidth of 3.6 kHz.

H(f ) = ( 1

2



1 + cos

πf fh



for|f| ∈ [0, fh]

0 otherwise (26)

where :

• fh = 7.2kHz

As it can be seen on Fig. 7-15, the eye-diagram shows that the transmission filter is not a Nyquist filter, however, there is solely small inter-symbol interference, so no equalization is used to demodulate the signal.

−2 −1.8−1.6−1.4−1.2 −1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

−1.2

−1

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1 1.2

Inphase

Quadrature

Figure 7-14: DQPSK constellation

−120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120

−8

−6

−4

−2 0 2 4 6 8

Time (µs)

Figure 7-15: DQPSK eye-diagram

Compared to the CQPSK modulation scheme which is also an amplitude modulation, it can be observed on the eye-diagram Fig.7-15 is relatively wider than for a CQPSK, however the symbol time is reduced, therefore it may not be more resistant to delay spread. If the eye- diagram is wide, this also means that the level transitions are very short, and therefore the spectrum efficiency compared to a CQPSK modulator, is reduced. It can be observed that the signal PSD Fig.7-17 is wider.

(33)

7.2 Phase 2 modulation 7 MODULATION - DEMODULATION

−800 −700 −600 −500 −400 −300 −200 −100 0 100 200 300 400 500 600 700 800

−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

Time (µs)

Amplitude

Transmission filter impulse response

Figure 7-16: DQPSK transmission filter impulse response

−30 −25 −20 −15 −10 −5 0 5 10 15 20 25 30

−100

−90

−80

−70

−60

−50

−40

−30

−20

−10 0

Frequency (kHz)

PowerSpectralDensity(dB)

Figure 7-17: PSD of DQPSK transmitted baseband signal

7.2.2 D8PSK modulator

D8PSK stands for π8 differential phase shift keyed modulation. The baseband formula for a D8PSK signal is:

s(t) =

Z r Es

Ts

exp(jφ(u, I))h(t− u)du (27)

where :

φ(t, I) = π 8

XIk (28)

where :

• Es : Energy per symbol

• Ts : Symbol time, Ts= 250µs

• {Ik} are the symbols defined in table 4

h(t) defines a filter applied to the Inphase and Quadrature signals, thus it defines the spectral spread of the baseband modulated signal s(t). It is defined as a Raised-Cosine with a roll-off coefficient α = 1 and a bandwidth of 2.5 kHz.

H(f ) = ( 1

2

1 + cos

πf fh

 for|f| ∈ [0, fh]

0 otherwise (29)

where :

• fh = 5kHz

As it can be seen on Fig. 7-19, the eye-diagram shows that the transmission filter is not a Nyquist filter, however, there is solely small inter-symbol interference, so no equalization is used to demodulate the signal.

(34)

7.2 Phase 2 modulation 7 MODULATION - DEMODULATION

Information Bits Symbols

010 +7

011 +5

001 +3

000 +1

100 −1

101 −3

111 −5

110 −7

Table 4: D8PSK mapping table

−2 −1.8−1.6−1.4−1.2 −1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

−1.2

−1

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1 1.2

Inphase

Quadrature

Figure 7-18: D8PSK constellation

−120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120

−8

−6

−4

−2 0 2 4 6 8

Time (µs)

Figure 7-19: D8PSK eye-diagram

−1,000 −800 −600 −400 −200 0 200 400 600 800 1,000

−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

Time (µs)

Amplitude

Transmission filter impulse response

Figure 7-20: D8PSK transmission filter im- pulse response

−20 −18 −16 −14 −12 −10 −8 −6 −4 −2 0 2 4 6 8 10 12 14 16 18 20

−120

−100

−80

−60

−40

−20 0

Frequency (kHz)

PowerSpectralDensity(dB)

Figure 7-21: PSD of D8PSK transmitted baseband signal

The constellation Fig.7-18 shows some transitions that get really close to zero, and therefore

(35)

7.2 Phase 2 modulation 7 MODULATION - DEMODULATION

7.2.3 HCPM modulator

H-CPM stands for Harmonized Continuous Phase modulation and is a form of Continuous Phase Modulation (CPM) operating at 12 kbit/s. The baseband formula for a CPM signal is:

s(t) =r Es Ts

exp(jφ(t, I)) (30)

where :

• Es : Energy per symbol

• Ts : Symbol time, Ts' 167µs

The information is carried by the signal phase φ(t, I), I being the sequence of symbols sent, I ={Ik}∀k ∈ Z, Ik∈ {−3, −1, 1, 3}. This phase can be expressed as :

φ(t, I) = 2πhX

k∈Z

Ikq(t− kTs) (31)

where :

• h : Modulation index

• q : Phase response of H-CPM, given by the following formula :

q(t) =

 0 for t < 0

1

2 for t > LTs (32)

• L = pulse response length in symbols.

q(t) is more precisely defined as the integral of a frequency impulse response g(t) defined as follows :

q(t) = Z t

0

g(v)dv (33)

g(t) = ( 1

G

h sinc

λ

Ts t−LT2s cos2

π

LTs t−LT2si

for t∈ [0, LTs]

0 otherwise (34)

H-CPM modulation is defined with parameters : G = 4.345510−4, λ = 34, h = 13 and L = 4.

(36)

7.2 Phase 2 modulation 7 MODULATION - DEMODULATION

−1.4 −1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

−1

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

Inphase

Quadrature

Figure 7-22: HCPM constellation

−120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120

−8

−6

−4

−2 0 2 4 6 8

Time (µs)

Figure 7-23: HCPM eye-diagram

−800 −700 −600 −500 −400 −300 −200 −100 0 100 200 300 400 500 600 700 800

−0.5 0 0.5 1 1.5 2 2.5 3 3.5 4

·10−2

Time (µs)

Amplitude

Transmission filter impulse response

Figure 7-24: HCPM transmission filter im- pulse response

−30 −25 −20 −15 −10 −5 0 5 10 15 20 25 30

−140

−120

−100

−80

−60

−40

−20 0

Frequency (kHz)

PowerSpectralDensity(dB)

Figure 7-25: PSD of HCPM transmitted baseband signal

As it can be seen in Fig.7-23, the eye-diagram obtained with the discriminator receiver shows that the transmission filter is not a Nyquist filter, inter-symbol interference at sampling time is considerable and an equalizer is required to eliminate, or at least reduce, those interference.

Similarly to a C4FM modulation, the baseband signal PSD is wide and will therefore be altered by the channel filter. As expected the constellation shows a perfect circle as the signal has a constant envelope. The transmission filter length is defined by the standard and lasts L = 4 symbols.

(37)

7.3 Phase 1 demodulation 7 MODULATION - DEMODULATION

7.3 Phase 1 demodulation

Let y(t) be the baseband signal received after transmission over the channel. This signal is filtered by a Low-Pass filter to reject a maximum of noise and keep the useful signal. Then this signal is normalized to yield a constant envelope signal, this is necessary before using a discriminator method.

If there is no fading or noise, y(t) = s(t) where s(t) is the baseband signal before transmission over the channel.

The discriminator method consists in computing : 1

2πTosiy(t)(y(t + Tos)− y(t)) (35) When developed it yields :

1

2πTosiy(t)(y(t + Tos)− y(t)) = eiθ(t+Tos)− eiθ(t) 2πTosieiθ(t) ' φ(t + Tos)− φ(t)

2πTos ' 1 2π

dφ(t)

dt = hP akp(t− kTs) Tos

(36)

After filtering by the receiving filter, the obtained signal does not have ISI and thus at sampling time the signal value is :

Chak0

Tos

(37) Where C is a constant depending on the transmitting filter, thus C is known and akcan be found.

In order to yield the best results, the demodulator should not be the same for a C4FM modu- lator and a CQPSK modulator.

In the first case, the signal after discriminator should be filtered by the inverse shaping filter 1/P (f ).

In the second case, the signal should be filtered by an averaging filter, with length equal to the number of samples per symbol.

However, the inverse shaping filter 1/P (f ) is a truncated sinc function, thus its Fourier Trans- form is the averaging filter defined above, convolved with a sinc function.

The assumption that this sinc function is a Dirac is made. It deteriorates the C4FM modulation performances, but gives the best performances for a CQPSK modulator.

Figure 7-26: C4FM and CQPSK demodulator

(38)

7.4 Phase 2 demodulation 7 MODULATION - DEMODULATION

7.4 Phase 2 demodulation

DQPSK and D8PSK :

In P25 Phase 2, all the modulators face ISI. However, as it can be seen in Fig.7-15 and Fig.7-19, for both DQPSK and D8PSK modulators, the eye-diagram is not closed and since they both are QPSK modulations, they can be demodulated using the non-coherent approach described in the previous section. This is the method that was exploited in the simulation, it yields decent results for a low-complexity demodulator.

Figure 7-27: H-CPM non-coherent demodulator H-CPM :

Concerning the H-CPM modulator, the eye-diagram is completely closed as shown in Fig.7-23, therefore an equalizer is required to remove or at least attenuate ISI. Five different equalizers have been implemented and benchmarked to find the best trade-off between low-complexity and satisfying results.

Those equalizers are listed below :

• Linear Zero-Forcing equalizer (L-ZF)

• Linear Minimum Square Error Equalizer (L-MSE)

• Decision Feedback Zero-Forcing equalizer (DFE-ZF)

• Decision Feedback Minimum Square Error Equalizer (DFE-MSE)

• Maximum Likelihood Sequence Equalizer (MLSE)

As described in section 6, 4 symbols are present at the beginning of a frame, and 4 at the end.

They may be used by some equalizers.

• Zero-forcing

The Zero-Forcing equalizers use an a priori model of the channel, therefore they do not use the knowledge of those symbols.

• MSE

Both MSE equalizers need an estimate of the channel autocorrelation matrix, a training sequence is used to define the filter which is then used whichever the conditions. That

(39)

7.4 Phase 2 demodulation 7 MODULATION - DEMODULATION

• MLSE

The MLSE equalizer uses the symbols to open and close the trellis, it helps staying on the correct path while demodulating. Nevertheless, the channel is not estimated either with this method.

Details about those different equalizers can be found in [6]. The BER vs NEb

0 results in static condition with AWGN are shown in Fig.7-28 for the different equalizers.

At high SNRs, MSE and Zero-forcing equalizers should behave equally which is not what is observed. This is explained by the fact that the MSE takes into account the channel filter effect unlike the zero-forcing equalizer which uses the hard-coded transmission filter response unaltered by the channel filter.

−5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

10−4 10−3 10−2 10−1 100

EbNo (dB)

BER

BERs as a function of EbNo (dB)

HCPM static, speed 0, enc RAW, eq ZF HCPM static, speed 0, enc RAW, eq DFEZF HCPM static, speed 0, enc RAW, eq MSE HCPM static, speed 0, enc RAW, eq DFEMSE HCPM static, speed 0, enc RAW, eq MLSE

Figure 7-28: Performances of H-CPM non-coherent demodulation depending on equalizers The results for the H-CPM modulation scheme presented in this report were done using a MLSE equalizer, since it gives significantly better results than the other equalizers. Its higher complexity does not considerably slow down the simulation, however it should be improved to yield better results as it does not meet every single standard requirements as pointed further in this report.

References

Related documents

[r]

We have to conducted interviews with journalists and reporters in Thailand to see how they work under the restrictions on media set in place by the military government, and

(Sunér Fleming, 2014) In data centers, it is common to use Uninterruptible Power Supply (UPS) systems to ensure stable and reliable power supply during power failures (Aamir et

For codes where more errors is possible the direct method needs to calcu- late the determinant for larger matrices to find the number of errors, then this method potentially needs

Time of decoding depends on number of occurred errors in received vector and on error correction capability, it doesn’t depend on length of codeword, number of information

According to Shore &amp; Warden (2008, pp. 177,183) important practices applicable in the eld of extreme programming from the perspective of source code management systems and

Right: Mean altitude of minimum relative humidity gradient calculated from corresponding ECMWF data.. Altitudes are with respect to

När värdering sker av immateriella tillgångar finns det många saker som kan påverka värderingen detta kan till exempel vara vilken syn den person som värderar har på