Continuous Phase ModulationA short Introduction

Charles-Ugo Piat12 & Romain Chayot123

1TeSA, 2CNES, 3TAS

19/04/17

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 1/23

Table of Content

CPM ModulationSystem ModelNotable CPM schemesInterestsTrellis representation

Decomposition and Detection of CPMRimoldi’s DecompositionPAM Decomposition

Thesis ContributionThesis Charles-UgoThesis Romain

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 2/23

System Model

I The complex envelop of the transmitted signal for CPMsystems in baseband can be described as follows:∀ t,

s(t) =

√EsT· e jφ(t,α)

I The information-carrying phase is:

φ(t, α) = 2πhN−1∑i=0

αiq(t − iT )

αi ∈ {±1, ...,±(M − 1)} the information symbols, Es is the symbolenergy, T is the symbol period, h the modulation index (h = P

Q ,with P and Q are relatively prime).

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 3/23

Phase Response

I Keeps the phase of the CPM signal continuous.

I Satisfies the following equation:

q(t) =

0, t ≤ 0∫ t

0 g(u)du, 0 < t ≤ LT12 , t > LT

Where g(t) is the pulse response. It defines the shape of thetrajectory.

The spectral efficiency is highly dependent on this parameter.

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 4/23

Phase and Pulse Response examples

Figure: Phase g(t) and pulse q(t) response of some CPM

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 5/23

CPM parameters

I L is the CPM memory.I support length of the pulse responseI the number of past symbols required to determine the signal

waveformI L = 1 total response CPM, L > 1 partial response.I Greater L leads to less out-of-band energy (smaller side lobes)

Figure: Influence of parameter L for a RC h=0.5

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 6/23

CPM parameters

I h is the modulation indexI Usually rational number < 1I small h leads to narrow occupied bandwidth

Figure: Influence of parameter h for a REC L=2

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 7/23

Notable CPM schemes and some application

I CPFSK: Telemetry

I SOQPSK: UHF SatCom (MIL-STD-188-181A)

I GMSK: Global System for Mobile Communication (GSM),Automatic Identification System (AIS)

I mixed RC/REC: Satellite Communication (DVB-RCS2)

I MSK, SFSK: considered for deep space communication

I Generalized MSK: Bluetooth data transmission

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 8/23

Interests

I Constant envelop waveform.I The transmitted power is constant.

Figure: Binary 3RC h=2/3 in a three dimensional plan

I Phase continuity.I High spectral efficiency.

I Memory.I Fit to turbo decoding.

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 9/23

Trellis representation

I How to detect the emitted sequence?I Maximum Likelihood (ML) Detection

s = argmax

∫r(t)s∗(t)dt

I Need a trellis representation to perform a Viterbi algorithm

I Decomposition of the phase, at t ∈ [kT ; (k + 1)T [

φ(t, α) = hπk−L∑i=0

αi︸ ︷︷ ︸=φk

+2hπk∑

i=k−L+1

αiq(t − iT )

The signal can be modelled only fromσk = {φk , αk−L+1, . . . , αk−1} which forms a state of ourtrellis and αk the current symbol.

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 10/23

Example of Trellis representation

I MSK scheme (M=2, L=1, h=1/2 and REC pulse shape)

I state σk = {φk}I φk = πh

∑k−1i=0 αi takes 4 values modulo 2π {0, π2 , π,

3π2 }

I Time-variant trellis (only 2 of the 4 states are accesible ineach symbol period)

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 11/23

Rimoldi’s Decomposition

I Time invariant phase trellis for CPM can be obtained bydefining the tilted phase ψ

ψ(t, α) = φ(t, α) +πh(M − 1)t

T

I The modified data sequence is introduced and defined as:

ui =αi + (M − 1)

2

ui ∈ {0, 1, ...,M − 1} is called the tilted symbol and ψ the tiltedphase.

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 12/23

Rimoldi’s Time-invariant trellis

Figure: (a) Tilted-phase tree of MSK (b) Physical tilted-phase trellis ofMSK

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 13/23

CPM Detection using Rimoldi’s Representation

I BCJR Algorithm with a maximum a posteriori (MAP) criteriaI Turbo DemodulationI BER minimisation

I State is defined as follows: δk = {uk−1, ..., uk−L+1, φk}I Transition {δk → δk+1} is done such that

I φk+1 = φk + 2πhuk−L+1.I Symbol uk emitted

I Complexity Q ·ML−1

φk φk+1 · · · φk+L−2 φk+L−1 φk+L

uk−L+1 uk−1 uk

δk = {φk , uk−L+1, ..., uk−1}

δk+1 = {φk+1, uk−L+2, ..., uk}

Figure: State Diagram of the usual BCJR

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 14/23

PAM Decomposition and complexity reduction

I Developed by Laurent for binary CPMs, extended to M-aryCPMs by Mengali and Morelli

I Idea: CPM = sum of modulated PAM

s(t) =K−1∑k=0

ak,ngk(t − nT )

{ak,n} can be expressed in closed form from {αn} and h{gk} can be obtained in closed form from q(t) and h

I Most signal power in the first M − 1 components (known asprincipal components)

I can be used to design the detectionI for k ∈ [0;M − 2], {ak,n} can be expressed only from a0,n−1

and αn

I only Q states in the detection!I only M − 1 matched filters!

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 15/23

PAM Decomposition: Example

I 2REC, h = 1/4 and M = 4

Figure: Laurent pulsesIntroduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 16/23

Thesis Charles-Ugo

I Thesis co-funded by CNES and CNRSI Academic supervisors: M.-L. Boucheret, C. Poulliat and N.

ThomasI Application: Launchers Telemetry system (Ariane, Vega and

Soyuz)

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 17/23

CPM for telemetry launchers

I ContextI Low data transmission rateI ’Effets Flammes’I Channel undergoes an unknown phase rotation θ

I Modulation : CPFSKI Memory L=1.I g(t) is a rectangular phase response.

I Key pointsI Deal with the phase shifting.I Channel characterisation.I Increase the Rate.

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 18/23

Thesis Romain

I Thesis co-funded by CNES and TASI Academic supervisors: M.-L. Boucheret, C. Poulliat and N.

ThomasI Application: Unmanned Air Vehicle (UAV)

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 19/23

Equalization and Synchronization for CPM

I System Model

I Key points

I More information (research context, publication, teaching...)are available here

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 20/23

Thanks for your attention!

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 21/23

References I

Bixio E. Rimoldi, A Decomposition Approach to CPM, IEEETrans. on Information Theory, vol. 34, no. 2, March. 1988.

Pierre Laurent, Exact and approximate construction of digitalphase modulations by superposition of amplitude modulatedpulses (AMP), IEEE Trans. on Communications, vol. 34, no.2, 1986.

Umberto Mengali & Michele Morelli, Decomposition of M-aryCPM signals into PAM waveforms, IEEE Trans. onInformation Theory, vol. 41, no. 5, 1995.

Ridha Chaggara, Les Modulations a Phase Continue pour laConception d’une Forme d’Onde Adaptative Application auxFuturs Systemes Multimedia par Satellite en Bande Ka, PhDDissertation, ENST Paris, 2004

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 22/23

References II

Tarik Benaddi, Sparse Graph-Based Coding Schemes forContinuous Phase Modulations, PhD Dissertation,INP-Toulouse, 2015

Malek Messai, Application des signaux CPM pour la collectede donnees a grande echelle provenant d’emetteurs faible cout,PhD Dissertation, Telecom Bretagne, 2015

Introduction to CPM 19/04/17 C. Piat & R. Chayot TeSA, CNES, TAS 23/23