Lecture boğaziçi üniversitesi 2016 presentation - offline ping-pong optimized pulse shaping for...

1

Offline Ping-Pong Optimized Pulse Shaping for

Future 5G Systems: POPS-FBMC

Mohamed Siala

MEDIATRON Laboratory

Higher School of Communication of Tunis (SUP’COM)

Carthage University - Tunisia

Boğaziçi Üniversitesi

Beşiktaş/İstanbul - Türkiye

May 11, 2016

Outline

Motivation of Research Activities on Pulse Shaping for 5G

OFDM/OFDMA

5G Challenges and Requirements

POPS-OFDM to Systematically Respond to 5G Radio Interface

Challenges

Conclusion and Perspectives for Future Research Work on 5G

2

Motivation of Research Activities on Pulse

Shaping for 5G OFDM/OFDMA

3

5G Challenges and Requirements 1/2

4

5G Challenges and Requirements 2/2

5

4G (LTE-A) Pitfalls

LTE is tailored to maximize performance by enforcing strict synchronism and perfect orthogonality

Machine-type communication (MTC) requires bulky procedures to

ensure strict synchronism

Collaborative schemes (e.g. CoMP) use tremendous efforts to

collect gains under strict synchronism and orthogonality

Digital Agenda/Carrier aggregation forces systems to deal with

fragmented spectrum

6

Need for Non-Orthogonal Waveforms

Non-orthogonal waveforms on the physical layer will enable:

Asynchronous MTC traffic with drastically reduced signalling and

increased life time

The provision of asynchronous coordinated multi-point (CoMP) /

Heterogeneous Networking (HetNet)

Implementation of asynchronous carrier aggregation concepts with

well frequency localization

A (filtered) multicarrier approach will enable:

The mix of synchronous/asynchronous and orthogonal/non-

orthogonal traffic types

The aggregation of non-contiguous spectrum thanks to low out-of-

band emissions of the non-orthogonal waveforms

7

Workload of Current Mobiles

8

Outer receiver consists of channel decoder and de-interleaver

Projects on 5G

From 2007 to 2013, the European Union set aside €700 million of

funding (FP7) for research on future networks, half of which was

reserved for the development of 4G and beyond-4G technologies.

METIS, 5GNOW, iJOIN, TROPIC, Mobile Cloud Networking,

COMBO, MOTO and PHYLAWS are some of the latest EU research

projects that address the architecture and functionality needs of 5G

networks, representing some €50 million EU investment.

European Union’s FP7 project, PHYDYAS (Duration: 30 months,

Start: January 2008, End: October 2010, Total Cost: 4 093 483€),

investigated Filter Bank Multi-Carrier (FBMC) and corresponding

transceiver functionalities.

9

5GNOW Candidate Waveforms

European Union’s FP7 projects, 5GNOW (5th Generation Non-

Orthogonal Waveforms for Asynchronous Signaling), (Start:

September 2012, End: February 2015, Total Cost: 3 526 991 €),

investigated 4 candidate waveforms:

Generalized Frequency Division Multiplexing (GFDM)

Universal Filtered Multicarrier (UFMC)

Filter Bank Multi-Carrier (FBMC)

Bi-orthogonal Frequency Division Multiplexing (BFDM)

10

GFDM: Generalized Frequency Division

Multiplexing

11

UFMC: Universal Filtered MultiCarrier

12

Spectral behavior within a single sub-band

Single PRB compared to OFDM

5G Challenges and Requirements

13

Requirements for 5G: Coordinated MultiPoint

(CoMP)

Joint Processing (JP):

Coordination between multiple BSs

MSs are simultaneously transmitting or receiving to or from

multiple BSs

Coordinated Scheduling/Coordinated Beamforming (CS/CB):

Coordination between multiple BSs

MSs are transmitting or receiving to or from a single transmission

or reception BS

14


(CoMP) – Overlapping in Time

15

timeAt the BSs

MS2MS1

time

TDOA Overlapping in time

Artificial delay spread

Inter-Symbol Interference

At MS2

time

At MS1TDOA: Time Difference of Arrival

Applicable even for fully

time synchronous BSs


(CoMP) – Overlapping in Frequency

16

MS

frequency

Carrier Frequency Offset Overlapping in frequency Artificial Doppler spread

Inter-Carrier Interference (ICI)

At MS

From BS1

frequency

frequency

From BS2

From BS3Applicable only for non fully

frequency Synchronous BSs

Requirements for 4G, 5G and DVB-T: MBMS

and SFN 1/2

17Overlapping replicas Artificial delay spread Interference

time

At the BSs/DVB-T TV Station

time

At the TV Set

(SFN)

At the MS

(MBMS)

SFN: Single Frequency

Network

MBMS: Multimedia Broadcast

Multicast Service

Requirements for 4G, 5G and DVB-T: MBMS

and SFN 2/2

18

MBMS: Replicas of the same modulated

signal arriving at different delays at the MS

Delay spread

Aggregate “artificial » delay spread

Requirements for 5G: Sporadic Traffic and Fast

Dormancy 1/5

2G, 3G and 4G systems continuously transmit reference signals and

broadcast system information that is used by terminals as they move

across cells

The more signaling the cellular standard requires, the more complex

and power-hungry will be the devices

With denser deployment and more network nodes (MTC), such

“always-on” transmissions are not attractive from an interference and

energy consumption perspective

Maximizing the devices’ sleep opportunities, through sporadic

access, minimizes energy consumption, leading to long battery life

19


Dormancy 2/5

Sporadic access poses a significant challenge to mobile access

networks due to fast dormancy:

Fast dormancy is used to save battery power: The mobile breaks

ties to the network as soon as a data piece is delivered

When the mobile has to deliver more pieces of data it will always

go through the complete synchronization procedure again

This can happen several hundred times a day, resulting in

significant control signaling growth and network congestion threat

20


Dormancy 3/5

21Nokia Siemens Networks, Understanding Smartphone Behavior in the Network,

White Paper, 2011, [Available: http://www.nokiasiemensnetworks.com/sites/default/files

Comparisons of Data and Signaling Traffic


Dormancy 4/5

It is desirable to achieve “zero-overhead” communications by

providing channel access with minimal signaling

Get rid of closed-loop timing control (which costs energy and

signaling overhead, being undesirable for MTC) and use open loop

timing control mechanisms: The device uses the downlink pilot signals

by the BS for a rough synchronization (RSSI: Received Signal

Strength Indication)

22


Dormancy 5/5

23

Overhead Payload (Useful information)

High data rate service with “always-on” transmission: Overhead << PayloadTime

Overhead Payload (Useful information)

TimeLoss of synchronization

Delayed

transmission

Sporadic access with fast dormancy and no synchronization procedure

Payload (Useful information)

TimeLoss of synchronization

Sporadic access with fast dormancy using a complete synchronization procedure:

Overhead >> Payload


Dormancy – Relaxed Frequency Synchronization

24

MS2

Reduced synchronization overhead Relaxed frequency synchronization

Carrier Frequency Offset Overlapping in frequency

Inter-user interference in frequency

From MS1

frequency

MS1MS3

frequencyFrom MS2

frequencyFrom MS3

At BS

frequency

Inter-user interference

Unaligned carrier frequencies


Dormancy – Relaxed Time Synchronization

25

MS2

Reduced synchronization overhead Relaxed time synchronization

Overlapping in time

Inter-user interference in time

MS1

From MS1

time

timeFrom MS2

At BS

time

Inter-user interference

Requirements for 5G: Asynchronous Signaling in

the Uplink – RACH 1/3

26

MS2MS1

RACH random access

MS2 experiences a higher round-trip delay than MS1



27

time

No synchronization overhead Strong overlapping in time

Inter-user interference in time

To/from BS

time

To/from MS1

To/from MS2

Inter-Burst interference

time

Synchronization

channel

RACH burst

from MS2

RACH burst

from MS1Propagation

delay to MS1

Propagation

delay to MS2



28

Use of open loop timing control: The device uses the RSSI for a rough synchronization Shadowing disturbance Partially alleviated

asynchronism

RSSI: Received Signal Strength Indication

Ideal pathloss

Path loss

+ shadowingIdeal arrival at the BS

(No overlapping)

Actual arrival at the BS

(Overlapping in time)

Time

Requirements for 5G: Spectrum Agility and

Carrier Aggregation 1/2

TV White Spaces (TVWS) exploration can represent a new niche

markets if it overcomes, with spectrum agility, the rigorous

implementation requirements of low out-of-band (OOB) radiations for

protection of legacy systems

The LTE-A waveform imposes generous guard bands to satisfy

spectral mask requirements which either severely deteriorate spectral

efficiency or even prevent band usage

5G will address carrier aggregation by implementing non-orthogonal

waveforms, with low OOB emissions, in order not to interfere with

other legacy systems and conform to tight spectral masks

29

Requirements for 5G: Spectrum Agility and

Carrier Aggregation 2/2

30

OFDM vs. ESM: Loss of efficiency of traditional OFDM to fit in an ESM

(Emission Spectrum Mask) due to its non-negligible side lobes

55 dB protection

Requirements for 5G: Low Latency 1/2

4G offers latencies of multiple 10 ms between terminal and BS that

originate from resource scheduling, frame processing, retransmission

procedures, and so on.

The access latency offered by LTE is not sufficient for latency-critical

applications, such as tactile internet (motivated by the tactile sense of

the human body, which can distinguish latencies on the order of 1 ms

accuracy), traffic safety and infrastructure protection.

To ensure support for such mission-critical MTC applications, next-

generation wireless access should allow for latencies on the order of 1

ms or less.

31

Requirements for 5G: Low Latency 2/2

A 1 ms round-trip time for a typical tactile interaction requires a time

budget of maximum 100 µs on the physical layer

Far shorter than LTE-A allows, missing the target by nearly two

orders of magnitude

Clear motivation for an innovative and disruptive redesign of

the PHY layer

Lower latency over the radio link can be achieved by reducing

transmission-time intervals and widening the bandwidth of radio

resource blocks in which a specific amount of data is transmitted

32

Requirements for 5G: Lower Latency vs Doppler

Spread-Delay Spread Balancing 1/2

33

Time

F

T

Frequency

Doppler shift

Time delayDB

mT

Reduced global ICI+ISI Good balancing between T and F

Increased Latency

ICI

ICI

ISIISI

Processing

Time at the Rx2

mTmin

Contribution of the PHY to the latency

Requirements for 5G: Lower Latency vs Doppler

Spread-Delay Spread Balancing 2/2

34

Time

F

T

Frequency

Doppler shift

Time

delayDB

mT

Decreased Latency

Bad balancing between

T and F

Increased global

ICI+ISI

ISIISI

Processing

Time at the Rx2

mTmin

Contribution of the PHY to the latency

ICI

ICI

POPS-OFDM to Systematically Respond to 5G

Radio Interface Challenges

35

POPS-OFDM Categories

36

POPS-OFDM

Continuous DiscreteTime

Optimum

exploration space2 ( ) 2 ( )

Practical

exploration space

1

0Vect({ ( )} )N

k kt

1

0Vect({ ( )} )N

k kt

0{ ( )}k kt

0{ ( )}k kt

: Hermite functions

: Prolate Spheroidal Wave Functions (PSWF)

To be explored next

2 ( )I

33φ32φ31φ30φ

23φ22φ21φ20φ

13φ12φ11φ10φ

OFDM Time-Frequency Lattice: Transmitter

Side

Time

Frequency

Signal

00 φ φ 01φ 02φ 03φ

Time Shift by TTime Shift by 2TTime Shift by 3T

Frequency

Shift by F

Frequency

Shift by 2F

Frequency

Shift by 3F

Symbol Period T

=

Symbol Spacing

Symbol Bandwidth F = Subcarrier Spacing

: Transmitter Prototype Waveformφ

mnφ

Subcarrier Index Symbol Index

Frequency shift of by mF Time shift of by nT37

30 30a φ

20 20a φ

10 10a φ

00 00a φ

1

0 0

0

Q

m m

m

a

φ

OFDM Transmitted Signal

Time

Frequency

Signal21 21a φ

11 11a φ

01 01a φ

31 31a φ

1

1 1

0

Q

m m

m

a

φ

1

0

: Sampled Version of the Transmitted OFDM SignalQ

mn mn

n m

a

e φ

1

2 2

0

Q

m m

m

a

φ

32 32a φ

22 22a φ

12 12a φ

02 02a φ

1

3 3

0

Q

m m

m

a

φ

33 33a φ

23 23a φ

13 13a φ

03 03a φ

SubcarriersQ

38

Propagation Channel Characteristics: Delay and

Doppler Spreads

Mobile speed

( , )S p

p

dB : Doppler spread

Doppler spread spectrum

: Discrete time delay

: Doppler frequency shift

( , )S p : Channel scattering function

: Discrete time delay spreadmT 39

30 30a φ

20 20a φ

10 10a φ

00 00a φ

1

0 0

0

Q

m m

m

a

φ

OFDM Received Signal

Time

Frequency

Signal

1

0

: Sampled Version of the Received OFDM SignalQ

mn mn

n m

a

r φ n

21 21a φ

11 11a φ

01 01a φ

31 31a φ

1

1 1

0

Q

m m

m

a

φ

: Additive White Gaussian Noisen

: Channel distorted version of mn mnφ φ

40

ISIICI

Decision variables

: Receiver Prototype Waveform (Vector)ψ

klψ

Subcarrier Index Symbol Index

Frequency shift of by kF Time shift of by lT

H

kl kl ψ r : Decision variable on kla

( , ) ( , )Noise TermUseful Term

Interference Term

H H H

kl kl kl kl mn kl mn kl

m n k l

a a

ψ φ ψ φ ψ n

41

Signal-to-Interference and Noise Ratio (SINR)

S

I N

PSINR

P P

: Average power of the Useful Term

: Average power of the Interference Term

: Average power of the Noise Term

S

I

N

P

P

P

( , )

( , )

1

H

S p

H

S p

SINR

SNR

φ

φ

ψ KS ψ

ψ KI I ψ

: Ratio of two definite positive quadratic

forms on for a given

( , )

( , )

1

H

S p

H

S p

SINR

SNR

ψ

ψ

φ KS φ

φ KI I φ

: Ratio of two definite positive quadratic

forms on for a given

0

: Signal to Noise RatioE

SNRN

42

Offline Ping-pong Optimization Philosophy

1/2

Transmitter Side Receiver Side(0)φ

(0 )

(0)

( , )

( , )

Maximize 1

H

S p

H

S p

SINR

SNR

φ

φ

ψ KS ψ

ψ KI I ψ (0)ψ

(0 )

(0 )

( , )

( , )

Maximize 1

H

S p

H

S p

SINR

SNR

ψ

ψ

φ KS φ

φ KI I φ(1)φ

(1)

(1)

( , )

( , )

Maximize 1

H

S p

H

S p

SINR

SNR

φ

φ

ψ KS ψ

ψ KI I ψ (1)ψ

(1)

(1)

( , )

( , )

Maximize 1

H

S p

H

S p

SINR

SNR

ψ

ψ

φ KS φ

φ KI I φ(2)

φ 43

Offline Ping-pong Optimization Philosophy

2/2

φ

ψ

(0)φ

(0)ψ

(1)φ

(1)ψ

(2)φ

44SINR

Equal-SINR curves

(Contour plot of SINR)

SINR maximum

First Optimization Technique

SINR

0

ψ

( , ) ( , )

1S p S p

SINR φ φ

KI ψ KS ψ

Generalized Eigenvalue Problem

Find the eigenvector with the smallest eigenvalue

SINR

0

φ

( , ) ( , )

1S p S p

SINR ψ ψ

KI φ KS φ

45

Second Optimization Technique

( , )

( , )

H

S p

H

S p

SINR

φ

φ

ψ KS ψ

ψ KIN ψ

( , )

H

S p φKIN UΛU

: Unitary Matrix

: Diagonal Positive Matrix

U

Λ

( , )

H H H H

S p φψ KIN ψ ψ UΛU ψ u u

1/2 Hu Λ U ψ

H

HSINR

u Φu

u u

1/2 1/2

( , )

H

S p

φΦ Λ U KS UΛ

maxFind the eigenvector of with maximum eigenvalueu Φ

1/ 2

max

1/ 2

max

opt

UΛ uψ

UΛ u46

Signal and Interference Kernel Computation

1/3

1

( , )

0

( )k

KH

S p nN k p

n k

φ

K Σ Σ φφ Ω

0 ( ( )) if ( )mod 0

0 else

D s

pq

QJ B T p q p q Q

1

0 ( , )

0

( )k

KH

S p k p

k

φ

K Σ φφ Π

0( ( ))pq D sJ B T p q

( , ) 0 ( , )S p S p φ φKS K ( , ) ( , ) 0 ( , )S p S p S p φ φ φ

KI K K

Π Q Ω

Dependence on channel Doppler (Computed once)

DN Q

47


2/3

φ H φφ

1

0

( )k

KH

k p

k

Σ φφ

Duration: DT

DN samples

48

Matrix shifts according to

the multipath power profile


3/3

Matrix shifts according to

the normalized symbol duration N

49

1

0

( )k

KH

nN k p

n k

Σ Σ φφ

Numerical Results: Impact of Initialization and

Existence of Local Maxima

50

Local maxima

Conjecture to

be the global

maximum

Numerical Results: Evolution of Transmit and

Receive Pulse Shapes Through the Iterations

51

Iterations: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,…,20,…,30,…,100

φ ψ

Initialization: Gaussian pulse

Numerical Results: Doppler Spread-Delay Spread

Balancing

52

Best balancing

Numerical Results: Optimized Waveforms

53

Numerical Results: Optimized Waveforms

54

Numerical Results: Performance and Gain in

SINR – Identical Pulse Shape Durations

55

Gain > 5dB

Numerical Results: Uneven Distribution of PHY

Delay/Complexity Between Transmitter and

Receiver 1/2

56

PHY delay = (D+D)/2 = 3T

Numerical Results: Uneven Distribution of PHY

Delay/Complexity Between Transmitter and

Receiver 2/2

57

PHY delay = (D+D)/2 = 5T

Numerical Results: Spectrum of One Subcarrier

58

~ 60 dB

Numerical Results: Spectrum of 64 Subcarriers

59

~ 60 dB

Numerical Results: Sensitivity to an Estimation

Error on BdTm

60

Numerical Results: Sensitivity to Synchronization

Errors in Frequency

61

Tolerence margin > 10%

Numerical Results: Sensitivity to Synchronization

Errors in Time

62

38-sample error tolerence

34-sample error tolerence

Staggered (Hexagonal/Quincunx) Time-

Frequency Lattice 1/9

63

T

F

2F

( , )

( , )

/ 2

0

n m

n m

t T T n

f F m

T/2



1

0 ( , )

0

( )k

KH

S p k p

k

φ

K Σ φφ Π

0( ( ))pq D sJ B T p q

Π

Dependence on channel Doppler for the 0th Kernel

DN

64



1 1

( , ) /2

0 0

( ) ( )k k

K KH even H odd

S p nN k p nN N k p

n k n k

φ

K Σ Σ φφ Ω Σ Σ φφ Ω

0 ( ( )) if ( )mod 02 2

0 else

even D s

pq

Q QJ B T p q p q

Dependence on channel Doppler for the infinite kernel65

0

0

( ( )) if ( )mod 02

( ( )) if ( )mod2 2

0 else

D s

odd

pq D s

QJ B T p q p q Q

Q QJ B T p q p q Q



2

even Q Ω

Dependence on channel Doppler for the infinite kernel

/ 2Q

66

2

odd Q Ω

/ 2Q

Even carrier contribution mask Odd carrier contribution mask



67

1

0

( )k

KH

nN k p

n k

Σ Σ φφ

1

/2

0

( )k

KH

nN N k p

n k

Σ Σ φφ

Selection on which is

based kernel computation

Even carrier contribution

Odd carrier contribution



68



69

Rectangular lattice

Hexagonal/quincunx

lattice



70



71

Transmit and Receive Waveforms with Unequal

Durations 1/7

72

MSBS

Waveforms for the Downlink

MSBS

Waveforms for the Uplink

t t t t

D D D D

φφ ψ ψ

The BS can afford more complexity in terms of filtering than the MS


Durations 2/7

73

x =D N

D N

ψ Hψ

Hψψ

Assumption: D D

Given , we search for ψ φ


Durations 3/7

74

D N

D N


based the kernel for

the computation of φ


Durations 4/7

75

x =

D N

D N

φ Hφ

Hφφ

Assumption: D D

Given , we search for φ ψ


Durations 5/7

76

D N

D N


based the kernel for

the computation of ψ


Durations 6/7

77


Durations 7/7

78

SINR Kernal Characteristics and Consequences

1/4

79

( , ) ( , )

( , ) ( , )

1 1

H H

S p S p

H H

S p S pSNR SNR

ψφ

ψφ

ψ KS ψ φ KS φ

ψ KI I ψ φ KI I φ

Time reverse of φ

Time reverse of ψ


2/4

80

φ ψφψ

In terms of noise correlation at the receiver

φ ψφψ

In terms of SINR

Not always equivalent


3/4

81

PC

Timeφ

ψ Time

CP-OFDM

Timeφ

ψ Time

ZP-OFDM

ZP

Only in terms of SINR

Time

reversing

CP-OFDM and ZP-OFDM are duals of each other


4/4

82

If the optimum couple (, ), maximizing the SINR, is unique, then

ψ φ

Adaptive Waveform Communication: A New

Link Adaptation Paradigm 1/5

83d mB T

SINR [dB]

Best achieved SINR for each BdTm,

using always the optimum pair (, )

1( )d mB T 2( )d mB T

SINR performance for pair (1, 1)

optimized for (BdTm)1

SINR performance for pair (2, 2)

optimized for (BdTm)2



84d mB T

SINR [dB]

Best achieved SINR for each BdTm,

using always the optimum pair (, )

Use of pair (1, 1) Use of pair (2, 2)

Waveform Codebook



85d mB T

SINR [dB] Instantaneous and average losses in SINR

A priori distributions of BdTm

Most seen SINR loss

for the red a priori

Most seen SINR loss

for the blue a priori



86d mB T

SINR [dB]Codebook optimization:

Notion of multiple codebooks

2 different services 2 different a priori distributions of BdTm

Codebook #1

Codebook #2

A priori distribution

for service #1

A priori distribution

for service #2



87With full characterization of the scattering function

dB

mT

A priori distributions

of (Bd, Tm) corresponding

to different services

(Bd, Tm) values for which

pairs of waveforms

constituting the

codebook are optimized

Conclusion and Perspectives for Future Research

Work on 5G

88

Conclusion

We proposed a new and straightforward technique for the

systematic offline optimization of transmit and receive

waveforms for OFDM/FBMC systems

Increased SINR

6 orders of magnitude reduction in out-of-band emissions

using rectangular time-frequency lattice

7 orders of magnitude reduction in out-of-band emissions

using hexagonal time-frequency lattice

Unequal time durations for transmit and receive

waveforms to adapt to affordable computational resources

Robustness to synchronization errors89

Ongoing Research Work

Current extensions to:

OFDM/OQAM

Reverse-time channel

Unequal-duration waveforms

Hexagonal-lattice OFDM/QAM

Partial equalization

Single-carrier (satellite) communications

OFDMA/QAM

Multi-pulse OFDM/QAM

Windowed OFDM

Faster-than-Nyquist (FTN) signalling

Unique-Word OFDM90

Perspectives

Future extensions to:

Multi-pulse OFDM/OQAM

Hexagonal-lattice OFDM/OQAM

Underwater acoustic communications

Relaxed synchronization (RACH, MTC)

Carrier aggregation and reduced out-of band emissions

Low latency communications

RADAR/SONAR

5G interface optimization (Standardization inside 3GPP RAN-L1)

91

92

Thank You for Your Attention!

Mohamed Siala

MEDIATRON Laboratory

Higher School of Communication of Tunis (SUP’COM)

Carthage University - Tunisia

Boğaziçi Üniversitesi

Beşiktaş/İstanbul - Türkiye

May 11, 2016

References 1/4

M. Siala, T. Kurt, and A. Yongaçoglu, “Orthonormalization for Multi-Carrier Transmission,”

Canadian Workshop on Information Theory 2005 (CWIT’05), Montreal, Quebec, Canada, June 2005.

T. Kurt, M. Siala, and A. Yongaçoglu, “Multi-Carrier Signal Shaping Employing Hermite

Functions,” European Signal Processing Conference 2005 (EUSIPCO’05), Antalya, Turkey,

September 2005.

N. Debbabi, M. Siala, and H. Boujemâa, “Optimization of the OFDM Prototype Waveform for

Highly Time and Frequency Dispersive Channels Through a Maximization of the SIR,” 12th

IEEE International Conference on Electronics, Circuits and Systems 2005 (ICECS’05), Gammarth,

Tunisia, December 2005.

A. Ben Salem, M. Siala, and H. Boujemâa, “Performance Comparison of OFDM and

OFDM/OQAM Systems Operating in Highly Time and Frequency Dispersive Radio-Mobile

Channels,” 12th IEEE International Conference on Electronics, Circuits and Systems 2005

(ICECS’05), Gammarth, Tunisia, December 2005.

M. Siala, T. Kurt, and A. Yongaçoglu, “A Unified Framework for the Construction of

OFDM/OQAM Systems,” 12th IEEE International Conference on Electronics, Circuits and Systems

2005 (ICECS’05), Gammarth, Tunisia, December 2005.

93

References 2/4

A. Ben Salem, M. Siala, and H. Boujemâa, “OFDM systems with hexagonal time-frequency

lattices and well time frequency localized prototype functions,” Third International Symposium

on Image/Video Communications over fixed and mobile networks 2006 (ISIVC’06), Hammamet,

Tunisia, September 2006.

M. Siala, “Novel OFDM/OQAM system with hexagonal time-frequency lattice,” Third

International Symposium on Image/Video Communications over fixed and mobile networks

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