The document discusses 'pops-ofdm,' a pulse shaping method for Orthogonal Frequency Division Multiplexing (OFDM) aimed at addressing challenges in 5G cellular systems. It highlights the motivation for research, the need for non-orthogonal waveforms, and outlines various recent EU research projects in wireless technology. Key issues include the growing demands of the Internet of Things, low-latency requirements, and the inefficiencies in current LTE technologies.

1. 1
POPS-OFDM:
Ping-Pong Optimized Pulse Shaping OFDM for
5G Cellular Systems and Beyond
Mohamed SIALA
Ecole Supérieure des Communications de Tunis (SUP’COM)
12th International Multi-Conference on Systems, Signals &
Devices (SSD’2015)
March 16 - 19, 2015 - Mahdia, Tunisia

2. Outline
 Motivation of Research Activities on Pulse Shaping for OFDM
 Background on Multi-Carrier Systems
 5G Challenges and Requirements
 POPS-OFDM
 Conclusion and Perspectives
2

3. Motivation of Research Activities on Pulse
Shaping for OFDM
3

4. 5G Challenges and Requirements 1/5
4
5GNOW

5. 5G Challenges and Requirements 2/5
5
5GNOW

6. 5G Challenges and Requirements 3/5
6
5GNOW

7. 5G Challenges and Requirements 4/5
7
5GNOW

8. 5G Challenges and Requirements 5/5
 The main drivers for 5G are:
 Tactile Internet: The human tactile sense distinguishes latencies in
the order of 1ms  1ms round trip time requires a time budget on
PHY of maximum 100 µs.
 Internet of Things (IoT): A scalability problem (>100k MTC nodes
in a cell) under cost, coverage, energy (life time) and privacy
constraints.
 Gigabit Wireless Connectivity: Quick downloads (streaming
content with data rates in the order of ~100 Mbit/s)  Download
times in the order of ~ 10 Gbit/s.
 Fragmented Spectrum and the Spectrum Paradox: Spectrum is
scarce and expensive but underutilized. With White Spaces
Communication, a 100x better localization is expected.
8

9. 4G (LTE-A) Pitfalls
 LTE is tailored to maximize performance by enforcing strict
synchronism and orthogonality 
 Machine-type communication (MTC) communications 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
9

10. 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
10

11. Workload of Current Mobiles
11
Outer receiver consists of channel decoder and de-interleaver

12. 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 wireless technologies and 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 projects, 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
12

13. 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): UFMC applies filtering
to subsets of the complete band instead of single subcarriers
(GFDM) or the complete band (Filtered OFDM)
 Filter Bank MultiCarrier (FBMC)
 Bi-orthogonal Frequency Division Multiplexing (BFDM)
13

14. GFDM: Generalized Frequency Division
Multiplexing
14

15. UFMC: Universal Filtered MultiCarrier
15
Spectral behavior within a single sub-band
Single PRB compared to OFDM

16. Background on Multi-Carrier Systems
16

17. 17
History of OFDM
 Late 50’s: Concept of multicarrier without overlapping in frequency
 Late 60’s: Orthogonal multicarrier [Chang66, Salzberg67]
 Early 70’s: Use of the Fast Fourier Transform (FFT) [Weinstein &
Ebert71] - Concept of Guard Interval (GI)
 Early 80’s: Concept of Cyclic Prefix (CP) [Peled & Ruiz80]
 Early 90’s: DAB standardization
 Late 90’s: Standardization of ADSL, DBV-T and WIFI

18. 18
Applications of OFDM
 Wireless applications :
 Broadcasting for digital terrestrial television (DVB- T, DVB- H)
 Digital Audio Broadcasting (DAB) and Digital Radio Mondiale
(DRM)
 802.11a wireless networks (WIFI5) , 802.16 (WiMAX) and
HiperLAN/2
 New generation radio mobile networks (LTE, LTE-A)
 Wireline applications:
 ADSL
 PLC (Power-Line Communications)

19. Classification of Multi-Carrier Systems
19
Multi-carrier systems
Filter Lattice Symbol
Orthogonal
Hexagonal
Biorthogonal
Rectangular
Non-orthogonal
Staggered
Complex
Real
OFDMw/oGI
OFDMw/CP
OFDM/QAM
OFDM/OQAM
OFDMw/ZP
Pulse
Mono-pulse
Multi-pulseUFMC
OFDMOQAM: Offset Quadrature Amplitude Modulation
CP: Cyclic Prefix, ZP: Zero Padding, GI/ Guard Interval
TimeContinuous
Discrete

20. 20
Pulse Shaping for OFDM without Guard Interval
 Rectangular pulse shaping filter with duration T :
1/T
t
[0, [( ) rect ( ) /Tt t T 
1
ˆ( ) sinc( )f fT 
1/T
T
… …
f
Fourier Transform

21. 21
OFDM without Guard Interval
t
f
nT ( 1)n T0 0f 
/mf m T
1 ( 1)/Nf N T  
… …
0 ( )n t
1, ( )N n t 
t
nT ( 1)n T
… …
( 1)n T ( 2)n T
OFDM symbol between nT and (n+1)T
Modulated Signal ee(t)
Orthogonal
sinusoidal
functions
( )mn t

22. Time-Frequency Lattice Layout: OFDM without
Guard Interval (GI)
22
Frequency
Time
1/ uF T
uT T
Area (1/ ) 1u uFT T T  
Lattice density 1/ 1FT    Critical density
0 & π/2 0 & π/20 & π/20 & π/2
0 & π/2 0 & π/20 & π/20 & π/2
0 & π/2 0 & π/20 & π/20 & π/2
0 & π/2 0 & π/20 & π/20 & π/2
Inphase and quadrature
components

23. 23
Power Spectral Density of OFDM without Guard
Interval 1/2
 Subcarrier spacing : f = 1/T
1/f T 
f

24. Power Spectral Density of OFDM without Guard
Interval 2/2
24
16N 
0gT 
32N 
64N  128N 

25. 25
Analog Transmitter for OFDM
 Complex implementation: Use of a battery of N costly analog filters
ka
0na
mna
1,N na 
S
/
P
( )t
( )t
( )t
0exp( 2 )j f t
exp( 2 )mj f t
1exp( 2 )Nj f t  exp( 2 )cj f t
{} 
( )ee t ( )e t
S/P : Serial-to-Parallel Converter
0m
m
f f
T
 
0 0f  in general

26. 26
Vectorial Equivalent of the OFDM Transmitter
ka
0na
mna
1,N na 
S
/
P
exp( 2 )cj f t
{} 
( )ee t ( )e t
0 ( )n t
( )mn t
1, ( )N n t 

27. 27
Analog Receiver for OFDM
 Complex implementation: Use of a battery of N costly analog filters
ˆkaP
/
S
( )t
0exp( 2 )j f t
exp( 2 )mj f t
1exp( 2 )Nj f t 
exp( 2 )cj f t
( )x t
P/S : Parallel to Serial Converter
0
ˆ na
ˆmna
1,
ˆN na 
( )t
( )t
*
( ) ( )t T t  

28. 28
Vectorial Equivalent of the OFDM Receiver
ˆkaP
/
S
exp( 2 )cj f t
( )r t
0
ˆ na
ˆmna
1,
ˆN na 
*
( ), ( ) ( ) ( )u t v t u t v t dt


0 ( ),n t 
( ),mn t 
1, ( ),N n t  

29. 29
No Interference in the Gaussian Channel –
Orthogonality Contraints
 Modulated signal:
 Symbol amn transported by function :
 Absence of Inter-Symbol Interference (ISI) and Inter-Carrier
Interference (ICI) equivalent to orthogonality conditions:
 Functions {mn(t)} form un orthonormal base of the space of
modulated signals
1
0
( ) ( )
N
e mn mnn m
e t a t


  
( ) ( )exp( 2 )mn mt t nT j f t   
*
( ), ( ) ( ) ( )kl mn kl mn km lnt t t t dt     

 

30. Balian-Low Theorem for a Time-Frequency
Critical Lattice Density

30
( ) ( )exp( 2 )mn t t nT j mFt   
2 22 2
ˆ( ) ( )t t dt or f f df     
Fourier transform of ( )t

31. 31
Behavior of an OFDM System without GI in the
Presence of Time Dispersive Channel
t
f
nT ( 1)n T0 0f 
/mf m T
1 ( 1)/Nf N T  
… …
t
nT ( 1)n T
… …
( 1)n T ( 2)n T
Noiseless received
signal

( )c 
Channel
Inter-Symbol Interference
(ISI)
Loss
of orthogonality!
mT0
0 ( )n t
1, ( )N n t 
( )mn t

32. 32
Interference Suppression: Guard Interval Insertion with
Zero Padding (ZP)
t
f
… …
t
nT ( 1)n T
… …
( 1)n T
1, ( )N n t 
( )mn t
0 ( )n t
T
gTuT

( )c 
Channel
mT0
g mT T
Guard Interval
Zero Padding

33. 33
Interference Suppression: Guard Interval Insertion with
Zero Padding (ZP)
t
… …
No Inter-Symbol
Interference (ISI)
Persistent loss of
orthogonality!
t
f
… …
g mT T
T

34. 34
Interference Suppression: Guard Interval Insertion with
Cyclic Prefix (CP)
t
… …
t
nT ( 1)n T
… …
( 1)n T
0 ( )n t
T
gT uT

( )c 
Channel
mT0
f
Cyclic Prefix
1, ( )N n t 
( )mn t
nT ( 1)n T( 1)n T

35. Time-Frequency Lattice Layout: OFDM with
Cyclic Prefix (CP)
35
Time
1/ uF T
u gT T T 
Area (1/ )( ) 1 / 1u u g g uFT T T T T T     
Lattice density 1/ 1FT   
Frequency
uTgT
Cyclic Prefix Useful part

36. Power Spectrum Density of Conventional OFDM
36
16N 
/ 4g uT T
32N 
64N 
128N 

37. 37
Interference Suppression: Guard Interval Insertion with
Cyclic Prefix (CP)
t
… …
t
nT ( 1)n T
… …
( 1)n T
T
gT uT
f
Overlapping restricted
to the Guard Interval
0 ( )n t
1, ( )N n t 
( )mn t

38. 38
Interference Suppression: Guard Interval Insertion with
Cyclic Prefix (CP)
t
… …
t
… …
f
Recovered
orthogonality
t
… …
( 1)n T( 1)n T
Cyclic Prefix Suppression
1, ( )N n t 
( )mn t
0 ( )n t
nT

39. 39
OFDM/OQAM with Square Lattice
 The used shaping filter filtre is generally a root-raised cosine filter with
roll-off  (typically equal to 1)
 OFDM with Offset QAM (OQAM) alternately transmit phase and
quadrature
t
1/f T 
QAM
Symbol
f
T
/ 2T
: In-phase component : Quadrature component

40. Time-Frequency Lattice Layout: OFDM/OQAM
with Square Lattice
40
Frequency
Time
1/ uF T
/ 2uT T
Surface (1/ )( / 2) 1/ 2u uFT T T  
Lattice density 1/ 2FT    Critical density
π/2
π/2
π/2
π/2
π/2
π/2
π/2
π/2
π/2
π/2
π/2
π/2
π/2
π/2
π/2
π/2
Quadrature componentInphase component

41. Time-Frequency Lattice Layout: OFDM/OQAM
with Hexagonal Lattice
41
Frequency
Time
3π/4
π/2 0
π/4 3π/4
π/2 0
π/43π/4
π/2 0
π/4
3π/4
π/2 0
π/4 3π/4
π/2 0
π/43π/4
π/2 0
π/4
Lattice density 1   Critical density
[1] M. Siala, “Novel OFDM/OQAM system with hexagonal time-frequency lattice,” Third International Symposium on
Image/Video Communications over fixed and mobile networks (ISIVC’06), Hammamet, Tunisia, September 2006.
[2] M. Siala and A. Yongaçoglu, “Prototype waveform optimization for an OFDM/OQAM system with hexagonal
time-frequency lattice structure,” 9th International Symposium on Signal Processing and its Applications (ISSPA’07),
Sharjah, United Arab Emirates, February 2007.

42. Waveforms for OFDM/OQAM
42
Linear decreasing in the
logarithmic scale
 Exponential decrease in
time and frequency
Gaussian waveform
Hexagonal lattice waveform
[1] M. Siala, “Novel OFDM/OQAM system with hexagonal time-frequency lattice,” Third International Symposium
on Image/Video Communications over fixed and mobile networks (ISIVC’06), Hammamet, Tunisia, September 2006.

43. Small-Scale Propagation: Multipath Rayleigh
Fading 1/2
43
Time
F
T
Frequency
Doppler shift
Time delay
min
min Df  
max Df  
max
: Doppler spread
DB
mT
: Delay spread
DB
mT
Scattering function

44. Small-Scale Propagation: Multipath Rayleigh
Fading 2/2
44
Time
F
T
Frequency
Doppler shift
Time delay
: Channel spread
DB
mT
D mB T 
(Diffuse) Scattering function
ISIISI
ICI
ICI
ISI: Inter-Symbol Interference
ICI: Inter-Carrier Interference

45. Doppler Spread-Delay Spread Balancing 1/3
45
Time
F
T
Frequency
Doppler shift
Time delayDB
mT
Reduction in F & Increase in T
 Substantial increase in ICI
 Global increase in ICI+ISI
ISIISI
ICI
ICI

46. Doppler Spread-Delay Spread Balancing 2/3
46
Time
F
T
Frequency
Doppler shift
Time delayDB
mT
ISI
ICI
ICI
ISI
Reduction in T & Increase in F
 Substantial increase in ISI
 Global increase in ICI+ISI

47. Doppler Spread-Delay Spread Balancing 3/3
47
Time
F
T
Frequency
Doppler shift
Time delayDB
mT
ISIISI
ICI
ICI
 Good balancing between T and F
 Global reduction in ICI+ISI
mD TB
F T


48. 5G Challenges and Requirements
48

49. 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
49

50. Requirements for 5G: Coordinated MultiPoint
(CoMP) – Overlapping in Time
50
time
At the BSs
MS2MS1
timetime
TDOA  Overlapping in time
 Artificial delay spread
 Inter-Symbol Interference
At MS2
At MS1
TDOA: Time Difference of Arrival
Applicable even for fully
time synchronous BSs

51. Requirements for 5G: Coordinated MultiPoint
(CoMP) – Overlapping in Frequency
51
MS
frequency
Carrier Frequency Offset 
Overlapping in frequency  Artificial Doppler spread
 Inter-Carrier Interference (ICI)
At MS
From BS1
frequency
frequency
From BS2
From BS3
Applicable only for not fully
frequency Synchronous BSs

52. Requirements for 4G, 5G and DVB-T: MBMS
and SFN
52
time
At the BSs/DVB-T TV Station
Overlapping replicas  Artificial delay spread  Interference
time
At the TV Set
(SFN)
At the MS
(MBMS)
SFN: Single Frequency
Network
MBMS: Multimedia Broadcast
Multicast Service

53. Requirements for 5G: Sporadic Traffic and Fast
Dormancy 1/4
 2, 3 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, can minimize energy consumption, leading to long battery life
53

54. Requirements for 5G: Sporadic Traffic and Fast
Dormancy 2/4
 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
  It is desirable to achieve “zero-overhead” communications by
providing channel access with minimal signaling
54

55. Requirements for 5G: Sporadic Traffic and Fast
Dormancy 3/4
  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
55

56. Requirements for 5G: Sporadic Traffic and Fast
Dormancy 4/4
56Nokia 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

57. Requirements for 5G: Sporadic Traffic and Fast
Dormancy – Relaxed Frequency Synchronization
57
MS2
frequency
Reduced synchronization overhead 
Relaxed frequency synchronization 
Carrier Frequency Offset 
Overlapping in frequency 
Inter-user interference in frequency
From MS1
frequency
From MS2
MS1
MS3
frequency
From MS3
At BS
frequency
Inter-user interference
Unaligned carrier frequencies

58. Requirements for 5G: Sporadic Traffic and Fast
Dormancy – Relaxed Time Synchronization
58
MS2
time
Reduced synchronization overhead
 Relaxed time synchronization
 Overlapping in time
 Inter-user interference in time
From MS1
time
From MS2
MS1
At BS
time
Inter-user interference

59. Requirements for 5G: Asynchronous Signaling in
the Uplink – RACH 1/2
59
MS2MS1
RACH random access

60. Requirements for 5G: Asynchronous Signaling in
the Uplink – RACH 2/2
60
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 MS1
Propagation
delay to MS1
Propagation
delay to MS2

61. Requirements for 5G: Spectrum Agility and
Carrier Aggregation 1/2
 TV White Spaces (TVWS) exploration can represent a new niche
markets if it overcome, with spectrum agility, the rigorous
implementation requirements of low out of band radiation 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 at all
 5G will address carrier aggregation by implementing non-orthogonal
waveform, with low out-of-band emissions, in order not to interfere
with other legacy systems and tight spectral masks
61

62. Requirements for 5G: Spectrum Agility and
Carrier Aggregation 2/2
62
OFDM+CP vs. ESM: Loss of efficient of traditional OFDM with CP to fit in
an ESM (Emission Spectrum Mask) due its non-negligible side lobes

63. 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.
63

64. 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 allow, 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
64

65. Requirements for 5G: Lower Latency vs Doppler
Spread-Delay Spread Balancing 1/2
65
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
mT
min
Contribution of the PHY to the latency

66. Requirements for 5G: Lower Latency vs Doppler
Spread-Delay Spread Balancing 2/2
66
Time
F
T
Frequency
Doppler shift
Time
delay
DB
mT
Decreased Latency
 Bad balancing between
T and F
 Increased global
ICI+ISI ISIISI
Processing
Time at the Rx
2
mTmin
Contribution of the PHY to the latency 
ICI
ICI

67. POPS-OFDM
67

68. POPS-OFDM Categories
68
POPS-OFDM
Continuous DiscreteTime
Optimum
exploration space
2
( ) 2
( )
Practical
exploration space
1
0Vect({ ( )} )N
k kt 

1
0Vect({ ( )} )N
k kt 

2
( )I 
0{ ( )}k kt 

0{ ( )}k kt 

: Hermite functions
: Prolate Spheroidal Wave Functions (PSWF)
To be explored next

69. 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 Waveform (Vector)φ
: (OFDM) Symbol PeriodT
: Subcarrier SpacingF
mnφ
Subcarrier Index Symbol Index
Frequency shift of  by mF Time shift of  by nT69

70. 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
Signal
21 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 Signal
Q
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
70

71. 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 71

72. 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 Signal
Q
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 ofmn mnφ φ
72
ISIICI

73. 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
73

74. Signal-to-Interference and Noise Ratio (SINR)
S
I N
P
SINR
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 Ratio
E
SNR
N

74

75. Optimization Philosophy
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 75

76. Optimization Philosophy
φ
ψ
(0)
φ
(0)
ψ
(1)
φ
(1)
ψ
(2)
φ
76SINR
Equal-SINR curves
(Contour plot of SINR)
SINR maximum

77. First Optimization Technique
SINR


0
ψ
( , ) ( , )
1
S p S p
SINR
 φ φ
KI ψ KS ψ
Generalized Eigenvalue Problem
Find the eigenvector with the smallest eigenvalue
SINR


0
φ
( , ) ( , )
1
S p S p
SINR
    ψ ψ
KI φ KS φ
77

78. Second Optimization Technique
( , )
( , )
H
S p
H
S p
SINR



φ
φ
ψ KS ψ
ψ KIN ψ
( , )
H
S p  φ
KIN UΛU
: Unitary Matrix
: Diagonal Positive Matrix
U
Λ
( , )
H H H H
S p   φ
ψ KIN ψ ψ UΛU ψ u u 1/2 H
u Λ U ψ
H
H
SINR 
u Φu
u u
1/2 1/2
( , )
H
S p 
 
 φ
Φ Λ U KS UΛ
maxFind the eigenvector of with maximum eigenvalueu Φ
1/2
max
1/2
max
opt



UΛ u
ψ
UΛ u
78

79. Signal and Interference Kernel Computation
1/3
1
( , )
0
( )k
K
H
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
K
H
S p k p
k
 


 
  
 
φ
K Σ φφ Π
0 ( ( ))pq D sJ B T p q  
( , ) 0 ( , )S p S p φ φ
KS 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
79

80. Signal and Interference Kernel Computation
2/3
φ H
φφ  
1
0
( )k
K
H
k p
k



 Σ φφ
Duration: DT
 DN samples
80
Matrix shifts according to
The multipath power profile

81. Signal and Interference Kernel Computation
3/3
1
0
( )k
K
H
nN k p
n k



 
 
 
 Σ Σ φφ
Matrix shifts according to
the normalized symbol duration N
81

82. Numerical Results: Impact of Initialization and
Existence of Local Maxima
82
Local maxima

83. Numerical Results: Evolution of Transmit and
Receive Pulse Shapes Through the Iterations
83
Iterations: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,…,20,…,30,…,100
φ ψ
Initialization: Gaussian pulse

84. Numerical Results: Doppler Spread-Delay Spread
Balancing
84
Best balancing

85. Numerical Results: Doppler Spread-Delay Spread
Balancing
85

86. Numerical Results: Optimized Waveforms
86

87. Numerical Results: Optimized Waveforms
87

88. Numerical Results: Performance and Gain in
SINR – Identical Pulse Shape Durations
88
Gain > 5dB

89. Numerical Results: Performance and Gain in
SINR – Different Pulse Shape Durations
89

90. Numerical Results: Ventilation of Complexity
Between Transmitter and Receiver
90
PHY delay = (D+D)/2

91. Numerical Results: Spectrum of One Subcarrier
91
~ 60 dB

92. Numerical Results: Spectrum of 64 Subcarriers
92
~ 60 dB

93. Numerical Results: Sensitivity to an Estimation
Error on BdTm
93

94. Numerical Results: Sensitivity to Synchronization
Errors in Frequency
94

95. Numerical Results: Sensitivity to Synchronization
Errors in Time
95
38-sample error tolerence
34-sample error tolerence

96. Conclusion
 We proposed a new and straightforward technique for the
systematic optimization of transmit and receive waveforms
for OFDM/FBMC/GFDM systems
 Increased SINR
 6 orders of magnitude reduction in out-of-band emissions
 Robustness to synchronization errors
96

97. Perspectives
 Extension to OFDM/OQAM
 Extension to multi-pulse OFDM/QAM and OFDM/OQAM
 Extension to single-carrier communications
 Extension to underwater acoustic communications
 OFDM pulse shapes optimized for partial equalization
 OFDM tolerant to bursty communications with relaxed
synchronization
 OFDM pulse shapes optimized for carrier aggregation and reduced
out-of band emissions
 OFDM pulse shapes optimized for further OFDM pulse shapes
optimized for a lower latency
 Optimization of RADAR pulses
97

98. 98
Thank You for Listening
Mohamed SIALA
Ecole Supérieure des Communications de Tunis (SUP’COM)
12th International Multi-Conference on Systems, Signals &
Devices (SSD’2015)
March 16 - 19, 2015 - Mahdia, Tunisia

99. 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.
99

100. 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
(ISIVC’06), Hammamet, Tunisia, September 2006.
 I. Trigui, M. Siala, and H. Boujemâa, “Optimized pulse shaping for OFDM multi-user
communications over doubly dispersive channels,” 9th International Symposium on Signal
Processing and its Applications (ISSPA’07), Sharjah, United Arab Emirates, February 2007.
 M. Siala and A. Yongaçoglu, “Prototype waveform optimization for an OFDM/OQAM system
with hexagonal time-frequency lattice structure,” 9th International Symposium on Signal
Processing and its Applications (ISSPA’07), Sharjah, United Arab Emirates, February 2007.
 I. Trigui, M. Siala, S. Affes and A. Stephenne, “SIR Optimized Hermite-Based Pulses for BFDM
Systems in Doubly Dispersive Channels,” International Symposium on Signals, Systems and
Electronics (ISSSE’07), Montreal, Quebec, Canada, July 2007.
100

101. References 3/4
 R. Ayadi, I. Kammoun, and M. Siala, “Optimization of the pulse shape of OFDM systems Using
the Arrow-Hurwicz Algorithm,” 4th International Symposium on Wireless Communication
Systems (ISWCS’07), Trondheim, Norway, October 2007.
 R. Ayadi, M. Siala, and I. Kammoun, “Transmit/receive pulse-shaping design in BFDM systems
over time-frequency dispersive AWGN channel,” IEEE International Conference on Signal
Processing and Communications (ICSPC’07), Dubai, United Arab Emirates, November 2007.
 I. Trigui, M. Siala, S. Affes, A. Stephenne, and H. Boujemaa, “Optimum Pulse Shaping for
OFDM/BFDM Systems Operating in Time Varying Multi-Path Channels,” IEEE Global
Telecommunications Conference (GLOBECOM’07), Washington DC, USA, November 2007.
 M. Bellili, M. Siala, and L. Ben Hadj Slama, “Pulse design for maximizing SIR in partially
equalized OFDM/BFDM systems,” IEEE 19th International Symposium on Personal, Indoor and
Mobile Radio Communications (PIMRC’08), Cannes, France, September 2008.
 M. Bellili, L. Ben Hadj Slama, and M. Siala, “Multi-pulse/single-pulse design for maximizing SIR
in partially equalized OFDM systems over highly dispersive channels,” 16th IEEE International
Conference on Electronics, Circuits, and Systems, 2009 (ICECS 2009), Hammamet, Tunisia,
December 2009.
101

102. References 4/4
 R. Ayadi, I. Kammoun, and M. Siala, “Optimal OFDM Pulse Design, Analysis and
Implementation Over Doubly Dispersive Channel,” 21st European Signal Processing Conference
(EUSIPCO 2013), Marrakech, Morocco, September 9-13, 2013.
 M. Siala, F. Abdelkefi and Z. Hraiech, “Novel Algorithms for Optimal Waveforms Design in
Multicarrier Systems,” IEEE Wireless Communications and Networking Conference
(WCNC’2014), Istanbul, Turkey, April 2014.
 Z. Hraiech, M. Siala, and F. Abdelkefi, “Numerical Characterization for Optimal Designed
Waveform to Multicarrier Systems in 5G,” 22nd European Signal Processing Conference 2014
(EUSIPCO 2014), Lisbon, Portugal, 1-5 September 2014.
 Z. Hraiech, F. Abdelkefi, and M. Siala, “POPS-OFDM: Ping-pong Optimized Pulse Shaping-
OFDM for 5G systems,” accepted at IEEE International Conference on Communications (ICC’15),
London, UK, June 2015.
 Z. Hraiech, F. Abdelkefi, and M. Siala, “POPS-OFDM: Ping-pong Optimized Pulse Shaping-
OFDM for 5G systems,” Accepted at IEEE Vehicular Technology Conference – Spring 2015
(VTC’S15), Glasgow, Scotland, May 2015.
102