FILTER BANK MULTICARRIER WITH LAPPED TRANSFORMS

Maurice Bellanger, CNAM

Davide Mattera, Mario Tanda, Univ.Napoli

March 2015

Objectives

A multicarrier approach to

• improve on OFDM for future wireless systems- asynchronous multi-user access

- spectral separation for coexistence

- robustness to channel impairments – CFO

• keep most of OFDM features- spectral efficiency

- minimum delay

- simplicity of concept

- low computational complexity

Outline

• Lapped Transform: - definition

- implementation

• Transmission system performance- signal characteristics

- channel equalization

• Complex lapped transform for FBMC- implementation

- channel equalization

- carrier frequency offset compensation

• Open issues

Lapped transform

Introduced decades ago to improve the discrimination of critical spectral

components in signal compression

n: time domain ; k: frequency domain

• perfect decomposition-reconstruction

• overlapping factor: K=2

• real processing

novelty in communications: frequency domain equalization

])21)(

221cos[()(),(

MkMnnhknT π−+−=

MkMn ≤≤≤≤ 1;21

]2

)21sin[()(

Mnnh π−−=

LT in communications

• Real lapped transform – QAM modulation

Lapped-OFDM

• Complex lapped transform – PAM modulation

FBMC-PAM

MnkenhknTc MkMnj

2,1;)(),()

21)(

221( ≤≤= −+− π

Frequency response

Response of sine filter h(n):

• M pairs of symmetrical carriers instead of M carriers for the DFT

2)22(1)2cos(2)(

MfMffH L −= π

π

0 5 10 15 20 25 30-90

-80

-70

-60

-50

-40

-30

-20

-10

0Amplitude

dB

Frequency (unit=sub-carrier spacing)

OFDM

Lapped-OFDM

LT in transmission

Multi-carrier transmission with T(n,k)

• QAM modulation can be used- independent real processing of real and imaginary parts of data

• FBMC scheme with overlapping K=2- delay: 2 M

• equalization in the receiver can be performed in the frequency domain (no additional delay)

• frequency domain residual CFO compensation in

multi-user scenario

Implementation

Objective: use a 2M-DFT for frequency domain equalization

Expression of the transform

and

2M-DFT + frequency domain filtering + phase shifts

( coefficients [1 –1] )

]][[4

),()

21)(

221()

21)(

221(

2)

21(

2)

21(

MkMnj

MkMnj

Mnj

Mnj

eeeejknTππππ −+−−−+−−−− +−=

]][

][[4

),(

)1()1(222

)2

1(

)1()1(222

)2

1(

Mkjnk

Mj

Mjnkk

Mjkj

Mkjnk

Mj

Mjnkk

Mjkj

eeeee

eeeeej

knT

πππππ

πππππ

−−−−−−

−−−−−

−−

−=

Transceiver structure

• emitted symbols of 2M samples overlap by M samples

• symbol rate: 1/M

• equalization at FFT output

data

out

S/P

+

QAM

Transpose

Lapped

Transform

Overlap

/ add

+

P/S

S

/

P

FFT(2M)

Equalization

Sine

filter

Post

process.

QAM

detect+P/S

data

in

channel

Transmitter Receiver

Lapped Transform

Emitted spectrum

• The lapped transform defines 2M sub-carriers- a sub-channel consists of 2 parts: k and 2M-k

• Spectrum: continuous / fragmented

0 11/2

A

fk/2M 1-k/2M

f1 f2 1-f2 1-f2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5Amplitude

Frequency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5Amplitude

Frequency

Transmission system performance

Impact of timing offset

Envelop of emitted signal

Timing offset: to ; signal-to-interference ratio

OFDM:(GT: guard time)

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 00

0 . 2

0 . 4

0 . 6

0 . 8

1

1 . 2

M T O

t i m e

a m p li tu d e

ππ 2/)2/2sin(2/2/1

MtoMtoSIRL −=

MGTtoSIROFDM /)(

2/1−=

Half rate schemes

Signal-to-interference ratio – half rate

Emitted signal envelop

full rate half rate

)/2sin(161)/sin(2

183

2/1MtoMto

Mto

SIR LHRππππ +−

=

0 1 00 2 00 30 0 4 00 5 00 60 00

0 .2

0 .4

0 .6

0 .8

1

1 .2A m p litud e

tim e

re a l im a g ina ry

0 100 200 300 400 500 6000

0.2

0.4

0.6

0.8

1

1.2A m plitude

tim e

M

SIR curves

Signal-to-interference ratio

Max. to = M/2 SIR = 7.4 dB BER = 0.015 (4-QAM)

0 20 40 60 80 100 1200

5

10

15

20

25

30

35

40SIR

dB

Timing offset (M=256)

OFDM-GT=16 (1/16)

OFDM-GT=32 (1/8)

Lapped-OFDM-half rate

Lapped-OFDM

Multipath channel equalization

channel transfer function

interference power

SNR: multiply interference+noise by equalizer response

iP

ii ZcZC −

=∑=

0

)(

)]1()([2

1

−−= ∑ ∑= =

jfjfcPP

i

P

ijjiP

ππ 2/)2/2sin(2/)( MiMiif −=

Bit error rate

• M=256 sub-channels

• Channel: ITU-R veh.B – max.delay: 0.22M (< M/4)

• Profile: delay: 0 1 25 36 48 56

ampl.: 0.75 1 0.23 0.316 0.055 0.16

4-QAM 64-QAM

Asynchronous access

• OFDM – CP = 64 (1/4)

• One-tap FBMC: OQAM ; single tap equalizer ; K=2

• FS-FBMC: OQAM ; frequency domain equalization

• OFDM-lap: QAM ; lapped transform

Channel ITU-R

veh.B

Eb/No=20 dB

4-QAM

Symmetry

PAPR

• Peak-to-average power ratio

• Complementary cumulative distribution function

1.5 2 2.5 3 3.5 4 4.5 5-30

-25

-20

-15

-10

-5

0

5

amplitude

CCDF

dB

L-OFDMreal data

L-OFDMreal/imaginary data

L-OFDM complex data(full rate)

OFDM

Complex lapped transform for FBMC

Complex transform and implementation

Definition

Factorization

Implementation

• Phase shifts by multiples of π/2

• Frequency domain filtering , coefficients: [1 –1]

• Multiply by (time shift: ½)

• Inverse FFT of size 2M

• Overlap and add (overlapping factor K=2)

MnkeM

nknTc MkMnj

2,1;]2

)21sin[(),(

)21)(

221(

≤≤−=−+− ππ

2)

23(

22)1(

2)1(

22

2 ][21),(

πππππ −−−−− −= kjM

kjnM

kjM

jnkM

jkeeeeeknTc

Mkj

e 2)1( π−−

Transmitter structure

Multicarrier transmitter

• PAM modulation

• Multicarrier symbol length:2M

• Symbol rate: M

Phase

shifts

Filter

iFFT

(2M)

overlap+add

d(k)

(real)

S/P

(2M)

P/S

(M)

y(n)

(channel)

Emitted spectrum

M=256 ; Number of used sub-channels: 230x2 ;

binary data ; 460 bits per symbol ; rate: 1/M

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4Amplitude

Frequency

Receiver structure

Multicarrier receiver

• Frequency domain equalization

• Sub-channel filtering after equalization

• CFO compensation: interpolated filter coefficients

phase

shifts

filter

FFT

(2M)

detection

S/P

(M)

y(n) d(k)

input

buffer

equalizer

P/S

(2M)

System impulse response

frequency

time

Total imaginary interference power: unity

-0.021 j0.106 j-0.25 j0.318 j-0.25 j0.106 j-0.021 jn+1

000.5 j1-0.5 j00 n

0.021 j-0.106 j-0.25 j-0.318 j-0.25 j-0.106 j0.021 jn-1

k+4k+2k+1kk-1k-2k-4

SIR curves

Signal-to-interference ratio / timing offset

Maximum timing offset: M/2 ; BER = 0.015 (binary data)

asynchronous access

0 20 40 60 80 100 1200

5

10

15

20

25

30

35

40SIR

Timing offset (M=256)

dB OFD M -GT=16 (1/16)

OFD M-GT=32 (1/8)

FBMC -PAM

Bit error rate

• M=256 sub-channels

• Channel: ITU-R veh.B – max.delay: 0.22M (< M/4)

• Profile: delay: 0 1 25 36 48 56

ampl.: 0.75 1 0.23 0.316 0.055 0.16

4-QAM / 2-PAM 64-QAM / 8-PAM

Carrier frequency offset

Compensation at sub-channel level in multi-user scenario

• CFO = δf ; Filter output at time n0

• for n0 = Mm0 + (M+1)/2

• Receiver filter coefficients (time domain)

In the frequency domain: interpolation of initial set [1 –1]

)(20

12

00

0)()( infjr

M

irir einxhny −

−

=

−= ∑δπ

ifjr

M

Miri

nfjr einxheny δπδπ 2

0

2/1

2/1

20 )()( 0 −= ∑

−

+−=

Mnnhenh fMnjCFO 21;)()( )2/1(2 ≤≤= −− δπ

CFO compensation

Compensation per sub-channel or group of sub-channels

Phase shift + interpolated filter coefficients

0 0.05 0.1 0.15 0.2 0.250

5

10

15

20

25

30

35

40

45

50 SIR

dB

CFO (unit:sub-carrier spacing)

interpolation:6 coefficients

interpolation:4 coefficients

no filter coefficient interpolation

OFDM

BER versus CFO

Performance of OFDM, lapped OFDM, FBMC-PAM

4-QAM/2-PAM

Eb/No = 8dB

Normalized CFO

C: full compensation

C3: 3 coefficients

C5: 5 coefficients

C7: 7 coefficients

Open issues

Algorithmic aspects

• Generalization – extended lapped transform

• Other system options and parameter selection

• Optimization of the structure

• Efficient implementation – minimal complexity

• Performance analysis – multiple asynchronous users

• Comparison with enhanced OFDM techniques

(filtered OFDM, universal filtered multicarrier, generalized FDM)

Open issues

Networking aspects

• Single carrier techniques

• Preamble and pilots for burst transmission

• Duplexing: TDD, FDD, full duplex

• MIMO and massive MIMO

• Compatibility with OFDM

• Capability to meet 5G performance objectives(100 µs time budget for PHY, 55 dB ACLR, short bursts, …)