D IGITAL PROCESSING ALGORITHMS AND ARCHITECTURES FOR UWB LOW COST COMMUNICATION SYSTEM S AMI MEKKI Télécom ParisTech (ENST)

July 3rd, 2009

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

O UTLINE

1

I NTRODUCTION AND M OTIVATION

2

E NERGY D ETECTION R ECEIVER

3

P ROBABILISTIC UWB E QUALIZER

4

C HANNEL PARAMETERS E STIMATION

5

A RCHITECTURE F EASIBILITY

6

C ONCLUSIONS

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

2 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

1

I NTRODUCTION AND M OTIVATION

2

E NERGY D ETECTION R ECEIVER

3

P ROBABILISTIC UWB E QUALIZER

4

C HANNEL PARAMETERS E STIMATION

5

A RCHITECTURE F EASIBILITY

6

C ONCLUSIONS

Sami MEKKI

Architecture Feasibility

Digital processing algorithms and architectures for UWB low cost communication system

Conclusions

July 3rd, 2009

3 / 39

Introduction and Motivation

Energy Detection Receiver

I NDOOR UWB

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

APPLICATIONS

Wireless personal area network (WPAN)

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

4 / 39

Introduction and Motivation

Energy Detection Receiver

T HE SPECTRUM

Probabilistic UWB Equalizer

OF THE

UWB

Channel Parameters Estimation

Architecture Feasibility

Conclusions

SIGNALS VERSUS CONVENTIONAL

SIGNALS

PSD

Power Spectrum Density

Conventional radio signals

UWB radio signal

Frequency

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

5 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

D EFINITION UWB D EFINITION UWB systems transmit signals whose bandwidths exceed 20% of their center (f −f ) frequency fc (i.e Hf L > 20%), or have a −10dB bandwidth of more than 500 MHz c

Scholtz monocycle with τ = 0.13ns m

1.5 pS(t)

0 −5 Relative Power (dB)

Signal Amplitude

1

0.5

0

−0.5

−10

Bandwidth

−15 −20 −25 −30

−1

fH

fL

−35

pS(t) FCC Mask

−1.5 −2

−1.5

−1

−0.5

0 Time [s]

0.5

1

1.5

2 −10

x 10

1

2

3

4

5 6 7 8 Frequency (GHz)

9

10

11

12

F IGURE : Scholtz monocycle in time domain and in frequency domain for τ = 0.13 ns.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

6 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

O BJECTIVES

G OALS Design an Impulse Radio (IR) UWB receiver based on low cost analog components. Transmit at high data rate (≥ 100 Mbps) with M -PPM modulation. Define new equalization algorithm with energy detection. Develop new methods for channel parameters estimation based on energy detection. Study the associated architecture for hardware implementation

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

7 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

D IFFICULTIES 1

UWB Channel Models (CM) [IEEE 802.15.3a].

CM1

CM4

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

−0.1

−0.1

−0.2

−0.2

−0.3

−0.3

−0.4

−0.4

−0.5

0

50

100

150 Time (nS)

200

250

−0.5

0

50

100

150

200

250

Time (nS)

F IGURE : Impulse responses for Channel Model CM1 and CM4. Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

8 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

D IFFICULTIES 1

UWB Channel Models (CM) [IEEE 802.15.3a].

2

Use of M -PPM modulation for high data transmission (i.e. transmit at 100 Mbps with a 4-PPM).

Time Symbol Ts Time Slot Tslot

Binary Sequence 00

01

10

11

01

F IGURE : An example of 4−PPM modulation and straight binary mapping.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

8 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

D IFFICULTIES 1

UWB Channel Models (CM) [IEEE 802.15.3a].

2

Use of M -PPM modulation for high data transmission (i.e. transmit at 100 Mbps with a 4-PPM). Transmitted data

Ts= 4.Tslot 1

e(t) 0

0

20

40

60

80

100

120

140

160

180

200

220

Time(nS)

Transmitted symbol: 00 0.3

x

(t) n−2

0

−0.3

0

20

40

60

80

100 120 Time(nS) Transmitted symbol: 10

140

160

180

200

220

0

20

40

60

80

100 120 Time(nS) Transmitted symbol: 00

140

160

180

200

220

0

20

40

60

80

140

160

180

200

220

0.3

x

(t)

n−1

0

−0.3

0.3

xn(t)

0

−0.3

100

120 Time(nS)

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

8 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

D IFFICULTIES 1

UWB Channel Models (CM) [IEEE 802.15.3a].

2

Use of M -PPM modulation for high data transmission (i.e. transmit at 100 Mbps with a 4-PPM). Transmitted data

Ts= 4.Tslot 1

e(t) 0

0

20

40

60

80

100

120

140

160

180

200

220

120

140

160

180

200

220

Time(nS)

0.3

0.2

0.1

0

−0.1

−0.2

−0.3

0

20

40

60

80

100 Time(nS)

(b) Inter-Symbol Interference (ISI) and Inter-Slot Interference (IStI).

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

8 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

D IFFICULTIES 1

UWB Channel Models (CM) [IEEE 802.15.3a].

2

Use of M -PPM modulation for high data transmission (i.e. transmit at 100 Mbps with a 4-PPM). Transmitted data

Ts= 4.Tslot 1

e(t) 0

0

20

40

60

80

100

120

140

160

180

200

220

Time(nS)

The resulting signal 0.3

0.2

0.1

0

−0.1

−0.2

−0.3

0

20

40

60

80

100

120

140

160

180

200

220

Time(nS)

(c) The resulting signal sn (t).

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

8 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

R ECEIVER T YPES 1

Rake Receiver used for DS-UWB (coherent receiver).

Channel impulse response: h(t) = Drawbacks:

PK−1

`=1 a` e

jθ` δ(t − τ

RT

`)

0

a1e−jθ1

c∗(t − τ1 )

RT

A lot of Rake fingers is required to capture energy (up to 50 resolvable dominant paths in NLOS) [Win

0

Σ

Decision

and Scholtz, 1998, 2002] Using a single LOS path signal as template is suboptimal [Win and Scholtz, 1997] High sampling rate is required for channel estimation (14 Ghz [Nikookar and Prasad, 2009]).

⇒ Increase the complexity and cost of the receiver

a2 e−jθ2 ...

c∗(t − τ2 )

RT 0

aK−1e−jθK−1

c∗(t − τK−1)

F IGURE : Rake Receiver for DS-UWB. Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

9 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

R ECEIVER T YPES 1

Rake Receiver used for DS-UWB (coherent receiver).

2

Transmit Reference (T-R) receiver is pilot-based receiver (non-coherent receiver).

Two transmitted pulses are used: 1

reference pulse

2

data pulse

t

Drawbacks:

D

T-R receivers is poor at low signal-to-noise ratios or in the presence of narrow band interference [Dowla al. 2004]

1

⇒ Not Low Cost! Sami MEKKI

D

D

1

Mixer Filter and Amplifier

Half of the transmitted waveform is used as pilot. A mixer and a delay line are necessary.

D

0

Z

D 1

0

Differential data: "1 1 0 1 0" A/D T

Delay D

F IGURE : A DPSK sequence and TR-UWB receiver.

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

9 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

R ECEIVER T YPES 1

Rake Receiver used for DS-UWB (coherent receiver).

2

Transmit Reference (T-R) receiver is pilot-based receiver (non-coherent receiver).

3

Energy Detection (ED) receiver (non-coherent receiver).

Based on energy detection. Typically used for low data rate (Wireless Sensor Networks) Drawbacks:

(.)2

ADC

DSP

de

0

Suffers more from noise due to a square-law device. Dedicated for low data rate transmission.

ZT

F IGURE : Typical ED receiver.

⇒ Low cost receiver (analog components point of view)

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

9 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

R ECEIVER T YPES 1

Rake Receiver used for DS-UWB (coherent receiver).

2

Transmit Reference (T-R) receiver is pilot-based receiver (non-coherent receiver).

3

Energy Detection (ED) receiver (non-coherent receiver).

⇒ ED receiver is the best choice for low cost analog components.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

9 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

1

I NTRODUCTION AND M OTIVATION

2

E NERGY D ETECTION R ECEIVER

3

P ROBABILISTIC UWB E QUALIZER

4

C HANNEL PARAMETERS E STIMATION

5

A RCHITECTURE F EASIBILITY

6

C ONCLUSIONS

Sami MEKKI

Architecture Feasibility

Digital processing algorithms and architectures for UWB low cost communication system

Conclusions

July 3rd, 2009

10 / 39

Introduction and Motivation

Energy Detection Receiver

T RANSMITTER

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

AND RECEIVER DESIGN .

Channel

zn (t) Data

Encoder

Modulator

Pulse Generator

{en−k (t)}

Channel Filter

sn (t)

H

SISO Decoder

Equalizer

En,m

Z

(.)2 Tslot

F IGURE : Block diagram of transmission and reception with an equalizer and SISO decoder.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

11 / 39

Introduction and Motivation

Energy Detection Receiver

T RANSMITTER

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

AND RECEIVER DESIGN .

Channel

zn (t) Data

Encoder

Modulator

Pulse Generator

{en−k (t)}

Channel Filter

sn (t)

H

SISO Decoder

Equalizer

En,m

Z

(.)2 Tslot

F IGURE : Block diagram of transmission and reception with an equalizer and SISO decoder.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

11 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

The output of the channel filter is sn (t) =

Z En,m

Channel Parameters Estimation

PK−1

k=0 xn−k (t) (sum of

nTs +(m)Tslot

=

Architecture Feasibility

Conclusions

K interfered symbols).

(sn (t) + zn (t))2 dt

(1)

nTs +(m−1)Tslot

According to [Urkowitz-67]:

En,m =

2L X

(s`n,m + z`n,m )2

(2)

`=1

where 2L = 2Tslot W (i.e. 2L is the Degree of Freedom (DoF) over Tslot ).

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

12 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

E NERGY DISTRIBUTION From (2) χ` = s`n,m + z`n,m ∼ N (s`n,m , σ2 ). ⇒ The energy En,m follows a Chi2 (χ2 ) distribution with 2L DoF, the pdf is given [Proakis, 2000]: 1

if Bn,m =

` 2 `=1 (sn,m )

P2L

, 0 (non-centrality parameter)

1 En,m p(En,m |Bn,m ) = 2σ2 Bn,m 2

if Bn,m =

` 2 `=1 (sn,m )

P2L

! L−1 2

−

e

(En,m +Bn,m ) 2σ2

p   Bn,m En,m    IL−1  σ2

(3)

=0 p(En,m |0) =

1

σ2L 2L Γ(L)

EL−1 n,m e

−En,m 2σ2

(4)

where IL−1 (u) and Γ(z) are respectively the (L − 1)th -order modified Bessel function of the first kind and the Gamma function [Abramowitz, 1964].

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

13 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

1

I NTRODUCTION AND M OTIVATION

2

E NERGY D ETECTION R ECEIVER

3

P ROBABILISTIC UWB E QUALIZER

4

C HANNEL PARAMETERS E STIMATION

5

A RCHITECTURE F EASIBILITY

6

C ONCLUSIONS

Sami MEKKI

Architecture Feasibility

Digital processing algorithms and architectures for UWB low cost communication system

Conclusions

July 3rd, 2009

14 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

M OTIVATION Manage the Inter-Symbol Interference (ISI) and intra-Symbol Interference induced by the channel models (defined by IEEE802.15.3a).

P ROPOSAL Develop a new probabilistic equalizer based on ED. 1

The equalizer computes p(En |xn ).

2

This probability (after normalization) is forwarded to the SISO (Soft-Input Soft Output) decoder to compute the extrinsic probability.

3

The equalizer computes again p(En |xn ) taking into account the probabilities provided by the decoder previously. Steps 2 and 3 are iterated until convergence.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

15 / 39

Introduction and Motivation

H OW

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

THE PROBABILISTIC EQUALIZER WORKS !

The probabilistic equalizer takes into account all the possible interference and computes p(En |xn ) as follows

p(En |xn ) =

X

 M  K−1 Y  Y   p(En,m |Bn,m ) π(xn−k ) 

xn−1 ,...,xn−K+1 m=1

(5)

k =1

where π(xn−k ) is the a priori probability of xn−k and Bn,m ∈ B = {βj }. TABLE : Exhaustive Listing of Energy Patterns βj for two consecutive 4-PPM interfering symbols, K = 2.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

16 / 39

Introduction and Motivation

H OW

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

THE PROBABILISTIC EQUALIZER WORKS !

The probabilistic equalizer takes into account all the possible interference and computes p(En |xn ) as follows

p(En |xn ) =

X

 M  K−1 Y  Y   p(En,m |Bn,m ) π(xn−k ) 

xn−1 ,...,xn−K+1 m=1

(5)

k =1

where π(xn−k ) is the a priori probability of xn−k and Bn,m ∈ B = {βj }. TABLE : Exhaustive Listing of Energy Patterns βj for two consecutive 4-PPM interfering symbols, K = 2.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

16 / 39

Introduction and Motivation

H OW

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

THE PROBABILISTIC EQUALIZER WORKS !

The probabilistic equalizer takes into account all the possible interference and computes p(En |xn ) as follows

p(En |xn ) =

 M  K−1 Y  Y   p(En,m |Bn,m ) π(xn−k ) 

X

xn−1 ,...,xn−K+1 m=1

(5)

k =1

where π(xn−k ) is the a priori probability of xn−k and Bn,m ∈ B = {βj }.

TABLE : Relation between the presumed number of interfering symbols K and |B|

Sami MEKKI

K

P

|B|

2 3 4

5 9 13

15 88 424

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

16 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

P ROBABILISTIC E QUALIZER S UMMARY IN P ERFECT CSI

Encoder

Decoded bits {dei}

z(t)

codeword

Data{di}

SISO Decoder

c

Mapper Pulse Generator

p(En|xn )

{pn−k (t)}

Channel Filter H

En,m

Equalizer

s(t)

Z

(.)2 Tslot

π(xk )

Mem

{βj } σ2

χ2 Table p(En,m|Bn,m )

F IGURE : Probabilistic equalizer procedure

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

17 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

S IMULATIONS WITHOUT CHANNEL CODING IN P ERFECT CSI Energetic Equalization with Perfect CSI without Channel Coding at 100Mbps and P=5 100

Bit Error Rate (information)

10-1

10-2

10-3

CM1 with Equalization CM1 without equalization CM2 with Equalization CM2 without equalization CM3 with Equalization CM3 without equalization CM4 with Equalization CM4 without equalization

10-4

10-5

6

8

10

12 Eb/N0 (dB)

14

16

18

20

BER vs Eb /N0 for different channel models IEEE802.15.3a for K = 2 at 100Mbit/s (Tslot = 5ns) using a 4-PPM modulation, W = 3 GHz (2L = 30). Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

18 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

S IMULATIONS WITHOUT CHANNEL CODING IN P ERFECT CSI Energetic Equalization with Perfect CSI without Channel Coding at 100Mbps and P=9 100

Bit Error Rate (information)

10-1

10-2

10-3

10-4

10-5

CM1 with Equalization CM2 with Equalization CM3 with Equalization CM4 with Equalization 6

8

10

12 Eb/N0 (dB)

14

16

18

20

BER vs Eb /N0 for different channel models IEEE802.15.3a for K = 3 at 100Mbit/s (Tslot = 5ns) using a 4-PPM modulation, W = 3 GHz (2L = 30). Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

18 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

S IMULATIONS WITHOUT CHANNEL CODING IN P ERFECT CSI Energetic Equalization with Perfect CSI without Channel Coding at 100Mbps and P=13 100

Bit Error Rate (information)

10-1

10-2

10-3

10-4

10-5

CM1 with Equalization CM2 with Equalization CM3 with Equalization CM4 with Equalization 6

8

10

12 Eb/N0 (dB)

14

16

18

20

BER vs Eb /N0 for different channel models IEEE802.15.3a for K = 4 at 100Mbit/s (Tslot = 5ns) using a 4-PPM modulation, W = 3 GHz (2L = 30). Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

18 / 39

Introduction and Motivation

Energy Detection Receiver

S IMULATIONS WITH

Probabilistic UWB Equalizer

Channel Parameters Estimation

CHANNEL CODING IN

Architecture Feasibility

Conclusions

P ERFECT CSI

P=5, BICM (23,35) at rate 1/2, 10 SISO iterations and Energetic Equalization in Perfect CSI at 100Mbps 100

Bit Error Rate (information)

10-1

10-2

10-3

10-4

10-5

CM1 CM2 CM3 CM4 6

8

10

12 Eb/N0 (dB)

14

16

18

20

BER vs Eb /N0 for different channel models using BICM(23,35) with code rate 1/2 length N=1024 bits, 10 iterations of the SISO decoder for K = 2, data rate 100Mbit/s and a 4-PPM modulation, W = 3 GHz (2L = 30). Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

19 / 39

Introduction and Motivation

Energy Detection Receiver

S IMULATIONS WITH

Probabilistic UWB Equalizer

Channel Parameters Estimation

CHANNEL CODING IN

Architecture Feasibility

Conclusions

P ERFECT CSI

P=9, BICM (23,35) at rate 1/2, 10 SISO iterations and Energetic Equalization in Perfect CSI at 100Mbps 100

Bit Error Rate (information)

10-1

10-2

10-3

10-4

10-5

CM1 CM2 CM3 CM4 6

8

10

12 Eb/N0 (dB)

14

16

18

20

BER vs Eb /N0 for different channel models using BICM(23,35) with code rate 1/2 length N=1024 bits, 10 iterations of the SISO decoder for K = 3, data rate 100Mbit/s and a 4-PPM modulation, W = 3 GHz (2L = 30). Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

19 / 39

Introduction and Motivation

Energy Detection Receiver

S IMULATIONS WITH

Probabilistic UWB Equalizer

Channel Parameters Estimation

CHANNEL CODING IN

Architecture Feasibility

Conclusions

P ERFECT CSI

P=13, BICM (23,35) at rate 1/2, 10 SISO iterations and Energetic Equalization in Perfect CSI at 100Mbps 100

Bit Error Rate (information)

10-1

10-2

10-3

10-4

10-5

CM1 CM2 CM3 CM4 6

8

10

12 Eb/N0 (dB)

14

16

18

20

BER vs Eb /N0 for different channel models using BICM(23,35) with code rate 1/2 length N=1024 bits, 10 iterations of the SISO decoder for K = 4, data rate 100Mbit/s and a 4-PPM modulation, W = 3 GHz (2L = 30). Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

19 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

1

I NTRODUCTION AND M OTIVATION

2

E NERGY D ETECTION R ECEIVER

3

P ROBABILISTIC UWB E QUALIZER

4

C HANNEL PARAMETERS E STIMATION

5

A RCHITECTURE F EASIBILITY

6

C ONCLUSIONS

Sami MEKKI

Architecture Feasibility

Digital processing algorithms and architectures for UWB low cost communication system

Conclusions

July 3rd, 2009

20 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

M OTIVATION Estimate the channel parameters (B and σ2 ) for equalization application.

P ROPOSALS 1

Apply the expectation-maximization (EM) algorithm [Dempster, Laird and Rudin, 1977] to obtain the maximum likelihood of estimates that might not be available otherwise.

2

Transmit special training sequences to estimate the channel parameters.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

21 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

EM A LGORITHM

This algorithm allows to compute maximum-likelihood estimate of parameters when direct access to the full data necessary to make the estimate is impossible. Equalization needs to access to B = {βj } and σ2 .

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

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Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

EM A LGORITHM

This algorithm allows to compute maximum-likelihood estimate of parameters when direct access to the full data necessary to make the estimate is impossible. Equalization needs to access to B = {βj } and σ2 . ⇒ The EM algorithm is ideally suited to problems of this sort.

y is the incomplete data (received data); x is the missing data (transmitted data); (x, y) is the complete data. θ is the parameter to be estimated (the channel parameters (B = {βj }, σ2 )).

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Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

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Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

A LGORITHM D ESCRIPTION The EM algorithm consists of two primary steps: an expectation step, followed by a maximization step. It proceeds as follows: 1

Choose an initial parameter θ(0)

2

E-step (Expectation step):Estimate unobserved data using θi

  Q(θ|θ(i) ) = Ex [log p(x, y|θ)|y, θ(i) ]

(6)

where Q is the auxiliary function. 3

M-step (Maximization step): compute maximum likelihood estimate of parameter θ(i+1) using estimated data.

θ(i+1) = arg max Q(θ|θ(i) )

(7)

θ

The E-step and the M-step are alternated until the parameter estimate has converged (no more change on the estimate).

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Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

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Introduction and Motivation

EM

Energy Detection Receiver

APPLICATION TO

Probabilistic UWB Equalizer

ED

Channel Parameters Estimation

Architecture Feasibility

Conclusions

MODEL

The auxiliary function with ED is Q(θ|θi )

=

N X M XX x

log p(En,m |Bn,m , θ)APP(x)

(8)

n m=1

The update channel parameters are 2  N M q  X X  (i)  (i)  f (En,m , 2Lσ2 ) pi (Bn,m = βj )      n=1 m=1 (i+1) βj ≈   N M  XX  (i)   pi (Bn,m = βj ) 

(9)

n=1 m=1

σ2

(i+1)

=

N M 1 XXX (i) (i) (En,m − βj )pi (Bn,m = βj ) 2LMN n=1 m=1 (i)

(10)

Bj

where f (En,m

Sami MEKKI

   En,m − 2Lσ2 (i)    0

 (i) , 2Lσ2 ) =

if En,m > 2Lσ2

(i)

if En,m ≤ 2Lσ2

(i)

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

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Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

E QUALIZER AND EM ALGORITHM

Encoder

SISO Decoder

Architecture Feasibility

Conclusions

DESIGN

z(t)

codeword

Data{di}

Decoded bits

Channel Parameters Estimation

c

Mapper Pulse Generator

p(En|xn )

{pn−k (t)}

Channel Filter H

En,m

Equalizer

s(t)

Z

(.)2 Tslot

AP Pi (x) π(x) Mem

EM

θ

i

{βj } σ

2

χ2 Table p(En,m|Bn,m )

F IGURE : Transmitter and receiver design with joint channel parameters estimation and energy equalization.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

25 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

K=2, BICM (23,35) at rate 1/2, 10 SISO iterations and Energy Equalization with 1 iteration of EM at 100Mbps 100

Bit Error Rate (information)

10-1

10-2

10-3

10-4

10-5

CM1-Perfect CSI CM1-EM Algorithm CM2-Perfect CSI CM2-EM Algorithm CM3-Perfect CSI CM3-EM Algorithm CM4-Perfect CSI CM4-EM Algorithm 6

8

10

12 Eb/N0 (dB)

14

16

18

20

BER for different channel models using BICM(23,35) with code rate 1/2, N=1024 with K = 2, 10 SISO decoder iterations with one iteration of the EM algorithm per decoder iteration (10 EM iterations). 10 symbols for EM initialization, EM algorithm versus Perfect CSI at 100 Mbps using 4-PPM modulation. Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

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Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

K=3, BICM (23,35) at rate 1/2, 10 SISO iterations and Energy Equalization with 1 iteration of EM at 100Mbps 100

Bit Error Rate (information)

10-1

10-2

10-3

10-4

10-5

CM1-Perfect CSI CM1-EM Algorithm CM2-Perfect CSI CM2-EM Algorithm CM3-Perfect CSI CM3-EM Algorithm CM4-Perfect CSI CM4-EM Algorithm 6

8

10

12 Eb/N0 (dB)

14

16

18

20

BER for different channel models using BICM(23,35) with code rate 1/2, N=1024 with K = 3, 10 SISO decoder iterations with one iteration of the EM algorithm per decoder iteration (10 EM iterations). 10 symbols for EM initialization, EM algorithm versus Perfect CSI at 100 Mbps using 4-PPM modulation. Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

26 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

1

I NTRODUCTION AND M OTIVATION

2

E NERGY D ETECTION R ECEIVER

3

P ROBABILISTIC UWB E QUALIZER

4

C HANNEL PARAMETERS E STIMATION

5

A RCHITECTURE F EASIBILITY

6

C ONCLUSIONS

Sami MEKKI

Architecture Feasibility

Digital processing algorithms and architectures for UWB low cost communication system

Conclusions

July 3rd, 2009

27 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

M OTIVATIONS AND P ROPOSALS M OTIVATION Study and reduce the hardware implementation complexity (computational complexity) of the developed algorithm. Optimize the size of variables (number of bits) required for the operations.

T HE PROBLEMS The χ2 pdf will occupy a very large memory (448 Mbit). Keep reasonable amount of operators (3.2 GMultip/s).

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

28 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

M OTIVATIONS AND P ROPOSALS M OTIVATION Study and reduce the hardware implementation complexity (computational complexity) of the developed algorithm. Optimize the size of variables (number of bits) required for the operations.

T HE PROBLEMS The χ2 pdf will occupy a very large memory (448 Mbit). Keep reasonable amount of operators (3.2 GMultip/s).

P ROPOSALS Approximate the χ2 pdf by a function easier to implement (reduce the required memories, i.e. ROM). Compute in the logarithm domain (additions become Log-Sum or max*10 operations and multiplications become additions). Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

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Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

χ2 A PPROXIMATION According to the central limit theorem, for large 2L, the distribution of En,m is asymptotically Gaussian [Marcuse-90]. When φ is used to approximate ψ, it is equivalent to match the mean and variance [Jin-Ting Zhang-05]. Mean and variance of χ2 distribution:

mχ2 σ2χ2

= 2Lσ2 + Bn,m 4

(11)

2

= 4Lσ + 4σ Bn,m

p(En,m |Bn,m ) ≈ e p(En,m |Bn,m ) = q

1 2πσ2χ2

(12)

   (En,m − m 2 )2  χ   exp −  2σ2

(13)

χ2

i.e. En,m ∼ N (mχ2 , σ2 2 ) χ

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Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

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Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

χ2 A PPROXIMATION E RROR

WITH

Channel Parameters Estimation

Architecture Feasibility

Conclusions

σ2 = 1 ( LOW Eb /N0 )

10−3

4

3

Error 2

1,000

1 750

Bnm

500 250 00 0

100

300

200

400

500

Enm

Error measured by |p(En,m |Bn,m ) −e p(En,m |Bn,m )| ∀ En,m ≥ 0, ∀ Bn,m > 0 and σ2 = 1. Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

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Introduction and Motivation

Energy Detection Receiver

A PPROXIMATED χ2

log(En,m )

ROM

En,m

10x



Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

IMPLEMENTATION

En,m − mχ2



ROM

φ(x) =

2 √1 e−x 2π

pe(En,m |Bn,m )

Bn,m

q1 σ2 2



χ

log(2Lσ 2 )

ROM

σχ2 2

mχ 2

10x



2Lσ 2

ROM √1 x



1 L

: Stands for trivial Multiplication by a power of 2 : Stands for non-trivial Multiplication

F IGURE : Approximated Energy distribution architecture for the linear equalizer with χ2 approximation. The linear equalizer requires 12.8 GMultip/s and 30.25 Kbit per level of parallelism. Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

31 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

TC Frame Type 864 with rate 1/2 at 100Mbps (Chi-2 vs Fixed Chi2 approximation) 100

Bit Error Rate (information)

10-1

10-2

CM1-float Chi2 CM1-Fixed Gauss Approx CM2-float Chi2 CM2-Fixed Gauss Approx CM3-float Chi2 CM3-Fixed Gauss Approx CM4-float Chi2 CM4-Fixed Gauss Approx

10-3

10-4

8

10

12

14 Eb/N0 (dB)

16

18

20

χ2 float precision versus the Gaussian approximation in fixed point precision for K = 2. A duo-binary turbo code with encoded data of 864 bits at rate 1/2, 4-PPM modulation at 100 Mbps Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

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Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

L OG -S UM OR max*10 O PERATOR The logarithmic domain allows to replace linear multiplications by log additions and the linear additions have to be replaced by the Log-Sum (max*10 ) operation [Viterbi, 1998]: ∆

max*10 (a, b) = log10 (10a + 10b ) ∆

= max(a, b) + log10 (1 + 10−|a−b| )

(14)

The new probabilistic equalizer in the logarithm domain is

log p(En |xn ) =

*

 M  K−1 X  X   log p(En,m |Bn,m ) + log π(xn−k ) 

max10 xn−1 ,...,xn−K+1 m=1

(15)

k =1

where h i loge p(En,m |Bn,m ) ∝ − 12 max*10 log(2Lσ2 ), log 2 + log Bn,m − 2 lnL10 (En,m − mχ2 )2 10−γ and γ = log(2Lσ2 ) + max*10 [log(2Lσ2 ), log 2 + log Bn,m ]

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Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

33 / 39

Introduction and Motivation

Energy Detection Receiver

A PPROXIMATED χ2

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

IMPLEMENTATION − 2 lnL10

log(En,m )

10x

2

log(2Lσ )

log Bn,m

ROM

En,m

ROM

2Lσ 2

10x



ROM

Bn,m

10x



log pe(En,m |Bn,m )

mχ 2





γ

−γ

ROM



10x

10−γ

−1 log 2

log 2 + log Bn,m

max∗10

−1/2

: Stands for trivial Multiplication by a power of 2 : Stands for non-trivial Multiplication

max∗10

≡

d

sign

ROM

log(1 + 10−|d|)



F IGURE : Energy distribution architecture for logarithmic equalizer. The logarithmic equalizer requires 6.4 GMultip/s and 16.25 Kbit per level of parallelism. Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

34 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

TC Frame Type 864 with rate 1/2 at 100Mbps and K=2 (Chi-2 vs Fixed Log approximated Chi2) 100

Bit Error Rate (information)

10-1

10-2

CM1-float Chi2 CM1-Fixed CM2-float Chi2 CM2-Fixed CM3-float Chi2 CM3-Fixed CM4-float Chi2 CM4-Fixed

10-3

10-4

8

10

12

14 Eb/N0 (dB)

16

18

20

χ2 float precision versus the logarithmic approximated χ2 in fixed point precision for K = 2. A duo-binary turbo code with encoded data of 864 bits at rate 1/2, 4-PPM modulation at 100 Mbps Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

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Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

A RCHITECTURE F EASIBILITY S UMMARY

TABLE : Complexity Requirement with 4-PPM and K = 2

Functions

Linear

Number of Multiplications Linear Logarithmic χ2 approximated χ2 approximated

(M + K − 2)M K 3.2 GMultip/s 0

p(En |xn ) p(En,m |Bn,m ) Total Equalizer Multiplications Total required memory per level of parallelism

Sami MEKKI

χ2

3.2 GMultip/s

(M + K − 2)M K 3.2 GMultip/s 3M K +1 9.6 GMultip/s 12.8 GMultip/s

2M K +1 6.4 GMultip/s 6.4 GMultip/s

448 Mbit

30.25 Kbit

16.25 Kbit

Digital processing algorithms and architectures for UWB low cost communication system

0

July 3rd, 2009

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Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

1

I NTRODUCTION AND M OTIVATION

2

E NERGY D ETECTION R ECEIVER

3

P ROBABILISTIC UWB E QUALIZER

4

C HANNEL PARAMETERS E STIMATION

5

A RCHITECTURE F EASIBILITY

6

C ONCLUSIONS

Sami MEKKI

Architecture Feasibility

Digital processing algorithms and architectures for UWB low cost communication system

Conclusions

July 3rd, 2009

37 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

C ONCLUSION We proposed the probabilistic UWB equalizer with energy detection that improves the receiver performance at high data rate.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

38 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

C ONCLUSION We proposed the probabilistic UWB equalizer with energy detection that improves the receiver performance at high data rate. We implemented the EM algorithm for channel parameters estimation necessary to equalization.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

38 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

C ONCLUSION We proposed the probabilistic UWB equalizer with energy detection that improves the receiver performance at high data rate. We implemented the EM algorithm for channel parameters estimation necessary to equalization. We defined a special training sequence capable to get a good estimate of channel parameters with very low complexity channel estimation with regards to the EM method.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

38 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

C ONCLUSION We proposed the probabilistic UWB equalizer with energy detection that improves the receiver performance at high data rate. We implemented the EM algorithm for channel parameters estimation necessary to equalization. We defined a special training sequence capable to get a good estimate of channel parameters with very low complexity channel estimation with regards to the EM method. Equalization with the proposed Gaussian approximation achieves the equalization performance.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

38 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

C ONCLUSION We proposed the probabilistic UWB equalizer with energy detection that improves the receiver performance at high data rate. We implemented the EM algorithm for channel parameters estimation necessary to equalization. We defined a special training sequence capable to get a good estimate of channel parameters with very low complexity channel estimation with regards to the EM method. Equalization with the proposed Gaussian approximation achieves the equalization performance. We reduced the memory size and the number of multipliers by performing the calculation in the logarithm domain.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

38 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

C ONCLUSION We proposed the probabilistic UWB equalizer with energy detection that improves the receiver performance at high data rate. We implemented the EM algorithm for channel parameters estimation necessary to equalization. We defined a special training sequence capable to get a good estimate of channel parameters with very low complexity channel estimation with regards to the EM method. Equalization with the proposed Gaussian approximation achieves the equalization performance. We reduced the memory size and the number of multipliers by performing the calculation in the logarithm domain.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

38 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

C ONCLUSION We proposed the probabilistic UWB equalizer with energy detection that improves the receiver performance at high data rate. We implemented the EM algorithm for channel parameters estimation necessary to equalization. We defined a special training sequence capable to get a good estimate of channel parameters with very low complexity channel estimation with regards to the EM method. Equalization with the proposed Gaussian approximation achieves the equalization performance. We reduced the memory size and the number of multipliers by performing the calculation in the logarithm domain. This study shows the feasibility of IR-UWB receiver based on energy detection for high data rate transmission. Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

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Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

O PEN I SSUES

Reduce the energy coefficient in the equalizer to optimize the digital processing cost.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

39 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

O PEN I SSUES

Reduce the energy coefficient in the equalizer to optimize the digital processing cost. Study the feasibility of a multi-user receiver based on energy detection.

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

39 / 39

Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

O PEN I SSUES

Reduce the energy coefficient in the equalizer to optimize the digital processing cost. Study the feasibility of a multi-user receiver based on energy detection. Extend the application of this work in any field dealing with energy detection (wireless optical communication).

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

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Introduction and Motivation

Energy Detection Receiver

Probabilistic UWB Equalizer

Channel Parameters Estimation

Architecture Feasibility

Conclusions

Thank you for your attention! Questions?

Sami MEKKI

Digital processing algorithms and architectures for UWB low cost communication system

July 3rd, 2009

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