Introduction to a Multichannel Noncoherent Autocorrelation ... · TU Graz - Signal Processing and Speech Communication Laboratory Introduction to a Multichannel Noncoherent Autocorrelation

TU Graz - Signal Processing and Speech Communication Laboratory

Introduction to a Multichannel NoncoherentAutocorrelation UWB Receiver using OFDM

Andreas Pedross, Klaus Witrisal

Signal Processing and Speech Communication Laboratory

May 05, 2011

Andreas Pedross, Klaus Witrisal May 05, 2011 page 1/23


Outline

Introduction

Architecture

Receiver Signal Processing

Conclusions



Introduction – What’s the goal?

Receiver Design Constraints

We want:

1.

2.





We want:

1. High Data-Rate: 437.5 Mbps

2.





We want:


2. Low-Power!





We want:


2. Low-Power!

How to achieve?





We want:


2. Low-Power!

How to achieve?

◮ Ultra-Wide Band: BW 1.75 GHz @ 4 GHz center





We want:


2. Low-Power!

How to achieve?

◮ Ultra-Wide Band: BW 1.75 GHz @ 4 GHz center

◮ Multidimensional Noncoherent Signaling Scheme!



Outline

Introduction

Architecture


Conclusions



Architecture – General Signal (1)

Signaling Scheme

s(t) = ℜ

e+jωct

+ K−1

2∑

k=−K−1

2

skΘk(t)

with:

◮ ωc ... carrier frequency

◮ K ... dimension of signal space

◮ Θk(t) ... k-th orthogonal basis function

◮ sk ... k-th symbol element




Received Signal

r(t) = hch(t) ∗ s(t) + n(t)

= ℜ

e+jωct

+ K−1

2∑

k=−K−1

2

skΘ̃k(t)

+ n(t)

with:

◮ hch(t) ... communication channel

◮ Θ̃k(t) ... k-th convolved basis function

◮ n(t) ... noise




Which Noncoherent Receiver Design?

◮ Energy Detector?

z[n] =

∫ nTs

λ=(n−1)Ts

r2(λ)dλ

No separation between basis functions possible!

◮ Autocorrelation?

zk[n] =

∫ nTs

λ=(n−1)Ts

Θ̃k(λ)Θ̃∗k(λ − τm)dλ

Seems feasible...



Architecture – System View

Linear

Combiner

Front End

Filterτ0

τ1

τ2

τ3

τ4

LP

ADC

ADC

ADC

ADC

ADC

ADC

LP

LP I&D

LP I&D

LP I&D

LP I&D

LP I&D

LP I&D

ADCI&D

ADCI&D



Architecture – System Parameters

Receiver

◮ 8x AcR Channels (4x I&Q)

◮ Delay Lines: 1x 62.5 ps, 1x 250 ps, and 3x 500 ps

Signaling

◮ OFDM

◮ 4 GHz Carrier

◮ 7 Sub-Carriers, 250 MHz spacing

◮ 16 ns Symbol Period with Zero Guard Interval

◮ Truncated Root Raised Cosine Pulses

◮ OOK/PPM



Outline

Introduction

Architecture


Conclusions



Receiver Signal Processing – OFDM

Signaling Scheme

s(t) = ℜ

e+jωct

+ K−1

2∑

k=−K−1

2

skϕ(t)e+jkωsct

with:

◮ ωc ... center frequency

◮ ωsc ... sub-carrier spacing

◮ K ... number of sub-carriers

◮ ϕ(t) ... pulse shape

◮ sk ... k-th symbol element



Receiver Signal Processing – Signaling

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

x 10−8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time [s]

ϕ(t

)

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1

x 109

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

frequency [Hz]

magnitude o

f baseband s

ub−

carr

ier

puls

es

(left) Baseband Pulse in Time Domain, (right) BasebandSub-Carriers in Frequency Domain



Receiver Signal Processing – Autocorrelation (1)

Delay & Multiplication

xm(t) = r(t) · r(t − τm)

=1

2

∑

k

∑

l

skslℜ{

Θ̃k(t)Θ̃∗l (t − τm)e+jωcτm

}

+

+1

2

∑

k

∑

l

skslℜ{

Θ̃k(t)Θ̃l(t − τm)e+2jωcte−jωcτm

}

+

+∑

k

skℜ{

Θ̃k(t)e+jωct

}

· n(t − τm)+

+∑

l

slℜ{

Θ̃l(t − τm)e+jωcte−jωcτm

}

· n(t)+

+ n(t) · n(t − τm)





xm(t) = r(t) · r(t − τm)

=1

2

∑

k

∑

l

skslℜ{


}

+

+1

2

∑

k

∑

l

skslℜ{


}

+

+∑

k

skℜ{

Θ̃k(t)e+jωct

}

· n(t − τm)+

+∑

l

slℜ{


}

· n(t)+

+ n(t) · n(t − τm)





xm(t) = r(t) · r(t − τm)

=1

2

∑

k

∑

l

skslℜ{


}

+

+1

2

∑

k

∑

l

skslℜ{


}

+

+∑

k

skℜ{

Θ̃k(t)e+jωct

}

· n(t − τm)+

+∑

l

slℜ{


}

· n(t)+

+ n(t) · n(t − τm)




Lowpass-Filtering

x̃m(t) = hlp(t) ∗ xm(t)

≈1

2

∑

k

s2kℜ

{

hlp(t) ∗[

Θ̃k(t)Θ̃∗k(t − τm)

]

e+jωcτm

}

+

+1

2

∑

k

∑

l,l 6=k

skslℜ{

hlp(t) ∗[

Θ̃k(t)Θ̃∗l (t − τm)

]

e+jωcτm

}

+

+∑

k

skhlp(t) ∗[

ℜ{

Θ̃k(t)e+jωct

}

· n(t − τm)]

+

+∑

l

slhlp(t) ∗[

ℜ{


}

· n(t)]

+

+ hlp(t) ∗ [n(t) · n(t − τm)]




Lowpass-Filtering


≈1

2

∑

k

s2kℜ

{

hlp(t) ∗[


]

e+jωcτm

}

+

+1

2

∑

k

∑

l,l 6=k

skslℜ{

hlp(t) ∗[


]

e+jωcτm

}

+

+∑

k

skhlp(t) ∗[

ℜ{

Θ̃k(t)e+jωct

}

· n(t − τm)]

+

+∑

l

slhlp(t) ∗[

ℜ{


}

· n(t)]

+

+ hlp(t) ∗ [n(t) · n(t − τm)]




Lowpass-Filtering


≈1

2

∑

k

s2kℜ

{

hlp(t) ∗[


]

e+jωcτm

}

+

+1

2

∑

k

∑

l,l 6=k

skslℜ{

hlp(t) ∗[


]

e+jωcτm

}

+

+∑

k

skhlp(t) ∗[

ℜ{

Θ̃k(t)e+jωct

}

· n(t − τm)]

+

+∑

l

slhlp(t) ∗[

ℜ{


}

· n(t)]

+

+ hlp(t) ∗ [n(t) · n(t − τm)]



Receiver Signal Processing – Mixers

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2

x 109

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

frequency [Hz]

magnitude o

f co−

and c

ross−

term

s

Mixing Product



Receiver Signal Processing – Mixers

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2

x 109

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

frequency [Hz]

magnitude o

f co−

and c

ross−

term

s

Mixing Product




Integrate ... and Dump

ym[n] = ym(nTs)

= hint(t) ∗ x̃m(t)|t=nTs

≈1

2

∑

k

s2kℜ

{

hlp(t) ∗ Φ̃mkk(nTs)e

+jωcτm

}

+

+1

2

∑

k

∑

l,l 6=k

skslℜ{

hlp(t) ∗ Φ̃mkl(nTs)e

+jωcτm

}

+

+ νs×n(nTs)+

+ νn×s(nTs)+

+ νn×n(nTs)




with the Autocorrelation Function

Φ̃mkl(t) = hint(t) ∗

[

Θ̃k(λ)Θ̃∗l (λ − τm)

]

=

∫ t

λ=t−Tint

Θ̃k(λ)Θ̃∗l (λ − τm)dλ

and Ideal Integration Filter

hint(t) = σ(t) − σ(t − Tint)

σ(t)... Heaviside function



Receiver Signal Processing – Integrate & Dump

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2

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0

0.1

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0.5

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0.8

0.9

1

frequency [Hz]

magnitude o

f co−

and c

ross−

term

s

Signal after Integration



Receiver Signal Processing – Integrate & Dump

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2

x 109

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

frequency [Hz]

magnitude o

f co−

and c

ross−

term

s

Signal after Integration



Receiver Signal Processing – MIMO

Typical Memoryless MIMO System

y[n] = Hs[n] + G (s[n] ⊗ s[n]) + ν[n]

G vanishes for orthogonal basis functions!

Basis Function Separation

Separation possible for H with rank K: use Linear Combiner W!

z[n] = Wy[n]

= WHs[n] + Wν[n]

Design Methods for W: ZF, MMSE, ...



Receiver Signal Processing – Performance

4 6 8 10 12 14 16 18 20 22 2410

−4

10−3

10−2

10−1

100

avera

ge b

it−

err

or−

rate

BE

R

average Eb/N

0 [dB]

MC UWB w/ MMSE

MC UWB w/ ZF

wideband UWB w/ ED

UWB subcarrier w/ ED



Outline

Introduction

Architecture


Conclusions



Conclusions – Finally!?

◮ A Noncoherent Multichannel Autocorrelation Receiver wasintroduced

◮ We took a close look on the Receiver Signal Processing

◮ Receiver Architecture shows a promissing performance



Conclusions – Finally!?

◮ A Noncoherent Multichannel Autocorrelation Receiver wasintroduced

◮ We took a close look on the Receiver Signal Processing

◮ Receiver Architecture shows a promissing performanceEspecially for Noncoherent OFDM!!Even for not perfectly orthogonal basis functions!!



References

K. Witrisal,

“Noncoherent Autocorrelation Detection of Orthogonal Multicarrier UWB signals“,IEEE International Conference on Ultra-Wideband 2008, Sept. 2008, vo. 2, pp. 161–164.

P. Meissner, and K. Witrisal,

“Analysis of a Noncoherent UWB Receiver for Multichannel Signals”,IEEE Vehicular Technology Conference, VTC2010-Spring, May 2010.

K. Witrisal, G. Leus, G. Janssen, M. Pausini, F. Troesch, T. Zasowski, and J. Romme,

“Noncoherent Ultra-Wideband Systems“,IEEE Signal Processing Magazine, vol. 26, no. 4, p. 48–66, July 2009.


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Introduction to a Multichannel Noncoherent Autocorrelation ... · TU Graz - Signal Processing and Speech Communication Laboratory Introduction to a Multichannel Noncoherent Autocorrelation