DSP Group, EE, Caltech, Pasadena CA IIR Ultra-Wideband Pulse Shaper Design Chun-yang Chen and P.P....

DSP Group, EE, Caltech, Pasadena CA

IIR Ultra-Wideband Pulse Shaper Design

Chun-yang Chen and P.P. Vaidyananthan

California Institute of Technology


The UWB communications

In 2002, the Federal Communication Community (FCC) approved a spectral mask for operation of UWB devices.

It allows UWB devices operate on 3.1GHz ~ 10.6GHz under -41.3dBm.


Impulse radio system for UWB

Impulse radio system transmits very short pulses p(t) without RF carriers.

The radiated power spectrum of impulse radio system can be expressed by

22)()()()( fPfSfHfS meq )( fM

Fourier transform of

the pulse

Depends on the modulation method

Transfer function from modulated

pulse train to radiated signal


Example of Gaussian monocycle pulse

For example, if we use the Gaussian monocycle pulse (derivative of a Gaussian pulse), then

Assume

2)(2

2)( g

t

g

et

etp

1)()( fSfH meq

Then the radiated power spectrum is2222

)2

exp()( gfffS


Example of Gaussian monocycle pulse (2)

The power spectrum for using Gaussian monocycle pulse

0 2 4 6 8 10 12-100

-90

-80

-70

-60

-50

-40

Pow

er(d

Bm

)

Frequency(GHz)

Maskg=10ns

g=50ns

g=100ns

The transmitting power is very

small.

2222

)2

exp()( gfffS


The optimization problem

To utilize the bandwidth, the optimal pulse should be designed so that the transmitting power is maximized.

)()()()( subject to

)()()(max

22

22

)(

max

min

fMfPfSfH

dffPfSfH

meq

F

F

meqtp

)()()()( 22

fMfPfSfH meq

The ideal solution to this problem is the pulse such that


Mask filling efficiency

The mask filling efficiency [Lewis et al. 2004] is defined as

max

min

max

min

)(

)()()(22

F

F

F

F meq

dffM

dffPfSfH

)()()()( 22

fMfPfSfH meq

The ideal solution

yields 100% of efficiency.


Pulse shaper

However, we cannot generate pulse with arbitrary with analog circuits.)( fP

We can generate the pulse by shaping the available waveforms by

M

nn nTtgbtp

0

)()(

This waveform can be directly generated by

analog circuit.


The scheme of FIR pulse shaper

D denotes the analog delay.

M

nn nTtgbtp

0

)()(


Power spectrum of the radiated signal

The Fourier transform of the pulse is

.)()(0

2

M

n

fT

ni

n fGebfP

M

nn nTtgbtp

0

)()(

).()()()(22

2

0

2

fSfHfGebfS meq

M

n

fT

ni

n

The power spectrum of the radiated signal is


Design of the pulse shaper To approximate the ideal solution, we choose

the shaper so that

).()()()()(22

2

0

2

fMfSfHfGebfS meq

M

n

fT

ni

n

}{ nb

It reduces to an FIR filter design problem. Standard technique such as the Parks-McClella

n algorithm can be used to design such a filter [Luo et all. 2003].


Results of using the pulse shaper

0 2 4 6 8 10 12-80

-75

-70

-65

-60

-55

-50

-45

-40

Frequency (GHz)

Pow

er (

dBm

)

The multipliers of the shaper is 17.

Gaussian monocycle

pulse

Gaussian monocycle pulse shaped by the minimax FIR filt

er

M

nn nTtgbtp

0

)()(


IIR pulse shaper

With the same complexity, IIR filters has better frequency response than FIR filters.

We can generate the pulse by summing the delay version of the elementary waveforms and the feedback

N

nn

M

nn nTtpanTtgbtp

10

)()()(


The scheme of IIR pulse shaper

D denotes the analog delay.

N

nn

M

nn nTtpanTtgbtp

10

)()()(


Power spectrum of the radiated signal

The Fourier transform of the pulse is

).()(

0

20

2

fG

ea

ebfP

M

n

fT

ni

n

M

n

fT

ni

n

N

nn

M

nn nTtpanTtgbtp

10

)()()(

).()()()(22

2

0

20

2

fSfHfG

ea

ebfS meqN

n

fT

ni

n

M

n

fT

ni

n

The power spectrum of the radiated signal is


Design of the IIR pulse shaper To approximate the ideal solution, we choose the

shaper and so that

).()()()()(22

2

0

20

2

fMfSfHfG

ea

ebfS meqN

n

fT

ni

n

M

n

fT

ni

n

Mnnb 0}{

It reduces to an IIR filter design problem.

Nnna 1}{

However, there is no standard technique to design IIR filter to fit arbitrary magnitude response.


Design of IIR pulse shaper using Elliptic filters

There are standard techniques to design IIR filters to fit bandpass magnitude responses such as elliptic IIR filters.

0 2 4 6 8 10 12-80

-75

-70

-65

-60

-55

-50

-45

-40

Frequency (GHz)

Pow

er (

dBm

)

Gaussian monocycle pulse shaped by a minimax FIR

filter.Filling efficiency: 74.96%

Gaussian monocycle pulse shaped by an elliptic

IIR filter. Filling efficiency: 68.29%

Both filters have 17 multipliers.


Comparison Elliptic shaper and minimax FIR shaper

0 2 4 6 8 10 12-55

-50

-45

-40

Frequency (GHz)

Pow

er (

dBm

)Elliptic IIR shaper has sharp transition band but cannot compensate the nonflatness of the transfer functions.

Minimax FIR shaper has the flexibility to compensate the nonflatness. But the transitio

n band is wide.

We can combine these two ideas to get both of their benefits.


IIR shaper design We divided the problem into two parts.

The first part is designing the Elliptic IIR filter H1

to fit the transition band of the mask .)( fM

The second part is designing the minimax FIR filter H2 to fix the nonflatness of the transfer functions . )()()(

2fSfHfG meq

).()()()()()()(22

22

2

22

1 fMfSfHfGeHeHfS meq

fT

nif

T

ni


0 2 4 6 8 10 12-60

-55

-50

-45

-40

Frequency (GHz)

Pow

er (

dBm

)

Results

Minimax FIR shaper: efficiency = 74.

96%

Elliptic IIR shaper: efficiency =

68.29%

Combination method: efficiency

= 78.92%

All shapers have 17 multipliers.

Combination method uses

7 multipliers on minimax FIR shaper and

10 multipliers on Elliptic IIR shaper.


Transient response

The impulse response of the FIR shapers has a duration of 2.4ns.

The proposed method has only 1.5% of energy outside this duration.

The transient response is small.

0 2 4 6 8 10-0.1

-0.05

0

0.05

0.1

0.15FIR

imp.

res

p.

0 2 4 6 8 10-0.2

-0.1

0

0.1

0.2New method

imp.

res

p.

time(ns)

1.5% of the energy


Conclusions

The pulse design is to generate a pulse such that radiated power can be maximized.

The IIR based pulse shaper is introduced. An elliptic IIR filter and a minimax FIR filter ar

e combined to fit the mask and the transfer functions.

The transient response of the proposed IIR filter is small enough to be neglected.


References

Terry P. Lewis, Robert A. Scholtz, “An ultrawideband signal design with power spectral density constraints,” Proc. 38th IEEE Asilomar Conf. on Signals, Systems, and Computers, pp. 1521-25, Nov. 2004.

X. Luo., L. Yang, and G.B. Giannakis, “Designing optimal pulse-shapers for ultra-wideband radios, ” Proc. of IEEE Conf. on Ultra Wideband Systems and Technologies, pp. 349-353, Nov. 2003.

B. Parr, B. Cho, K. Wallace, and Z. Ding, “A Novel Ultra-Wideband Pulse Design Algorithm,” IEEE Comm. Letters, pp. 219-221, 2003.


Thank you.

DSP Group, EE, Caltech, Pasadena CA IIR Ultra-Wideband Pulse Shaper Design Chun-yang Chen and P.P....

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Transcript of DSP Group, EE, Caltech, Pasadena CA IIR Ultra-Wideband Pulse Shaper Design Chun-yang Chen and P.P....