IIR UltraWideband Pulse Shaper Design

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IIR Ultra-Wideband Pulse Shaper Design

• Chun-yang Chen and P.P. Vaidyananthan
• California Institute of Technology

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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.

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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

Transfer function from modulated pulse train to
radiated signal
Fourier transform of the pulse
Depends on the modulation method
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Example of Gaussian monocycle pulse

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

Then the radiated power spectrum is
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Example of Gaussian monocycle pulse (2)

• The power spectrum for using Gaussian monocycle
  pulse

The transmitting power is very small.
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The optimization problem

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

• The ideal solution to this problem is the pulse
  such that

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Mask filling efficiency

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

• The ideal solution
• yields 100 of efficiency.

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Pulse shaper

• However, we cannot generate pulse with arbitrary
  with analog circuits.

• We can generate the pulse by shaping the
  available waveforms by

This waveform can be directly generated by analog
circuit.
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The scheme of FIR pulse shaper

• D denotes the analog delay.

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Power spectrum of the radiated signal

• The Fourier transform of the pulse is

• The power spectrum of the radiated signal is

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Design of the pulse shaper

• To approximate the ideal solution, we choose the
  shaper so that

• It reduces to an FIR filter design problem.

• Standard technique such as the Parks-McClellan
  algorithm can be used to design such a filter
  Luo et all. 2003.

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Results of using the pulse shaper
Gaussian monocycle pulse shaped by the minimax
FIR filter
Gaussian monocycle pulse

• The multipliers of the shaper is 17.

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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

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The scheme of IIR pulse shaper

• D denotes the analog delay.

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Power spectrum of the radiated signal

• The Fourier transform of the pulse is

• The power spectrum of the radiated signal is

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Design of the IIR pulse shaper

• To approximate the ideal solution, we choose the
  shaper and so that

• It reduces to an IIR filter design problem.

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

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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.

Gaussian monocycle pulse shaped by an elliptic
IIR filter. Filling efficiency 68.29
Gaussian monocycle pulse shaped by a minimax FIR
filter. Filling efficiency 74.96

• Both filters have 17 multipliers.

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Comparison Elliptic shaper and minimax FIR shaper
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 transition
band is wide.

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

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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
  .

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

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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.

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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.

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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
  are combined to fit the mask and the transfer
  functions.
• The transient response of the proposed IIR filter
  is small enough to be neglected.

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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.

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Thank you.