IIR Ultra-Wideband Pulse Shaper Design

1. IIR Ultra-Wideband Pulse Shaper Design Chun-yang Chen and P.P. Vaidyananthan California Institute of Technology DSP Group, EE, Caltech, Pasadena CA

2. 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. DSP Group, EE, Caltech, Pasadena CA

3. 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 DSP Group, EE, Caltech, Pasadena CA

4. 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 DSP Group, EE, Caltech, Pasadena CA

5. Example of Gaussian monocycle pulse (2) • The power spectrum for using Gaussian monocycle pulse The transmitting power is very small. DSP Group, EE, Caltech, Pasadena CA

6. 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 DSP Group, EE, Caltech, Pasadena CA

7. Mask filling efficiency • The mask filling efficiency [Lewis et al. 2004] is defined as • The ideal solution yields 100% of efficiency. DSP Group, EE, Caltech, Pasadena CA

8. 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. DSP Group, EE, Caltech, Pasadena CA

9. The scheme of FIR pulse shaper • D denotes the analog delay. DSP Group, EE, Caltech, Pasadena CA

10. Power spectrum of the radiated signal • The Fourier transform of the pulse is • The power spectrum of the radiated signal is DSP Group, EE, Caltech, Pasadena CA

11. 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]. DSP Group, EE, Caltech, Pasadena CA

12. Results of using the pulse shaper Gaussian monocycle pulse shaped by the minimax FIR filter • The multipliers of the shaper is 17. Gaussian monocycle pulse DSP Group, EE, Caltech, Pasadena CA

13. 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 DSP Group, EE, Caltech, Pasadena CA

14. The scheme of IIR pulse shaper • D denotes the analog delay. DSP Group, EE, Caltech, Pasadena CA

15. Power spectrum of the radiated signal • The Fourier transform of the pulse is • The power spectrum of the radiated signal is DSP Group, EE, Caltech, Pasadena CA

16. 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. DSP Group, EE, Caltech, Pasadena CA

17. 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. DSP Group, EE, Caltech, Pasadena CA

18. Comparison Elliptic shaper and minimax FIR shaper EllipticIIR 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. DSP Group, EE, Caltech, Pasadena CA

19. 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 . DSP Group, EE, Caltech, Pasadena CA

20. 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. DSP Group, EE, Caltech, Pasadena CA

21. 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. DSP Group, EE, Caltech, Pasadena CA

22. 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. DSP Group, EE, Caltech, Pasadena CA

23. 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. DSP Group, EE, Caltech, Pasadena CA

24. Thank you. DSP Group, EE, Caltech, Pasadena CA