2. Contents 1. Introduction 2. UWB Signal processing 3. Compressed Sensing Theory 3.1 Sparse representation of signals 3.2 AIC (analog to information converter) 3.3 Waveform Matched dictionary for UWB signal 4. Eco detection sysytem 5. Experimental results 6. References

3. Introduction ultra-wide-band (UWB) signal processing is the requirement for very high sampling rate. This is major challenge. The recently emerging compressed sensing (CS) theory makes processing UWB signal at a low sampling rate possible if the signal has a sparse representation in a certain space. Based on the CS theory, a system for sampling UWB echo signal at a rate much lower than Nyquist rate and performing signal detection is proposed in this paper.

4. 2. UWB Signal processing ULTRA-WIDE-BAND (UWB) signal processing system is characterized by its very high bandwidth that is up to several gigahertzes. To digitize a UWB signal, a very high sampling rate is required according to Shannon- Nyquist sampling theorem, but it is difficult to implement with a single analog-to- digital converter(ADC) chip. To address this problem, some parallel ADCs are developed. Based on hybrid filter banks (HFBs), the use of a parallel ADCs system to sample and reconstruct UWB signal.

5. UWB Signal processing But this parallel ADCs system faces the following difficulty. The digital filters for signal synthesis require the exact transfer functions of the analog filters for signal analysis. This may not be possible in practice because of various uncertainties in the system.so an advance CS theory introduced.

6. 3. Compressed Sensing Theory Traditional sampling theorem requires a band-limited signal to be sampled at the Nyquist rate. CS theory suggested that, if a signal has a sparse representation in a certain space, one can sample the signal at a rate significantly lower than Nyquist rate and reconstruct it with overwhelming probability by optimization techniques. There are three key elements that are needed to be addressed in the use of CS theory. 1) How to find a space in which signals have sparse representation? 2) How to obtain random measurements as samples of sparse signal? 3) How to reconstruct the original signal from the samples by optimization techniques.

7. Sparse representation of signals Sparse representations are representations that account for most or all information of a signal with a linear combination of a small number of elementary signals called atoms. Often, the atoms are chosen from a so called over-complete dictionary. Formally, an over- complete dictionary is a collection of atoms such that the number of atoms exceeds the dimension of the signal space, so that any signal can be represented by more than one combination of different atoms. Sparseness is one of the reasons for the extensive use of popular transforms such as the Discrete Fourier Transform, the wavelet transform and the Singular Value Decomposition.

8. AIC (analog to information converter)

9. AIC offers a feasible technique to implement low-rate “information” sampling. It consists of three main components: a wideband pseudorandom modulator, a filter and a low-rate ADC. The goal of pseudorandom sequence is to spread the frequency of signal and provide randomness necessary for successful signal recovery.

10. 3.3 Waveform Matched dictionary for UWB signal To obtain a sparse representation of signal in a certain space, many rules were proposed to match the signal in question and the basis functions of the space. the use of waveform-matched rules to design a dictionary forUWBsignal. The receiver is aware of the exact model of transmitted signal. To achieve very sparse representation of echo signals, the a priori knowledge of transmitted signal and the echo signal model should be taken into account in the design of basis or dictionary. Without regard to other interferences, such as Doppler shift, an echo signal without noise can be simply modeled as the sum of various scaled, time-shifted versions of the transmitted signal. Based on above considerations, we can construct a matched dictionary for echo signal

11. 4. Eco detection sysytem  There are four main components in this system: the AIC for random sampling; the waveform-matched dictionary for sparse signal representation; the optimizator for signal reconstruction; the detector for echo detection. For signal recovery in this paper, linear programming and quadratic programming optimization techniques are used in the optimizator for clean signal and noisy signal, respectively For noise-free signal, target echoes can be detected directly according to the reconstructed coefficients with respect to the matched dictionary. But for noisy signal, more reconstructed coefficients are nonzero because of the influence of noise, which necessitates a threshold scheme for eco d.

12. 5. Experimental results

13. References [1] S. R. Velazquez, T. Q. Nguyen, and S. R. Broadstone, “Design of hybrid filter banks for analog/digital conversion,” IEEE Trans. Signal Process., vol. 46, no. 4, pp. 956–967, Apr. 1998. [2] L. Feng and W. Namgoong, “An adaptive maximally decimated channelized uwb receiver with cyclic prefix,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 10, pp. 2165–2172, Oct. 2005. [3] P. Lowenborg, H. Johansson, and L. Wanhammar, “Two-channel digital and hybrid analog digital multirate filter banks with very low-complexity analysis or synthesis filters,” IEEE Trans. Circuits Syst. II, Analog Digital Signal Process., vol. 50, no. 7, pp. 355–367, Jul. 2003. [4] M. Vetterli, P. Marziliano, and T. Blu, “Sampling signals with finite rate of innovation,” IEEE Trans. Signal Process., vol. 50, no. 6, pp. 1417–1428, Jun. 2002. [5] E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489–509, Feb. 2006. [6] D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289–1306, Apr. 2006.

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