**Author details**

H. Lu and H. Nikookar

*International Research Centre for Telecommunications and Radar (IRCTR), Dept. EEMCS, Delft University of Technology, Delft, The Netherlands* 

T. Xu

122 Ultra Wideband – Current Status and Future Trends

relay.

**7. Conclusions** 

10-6

10-5

10-4

10-3

Bit Error Rate

10-2

10-1

test and combine with a relay with one scale-lag diversity, power gain 3 *h* = 4 , which improves the BER performance, and satisfies the *<sup>e</sup> P* requirement. Therefore, we adopt this

Relay selection for cooperative wavelet communications

h1=4,h2=1,2-DF theory (original state) h1=4,h2=1,h3=0.04,3-DF theory (test case 1) h1=4,h2=1,h3=4,3-DF theory (test case 2)

**Figure 10.** Relay selection for cooperative 2-decomposition level wavelet wideband communication

0 5 10 15 20 25

Eb/No, dB

Wideband scale-lag channels can be found in many applications, including ultra-wideband communications and underwater acoustic communications. Signaling and reception schemes using the wavelet theory enable the multi-scale and multi-lag diversity in the wideband system. In this chapter, we designed a cooperative wavelet system to capture the joint cooperative-scale-lag diversity. We proposed the analytical BER expression for the cooperative wavelet wideband communication. The agreement between the analytical *Circuits and Systems Group (CAS), Dept. EEMCS, Delft University of Technology, Delft, The Netherlands* 

#### **8. References**

	- [9] Rickard S., Balan R., Poor V. & Verdu S., Canonical time-frequency, time-scale, and frequency-scale representations of time-varying channels. *J. Comm. Infor. Syst.*, vol. 5, no. 5, 2005, pp. 1–30.

[23] Blahut R. E., Miller W. Jr. & Wilcox C. H., Eds., *Radar and Sonar, Part I, IMA Volumes in* 

[24] Weiss L. G., Wavelets and wideband correlation processing, *IEEE Signal Process. Mag.*,

[26] Tsatsanis M. K. & Giannakis G. B., Time-varying system identification and model validation using wavelets, *IIEEE Trans. Signal Process.*, vol. 41, no. 12, Dec. 1993, pp.

[27] Iverson D. E., Coherent processing of ultra-wide-band radar signals, *Proc. Inst. Elect.* 

[28] Sharif B. S., Neasham J., Hinton O. R. & Adams A. E., A computationally efficient Doppler compensation system for underwater acoustic communications, *IEEE J. Oceanic* 

[29] Wornell G.W., Emerging applications of multirate signal processing and wavelets in

[30] Leus G. & van Walree P., Multiband OFDM for covert acoustic communications, *IEEE J.* 

[31] Li B., Zhou S., Stojanovic M., Freitag L. & Willett P., Multicarrier communication over underwater acoustic channels with nonuniform doppler shifts, *IEEE J. Oceanic. Eng.*,

[32] Martone M., Wavelet-based separating kernels for array processing of cellular ds/cdma

[33] Mitra U. & Leus G., Equalizers for multi-scale / multi-lag wireless channels, *Proc. of* 

[34] Yu L. & White L. B., Optimum receiver design for broadband Doppler compensation in multipath/doppler channels with rational orthogonal wavelet signaling, *IEEE T. Signal.* 

[35] Linfoot S. L., Ibrahim M. K. & Al-Akaidi M. M., Orthogonal wavelet division multiplex: An alternative to ofdm, *IEEE T Consum. Electr.*, vol. 53, no. 2, 2007, pp.

[36] Lu H., Nikookar H. & Lian X., Performance evaluation of hybrid DF-AF OFDM cooperation in Rayleigh Channel, *Proc. of European Wireless Technology Conference*, Sep.

[37] Cover T. M. & El Gamal, A. A. Capacity theorems for the relay channel, *IEEE Trans.* 

[38] Farhadi G. & Beaulieu N. C., On the Ergodic Capacity of Wireless Relaying System over Rayleigh Fading Channels, *IEEE Trans. Wireless Communications*, vol. 7, no. 11, Nov.

[39] Lin S. & Constello D. J., *Error Control Coding: Fundamentals and Applications*. Englewood

*Mathematics and its Applications*. New York: Springer-Verlag, 1991.

*Eng. Radar, Sonar, Navigation*, vol. 141, Jun. 1994, pp. 171–179.

digital communications, *Proc. of IEEE*, vol. 84, Apr. 1996, pp. 586–603.

signals in fast fading, *IEEE T. Commun.*, vol. 48, no. 6, 2000, pp. 979–995.

[25] Young R. K., *Wavelet Theory and Its Applications*. Norwell, MA: Kluwer, 1993.

vol. 11, no. 1, Jan. 1994, pp. 13–32.

*Eng.*, vol. 25, no. 1, Jan. 2000, pp. 52–61.

vol. 33, no. 2, 2008, pp. 198–209.

*Sel. Area. Comm.*, vol. 26, no. 9, 2008, pp. 1662–1673.

*IEEE Global Telecommunications Conference, 2010.* pp. 1–5.

*Inform. Theory*, vol. 25, no. 5, Sep. 1979, pp. 572-584.

*Proces.*, vol. 55, no. 8, 2007, pp. 4091–4103.

3512–3523.

278–284.

2010, Paris, France.

2008, pp. 4462-4467.

Cliffs, NJ: Prentice–Hall, 1983.


Grove, California, USA, Nov. 2010.

*Analysis*, Pittsburgh, PA, Oct. 1998, pp. 373–376

*AdvancesWireless Communications*, Mar. 2001, pp. 50–53.

*IEEE Global Telecommunications Conference, 2010.* pp. 1–5.

*Processing*, vol. 1, Germany, Apr. 1997, pp. 575–578

*Eng.*, vol. 25, no. 1, Jan. 2000, pp. 52–61.

*Vehicular Communications*, September 2007.

*Conference, 2004.* pp. 3813–3817.

Princeton, NJ, Nov. 2003

no. 5, 2005, pp. 1–30.

1375.

3559.

2567.

pp. 4308–4319.

[9] Rickard S., Balan R., Poor V. & Verdu S., Canonical time-frequency, time-scale, and frequency-scale representations of time-varying channels. *J. Comm. Infor. Syst.*, vol. 5,

[10] Jiang Y. & Papandreou-Suppappola A., Discrete time-scale characterization of wideband time-varying systems. *IEEE T. Signal. Proces.*, vol. 54, no. 4, 2006, pp. 1364–

[11] Margetts A. R., Schniter P., and Swami A., Joint scale-lag diversity in wideband mobile direct sequence spread spectrum systems. *IEEE T. Wirel. Commun.*, vol. 6, no. 12, 2007,

[12] Xu T., Leus G. & Mitra U., Othogonal wavelet division multiplexing for wideband timevarying channels. *Proc. of IEEE ICASSP*, Prague (Czech Republic), May 2011, pp. 3556-

[13] Leus G., Xu T. & Mitra U., Block Transmission over Multi-Scale Multi-Lag Wireless Channels. *Proc. of the Asilomar Conference on Signals, Systems, and Computers*, Pacific

[14] Rickard S., Time-frequency and time-scale representations of doubly spread channels, *Ph.D. dissertation*, Applied and Computational Mathematics Dept., Princeton Univ.,

[15] Bircan A., Tekinay S. & Akansu A., Time-frequency and time-scale representation of wireless communication channels, *Proc. of IEEE Int. Symp. Time-Frequency/Time-Scale* 

[16] Capoglu I. R., Li Y. & Swami A., Effect of doppler spread in OFDM based UWB systems, *IEEE Transactions on Wireless Communictations*, vol. 4, no. 5, Sep. 2005, pp. 2559–

[17] Zhang H., Fan H. H. & Lindsey A., A wavelet packet based model for time-varying wireless communication channels, *Proc. of IEEE Workshop Signal Processing* 

[18] Johnson M., Freitag L. & Stojanovic M., Improved Doppler tracking and correction for underwater acoustic communications, *Proc. of IEEE Int. Conf. Acoustic, Speech, Signal* 

[19] Sharif B. S., Neasham J., Hinton O. R. & Adams A. E., A computationally efficient Doppler compensation system for underwater acoustic communications, *IEEE J. Oceanic* 

[20] Mitra U. & Leus G., Equalizers for multi-scale / multi-lag wireless channels, *Proc. of* 

[21] Acosta G., Tokuda K. & Ingram M. A., Measured joint Doppler-delay power profiles for vehicle-to-vehicle communications at 2.4 GHz, *Proc. of IEEE Global Telecommunications* 

[22] Acosta G. & Ingram M. A., Six time- and frequency-selective empirical channel models for vehicular wireless LANs, *Proc. of 1st IEEE International Symposium on Wireless* 

	- [40] Lu H., Xu T., Lakshmanan M. and Nikookar H., Cooperative wavelet communication for multi-relay, multi-scale and multi-lag wireless channels, *Proc. of IEEE Vehicular Technology Conference (VTC)*, Budapest, Hungary, May, 2011, pp. 1-5.

**Chapter 7** 

© 2012 Liang, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

*f* (1)

*f* (2)

distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 Liang, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Ultra-Wideband Antenna and Design** 

Ultra-wideband (UWB) antennas are gaining prominence and becoming very attractive in modern and future wireless communication systems, mainly due to two factors. Firstly, people increasingly high demand for the wireless transmission rate and UWB properties such as high data rate, low power consumption and low cost, which give a huge boost to the UWB antennas' research and development in industry and academia since the Federal Communications Commission (FCC) officially released the regulation for UWB technology in 2002. Secondly, now the wireless portable device need antenna operated in different frequencies for various wireless transmission functions, and operation bands and functions are increasing more and more, which may result in challenges in antenna design, such as antenna space limitation, multi antennas interference, and etc. One UWB antenna can be used to replace multi narrow-band antennas, which may effectively reduce the antenna

The bandwidth is the antenna operating frequency band within which the antenna performances, such as input impedance, radiation pattern, gain, efficiency, and etc., are desired. The most commonly used definitions for the antenna bandwidth are the fractional bandwidth (for narrow or wideband definition) and the bandwidth ratio (for ultra-

> <sup>−</sup> = × *h l* 100% *c*

> > *l*

*<sup>f</sup> BW*

*f f BW*

Additional information is available at the end of the chapter

Xian Ling Liang

**1. Introduction** 

number.

wideband definition).

The fractional bandwidth is defined as

The bandwidth ratio is defined as

= : 1 *<sup>h</sup>*

http://dx.doi.org/10.5772/47805
