A Review of Wavelets Emerging Applications for Digital Wireless Communication
Abstract
The use of wavelets in digital wireless communication systems has benefited data compression, source and
channel coding, signal denoising, channel modeling, and transceiver design. During these applications, Wavelet's key
advantage its ability to precisely identify signals. This paper discusses recent trends and developments in the use of
wavelets in wireless communications. Among other applications, wavelets are employed to model wireless channels,
reduce interference, denoise, offer multiple access, transport ultra wideband data, transmit cognitive radio data, and
connect wireless networks. Structural performance and architectures that can handle enormous amounts of data have
become more challenging as a result of the merging of communication and information technology and the potential
for pervasive connectivity. The possibility of pervasive connectivity and the convergence of communication and
information technology have made it difficult to create technologies and systems that can handle massive amounts of
data while operating with severely constrained resources like electricity and bandwidth. Wavelets are the best solution
for this issue. Due to its scalability and versatility, wavelet technology has a bright future in wireless technology.
References
[2] Y. Tanaka and A. Sakiyama, “$M$ -Channel Oversampled Graph Filter Banks,” IEEE Trans. Signal Process., vol. 62, no. 14, pp. 3578–3590, Jul. 2014, doi: 10.1109/TSP.2014.2328983.
[3] A. Jamin and P. Mähönen, “Wavelet packet modulation for wireless communications,” Wirel. Commun. Mob. Comput., vol. 5, no. 2, pp. 123–137, Mar. 2005, doi: 10.1002/wcm.201.
[4] B. G. Negash and H. Nikookar, “Wavelet-based multicarrier transmission over multipath wireless channels,” Electron. Lett., vol. 36, no. 21, p. 1787, 2000, doi: 10.1049/el:20001263.
[5] M. A. Louis, “The Performance of Orthogonal Wavelet Division Multiplexing (OWDM) in Flat Rayleigh Fading Channel,” vol. 12, no. 1, 2008.
[6] M. Vetterli and J. Kovaˇcevic, “Wavelets and Subband Coding”.
[7] I. Daubechies, Ten Lectures on Wavelets. Society for Industrial and Applied Mathematics, 1992. doi: 10.1137/1.9781611970104.
[8] J.-P. Cornil, “‘Building an ADSL Modem, the Basics,’” in Analog Circuit Design, W. Sansen, J. Huijsing, and R. van de Plassche, Eds. Boston, MA: Springer US, 1999, pp. 3–47. doi: 10.1007/978-1-4757-3047-0_1.
[9] P. P. Vaidyanathan, Multirate systems and filter banks. Englewood Cliffs, N.J: Prentice Hall, 1993.
[10] S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 11, no. 7, pp. 674–693, Jul. 1989, doi: 10.1109/34.192463.
[11] I. Cohen, S. Raz, and D. Malah, “Orthonormal shift-invariant wavelet packet decomposition and representation,” Signal Process., vol. 57, no. 3, pp. 251–270, Mar. 1997, doi: 10.1016/S0165-1684(97)00007-8.
[12] M. Unser, “Fast Gabor-like windowed Fourier and continuous wavelet transforms,” IEEE Signal Process. Lett., vol. 1, no. 5, pp. 76–79, May 1994, doi: 10.1109/97.294384.
[13] A. Cohen and J. Kovacevic, “Wavelets: the mathematical background,” Proc. IEEE, vol. 84, no. 4, pp. 514–522, Apr. 1996, doi: 10.1109/5.488697.
[14] M. K. Lakshmanan, D. Karamehmedović, and H. Nikookar, “An Investigation on the Sensitivity of Wavelet Packet Modulation to Time Synchronization Error,” Wirel. Pers. Commun., vol. 58, no. 3, pp. 483–502, Jun. 2011, doi: 10.1007/s11277-010-0132-3.
[15] G. Groenewold, “Optimal dynamic range integrators,” IEEE Trans. Circuits Syst. Fundam. Theory Appl., vol. 39, no. 8, pp. 614–627, Aug. 1992, doi: 10.1109/81.168928.
[16] T. Q. Nguyen and P. P. Vaidyanathan, “Maximally decimated perfect-reconstruction FIR filter banks with pairwise mirror-image analysis (and synthesis) frequency responses,” IEEE Trans. Acoust. Speech Signal Process., vol. 36, no. 5, pp. 693–706, May 1988, doi: 10.1109/29.1579.
[17] S. Achard, M. Clausel, I. Gannaz, and F. Roueff, “New results on approximate Hilbert pairs of wavelet filters with common factors,” Appl. Comput. Harmon. Anal., vol. 49, no. 3, pp. 1025–1045, Nov. 2020, doi: 10.1016/j.acha.2019.06.001.
[18] J. M. H. Karel, R. L. M. Peeters, R. L. Westra, S. A. P. Haddad, and W. A. Serdijn, “WAVELET APPROXIMATION FOR IMPLEMENTATION IN DYNAMIC TRANSLINEAR CIRCUITS,” IFAC Proc. Vol., vol. 38, no. 1, pp. 1101–1106, 2005, doi: 10.3182/20050703-6-CZ-1902.00185.
[19] L. Thiele, “On the sensitivity of linear state-space systems,” IEEE Trans. Circuits Syst., vol. 33, no. 5, pp. 502–510, May 1986, doi: 10.1109/TCS.1986.1085951.
[20] T. Mai and Y. Tsividis, “Internally Non-LTI Systems Based on Delays, With Application to Companding Signal Processors,” IEEE Trans. Circuits Syst. II Express Briefs, vol. 59, no. 8, pp. 476–480, Aug. 2012, doi: 10.1109/TCSII.2012.2204113.