Construction of Optimum Wavelet Packets for Multi-Carrier Based Spectrum Pooling Systems

The growing popularity of wireless applications has placed enormous burden on valuable resources such as spectral bandwidth. This has brought about a major revamp of traditional resource allocation policies culminating in an explosion of research activity in the field of cognitive radio (CR) (Mitola, Cognitive radio: an integrated agent architecture for software defined radio, Doctoral dissertation, 2000; Haykin, J Sel Areas Commun 23:201–220, 2005). In this paper we demonstrate the operation of a Wavelet Packet based multi-carrier modulation (WP-MCM) scheme in the context of cognitive radio. The wavelet packet (WP) bases are derived from multistage tree-structured paraunitary filter banks. To enable the WP-MCM cognitive radio system to co-exist with other licensed users a common spectrum pool is maintained and the WP-MCM transmission waveform characteristics are shaped to communicate in the idle time-frequency gaps of the licensed user. This is achieved by dynamically deactivating wavelet packet carriers in and near the region of the licensed user spectrum. Various wavelets including the well-known families Daubechies, Coiflet, Symlet are applied and studied. The emphasis is on the design and development of optimal WP carriers that have narrow and well confined spectral footprints. To this end filter banks that are maximally frequency selective are derived through a modified Remez exchange algorithm. Through simulation results the ability of the proposed wavelet packet based mechanism in seamlessly cohabiting with licensed users is demonstrated. The Bit Error rate (BER) performance is shown to be comparable, and even at times better, to the conventional Fourier based OFDM system.