Design and performance of a flexible wavelet based multicarrier modulation for wireless communications

Abstract

In the last decade, progress in digital signal processing has led to major changes in the wireless communication world. In particular, the transition from single carrier to multicarrier has resulted in a significant improvement in performance. To this day, however, virtually no commercial application uses a multicarrier modulation based on anything else than Orthogonal Frequency Division Multiplex (OFDM). This thesis analyses the design and performance of the Wavelet Packet Modulation (WPM), an alternative multicarrier modulation based on the wavelet packet transform. While swapping sine waves for wavelets as subcarrier waveforms is conceptually a simple change, it does allow the new modulation scheme to benefit from the properties of the versatile transform that the WPT is. This study begins with the mathematical basis of the WPT, the core element of a WPM transceiver. Its design and implementation architecture are derived and compared. In particular, we show that the WPT has more degrees of freedom than the DFT, and we explain how this extra freedom can be exploited in a wireless communication system. The performance of this new scheme over various wireless channels are reported and the differences with OFDM are highlighted whenever relevant. The issue of equalisation for WPM signal is extensively discussed and quantitative comparison with the extremely efficient cyclic based OFDM equalisation method is made. As it is equally important for the successful deployment of commercial systems, characterisation of WPM performance under common system distortion such as sampling frequency offset and power amplifier non-linearity has almost been made. A synchronisation method capable of tolerating large sampling frequency offset is also proposed. Overall, the performance of WPM in wireless propagation channel is shown to be comparable to the OFDM scheme. Equalisation of the latter is however easier thanks to the use of a cyclic prefix. As the implementation complexity of both schemes is of the same order, the advantage of WPM resides undeniably in its degree of freedom. The possibility of choosing both a particular wavelet and an arbitrary decomposition in the time-frequency domain gives the opportunity to optimise the modulated signal according to the application at hand. Nevertheless, further work remains to be carried out on equalisation in order for WPM to have a role in next generation communication systems