The Design And Application Of Multi-kernel Sparse Dictionaries For Ultra-wideband Signals

As an important theoretical basis for the sampling theorem, Nyquist’s theorem points out that if we want to obtain the accurate reconstruction of original signal, the sampling rate must be at least twice the highest frequency of the signal. With the development of information tecnology, Ultra-Wideband (UWB) has been applied in many fields because of its higher ability of resistance to multipath fading, lower interception rate, lower power consumption, and higher safety performance. However, due to the extreme wide bandwidth of UWB signals, the receiver needs very high rate analog-to-digital converter (ADC) to sample the signals. What’s more, the multipath channel environment is complicated. Evidently, the sampling method based on the Nyquist’s theorem is difficult to be realized. Therefore, the problem faced by UWB signal sampling blocks the development of UWB systems.The emerging Compressive Sensing (CS) theory proposed by Donoho and Cands uses a method different from the traditional one to perform sampling. It provides a new way for the sampling of the UWB signals. The sampling rate of CS is lower than that of the Nyquist’s theorem. Under the framework of the CS theory, the sampling rate is no longer limited by the bandwidth of the target signal. The main work of this research is to study construction of sparse dictionaries for UWB applications. We put forward a construction method of multi-kemel sparse dictionaries and investigate its application in UWB channel estimation.The main contributions of this thesis include the following aspects:1. A construction method of multi-kernel sparse dictionaries is proposed. The multi-kernel sparse dictionaries are based on the multipath diversity based dictionary (MDD). Auxiliary dictionaries are constructed by using the derivatives of the transmitted UWB pulse waveform. Then, the constructed auxiliary dictionaries are combined with the MDD so as to gain multi-kernel sparse dictionaries. The simulation results show that the multi-kernel sparse dictionaries outperform the MDD dictionary. It affirms that our idea is feasible. Among the multi-kernel sparse dictionaries, the ones only containing the first derivative perform better than others. It means that the dual-kernel dictionaries are good choices in practice.2. For the dual-kernel dictionaries, we put forward two construction methods. The first scheme picks up the odd terms of the MDD and their corresponding terms of the auxiliary dictionary, and the resultant dictionary is called cross-derivative dictionary (CDD). The second scheme picks up the the first half-part terms of MDD and their corresponding terms of the auxiliary dictionary, and the resultant dictionary is named accessorial-derivative dictionary (ADD). We find by simulations that the correlation coefficients achieved by the constructed dual-kernel dictionaries are greater than that achieved by MDD. Moreover, ADD performes better than CDD. It is due to the fact that ADD matches the characteristics of UWB signals better. It is beneficial to improve the signal sparsity, reduce the sampling rate and decrease the reconstruction error.3. The ADD is employed to implement the CS-based channel estimation for UWB systems, where a pilot signal assisted scheme is adopted. Simulation results on the BER performance in CM1 and CM3 channels show that, compared with the traditional MDD, ADD can be used to gain better channel estimation and thus better BER performance.