Efthymoglou, George P.

This thesis presents a comprehensive analysis of a relatively new transform for discrete time signals, called the Discrete Wavelet Transform (DWT). We find how this transform is connected with the already existing theory of perfect reconstruction filter banks and the recently introduced theory of multiresolution analysis. We use the conditions obtained from these two theories in order to understand the construction of wavelet filters, which also generate continuous functions that prove to constitute an orthonormal basis for the L$\sp2$ space. We also investigate the connection of this transform to the sampled wavelet series of nonorthogonal functions with good time-frequency localization properties. Finally, we see the way that the DWT maps a discrete signal in the phase plane and the applications that such representations incorporate.

In this dissertation, new semi-analytical expressions for the diversity bit error rate performance of asynchronous direct sequence-code division multiple access (DS-CDMA) systems in multipath fading channels are derived. Also, the PN acquisition time of a DS system with offset frequency periods greater than the code period in a AWGN channel is measured via laboratory experiments. In Part I we consider DS-CDMA systems operating in a cellular environment with multipath reception. Multipath propagation is exploited through the use of RAKE receivers. Coherent, differentially coherent and noncoherent binary demodulation schemes are considered. The multiple access interference is modeled as AWGN, conditioned on the fading statistics of the received signal. The mobile radio channel introduces selective fading, and is modeled as a tapped delay line. The amplitude of each resolvable path is statistically described by the Nakagami distribution, which is a general solution to the random vector problem that causes rapid fading. However, we assume independent but nonidentical fading along the RAKE branches. Therefore our analysis supports unequal mean powers and different amount of fading in the multipath components combined by the receiver. Also, the results can be easily extended to account for diversity from multiple antennas or coding in the generalized Nakagami multipath fading environment. In Part II we consider a land mobile satellite channel. First, a laboratory experiment is setup to evaluate the PN acquisition performance of a digital IF receiver in a AWGN channel with large Doppler offset. The digital conversion receiver uses the inherent aliasing property of sampling to realize the baseband conversion using a single analog-to-digital converter. Thereafter, digital signal processing on the I and Q samples enable for design trade-offs in the acquisition of the PN code with Doppler periods greater than the code period. Two code phase selection criterions, namely the maximum criterion and the threshold crossing criterion, are investigated and their acquisition time is measured for different frequency offsets and input IF signal to noise ratios. We also derive semi-analytical expressions for the BER performance of coherent and differentially coherent systems operating in a mobile satellite channel. In this case the channel is modeled as a multipath nonselective channel, but diversity gain can still be obtained through path diversity. This is the scenario when a signal is transmitted to all satellites in view and the received replicas are independently demodulated and combined at the receiver. Our analysis extends previous results to the case of unequal mean powers and Rice factors in the combined signals; a valid assumption if we consider that the satellites are in view at different elevation angles. Furthermore, the effect of imperfect power control in such mobile satellite DS-CDMA systems is also considered.