An Investigation of Orthogonal Wavelet Division Multiplexing Techniques as an Alternative to Orthogonal Frequency Division Multiplex Transmissions and Comparison of Wavelet Families and Their Children

Recently, issues surrounding wireless communications have risen to prominence because of the increase in the popularity of wireless applications. Bandwidth problems, and the difficulty of modulating signals across carriers, represent significant challenges. Every modulation scheme used to date has had limitations, and the use of the Discrete Fourier Transform in OFDM (Orthogonal Frequency Division Multiplex) is no exception. The restriction on further development of OFDM lies primarily within the type of transform it uses in the heart of its system, Fourier transform. OFDM suffers from sensitivity to Peak to Average Power Ratio, carrier frequency offset and wasting some bandwidth to guard successive OFDM symbols. The discovery of the wavelet transform has opened up a number of potential applications from image compression to watermarking and encryption. Very recently, work has been done to investigate the potential of using wavelet transforms within the communication space. This research will further investigate a recently proposed, innovative, modulation technique, Orthogonal Wavelet Division Multiplex, which utilises the wavelet transform opening a new avenue for an alternative modulation scheme with some interesting potential characteristics. Wavelet transform has many families and each of those families has children which each differ in filter length. This research consider comprehensively investigates the new modulation scheme, and proposes multi-level dynamic sub-banding as a tool to adapt variable signal bandwidths. Furthermore, all compactly supported wavelet families and their associated children of those families are investigated and evaluated against each other and compared with OFDM. The linear computational complexity of wavelet transform is less than the logarithmic complexity of Fourier in OFDM. The more important complexity is the operational complexity which is cost effectiveness, such as the time response of the system, the memory consumption and the number of iterative operations required for data processing. Those complexities are investigated for all available compactly supported wavelet families and their children and compared with OFDM. The evaluation reveals which wavelet families perform more effectively than OFDM, and for each wavelet family identifies which family children perform the best. Based on these results, it is concluded that the wavelet modulation scheme has some interesting advantages over OFDM, such as lower complexity and bandwidth conservation of up to 25%, due to the elimination of guard intervals and dynamic bandwidth allocation, which result in better cost effectiveness

Nearly orthogonal, doppler tolerant waveforms and signal processing for multi-mode radar applications

In this research, we investigate the design and analysis of nearly orthogonal, Doppler tolerant waveforms for diversity waveform radar applications. We then present a signal processing framework for joint synthetic aperture radar (SAR) and ground moving target indication (GMTI) processing that is built upon our proposed waveforms. ^ To design nearly orthogonal and Doppler tolerant waveforms, we applied direct sequence spread spectrum (DSSS) coding techniques to linear frequency modulated (LFM) signals. The resulting transmitted waveforms are rendered orthogonal using a unique spread spectrum code. At the receiver, the echo signal can be decoded using its spreading code. In this manner, transmit orthogonal waveforms can be matched filtered only with the intended receive signals. ^ Our proposed waveforms enable efficient SAR and GMTI processing concurrently without reconfiguring a radar system. Usually, SAR processing requires transmit waveforms with a low pulse repetition frequency (PRF) rate to reduce range ambigu- ity; on the other hand, GMTI processing requires a high PRF rate to avoid Doppler aliasing and ambiguity. These competing requirements can be tackled by employing some waveforms (with low PRF) for the SAR mission and other waveforms (with high PRF) for the GMTI mission. Since the proposed waveforms allow separation of individual waveforms at the receiver, we can accomplish both SAR and GMTI processing jointl

Approximation of dual Gabor frames, window decay, and wireless communications

We consider three problems for Gabor frames that have recently received much attention. The first problem concerns the approximation of dual Gabor frames in $L_2(R)$ by finite-dimensional methods. Utilizing Wexler-Raz type duality relations we derive a method to approximate the dual Gabor frame, that is much simpler than previously proposed techniques. Furthermore it enables us to give estimates for the approximation rate when the dimension of the finite model approaches infinity. The second problem concerns the relation between the decay of the window function $g$ and its dual $\gamma$. Based on results on commutative Banach algebras and Laurent operators we derive a general condition under which the dual $\gamma$ inherits the decay properties of $g$. The third problem concerns the design of pulse shapes for orthogonal frequency division multiplex (OFDM) systems for time- and frequency dispersive channels. In particular, we provide a theoretical foundation for a recently proposed algorithm to construct orthogonal transmission functions that are well localized in the time-frequency plane

Characterization of Ultra Wideband Multiple Access Performance Using Time Hopped-Biorthogonal Pulse Position Modulation

The FCC\u27s release of its UWB First Report and Order in April 2002 spawned renewed interest in impulse signaling research. This work combines Time Hopped (TH) multiple access coding with 4-ary UWB Biorthogonal Pulse Position Modulation (TH-BPPM). Multiple access performance is evaluated in a multipath environment for both synchronous and asynchronous networks. Fast time hopping is implemented by replicating and hopping each TH-BPPM symbol NH times. Bit error expressions are derived for biorthogonal TH-BPPM signaling and results compared with previous orthogonal TH-PPM work. Without fast time hopping (NH = 1), the biorthogonal TH-BPPM technique provided gains equivalent to Gray-coded QPSK; improved BER at a given Eb/No and an effective doubling of the data rate. A synchronized network containing up to NT = 15 transmitters yields an average BER improvement (relative to an asynchronous network) of approximately -6.30 dB with orthogonal TH-PPM and approximately 5.9 dB with biorthogonal TH-BPPM. Simulation results indicate that doubling the number of multipath replications (NMP) reduces BER by approximately 3.6 dB. Network performance degrades as NT and NMP increase and synchronized network advantages apparent in the NMP = 0 case diminish with multipath interference present. With fast time hopping (NH \u3e 1) improves BER performance whenever NMP \u3c NH while reducing effective data rate by 1/NH. Compared to the NH = 1 synchronized network, TH-BPPM modulation using NH = 10 provides approximately 5.9 dB improvement at NMP = 0 and approximately 3.6 dB improvement at NMP = 5. At NMP = 10, the BER for the hopped and NH = 1 cases are not statistically different; with NH = 10 hops, BER improvement varies from approximately 0.57 to 0.14 dB (minimal variation between synchronous and asynchronous network performance)