New communication and adaptive system designs by time-frequency distributions and fractional Fourier transform

In the former parts of this thesis improved time-frequency analysis techniques are built up. Whereas, in the latter parts new communication models are developed and novel adaptive filter designs in the fractional Fourier domains are proposed.After introducing the short-time Fourier transform (STFT), Wigner distribution (WD), ambiguity function (AF), fractional Fourier transform (FrFT), and time-bandwidth product (TBP) in the second section, we evolve to novel studies of the thesis, namely, the investigation of the relationship between discrete evolutionary transform (DET) and the generalized time-bandwidth product optimum STFT. We have also determined the analysis window of the DET in an adaptive way, hence improving the DET representation.The latter part of the thesis is mainly based on the system model design using the ideas behind the time-frequency analysis. In this scope, two novel communication models are proposed and a new transform domain, the FrFT, is proposed for the adaptive filter paradigm, which is a breaking fresh ground idea.The efficient usage of the spectrum is a crucial issue. Therefore, in Sections 4 and 5, we propose two new communication models which increase the spectral efficiency by using time-frequency analysis techniques. In Section 4, we introduce the usage of weighted sum of Hermite-Gaussian functions associated with the data, which constitutes a toroidal waveform in the time-frequency space and thereby increase the spectral efficiency. We have selected the TBP as a measure of the spectral efficieny.Communication through wireless channels might face multi-path fading, shadowing, Doppler shift, and other distorting effects. Due to these destructive effects, the receiver might not demodulate the signal accurately, resulting in a decreased system performance. Therefore the channel estimation becomes pretty important. Generally, channel estimation procedure includes transmitting a sequence of pilot data before transmitting the actual data, which decreases the spectral efficiency. In Section 5, we propose a new channel estimation technique without the need of pilot signals, and therefore increasing the spectral efficiency. The transmitted waveform has a circular region, as opposed to the classical rectangular region, where chirp signals are used as base functions. The demodulation in the receiver process employs FrFT. When the chirp functions transmit the data, they also behave as pilot signals in which the characteristics of the communication channel can easily be estimated by only using the data signals. The channel estimation is achieved by using two important properties of the FrFT.In the last Section, we have proposed the fractional Fourier domain as a new transform domain for adaptive filters which are mostly realized in either time or Fourier domains. The performance of the proposed system is simulated by suppressing acoustic mechanical noise, which is an active noise control problem. Simulation results show that the proposed system suppresses the non-stationary noise better than that of the time-domain adaptive filter based systems.Key Words: Adaptive filters, ambiguity function (AF), chirp signals, discrete evolutionary transform (DET), fractional Fourier transform (FrFT), Hermite-Gaussians signals, multi-carrier communication, short-time Fourier transform, time-bandwidth product (TBP) toroidal lattice, Wigner distribution (WD).