Weighted-Type Fractional Fourier Transform And Its Applications In Communication Systems

The background of this thesis is formed from the two aspects decreasing perfor-mance of communication systems: one is the threat to information security induced bythe comprehensive political and economic factors, and a more important one is the inter-ferences caused by high information rate and complex communication environments.The traditional Low Probability Interception (LPI) communication techniques de-signed on time or frequency domain have existed for a long time that they are knownto most researchers, which impairs its capability for protecting communication signals.So there are exigent demands for new LPI techniques. The so called complex environ-ments means time-frequency doubly dispersive channels and varying channel fading typeswhen delivers high data rate in a high moving speed. The single carrier scheme andmulti-carrier scheme have different performance under channels of different fading types.However, few current systems is able to vary carrier scheme automatically that systemswith different techniques have to be adopted for the same services and customers. It isno doubt the waste of resources. In order to develop the current systems, I propose inthe thesis that: the proper time-frequency mathematical analysis tools and cooperationamong systems, techniques and domains should be adopted to solve the problems oc-curring in complex time-frequency channels by building up new communication theoriesand modes; while the mathematical tools themselves should be generalized to satisfy theengineering demands. In this thesis, I consider a rather new time-frequency mathematicaltool–Weighted-type Fractional Fourier Transform (WFRFT).Fractional Fourier Transform (FRFT), which is a mathematics tool for time-frequency analysis, has a variety of definitions. And the earliest one is chirp-type FRFT(CFRFT), which is notified by its name that has chirp signals as its orthogonal basis. Inthis thesis, whereas, we focus on a different kind of FRFT–WFRFT, which was proposedlater than CFRFT. WFRFT is a developing theory that its applications have never beenseen in communications. The thesis reveals the symmetrical time-frequency property ofWFRFT. Moreover, a creative work on the basic theory of WFRFT is done on the discretealgorithm of 4-terms WFRFT for continuous functions based on Discrete Fourier Trans-form (DFT), and also its restrict conditions for utilization. WFRFT matrix is obtained by defining the WFRFT for sequence. The structures of WFRFT digital communicationsystems are designed and proved to be compatible to current systems based on the gener-alization works on WFRFT.On the aspect of applications in communications, there are two major scenarioswith the considerations of WFRFT's structure and its signals'characters. One is thenew anti-interception techniques based on WFRFT. The other one is the carrier schemeconvergence and cooperation based on WFRFT's physical structure of hybrid modulationprocess with single carrier and multi-carrier scheme.With a view to the weakness of current LPI communication techniques, I suggest tomake WFRFT involve and analyze the anti-interception capability for WFRFT's signals.The constellation of WFRFT signals appears the rotation and fission property along withthe variation of WFRFT parameter. Meanwhile, when WFRFT parameter satisfies certainconditions, the signal constellation on the complex plane appears to have a quasi Gaus-sian probability density, which invalidates most of the blind detection methods based onhigher order cumulants. When the WFRFT parameter is scanned and detected one byone, WFRFT signals also appears convinced security. In With the combination of fre-quency hopping or Directed Sequence Spread Spectrum techniques, alterable parametersschemes are proposed in order to enhance the anti-interception capability of WFRFT sys-tems. Covert communication based on waveform overlay with WFRFT signals wouldalso improve the efficiency of traditional overlay systems.Although the single carrier and multi-carrier scheme are not compatible in currentcommunication systems, the convergence and cooperation of systems with different car-rier schemes is moving on. By analogy with Orthogonal Frequency-Division Multiplex-ing (OFDM) and Single Carrier with Frequency Domain Equalization (SC-FDE) system,the physical meaning of 4-WFRFT in digital communication is revealed: 4-WFRFT is acompatible process of multi-carrier and single carrier modulation. With respect to carrierschemes in current communication systems and the popular researches on relative tech-niques, I believe that convergence and cooperation of different carrier schemes are theforeseeing requirements which WFRFT can satisfy.The Peak-to-Average Power Rate of WFRFT signals is smaller than that of OFDMsignals. And WFRFT system has a comparative hardware complexity to that of OFDM orSC-FDE. The comparisons of bit error rate performance among different carrier schemes under fading channels are made in the thesis. WFRFT takes the second place under singledispersive channels, while it outperforms both of OFDM and single carrier system underdouble dispersive channels. The simulation results show that WFRFT system has the mostrobust performance under different kinds of fading channels. And the proper parameterof WFRFT that matches the channel will lead to the optimal cooperative carrier scheme.More creative works, such as cooperative carrier scheme communication system based ondistributed transmission antennae and equalization on the weighting fractional domain,can also be seen in the thesis.Beyond the contents of this thesis, there are more worthy subjects about the appli-cations of WFRFT in communications, especially when the property of hybrid carrierscheme modulation is considered. Channel estimation and equalization based on WFRFTare in the processes and the rudiments of WFRFT demo system have been established.