Research On Impulse Radio Ultra Wideband Systems Based On Fractional Fourier Transform

Recent years, many researches have focused on Impulse Radio Ultra-Wideband (IR-UWB) technology. It is different from the traditional continuous carrier communicationsystems that it adopts impulse waveforms to carry the information.The target of IR-UWB is to provide a novel data transmission technique with lowcost, low complexity and low power consumption. Nevertheless, IR-UWB usually worksin a varying and complex environment with dense multi-pathes. And to achieve the ob-jects of collecting multi-pathes energy and suppressing different kinds of interferenceswith cheap and simple techniques is very difficult. Hence, the actual data rate of UWBsystems is much lower than the theoretical one. As to the precise ranging and position-ing, although the time of arrival (TOA) estimation method based on time correlation hasa very high theoretical precision, the actual implementations of the prototypes are stilldominated by non-coherent energy detection due to complexity reasons. In a word, theIR-UWB targets for low cost and high performance could not unite under current techni-cal conditions.The dissertation tries to reconcile the con?ict between performance and complexityof IR-UWB systems from a new aspect. That is the adoption of a single signal processingmethod to suppress the in?uences of Multiple Access Interference (MAI), Sinusoid signalinterference and multi-path interference simultaneously, and improve the system perfor-mance with as less additional complexity as possible. To achieve this goal, IR-UWB sig-nals must be provided with some unique characteristics in order to be distinguished fromall the different types of interferences, and extraction of these features should be able toachieve with a simple receiver structure. Fractional Fourier Transform (FRFT) is thenchosen in this dissertation, because its fast digital calculation algorithm has a comparablecomplexity to Fast Fourier Transform (FFT), which meets the needs of low complexityand low power consumption for IR-UWB systems.FRFT which generalizes Fourier Transform in the way of eigenvalues fractionaliza-tion, and FRFT domains can be seen as the ones between time-domain and frequency-domain. The dissertation summarizes FRFT discrete algorithms and points out that thesampling-type discrete algorithm proposed by Ozaktas and others is suitable for digital communication systems for its comparable complex to FFT.Two basic theoretical issues occurring when FRFT is introduced into digital com-munication are studied. One is the dimensional normalization of discrete algorithm andthe other one is the spectrum of chirp functions on FRFT domain. As the bases of FRFT,the time infinite chirp functions will transform into impulse functions on certain FRFTdomains. Nevertheless, signals in communication are always time finite. A time finitechirp function can be seen as a multiplication of a time infinite chirp function and a win-dow function. The analytical expression of spectrum on FRFT domains of a time finitechirp function is deduced and then verified by simulations. FRFT in simulations is imple-mented by Ozaktas'discrete algorithm, which should dimensional normalize the signalsat first. So the analytical expressions of errors caused by two different dimensional nor-malization methods are also deduced and verified by simulations. All the above works laythe theoretical foundation of the application of FRFT in engineering.As to the chief question on the design of transmission waveforms in IR-UWB, thedissertation propose a scheme of weighted superposition of chirp functions, based on theanalysis of the relationship of FRFT and chirp functions. The designed waveforms willconcentrate on certain FRFT domains while the interferences will not, so filtering onthe FRFT domains is able to separate them. In this case, the designing objective is toincrease the emission power as high as possible while meeting power spectral constraintsof FCC (Federal Communications Commission). The optimization problem is solved bySDP algorithm and PM algorithm in filter designing. The dissertation also analyze thecharacteristics of Additive White Gaussian Noise (AWGN) on FRFT domains.Waveform design with chirp functions guarantees the separation of signal and inter-ferences on the FRFT domains. For the purpose of Multiple Access Interference (MAI)suppression, a novel Multiple Access (MA) scheme combined with FRFT domain MAand time hopping MA is proposed, in which the FRFT order is also determined as a pa-rameter to distinguish multi-user. A method separating IR-UWB signals and sinusoidsignals is proposed for sine interference suppression and spectral cognition. A binarychirp rate modulation and its non-coherent demodulation are proposed in order to reducethe influences of inter symbol interference and multi-path interference in one symbol.As to the ranging application of IR-UWB, the estimation precision of TOA is anessential parameter. So the dissertation studies and compares two TOA estimation meth- ods: (i) coherent method based on peak detection of correlation on FRFT domain and (ii)non-coherent method based on peak detection of spectrum on FRFT domain. Comparedwith correlation on time domain, correlation on FRFT domain has a shift-varying prop-erty, based on which the scope of ranging is able to be controlled. To meet the needs ofIR-UWB ranging nodes of simple device structure and low power consumption, a rangingmethod of peak detection on FRFT domain is proposed, which has lower complexity thantime correlation method. The theoretical deduction and simulation results verify that theproposed method and time correlation method have a comparable precision in high signalto noise ratio conditions. At last, the dissertation studies the estimation of time delay inthe presence of frequency offset. FRFT can display both of time delay and frequency off-set information simultaneously. So it can be used for a joint estimation of time delay andfrequency offset, in order to eliminate in?uence of frequency offset and improve precisionof time delay estimation.