Chaotic signals are ultra-wideband signals that can be generated with simple circuits in any frequency bands at arbitrary power level. The ultra-wideband property of chaotic carriers is beneficial in indoor and mobile applications where multipath propagation limits the attainable bit error rate. Another possible application is the ultra-wideband (UWB) radio, where the spectrum of transmitted signal covers an ultra-wide frequency band (a few GHz) and the power spectral density of transmitted UWB signal is so low that it does not cause any noticeable interference in the already existing conventional telecommunications systems sharing the same RF band. The UWB technology makes the reuse of the already assigned frequency bands possible. This chapter provides a unified framework for modeling, performance evaluation and optimization of UWB radios using either impulses or chaotic waveforms as carrier. The Fourier analyzer concept introduced provides a mathematical framework for studying the UWB detection problem. The autocorrelation receiver, the most frequently used UWB detector, is discussed in detail and an exact closed-form expression is provided for the prediction of its noise performance. Conditions assuring the best bit error rate with chaotic UWB radio are also given.