Optimal waveform design for UWB radios

With transmit power spectra strictly limited by regulatory spectral masks, the emerging ultra-wideband (UWB) communication systems call for judicious pulse shape design in order to achieve optimal spectrum utilization, spectral mask compatibility, and coexistence with other wireless services. Meanwhile, orthogonal pulse sets are often desired in order to apply high-rate multidimensional modulation and (carrier-free) orthogonal frequency-division multiple access. Motivated by these considerations, we suggest a digital finite impulse response (FIR) filter approach to synthesizing UWB pulses and propose filter design techniques by which optimal waveforms that satisfy the spectral mask can be efficiently obtained. For single pulse design, we develop a convex formulation for the design of the FIR filter coefficients that maximize the spectrum utilization efficiency in terms of both the bandwidth and power allowed by the spectral mask. For orthogonal pulse design, a sequential strategy is derived to formulate the overall pulse design problem as a set of convex subproblems, which are then solved in a sequential manner to yield a set of mutually orthogonal pulses. Our design techniques not only provide waveforms with high spectrum utilization and guaranteed spectral mask compliance but also permit simple modifications that can accommodate several other system objectives.