Design of the Family of Orthogonal and Spectrally Efficient UWB Waveforms

In this paper, a method for the design of nonlinear phase, full-band, ultra-wideband (UWB) pulses that satisfy the Federal Communications Commission's effective isotropic radiation power spectrum mask, or more generally, any other given mask, is introduced. The method uses convex programming in each step of the iterative procedure that updates the phase distribution of the goal function. Thanks to its mathematical structure, this method can be easily modified in order to be applied, in sequential fashion, to several different orthogonal UWB pulse-design problems, addressed later in the paper. The first among them is a problem considered in literature-design of multiple pulses, orthogonal when radiated. When employed for solving this problem, the method proposed here produces a considerably larger number of orthogonal pulses with high energy compared to the methods introduced before. As a novelty, the problem of designing pulses which are orthogonal in reception is considered. Then, a modification of our method is presented that can be used to solve this problem. We also introduce statistical criteria of robustness of pulses' orthogonality in reception, to the variation of the pulses' shape caused by the channel transfer function. After that, a modification of the proposed method is presented that is capable of producing a set of pulses with predefined maximum value of this criteria. Furthermore, it is shown that the method proposed can be used to efficiently design orthogonal pulses using a suboptimal value of the sample rate. All the concepts introduced are illustrated by design examples.