A Fast Waveform Design Method for Carrier-Free Ultrawideband Radio Sensors Based on OMP

Adaptive waveform design for carrier-free ultrawideband (UWB) signals can effectively improve the performance and anti-interference capability of sensor systems. To meet the real-time and low-complexity requirements for near detection of carrier-free UWB cognitive sensors, this article proposes a fast power spectrum fitting method based on the orthogonal matching pursuit (OMP) algorithm to meet the design requirements of combined Gaussian pulse waveforms for carrier-free UWB cognitive radio sensors. The method utilizes the formation properties of Gaussian pulses to construct a Gaussian pulse redundancy dictionary. Based on designing the optimal power spectrum, the combination of pulses that best matches the power spectrum template is quickly determined by the OMP algorithm, and its weighting coefficient is calculated. It essentially utilizes the orthogonality of the least squares method to achieve the best approximate representation of the power spectrum template using the atomic column space of the selected dictionary. The residual vector is updated during each iteration to maintain orthogonality with existing atoms, thereby accelerating the convergence speed of the algorithm. The simulation results demonstrate that the waveforms designed by the proposed algorithm exhibit superior anti-interference performance compared with other waveform design methods. In addition, the algorithm significantly reduces computational complexity and dramatically shortens the design time. These findings have significant implications for practical applications in waveform design.