| Active sensing applications such as radar, sonar and medical imaging, demand proper designs of the probing waveform. A well-synthesized waveform can significantly increase the system performance in terms of signal-to-interference ratio, spectrum containment, beampattern matching, target parameter estimation and so on. The focus of this work is on designing probing waveforms using computational algorithms.;We first investigate designing waveforms with good correlation properties, which are widely useful in applications including range compression, channel estimation and spread spectrum. We consider both the design of a single sequence and that of a set of sequences, the former with only auto-correlations and the latter with auto- and cross-correlations. The proposed algorithms leverage FFT (fast Fourier transform) operations and can efficiently generate long sequences that were previously difficult to synthesize. We present a new derivation of the lower bound for sequence correlations that arises from the proposed algorithm framework. We show that such a lower bound can be closely approached by the newly designed sequences.;A two-dimensional extension of the time-delay correlation function is the ambiguity function (AF) that involves a Doppler frequency shift. We give an overview of AF properties and discuss how to minimize AF sidelobes in a discrete formation.;Besides good correlation properties, we also consider the stopband constraint that is required in the scenario of avoiding reserved frequency bands or strong electronic jammer. We present an algorithm that accounts for both correlation and stopband constraints.;We finally consider transmit beampattern synthesis, particularly in the wideband case. We establish the relationship between a desired beampattern and underlying waveforms by using the Fourier transform. We highlight the increased design freedom resulting from the waveform diversity of a MIMO (multi-input multi-output) system. |
