Waveform design with controllable modulus dynamic range under spectral constraints

Abstract

Transmit waveform design under practical temporal and spectral constraints plays a prominent role in determining the performance of active sensing systems. In temporal domain, it is highly desirable to control the variation of waveform modulus within a small range to improve the transmit power efficiency. To this end, we introduce a new constraint, referred to as modulus dynamic range constraint (MDRC), to directly control the waveform magnitude variation, wherein the constant modulus (CM) is a special case. In spectrum domain, we examine the transmit waveform design with a desirable spectral shape under the MDRC. A flat spectrum that corresponds to low auto-correlation sidelobes (ACS) is considered first and then extended to arbitrary-shaped spectrum synthesis. We formulate the design as a least-square minimization of spectrum matching and a phase compensation technique is adopted to transform the non-smooth problem sequentially. A projected-gradient algorithm (PGA) is proposed to solve the first problem and any limit point of PGA is proved to converge to the KKT point. Two fast-version algorithms with a quadratic convergence rate are then developed for large-scale waveform design. Subsequently, PGA is extended to synthesize arbitrary-shaped spectrum. Finally, numerical experiments demonstrate the superiority of the proposed algorithms over the state-of-the-art methods.