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.

实际时间和频谱约束下的发射波形设计在确定有源传感系统的性能方面起着重要作用。在时域中，非常需要将波形模量的变化控制在小范围内以提高发射功率效率。为此，我们引入了一种新的约束，称为模量动态范围约束 (MDRC)，以直接控制波形幅度变化，其中恒模 (CM) 是一种特殊情况。在频谱域中，我们检查了在 MDRC 下具有理想频谱形状的发射波形设计。首先考虑对应于低自相关旁瓣 (ACS) 的平坦频谱，然后扩展到任意形状的频谱合成。我们将设计表述为频谱匹配的最小二乘最小化，并采用相位补偿技术来依次转换非平滑问题。提出了投影梯度算法（PGA）来解决第一个问题，并且证明PGA的任何极限点都收敛到KKT点。然后为大规模波形设计开发了两种具有二次收敛速度的快速版本算法。随后，PGA 扩展到合成任意形状的频谱。最后，数值实验证明了所提出的算法优于最先进的方法。然后为大规模波形设计开发了两种具有二次收敛速度的快速版本算法。随后，PGA 扩展到合成任意形状的频谱。最后，数值实验证明了所提出的算法优于最先进的方法。然后为大规模波形设计开发了两种具有二次收敛速度的快速版本算法。随后，PGA 扩展到合成任意形状的频谱。最后，数值实验证明了所提出的算法优于最先进的方法。