In this paper, we analyze the periodic transmission masks for MASked Modulation (MASM) in half-duplex integrated sensing and communication (ISAC), and derive their closed-form expected range-Doppler response $\mathbb{E}\{r(k,l,ν)\}$. We show that range sidelobes ($k\neq l$) are Doppler-invariant, extending the range-sidelobe optimality to the 2-D setting. For the range mainlobe ($k=l$), periodic masking yields sparse Doppler sidelobes: Cyclic difference sets (CDSs) (in particular Singer CDSs) are minimax-optimal in a moderately dynamic regime, while in a highly dynamic regime the Doppler-sidelobe energy is a concave function of the mask autocorrelation, revealing an inevitable tradeoff with mainlobe fluctuation.

翻译：本文分析了半双工集成感知与通信（ISAC）中掩码调制（MASM）的周期性传输掩码，并推导出其闭式期望距离-多普勒响应 $\mathbb{E}\{r(k,l,ν)\}$。我们证明距离旁瓣（$k\neq l$）具有多普勒不变性，从而将距离旁瓣最优性扩展至二维场景。对于距离主瓣（$k=l$），周期性掩码会产生稀疏的多普勒旁瓣：在中等动态场景中，循环差集（CDS）（特别是Singer CDS）具有极小极大最优性；而在高动态场景中，多普勒旁瓣能量是掩码自相关函数的凹函数，这揭示了其与主瓣波动之间不可避免的权衡关系。