基于诺伊曼级数的Zak-OTFS低复杂度均衡
Low-complexity Equalization of Zak-OTFS Via Neumann Series
- Duke University（杜克大学）
- Department of Electrical Engineering, Indian Institute of Technology Delhi（德里印度理工学院电气工程系）
- Cohere Technologies Inc.（Cohere科技有限公司）
- Department of Mathematics, University of Texas at Austin（德克萨斯大学奥斯汀分校数学系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出通过推广离散仿射傅里叶变换（GDAFT）选择Zak-OTFS载波波形的正交基，实现卫星、地对无人机等信道的低复杂度均衡，可最大化信道能量对角分量，对分数延迟和多普勒频移鲁棒。
AI中文摘要：
我们描述了一种选择载波波形正交基的通用方法，该方法可使基与无线信道的延迟/多普勒特性对齐。我们表明，该方法能为两类实际关注的信道实现低复杂度均衡：第一类是卫星通信，第二类是地面站到无人机（UAV）的通信。多普勒补偿后，这两种场景均具有一条零延迟、零多普勒频移的视距（LOS）路径，以及一条较弱的第二条路径。我们证明，该方法对分数延迟和多普勒频移具有鲁棒性。我们考虑的载波波形正交基，是通过对Zak-OTFS载波波形的Pulsone基应用离散仿射傅里叶变换（GDAFT）的推广形式得到的；该波形族包含为6G提出的AFDM及其他调制方式。这些基的区别在于，载波波形是离散延迟和多普勒移位的海森堡-外尔群的某个极大交换子群S的公共特征向量。我们描述了如何选择S以减轻载波间干扰的有害影响。我们用延迟-多普勒抽头表示无线信道，发现位于S内的信道抽头会将每个波形乘以一个复相位；若所有信道抽头都位于S内，则信道会将每个波形乘以一个复相位，此时单抽头均衡器即可支持可靠通信，线性时不变（LTI）信道即为此类情况，其中S为离散时间移位群，载波波形为离散音（OFDM）。一般而言，我们选择子群S以最大化信道能量的对角分量。
英文摘要：
We describe a general method for selecting an orthonormal basis of carrier waveforms that aligns the basis with delay / Doppler characteristics of a wireless channel. We show that our method enables low-complexity equalization for two channels of practical interest. The first is satellite communication and the second is communication from a ground station to an unmanned aerial vehicle (UAV). After Doppler compensation both scenarios are characterized by a first line of sight (LOS) path with zero delay and zero Doppler shift, and a second weaker path. We show that our method is robust to fractional delay and Doppler shifts. We consider orthonormal bases of carrier waveforms that are obtained from the pulsone basis of Zak-OTFS carrier waveforms by applying a generalization of the discrete affine Fourier transform (GDAFT). This family of waveforms includes AFDM and other modulations proposed for 6G. What distinguishes these bases is that the carrier waveforms are common eigenvectors of some maximal commutative subgroup S of a Heisenberg-Weyl group of discrete delay and Doppler shifts. We describe how to choose S to mitigate the damaging effects of interference between carriers. We represent the wireless channel by delay-Doppler taps and observe that a channel tap located within S multiplies every waveform by a complex phase. If all channel taps are located within S, then the channel multiplies every waveform by a complex phase, and a single tap equalizer supports reliable communication. This is the case for a linear time-invariant (LTI) channel, where S is the group of discrete time shifts and the carrier waveforms are discrete tones (OFDM). In general, we choose the subgroup S to maximize the diagonal component of the channel energy.
