标题： Zak-OFDM：双重扩展信道中OFDM载波的低复杂度联合均衡 显示英文标题

标题： Zak-OFDM: Low Complexity Joint Equalization of OFDM Carriers in Doubly-Spread Channels

摘要： 我们通过首先估计然后均衡有效信道来在无线信道上进行通信。 在Zak-OTFS（正交时频空间）调制中，载波波形是延迟-多普勒（DD）域中的脉冲，形式上是一个在延迟和多普勒方向上具有特定周期的准周期局部函数。 当信道延迟扩展小于延迟周期，并且信道多普勒扩展小于多普勒周期时，单个Zak-OTFS载波的响应可以提供散射环境的图像，并可用于预测所有其他载波的有效信道。 这使得信道估计变得简单，并且由于可以设计出相互无偏的数据和导频信号，因此不会损失频谱效率。 然而，均衡的朴素方法具有复杂度${\mathcal O}(M^3N^3)$，其中$M$和$N$分别是OTFS帧中的延迟和多普勒子块的数量。 我们通过将Zak-OTFS信息符号转换为CP-OFDM（循环前缀正交频分复用）调制来简化均衡。 为什么不直接使用CP-OFDM进行通信？ 在CP-OFDM中，载波间干扰（ICI）使得在移动和延迟扩展存在的情况下，获取子载波之间的完整频域（FD）信道响应非常具有挑战性。 我们通过从DD域中估计有效信道来避免这一困难，从而能够重建完整的FD信道响应。 我们利用CP-OFDM设计了一种${\mathcal O}(M^2N^2)$低复杂度的方法，联合均衡所有子载波，其中$MN$是子载波的数量。 我们的方法消除了CP-OFDM中传统导频的需要，并减少了随着移动性变化调整载波间隔的需求。 显示英文摘要

摘要： We communicate over wireless channels by first estimating and then equalizing the effective channel. In Zak-OTFS (orthogonal time frequency space) modulation the carrier waveform is a pulse in the delay-Doppler (DD) domain, formally a quasi-periodic localized function with specific periods along delay and Doppler. When the channel delay spread is less than the delay period, and the channel Doppler spread is less than the Doppler period, the response to a single Zak-OTFS carrier provides an image of the scattering environment and can be used to predict the effective channel at all other carriers. This makes channel estimation straightforward, and there is no loss in spectral efficiency since it is possible to design data and pilot signals that are mutually unbiased. However, the naive approach to equalization has complexity ${\mathcal O}(M^3N^3)$ where $M$ and $N$ are respectively the number of delay and Doppler bins in an OTFS frame. We simplify equalization by transforming Zak-OTFS information symbols to CP-OFDM (cyclic prefix orthogonal frequency division multiplexing) modulation. Why not simply communicate with CP-OFDM? Inter-carrier interference (ICI) in CP-OFDM makes it is very challenging to acquire the complete frequency domain (FD) channel response between subcarriers in the presence of mobility and delay spread. We avoid this difficulty by estimating the effective channel in the DD domain from which we are able to reconstruct the complete FD channel response. We take advantage of CP-OFDM to design an ${\mathcal O}(M^2N^2)$ low-complexity method of jointly equalizing all subcarriers, where $MN$ is the number of subcarriers. Our approach removes the need for traditional pilots in CP-OFDM and reduces the need to vary carrier spacing with mobility.