content
前言：和前面的類似，這部分依舊比較偏概念性的描述而缺少實際的公式和例子說明，是對延遲-多普勒信道符號耦合特性的描述
1.Definition定義
The wireless channel is governed by simple physics. It is composed of a collection of specular reflectors, some of which are static and some of which are moving. The transmitted waveform propagates through the medium and bounces off each reflector. The signal that arrives at the receiver is a superposition of the direct signal and the reflected echoes. Each of the reflected echoes arrives at the receiver at a delayed time (multipath effect) and possibly also shifted in frequency (Doppler effect) due to the relative velocity between the reflector and the transmitter/receiver. The channel physics is mathematically modeled through the delay-Doppler impulse response where each tap represents a cluster of reflectors with specific delay and Doppler characteristics, as shown in Figure 4. Our goal in this section is to describe the channel-symbol coupling (CSC for short) between the wireless channel and the OTFS carrier waveform given by a localized pulse in the delay-Doppler representation. As a motivation, we first discuss the channelsymbol coupling of the TDM and FDM pulses.
這個定義揭示的是信道和傳輸符號耦合的實質。即符號經過由多徑產生的時延以及多普勒產生的頻移的各個符號的疊加。
2.Example例子
2.1Channel symbol coupling of the TDM pulses
Transmitting a localized TDM pulse in the time representation gives rise at the receiver to a configuration of echoes which appear at specific time displacements which corresponds to the multipath delays imposed by the various reflectors. The phase and amplitude of
each echo depend on the initial position of the transmitted pulse and might change significantly among different coherence time intervals – a phenomenon referred to as time selectivity. There are two mechanisms involved. The phase of the echo changes due to the Doppler effect and the amplitude of the echo changes due to destructive superposition of numerous reflectors sharing the same delay but differing in Doppler, resulting from the inability of the TDM pulse to separate reflectors along Doppler. In Figure 9, counting the TDM echoes from left to right we see that the first and third echoes are due to static reflectors hence are time invariant, the fourth echo is due to moving reflector thus is time varying and the second echo is due to superposition of two reflectors, one of which is moving thus is fading.
解釋一下這段話的含義：
- 每個回波的相位和振幅取決於發射脈衝的初始位置，並可能在不同的相干時間間隔之間發生顯著變化，這種現象稱爲時間選擇性。
- 回波的相位由於多普勒效應而改變，而回波的振幅由於具有相同延遲但不同多普勒的多個反射器的破壞性疊加而改變，這是由於TDM脈衝無法沿多普勒分離反射器造成的
- 說明一下例子：
從時間維度來看- 一和三是靜態的反射器且只有一個，所以是時不變的
- 四因爲車在移動所以是時變的
- 二是兩個的疊加，一個動一個不動，所以是衰落
2.2Channel symbol coupling of the TDM pulses
Reciprocally, transmitting a localized FDM pulse in the frequency representation gives rise at the receiver to a configuration of echoes at specific frequency displacements which correspond to the Doppler shifts induced by the various reflectors. The phase and amplitude of each echo depends on the initial position of the transmitted pulse and might change significantly among different coherence frequency intervals – a phenomenon referred to as frequency selectivity. The phase of the echo changes due to the multipath effect and the amplitude of the echo changes due to destructive superposition of numerous reflectors sharing the same Doppler but perhaps differing in delay, resulting from the inability of the FDM pulse to separate reflectors along delay. For example, in Figure 9, counting the received FDM echoes from bottom up, we see that the first and third echoes are frequency varying and the second echo is due to superposition of three static reflectors thus is fading.
回波的相位由於多徑效應而改變，而回波的振幅由於共享同一多普勒但可能不同延遲的多個反射器的破壞性疊加而改變，也就是說從頻域來看，如果多普勒頻移一致，但是時延不同的話，就會導致不同的回波相位不同，可能就會導致疊加在一起的相位呈現出不同的特性。
2.3Channel symbol coupling of the OTFS pulses
Transmitting a localized OTFS pulse in the delay-Doppler representation gives rise at the receiver to a configuration of echoes that appear at specific delay-Doppler displacements, which corresponds to the delay and Doppler shifts induced by the various reflectors, as shown in Figure 10. In contrast to the previous two cases, the following properties now hold:
- CSC invariance: the phase and amplitude of the delay-Doppler echoes are independent of the location of the original pulse inside the fundamental domain, since the delay and Doppler periods are smaller than the coherence time and bandwidth of the channel respectively
- CSC separability: all the reflections are separated from one another along their delay and Doppler characteristics, hence their effects do not add up destructively and there is no loss of energy on the QAM symbol level.
- CSC orthogonality: the received echoes are confined to a small rectangular box around the transmitted pulse with dimensions equal the delay and Doppler spread of the channel which are much smaller than the outer delay and Doppler periods.??? As result, when two transmit pulses are geometrically separated at the transmitter they will remain orthogonal at the receiver.
An alternate way to express the OTFS channel-symbol coupling is as a two dimensional convolution between the delay-Doppler impulse response and the QAM symbols. This can be seen in Figure 11, which shows numerous delta functions (representing QAM symbols) convolved with the delay-Doppler impulse response of the channel.
這段話的意思是因爲具有時移和多普勒兩個維度的分辨能力，所以我們的OTFS脈衝具有了不變性，可分離性，正交性.但是爲什麼具有這個能力也沒有具體論述
