正交時頻空間（Orthogonal Time Frequency Space, OTFS）調變技術將資訊符號配置於延遲都卜勒（delay-Doppler, DD）域，藉由二維轉換在時頻域與延遲都卜勒域之間建立訊號表示，使其適合應用於高速移動與時變多路徑通道環境。然而，在實際 OTFS 系統中，多路徑延遲、都卜勒效應、通道估測誤差，皆會影響接收端訊號偵測與位元錯誤率效能。因此，本論文針對 OTFS 系統之通道估測、跨訊框干擾，以及時頻域（time-frequency, TF）等化方法進行分析與研究。

本論文首先由 OTFS 系統經 Wigner 轉換後之時頻域輸入輸出關係出發。在第三章的初始推導中，將時頻域輸入輸出關係假設為通道響應與傳送訊號之理想二維循環卷積關係，並據此利用二維快速傅立葉轉換將卷積關係轉換為乘法形式，以建立時頻域等化架構。然而，進一步檢視完整推導後發現，實際時頻域通道響應中仍包含與路徑延遲、都卜勒頻移以及時頻索引相互耦合之通道相關指數相位項，使通道核並不具有理想二維循環卷積所要求的平移不變性。因此，第三章所採用的二維循環卷積輸入輸出模型在一般時變多路徑通道下並不成立，而第四章建立於該模型上的殘留干擾功率、雜訊功率、有效訊雜干擾比及理論位元錯誤率等解析結果亦不具嚴格有效性。

為解決上述模型不符問題，本論文於第五章重新由連續時間接收訊號及 Wigner 轉換出發，在不忽略任何通道相關指數相位項的情況下，重新推導 OTFS 系統實際的時頻域輸入輸出關係。推導結果顯示，時頻域接收訊號應由一個同時依賴輸入與輸出時頻索引的通道核描述，而非簡化為僅與索引差值相關的二維循環卷積形式。基於此精確輸入輸出模型，本論文進一步提出精準時頻域等化（precise TF-domain equalization）方法，直接依據完整通道響應補償各時頻資源單元間由多路徑延遲與都卜勒效應所造成的干擾。值得注意的是，本研究所提出之精準時頻域等化系統並未配置循環字首（cyclic prefix, CP），而是利用所推導之完整時頻域通道模型與等化機制直接補償多路徑傳播所造成的訊號干擾，因此可避免循環字首所帶來的額外傳輸開銷與頻寬使用效率損失。不同於建立於理想卷積假設上的盲時頻域等化（blind TF-domain equalization）方法，精準時頻域等化保留完整的路徑相依相位資訊，並在無循環字首的系統架構下進行通道補償，以降低因通道模型近似及多路徑效應所造成的等化失配與殘留干擾。

模擬結果進一步比較精準時頻域等化、盲時頻域等化、傳統延遲都卜勒域零強迫（zero-forcing, ZF）等化，以及未等化 OTFS 系統在多種 3GPP TDL 通道模型下的位元錯誤率效能。結果顯示，採用完整時頻域輸入輸出模型之精準時頻域等化能夠更有效補償多路徑與都卜勒效應所造成的干擾，並在所考慮的通道與系統參數下獲得較佳的位元錯誤率效能。本論文亦進一步分析不同 OTFS 訊框大小、調變階數與子載波間距對精準與盲時頻域等化效能的影響，以評估不同系統參數設定下的傳輸可靠度。

除了時頻域等化之外，本論文亦探討數個與實際 OTFS 傳輸相關的重要議題。首先，針對延遲都卜勒域中的導頻與保護區配置進行通道估測分析，以取得接收端等化所需之通道狀態資訊。最後，為同時評估傳輸可靠度與頻寬資源使用情形，本論文引入聯合頻寬與能量效率（joint bandwidth--energy efficiency, JBEE）指標，將有效資料速率、頻寬使用效率與位元錯誤率共同納入考量，並比較具有循環字首之盲時頻域等化與無循環字首之精準時頻域等化在不同系統參數下的整體效能。

綜合而言，本論文首先指出將 OTFS 時頻域輸入輸出關係簡化為理想二維循環卷積所造成的模型限制，並進一步重新建立完整且精確的時頻域訊號模型。在此基礎上所提出之精準時頻域等化方法，可在不依賴理想循環卷積假設的情況下，直接處理多路徑通道所造成的干擾。模擬結果顯示，此方法在不同 OTFS 系統參數與 3GPP TDL 通道模型下具有良好的位元錯誤率與整體傳輸效率表現，顯示精準時頻域等化可作為高速移動 OTFS 通訊系統接收機設計的一種可行方法。

Orthogonal Time Frequency Space (OTFS) modulation maps information symbols onto the delay-Doppler (DD) domain and establishes signal representations between the time-frequency (TF) and DD domains through two-dimensional transforms, making it well suited for high-mobility communications over time-varying multipath channels. However, in practical OTFS systems, multipath delay, Doppler effects, channel estimation errors, and bit error rate (BER) performance. Therefore, this thesis investigates channel estimation, and TF-domain equalization for OTFS systems.

This thesis first investigates the TF-domain input-output relationship of an OTFS system after the Wigner transform. In the initial derivation presented in Chapter 3, the TF-domain input-output relationship was assumed to form an ideal two-dimensional circular convolution between the channel response and the transmitted signal. Based on this assumption, a two-dimensional fast Fourier transform (2D FFT) was employed to convert the convolution relationship into a multiplicative form, thereby establishing a TF-domain equalization framework. However, a further examination of the complete derivation reveals that the actual TF-domain channel response contains channel-dependent exponential phase terms that are jointly coupled with the path delays, Doppler shifts. Consequently, the resulting channel response and transmit signal in TF-domain does not valid for an ideal two-dimensional circular convolution. Therefore, the two-dimensional circular-convolution-based input-output model adopted in Chapter 3 does not hold in general multipath channels. As a consequence, the analytical results derived in Chapter 4 based on this model, including the residual interference power, noise power, effective signal-to-interference-plus-noise ratio (SINR), and theoretical BER, are not strictly valid.

To address this model mismatch, Chapter 5 re-derives the actual TF-domain input-output relationship of the OTFS system starting from the continuous-time received signal and the Wigner transform, while retaining all channel-dependent exponential phase terms throughout the derivation. The resulting expression shows that the received TF-domain signal must be characterized by a channel that depends jointly on both the input and output TF indices, rather than by a two-dimensional circular convolution that depends only on their index differences. Based on this precise input-output model, a precise TF-domain equalization scheme is further developed to compensate for the interference caused by multipath delay and Doppler effects among TF resource elements using the complete channel response. It is worth noting that the proposed precise TF-domain equalization system operates without a cyclic prefix. Instead, the derived complete TF-domain channel model and the corresponding equalization mechanism are employed to directly compensate for interference caused by multipath propagation, thereby avoiding the additional transmission overhead and loss of bandwidth utilization efficiency associated with CP insertion. In contrast to the blind TF-domain equalization scheme established under the ideal convolution assumption, the precise TF-domain equalization scheme retains the complete path-dependent phase information and performs channel compensation in a CP-free system, thereby reducing equalization mismatch and residual interference caused by channel-model approximation and multipath propagation.

Simulation results further compare the BER performance of the precise TF-domain equalization scheme, the blind TF-domain equalization scheme, conventional DD-domain zero-forcing (ZF) equalization, and the OTFS system without equalization under various 3GPP tapped delay line (TDL) channel models. The results demonstrate that the precise TF-domain equalization scheme based on the complete TF-domain input-output model can more effectively compensate for interference caused by multipath and Doppler effects and achieves improved BER performance under the considered channel conditions and system configurations. The effects of different OTFS frame sizes, modulation orders, and subcarrier spacings on the performance of the precise and blind TF-domain equalization schemes are also investigated to evaluate transmission reliability under different system parameter settings.

In addition to TF-domain equalization, this thesis investigates several important issues related to practical OTFS transmission. First, channel estimation based on pilot and guard-region allocation in the DD domain is analyzed to obtain the channel state information required for receiver equalization. Finally, to jointly evaluate transmission reliability and bandwidth resource utilization, a joint bandwidth--energy efficiency (JBEE) metric is introduced by jointly considering the effective data rate, bandwidth utilization efficiency, and BER. The overall performance of the CP-based blind TF-domain equalization scheme and the CP-free precise TF-domain equalization scheme is then compared under different system parameter configurations.

In summary, this thesis first identifies the model limitation associated with simplifying the OTFS TF-domain input-output relationship as an ideal two-dimensional circular convolution and subsequently establishes a complete and precise TF-domain signal model. Based on this model, the proposed precise TF-domain equalization scheme can directly mitigate interference caused by multipath propagation without relying on the ideal circular-convolution assumption. Simulation results demonstrate that the proposed scheme provides favorable BER and overall transmission-efficiency performance under different OTFS system configurations and 3GPP TDL channel models. These results indicate that precise TF-domain equalization provides a feasible receiver design approach for OTFS communication systems operating in high-mobility environments.

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