[LTE 筆記] OFDM 系統下的通道估測與誤差

在本文中, 我們預期從 5G NR 的 OFDM 通訊行為來分析通道與同步造成的收訊誤差與扭曲.

我們將以 SRS (Sound Reference Signal) 為例, 

SRS 並不是未知的資料訊號, 而是一種已知的 reference signal.

系統會先透過高層或 PHY 層配置決定 SRS 的參數,

例如: numerology, 子載波間距, SRS bandwidth, comb factor, 傳送的 OFDM symbol 位置等.

這些參數決定了 SRS 會出現在 resource grid 的哪些 resource elements 上.

在頻域中, SRS 會先形成一串已知序列 (Z-C Sequence), 接著映射到指定的子載波上. 

之後, OFDM transmitter 透過 IFFT 將頻域 resource grid 轉為 time-domain samples.

為了降低多路徑延遲造成的 inter-symbol interference, 

系統會將 OFDM symbol 尾端的一小段複製到前方, 形成 cyclic prefix. 

最後, 這段含有 CP 的時域訊號會經由 RF front-end 與天線送入無線通道.

接收端取得 time-domain IQ samples 後, 

會先進行時間與頻率同步, 再移除 CP, 並透過 FFT 回到頻域.

由於接收端知道 SRS 的時頻位置與原始序列, 因此可以從接收到的頻域訊號中抽取 SRS RE,

並將接收值除以已知的 SRS 符號, 得到該子載波上的 channel frequency response, 也就是 CFR.

如果進一步對 CFR 做 IFFT, 則可以得到 delay-domain 的 channel impulse response, 也就是 CIR.

整體的資料傳輸流程如下圖所示:

在圖中顯示了以 SRS 為例的 OFDM 訊號流程:

SRS 先在頻域產生與映射, 經 IFFT 與 CP insertion 形成時域 waveform,

經過無線通道後, 接收端再透過 FFT 回到頻域.

利用已知 SRS 估測 CFR, 並可進一步轉換為 CIR.

透過上述的通道模型, 

雖然在頻域上, 理想 OFDM 模型可以寫成簡潔的:

但這個模型成立的前提是接收端已經完成足夠準確的時間同步, 頻率同步與取樣時鐘同步.

實際系統中, 三種最常見且重要的同步誤差分別是:

Timing Offset, Carrier Frequency Offset (CFO) 與 Sampling Frequency Offset (SFO).

Timing offset 可以理解為接收端選取 FFT window 時, 

起點相對於理想 OFDM symbol boundary 發生偏移. 

如果偏移仍落在 CP 可容忍範圍內, 資料解調不一定會立刻失敗, 但 CFR 會出現線性相位斜率.

若再將此 CFR 轉為 CIR, 則可能觀察到 CIR peak 的位置發生平移.

這對一般通訊解調可能只是相位補償問題, 

但對定位與 sensing 而言, 會被誤認為 propagation delay (對應到距離) 的變化.

CFO 則來自傳送端與接收端本地振盪器頻率不完全一致, 或由 Doppler shift 所造成. 

CFO 在 time domain 會表現為每個 sample 持續累積的相位旋轉.

若 CFO 較小, 主要造成 common phase error. 

若 CFO 較大, 則會破壞 OFDM 子載波正交性, 使能量洩漏到鄰近子載波,

形成 inter-carrier interference.

SFO 則是傳送端與接收端的取樣頻率不一致, 

與 timing offset 不同的是, SFO 的影響會隨時間累積. 

剛開始取樣點可能只偏移一點點, 

但經過多個 OFDM symbols 或長時間 SRS 量測後, 取樣點會逐漸偏離理想位置. 

因此 SFO 特別容易影響長時間通道追蹤、SRS-based sensing 與定位估測.

在 5G NR 系統中, 同步與相位誤差如下圖所示:

上圖則說明真實系統中同步誤差對此流程的影響.

• TO 主要表現為 FFT window 偏移, 使 CFR 產生線性相位斜率並造成 CIR peak 平移.
• CFO 使 time-domain samples 持續相位旋轉, 進而造成 common phase error 與 ICI.
• SFO 則使取樣點隨時間逐漸漂移, 對長時間 SRS 量測與 delay estimation 造成累積性誤差.

由此可見, CFR 與 CIR 不只是通道估測結果, 也會同時反映系統同步誤差, 

因此在通訊解調, 通道量測與 OFDM radar / positioning 應用中,

都需要謹慎區分真實通道效應與同步誤差.

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