正交分頻多功技術 (orthogonal frequency division multiplexing) 具有對抗相鄰訊號干擾 (ISI) 和頻率選擇性的功效，因此經常使用於當今之無線通訊系統中。然而，此技術容易受到訊號上轉換和下轉換的過程中所產生的相位雜訊 (phase noise) 所影響。相位雜訊是振盪器相位的隨機擾動所造成，此雜訊會產生兩個不利於訊號偵測的效應，分別是: 共同相位誤差 (common phase error) 和載波間互相干擾 (intercarrier interference) 。此兩者除了造成傳輸訊號振幅不必要的改變外，還有載波間互相的正交性也被嚴重破壞。
因此在這篇論文裡，我們提出一種反覆交替估計相位雜訊和偵測傳輸訊號的疊代程序來改善和補償相位雜訊造成的問題。在偵測傳輸訊號的時候，上一階段所估計出來的相位雜訊會被當作完美的已知參數來使用；相同地，在對相位雜訊做估計的時候，上一階段被偵測出來的傳輸訊號會被當作正確的訊號而加以利用。為了做這些動作，我們使用了基於子空間和導引訊號穿插的方案，這樣的方案會把導引訊號安置在一個和傳輸訊號正交的子空間上面。過去文獻中所提出的方法習慣把導引訊號分配在數個指定的載波上面，這樣的方式也可視為基於子空間方法的一項特例。但是，這樣的方式對導引訊號和傳輸訊號的子空間來說可能不是最好的選擇。我們經由一些數值方法的模擬
來驗證所提出方案的成效，並比較不同子空間選擇的優劣。

Orthogonal frequency division multiplexing (OFDM) have been widely adopted in modern
wireless systems due to its ability to combat intersymbol interference (ISI) and frequency
selectivity. However, OFDM systems are extremely sensitive to phase noise that may exist
during the up and down-conversion at the transmitter and receiver sides. Phase noise causes
two main detrimental effects: common phase error (CPE) and intercarrier interference (ICI).
In this work, an iterative procedure is proposed where phase noise estimation (i.e., estimation
of CPE and ICI) and data detection are performed interchangeably. The estimated phase
noise parameters are assumed to be perfect when performing data detection and the detected
data symbols are assumed to be correct when performing the phase noise estimation. To do
this, we adopt the subspace-based pilot insertion scheme where pilot symbols are embedded
in a subspace orthogonal to that of the data symbols. The conventional scheme that allocates
a given number of subcarriers for pilot transmission can be viewed as a special case of the
subspace-based approach, but this may not be the best choice of pilot and data subspaces.
The efficacy of the proposed scheme is demonstrated through numerical simulations.

Bibliography
[1] A. G. Armada, “Understanding the effects of phase noise in orthogonal frequency division
multiplexing (OFDM),” IEEE Trans. Broadcast., vol. 47, pp. 153-159, 2001.
[2] D. Petetrovic, W. Rave, G. Fettweis, “Phase noise suppression in OFDM using a Kalman
filter,” in Proc. WPMC, Yokosuka, Japan, Oct. 2003.
[3] D. Petetrovic, W. Rave, G. Fettweis, “ Intercarrier interference due to phase noise
in OFDM - estimation and suppression,” Vehicular Technology Conference, 2004.
VTC2004-Fall. 2004 IEEE 60th, vol. 3.
[4] D. Petetrovic, W. Rave, G. Fettweis, “Phase noise suppression in OFDM including intercarrier
interference,” in Proc. Intl. OFDM Workshop, 2003.
[5] S. Wu, Y. Bar-Ness, “A phase noise suppression algorithm for OFDM-based WLANs,”
IEEE Commun. Letters, vol. 6, no. 7, Dec. 2002.
[6] S. Wu, P. Liu, Y. Bar-Ness, “Phase noise estimation and mitigation for OFDM systems,”
IEEE Trans. Wireless Commun., vol. 5, no. 12, Dec. 2006.
[7] Angiras R. Varma, Chandra R. N. Athaudage, Lachlan L.H Andrew, Jonathan H. Manton,
“Phase noise compensation for OFDM WLAN systems using superimposed pilots,”
Communication systems, 2006. ICCS 2006. 10th IEEE Singapore International Conference
on, pp.1-5, Oct. 2006.
[8] A. Goldsmith, ”Wireless Communications”. Cambridge University Press 2005.
29
[9] A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: a unifying
theory and numerical methods for characterisation,” IEEE Trans. Circuit Syst. I, vol.
47, no. 5, May 2000.
[10] C. Pirak, Z. Jane Wang, K. J. Ray Liu, and S. Jitapunkul, “A data-bearing approach
for pilot-embeddeding frameworks in space-time coded MIMO systems,” IEEE Trans.
Signal Process, vol. 54, no. 10, Oct. 2006.
[11] C. Pirak, Z. JaneWang, K. J. Ray Liu, and S. Jitapunkul, “Adaptive channel estimation
using pilot-embedded data-bearing approach for MIMO-OFDM systems,”IEEE Trans.
Signal Process., vol. 54, no. 12, Dec. 2006.
[12] P. Hoeher and F. Tufvesson, “Channel estimation with superimposed pilot sequence,”
IEEE Trans. Inform. Theory, vol.49, no.10, Apr. 2003, pages 951–964.
[13] S. C. Kay, ”Fundamentals of Statistical Signal Processing: Estimation Theory,” Prentice
Hall, 1993.
[14] C. Pirak, Z. J. Wang, “A data-bearing approach for pilot-embedding frameworks in
space-time coded MIMO systems,” IEEE Trans. Signal Process., vol. 54, no. 10, October
2006
[15] A. Hjorungnes, D. Gesbert, D. P. Palomar, ”Unified Theory of Complex-Valued Matrix
Differentiation,” Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE
International Conference on, vol.3, no., pp.III-345-III-348, 15-20 April 2007