應用於OFDM 系統之強健化 內部接收機架構設計 指導老師:高永安 學 生:蘇家弘 A Robust Inner Receiver Structure Design for OFDM Systems

Outline OFDM system block diagram OFDM baseband signal model Inner receiver structure Channel estimation LMS algorithm Selection of  Pilot-based phase estimator Dynamic simulation by Simulink 5.0 Conclusion and future work

OFDM system block diagram Up convert CFO SFO 強調兩顆震盪器 Eq . n: n-th sample point k: k-th subcarrier l: l-th subcarrier Down convert

Carrier Frequency Offsets CFO simulation CFO is due to the oscillator mismatch from up convert and down convert f

CFO calculation for IEEE 802.11a Maximum quantity of CFO = 20ppm for 5GHz k: k-th subcarrier, l: l-th OFDM symbol , N=64, n=80

Sampling Frequency Offsets SFO is caused by the oscillator mismatch between A/D & D/A converter SFO simulation TTX TRX When TRX > TTX

SFO calculation for IEEE 802.11a TTX=1/(20MHz 400Hz), TRX=1/(20MHz 400Hz) k: k-th subcarrier, l: l-th OFDM symbol , N=64, n=80

OFDM baseband signal model OFDM baseband signal after IFFT at the transmitter side The received OFDM baseband signal before FFT -------- (2) -------- (1) 要述說The CFO has been compensated in time domain, 所以after FFT 之後只有residual CFO n: n-th sample point k: k-th subcarrier l: l-th subcarrier

OFDM baseband signal model The received OFDM signal is influenced by channel effect, residual CFO, SFO, initial symbol timing offset and before FFT we can describe (2) as follows: -------- (3) Td : initial symbol timing offset Hk : frequency response of channel : residual CFO : initial phase offset Ts : sampling clock period at the transmitter Ts’: sampling clock period at the receiver CFO SFO 要述說The CFO has been compensated in time domain, 所以after FFT 之後只有residual CFO

OFDM baseband signal model The ICI produced by residual CFO is much smaller compared to Gaussian noise. N’k,l combine Ik,l and Nk,l and (3) can be modified as: -------- (4) 與AWGN相比,由殘餘CFO所造成的ICI非常小,所以…

OFDM baseband signal model The effect of CFO and SFO can be represented as : -------- (5) and

The difference between inner and outer receiver M. Speth, S. A. Fechtel, G. Fock and H. Meyr, “Optimum Receiver Design for Wireless Broad-band Systems Using OFDM-Part II,” IEEE Trans. Commun., vol. 49, pp.571-578, Apr. 2001. Decoding & demodulation

Inner receiver structure Input signal Frame detection:利用training sequence來作,找出frame Symbol timing:利用training sequence找出OFDM symbol的起始位置 Buffer:收到的訊號在此補償由訊框同步粗調和符元同步細調估計出的偏差量 FFT

Inner receiver structure Training sequence Initial coefficient FFT D a t Update coefficient of equalizer Phase compensation Frequency Domain Equalizer Pilot 1.訊號通過FFT之後,先將training sequence利用LSE(Least Square Error)的方法求出等化器初始值 2.然後將等化器初始值與接在training sequence後面的data部分相乘,補償通道效應和相角旋轉 3.雖然CFO已經在time domain預先補償過,但是仍舊會有殘餘的相角偏差,所以在此是以每個OFDM symbol中的pilot來估測 4.而經過等化過後的訊號, 補償由pilot估測出來的殘餘相角偏差 5.最後在送至outer receiver作解碼解調變的工作 ****************************************************************************************************************************************** 1.在這個架構中,等化器的部分是採用LMS演算法,其初始值是由training sequence利用LSE所求得 2.等化過後且補償過殘餘相角的訊號作為LMS的output signal,也就是Yk,l,其中k代表子載波,l代表OFDM symbol 3.Yk,l經過hard decision之後作為LMS等化器的desired signal, dk,l 4.因為每個子載波上的LMS等化器,可能會因為殘餘相角偏移量隨著OFDM symbol累積過大而追不上相角變化,所以input signal必須預先補償由前一個OFDM symbol估測出來的殘餘相角偏差,這也市此內部街收機架構的一大重點,使用pilot-based phase estimator來輔助LMS等化器追蹤相角 Pilot-based phase estimator Phase compensation Hard decision Outer receiver

Channel estimation by least square error Lk,l : transmitted training sequence Rk,l : received training sequence : equalized training sequence Hk : channel Nk,l : noise : equalizer initial coefficient Equalized training sequence  l : 2 long training symbol k : 52 subcarrier In 802.11a

Channel estimation by least square error Error between transmitted signal and equalized signal Find optimal Heq,k for minimum value of ek  Setting the partial derivative of ek

k is the step size that modified by channel condition LMS algorithm Filtering output: Yk=wkHXk Error estimation: ek=dk-Yk Tap-weight vector adaptation * After hard decision k is the step size that modified by channel condition

selection of  Normalized-LMS & time average Training sequence 0 <  < 1

Pilot-based phase estimator Received pilots After giving the appropriate weight Maximum ratio combination (MRC) pilot C’ Im Im A’ C A B B’ ∠2 ∠1 O Re O Re

Simulation by Simulink 5.0 從MathWork網站上download下來

1.沒有包括MAC/PHY介面和PLCP 標頭，傳送封包未含短訓練符元，每個OFDM symbol之間沒有時間加窗法 2.接收端的部分，不考慮訊框偵測、CFO估測和符元同步細調

Unequalized signal spacing plot Channel A (Ts=50ns, TRMS=50ns ) SNR=10dB Residual CFO =0.01 SFO=800Hz (Ts=1/(20MHz-400), =1/(20MHz+400 ) Code rate=1/2, QPSK 44 OFDM symbol per packet 1000 packet

Applied the proposed inner receiver structure After channel equalization 紅點

IEEE 802.11a PER v.s. SNR =0.15 =0.3 Channel A (Ts=50ns, TRMS=50ns ) Residual CFO =0.01 SFO=800Hz (Ts=1/(20MHz-400), =1/(20MHz+400 ) PSDU=256 bytes 1000 packet 每次傳256bytes,而不同調變會有不同的OFDM symbol數目產生,但是在這download下來的Simulink 5.0只適用在偶數個OFDM symbol的情況,所以某些調變為了配合會多或少一個OFDM symbol,經過測試之後結果並不會因為多或少一個OFDM symbol而有很大差異 曲線顯示的效能不理想 只以AWGN通道作測試時就是這樣,所以並非程式有誤

IEEE 802.11a PER v.s. SNR Channel B (Ts=50ns, TRMS=100ns ) Channel C (Ts=50ns, TRMS=150ns )

IEEE 802.11a PER v.s. SNR Channel D (Ts=50ns, TRMS=200ns ) Channel E (Ts=50ns, TRMS=250ns )

PER v.s. SNR with different  =0.3 Channel A (Ts=50ns, TRMS=50ns ) Residual CFO =0.01 SFO=800Hz (Ts=1/(20MHz-400), =1/(20MHz+400 ) 44 OFDM symbol per packet 1000 packet

PER v.s. SNR with different  Channel C (Ts=50ns, TRMS=150ns ) Channel E (Ts=50ns, TRMS=250ns )

PER v.s. SNR with different  =0.3 Channel A (Ts=50ns, TRMS=50ns ) Residual CFO =0.01 SFO=800Hz (Ts=1/(20MHz-400), =1/(20MHz+400 ) 200 OFDM symbol per packet 1000 packet

PER v.s. SNR with different  Channel C (Ts=50ns, TRMS=150ns ) Channel E (Ts=50ns, TRMS=250ns )

PER v.s.  with different channel =0.3 Channel A (Ts=50ns, TRMS=50ns ) Channel C (Ts=50ns, TRMS=150ns ) Channel E (Ts=50ns, TRMS=250ns ) SNR=10dB Residual CFO =0.01 SFO=800Hz (Ts=1/(20MHz-400), =1/(20MHz+400 ) 44 OFDM symbol per packet 1000 packet

PER v.s.  with different channel =0.3 Channel A (Ts=50ns, TRMS=50ns ) Channel C (Ts=50ns, TRMS=150ns ) Channel E (Ts=50ns, TRMS=250ns ) SNR=10dB Residual CFO =0.01 SFO=800Hz (Ts=1/(20MHz-400), =1/(20MHz+400 ) 200 OFDM symbol per packet 1000 packet

Conclusion A Robust Inner Receiver Structure Simulink 5.0  pilot-based phase estimator 1. Compensate the residual CFO 2. Assist the LMS equalizer in phase tracking  Dynamic simulation

Future work At present The future work Frequency selective fading channel LMS algorithm The future work Slow fading channel Other adaptive algorithms Decoding block of Simulink 5.0

Reference IEEE Std 802.11a-1999, Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications: High Speed Physical Layer in the 5GHz Band. Yung-An Kao; Chia-Hung Su; Shih-Kai Lee; Chung-Lung Hsiao; Po-Lin Chio, “A robust design of inner receiver structure for OFDM systems,” IEEE Conference. on Consumer Electronics, pp. 377-378, Jan. 2005. S. Haykin, Adaptive Filter Theory, Englewood Cliffs, NJ: Prentice-Hall, 2002, 4th Ed. M. Speth, S. A. Fechtel, G. Fock and H. Meyr, “Optimum Receiver Design for Wireless Broad-band Systems Using OFDM-Part I,” IEEE Trans. Commun., vol. 47, pp. 1668-1677, Nov. 1999. M. Speth, S. A. Fechtel, G. Fock and H. Meyr, “Optimum Receiver Design for Wireless Broad-band Systems Using OFDM-Part II,” IEEE Trans. Commun., vol. 49, pp.571-578, Apr. 2001. Doufexi, A.; Armour, S.; Butler, M.; Nix, A.; Bull, D.; McGeehan, J.; Karlsson, P., “A comparison of the HIPERLAN/2 and IEEE 802.11a wireless LAN standards,” IEEE Magazine on Comm. Vol. 40, pp.172-180, May 2002. 黃凡維, 2004, “一揭最小均方差頻域等化器應用於正交分頻多工系統之特性分析,” 長庚大學電機工程研究所碩士論文

Any Questions?

Channel estimation by LSE

Channel estimation by LSE Applying we obtain and R:real part I:imaginary part

Channel estimation by LSE

Comparison between the MRC pilot and the original pilot multiplication Only add MRC pilot

Comparison between the MRC pilot and the original pilot addition Original pilot multiplication After mutual multiplying

Channel A MRC pilot 4 pilot multiplying