• As mention above, we explore the correlation property of ICI outside the band and derive an approximate mathematical expression from it. We found that the correlation values are based solely on the ICI-to-noise ratio. It should be noted that the ICI correlation property derived applies not only to the flat fading, but also to the frequency selective fading. Furthermore, this property applies not only to classical multipath Rayleigh fading, but also to arbitrary different Doppler spectrum shapes in each path. The assumptions of approxi-mate expression of normalized ICI autocorrelation are so general that we can extend ICI correlation property to many applications. Even for different fre-quency offsets or Doppler spectrums coming from multiple transmitters and channels, this approximation of normalized ICI autocorrelation still works.
Some interesting topics arise and worth investigating:
– ICI and CFO mitigation in MIMO OFDM – ICI and CFO mitigation in Cooperative OFDM – ICI and CFO mitigation in OFDMA
• Through this assumption of perfect channel knowledge, the improvement of the detection performance confirms the substantial gains of numerical analysis in Sec. 4.1. On the other hand, we keep digging into most of our research based on the assumption of perfect channel knowledge until now. More detail of the actual implementation of ICI correlation property should be go through.
– We should incorporate the online estimation of covariance matrix of resid-ual ICI plus noise into the proposed detection.
– We may incorporate channel estimation into the proposed LMMSE de-tection, which may resolve the estimation error of CSI.
– We may also incorporate the FEC decoder into the proposed LMMSE de-tection with blockwise whitening of residual ICI plus noise. This scheme is a form of turbo equalization.
Appendix A: The Whiteners of Residual ICI Plus Noise
As mentioned in Chap. 4 and 5, we do blockwise whitening over windows of size 2q+1 by Kz, which depends on the settings of q, p, K. In this Appendix, we consider all Kz listed in the thesis and illustrate how these whitener are calculated from the properties of autocorrelation of residual ICI in Chap.3.
As defined in Chap. 4, we have Kz = E[zmzHm] and the aforesaid blockwise whitening of residual ICI plus noise zm is given by
e
A tradeoff between complexity and performance can be achieved by choosing q, p, and K. All the settings of {q, p, K} that have been used in the thesis are as follows:
• {K = 1, q = 1, p = 2},
• {K = 1, q = 1, p = 1},
Values of the Whiteners of Residual ICI (Infinite SNR)
At infinite SNR, consider the setting {K = 1, q = 1, p = 2} as (A.1), for which the
where σc02 = E[|cm,0|2] is the residual ICI power outside band K=0.
Next, we consider the setting {K = 1, q = 1, p = 1} as (A.3). By comparing Hm in (A.3) with (A.1), we note that the absent items am−1,m−2 and am+1,m+2, which should be considered by rearranging the terms of sum in (3.5) or (3.14).
Kz|{K=1,q=1,p=1}=
We note that the whiteners of residual ICI can be any scaled version of square root of K−1z given above. Consequently, the normalized autocorrelation matrix of residual ICI is a good choice instead of Kz. After normalizing Kz with σ2ck, the whiteners of residual ICI approximates to a constant matrix.
Values of the Whiteners of Residual ICI Plus Noise
At finite SNR, consider the setting {K = 1, q = 1, p = 2} as (A.1), for which the
After normalizing Kz given in (A.11), the whitener of residual ICI plus noise approximates to a matrix only depends on σ2c1/σW2 . It is straightforward to extend this propoerty to the other settings of {q, p, K}.
Gains of the Whiteners of Residual ICI
We consider the four cases
1. {K = 0, q = 1, p = 1}, 2. {K = 1, q = 1, p = 2}, 3. {K = 1, q = 1, p = 1},
4. {K = 2, q = 1, p = 1}, all at infinite SNR.
The corresponding Kz matrices are given above.
By (4.11), the resulting post- to pre-whitening SINR ratios are 2.0588, 2.9258, 8.7052, and 35.25, respectively.
Please note that the pre-whitening SINR of case (3) and (4) are worse than case (2). If we compare the post-whitening SINR of case (2), (3) and (4) with the conventional SINR Es/σc1 , the resulting SINR ratios of case (2), (3) and (4) will be 2.9258, 5.7146, and 24.94 times beter than Es/σc1, respectively. In Fig. 4.6, the difference of SINR between unwhitening and {K = 1, q = 1, p = 1} methods is close to 5.7146 (7.57 dB). Simulation confirms theory.
However, the mathematical relation between SINR and bit error rate (BER) is not straightforward. The proposed MLSE of {K = 2, q = 1, p = 1} indeed provides a lower error floor than {K = 1, q = 1, p = 1} with perfect CSI assumed. But Fig. 5.1 shows that the two proposed MLSE have very close and indistinguishable performances at practical SNR. As a result, we provide {K = 1, q = 1, p = 1}
as the default setting of the proposed MLSE detection. Furthermore, we provide {K = 2, q = 1, p = 1} as the default setting of the proposed MMSE/iterative MMSE for its significant SNR improvement.
Simulation of the Imperfect Whiteners
As mentioned, the whitener of residual ICI plus noise approximates to a matrix only depends on σ2c1/σW2 . For {K = 1, q = 1, p = 1}, we have the whitener as
It seems reasonable to assume that σW/c12 will be estimated first and apply to (A.12) and (A.13) when we estimate the whitener’s coefficients. We also assume a mismatch model of NIR: ]σW/c12 = γ × σW/c12 , where γ is a factor related to estimation error. When γ = 1, it means a perfect estimation σW/c12 without error. Figs. A.1 shows some simulation results for the TU6 channel. These results show that the mismatched NIR ]σW/c12 can be 0.25 times or 2 times as σ2W/c1 without performance loss in proposed MLSE {p = q = K = 1}. Similary, in proposed MMSE {p = q = K = 2}, the tolerance of mismatched NIR ranges form 0.7 to 1.05 times as σW/c12 .
10 15 20 25 30 10
−610
−510
−410
−310
−210
−1E
b/N
0(dB)
Bit Error Rate
Proposed MMSE, iter num=0 γ=1.05, MMSE, iter num=0 γ =0.7, MMSE, iter num=0 Proposed MMSE, iter num=1 γ=1.05, MMSE, iter num=1 γ =0.7, MMSE, iter num=1 Proposed MLSE K=1 γ =2, MLSE K=1 γ =0.25, MLSE K=1
Residual ICI−free bound,K=1
Figure A.1: Performance of proposed MLSE p = q = K = 1 and MMSE p = q = 1, K = 2, with imperfect whitener in the TU6 channel, at N = 128 and Tsa = 714 ns fdTsaN = 0.137 and under QPSK subcarrier modulation.
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簡
簡 簡 歷 歷 歷
Hai-wei Wang received the B.S. degree in control engineering and the M.S. degree in electronics engineering from National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 1995 and 1999, respectively. She was with Silicon Integrated Systems Corp., Hsinchu, during 1999–2002 and with Realtek Semiconductor Corp., Hsinchu, during 2002–2004. She is currently pursuing the Ph.D. degree in electronics engi-neering from the National Chiao Tung University. Her research interests are in the areas of digital communications and communication theory.
著
著 著 作 作 作 目 目 目 錄 錄 錄
• Journal articles
– H.-w. Wang, D. W. Lin, and T.-H. Sang, OFDM signal detection in dou-bly selective channels with whitening of residual intercarrier interference and noise, IEEE J. Sel. Areas Commun., vol. 30, no. 4, pp. 684-694, May 2012.
• Conference and proceeding papers:
– H.-w. Wang, D. W. Lin, and T.-H. Sang, OFDM signal detection in dou-bly selective channels with whitening of residual intercarrier interference and noise, in IEEE Veh. Technol. Conf., May 2010, pp. 1V5.
– H.-w. Wang, D. W. Lin, and T.-H. Sang, LMMSE detection of OFDM signals in time-varying channels with partial whitening of intercarrier interference and soft decision feedback in IEEE WPMC. Conf., 2012, accepted.
– H.-w. Wang, D. W. Lin, K.-C. Hung, and Y-T. Lee, ”Design and DSP software implementation of mobile WIMAX baseband transceiver func-tions,” in proceedings of the 2007 conference on Emerging direction in embedded and ubiquitous computing, ser. EUC’07. Berlin, Heidelberg:
Springer-Verlag, 2007, pp. 181-192.