• 沒有找到結果。

6.3 Channel Estimation

6.3.3 Numerical results

Reported in this subsection is some numerical simulation results for our channel estimation algorithm. Table 6.1 lists some simulation parameters. Fig. 6.5 shows the estimation result for one sub-channel for the case that the r.m.s. delay spread is 50ns.

The lower bound of the performance is also depicted in this figure. We can provide better performance by averaging because of the repeated preamble structure. For the cases that the channel response length is within the guard interval length, the optimal performance can be obtained, and it is independent of the channel response length. For the case that the channel response length is slightly longer than guard interval, the per-formance does not degrade seriously. Generally speaking, the channel gains with delay larger than guard interval length are small enough such that we can just ignore them.

Fig. 6.6 shows the simulation result for channels with different r.m.s. delay spread.

In this chapter, the channel estimation is done in time domain. Of course, we still can estimate the channel responses in frequency domain since the training sym-bols occupy different bands for different transmit antennas. However, the performance will degrade. Generally speaking, the time-domain channel estimator outperforms the frequency-domain channel estimator when the mean squared channel estimation error is considered [16][17]. In our case, if we want to estimate the channel response in fre-quency domain, the performance will degrade more than the cases in SISO systems.

This is because that we need some interpolation algorithms to estimate the frequency channel responses which are with no training tones. The “interpolation” will induce more estimation error.

Sample period 50ns Sequence parameters

Guard interval 16 (samples) K 4

Training symbol length

64 (samples) Nc(Nb2

) (AC period)

16

Table 6.1: Some simulation parameters adopted.

0 5 10 15 20 25 30 35

10−3 10−2 10−1 100

MSE for channel estimation (log−scale)

SNR (dB)

mean squared error of the channel estimator LS estimator

MSE lower bound (without averaging) LS estimator (noise reduced by averaging)

Figure 6.5: Mean squared channel estimation error. Noise variance can be reduced by averaging.

0 5 10 15 20 25 30 35 10−3

10−2 10−1 100

MSE for channel estimation (log−scale)

SNR (dB)

mean squared error of the channel estimator

max. dealy spread < GI

max. dealy spread > GI (r.m.s=200ns)

0 5 10 15 20 25 30 35 40 45

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Channel Tap Index n

Magnitude Response

Channel responses for r.m.s delay spread = 200ns

Figure 6.6: Mean squared channel estimation error for different channel delay spread.(Guard Interval = 16 samples.)

Chapter 7 Conclusion

A set of training sequences for a multiple antenna system should have perfect AC and CC properties within the maximum delay spread. This thesis presents a systematic transform domain approach for generating such sequences. Preambles based on these new sequences can be used in MIMO-OFDM WLAN systems. The new preamble se-quences can be regarded as a generalization of the PS sese-quences proposed in [3] for both can be generated by the same approach with different constraints. We show that the AC function and CC function are closely related to the DFTs of the desired sequences. Our method renders a natural interpretation and rigorous proof of the perfect AC function of the sequences proposed in [8].

The relationships between some parameters of the sequences and the system specifi-cations are established. Once the length of the OFDM guard interval is given, the length of training sequence is determined by the number of the transmit antennas. We provide a good solution when the elements of training sequence are limited to a finite constella-tion. We also propose synchronization and channel estimation algorithms based on the suggested preamble structure. Numerical simulation indicates that, since our preamble sequences possess the desired properties, our channel estimator yields optimal perfor-mance.

Several theoretical and implementation issues remain to be settled. For example, the effects of I-Q imbalance, nonlinear distortions, Doppler offset and Doppler spread are

likely to destroy and distort the original AC or CC properties, the robustness against these channel or signal jitters is of great concern to both practitioners and theorists. On the other hand, there are reports about the application of multi-dimensional signature sequences for MIMO-OFDMA or other MIMO MA systems. Multi-dimensional signa-ture sequences for Radar and sonar applications, though require different AC and/or CC properties, have been studied before as well. But the design of these sequences usually does not adopt the transform domain approach but involves a variety of other combi-natorial and ad hoc techniques. We believe that our approach can provide a avenue for discovering new sequences with desired properties.

Bibliography

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[2] R. A. Scholtz, and L. R. Welch, “Group characters: sequences with good correlation properties”, IEEE Trans. Inform. Theory, vol. IT-24, pp. 537-545, Sep. 1978.

[3] S. I. Park, S. R. Park, I. Song, and N. Suehiro, “Multiple-access interference re-duction for QS-CDMA systems with a novel class of polyphase sequences”, IEEE Trans. Inform. Theory, vol. 46, pp. 1448-1458, July 2000.

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[8] N. Suehiro and M. Hatori, “Modulatable orthogonal sequences and their application to SSMA systems,” IEEE Trans. Inform. Theory, vol. 34, pp. 93-100, Jan. 1988.

[9] P. Z. Fan and M. Darnell, Sequence design for communications applications, London, U.K.: Research Studies Press Ltd, 1996.

[10] A. van Zelst, T.C.W. Schenk, “Implementation of a MIMO OFDM-based wireless LAN system,” IEEE Trans. Signal Processing, vol. 52, no.2, pp. 82-88, Feb. 2004.

[11] T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun., vol. 45, pp. 1613-1621, Dec 1997.

[12] J.-J. van de Beek, M. Sandell, and P. O. Borjesson, “ML estimation of time and frequency offset in OFDM systems,” IEEE Trans. Signal Processing, vol. 45, pp.

1800-1805, July 1997.

[13] Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifi-cations, In IEEE Std 802.11-1999, 1999.

[14] B. M.Popovic, “Synthesis of power efficient multitone signals with flat amplitude spectrum,” IEEE Trans. Commun., vol. 39, pp. 1031-1033, July 1991.

[15] G. Caire and U. Mitra, “Training sequence design for adaptive equalization of multi-user systems,” in Proc. 32nd Asilomar Conf., vol. 2, pp. 1479-1483, 1998.

[16] W. Chen and U. Mitra, “Training sequence optimization: Comparisons and an alternative criterion,” IEEE Trans. Commun., vol. 48, pp. 1987-1991, Dec. 2000.

[17] Z. Cheng and D. Dahlhaus, “Time versus Frequency Domain Channel Estimation for OFDM Systems with Antenna Arrays,” Proc. of the 6th International Confer-ence on Signal Processing (ICSP’02), vol. 2, pp. 1340-1343, Aug. 26-30, 2002.

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ጰໜ౰ǴѠࠄѱΓǴ1980 ԃғǶ 1996 ~ 1998Ǻ࣪ҥѠࠄΒύǶ

1998 ~ 2002Ǻ୯ҥమ๮εᏢႝᐒπำᏢسǶ

2002 ~ 2004Ǻ୯ҥҬ೯εᏢႝߞπำᏢسᅺγ੤Ƕ

Graduate Course

1. Spread Spectrum Communications 2. Information Theory

3. Digital Communications 4. Random Process

5. Digital Signal Processing 6. Detection and Estimation 7. Array Signal Processing 8. Coding Theory

9. Design of Communication System VLSI Chips and Circuits 10.Digital Receivers

11.Analog Circuit Design

12.Digital Integrated Circuit Design and Modeling

13.Semiconductor Microwave Device

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