Maximum likelihood

Although we used parallel cross correlation and trellis search to find the best option of symbol boundary. But the performance isn’t good enough, due to bad correlation property in re-sampled training sequence. So we propose a method based on ML after trellis search. First, we found the CIR corresponds to each pattern from parallel cross correlation result. And the formula could be express as

*

But it is sensitive under CFO effects, so we must do CFO cancelation first to avoid CFO effects. We already have correlation output of each pattern from previous parallel correlation so we choose the pattern index j which has maximum correlation power in trellis survival path. Then we could divide the correlation between each

Then we could get the CFO information by the angle difference from z.

1 1 ( ) Fig 3.2.5 shows the Mean absolute error of CFO estimation. This CFO estimator may be not precise than general CFO estimator which used repeated symbol structure due to it suffer from inter symbol interference caused by multipath fading. But it is precise enough to do the CIR acquisition and maximum likelihood function.

Fig 3.2.5 Mean absolute error of CFO

After we get the CFO information by previous estimation method, the CIR acquisition by cross-correlation could consider the rotation caused by CFO to get more accuracy.

The formula of CIR acquisition would become

* pattern index order and it shown as Fig. 3.2.6. In order to recovery the original signal to make maximum likelihood function correctly, we must find the initial tap in CIR.

So we defined matrix H by the channel taps with circular shift that we get from correlation and matrix P which is the pattern sequence corresponds to the each channel taps.

Fig.3.2.6 CIR acquisition

{ , , , } And another ML function which is used to find the correct CIR is defined as below

2 Δ When the correct CIR is determined, we could check the symbol boundary candidate which is produce by previous trellis result. We defined a mask matrix corresponds to each symbol boundary candidate and a ML function to get the final decision about

m r e n trellis candidate









(3.22) Where M is a mask matrix correspond to each trellis candidate that we want to make decision from them. So the symbol boundary t corresponds to minimum value m in trellis candidate is the best option of the symbol boundary. But it is obviously that the complexity of those matrix computations in ML function is high, so we must reduce it complexity without performance loss in symbol boundary decision.

Fortunately, the second ML function could be reduce as follow

Δ Δ from ML. Under this formula derivation, the first ML which is used to find correct position of each taps in CIR is unnecessary because we only need to know which taps correspond to the which pattern index. As mentioned above, we could get some

complexity reduction to make this method more feasible. Table 3-1 shows the complexity derivation as mentioned above. Original ML means the original concept to do boundary detection and we could reduce the complexity by equation 3.23 and finally combine trellis result to reduce the region of detection.

Original ML ML reduction Combine

coarse detect

Chapter 4 Simulation

The simulation results for AGC, packet detection and boundary detection algorithms are shown in this chapter. MATLAB is chosen as simulation language, due to its ability to mathematics, such as matrix operation, numerous math functions, and easily drawing figures. And the parameters are shown in Table 4-1.

Parameter Value

Modulation 16 QAM

Coding Rate 2/3

PSDU Length 1024 Bytes

Packet No 2000

FFT size 512

width and depth of ADC 6 and 8

Path Loss -20dB to -80dB

Shadowing vibrate 3dB

Channel Model IEEE802.15.3c CM2

RMS delay spread 4 ns

Fig. 4-1 and Fig. 4-2 are the signal of VGA inputs and the signal of ADC outputs respectively. The signal is suffer from path loss and dynamic shadowing effects so the input signal will be very small and vibrates in time. After AGC control we could see that the signal of ADC outputs is more stable and keep in the dynamic range of ADC. At the noise level, AGC would let VGA achieve low power and avoid signal saturation when signal comes suddenly. At the signal level, AGC would track the rest range of VGA to get stable without saturation by 96 samplings.

Fig. 4-1 VGA input signal

Fig. 4-2 ADC output signal

Fig. 4-3 shows that the propose AGC adjustment result compare with desire VGA gain when shadowing period 2π within whole packets when SNR is 10dB.

AGC would track the shadowing effects such that the adjustment of VGA to form a sine wave. Although there are a little gain errors caused by AWGN effects but it still in acceptable region.

Fig. 4-3 Adjustment of VGA

Fig. 4-4 shows the performance of the proposed packet detection algorithm.

It’s Simulation in 48 sampling length as correlation windows. TH₂ and TH₃ is set 0.035 and 0.0325 as Fig. 3.1.3. We evaluate the performance of the algorithms by plotting the packet detect error rate against the SNR. Packet detection error rate means the number of packet detection error over the number of transmitted packets and misdetection means we detected the packet over 96 sampling of each packet when packet comes. Packet detection error includes false alarm and misdetection. On the Fig. 4-4, this approach would lower the quantization error to improve the performance of packet detection.

Fig. 4-4 Packet loss rate

Next we compare the performance between propose AGC and conventional AGC algorithm [1][2] which is constant reference power and without adaptive weight on the Fig. 4-5. When dynamic shadowing effects is 2π, the propose AGC is 0.8dB loss in SNR compare with ideal AGC at PER 1% and the conventional AGC is 2.6dB loss in SNR compare with ideal AGC. The propose AGC gain 1.8dB in SNR under dynamic shadowing effects. Regardless of propose AGC or conventional AGC the performance will get worse when dynamic shadowing effects become worse. But the resistance of dynamic shadowing effects is more obviously between them. There is 3.5dB loss of SNR at PER 1% between propose AGC and conventional AGC under dynamic shadowing effects is 2.5π.

Fig. 4-5 PER of AGC for different level of shadowing effects

4.2 Boundary detection

The settings of the proposed boundary detection are B=96, Z=6, K=3. We evaluate the performance of the algorithms by plotting the Boundary error rate against the SNR. The Boundary error is defined by sample offset is over two or more samples.

The correct symbol boundary of OFDM symbols can be tolerant of ±1 sample offsets.

Fig. 4-6 shows the performance of the proposed algorithm and conventional cross correlation metric reference as [7][8]. And Fig. 4-7 shows the estimated position with

respect to ideal position at SNR=5.

Fig. 4-6 Boundary error rate of different detect method

Fig.4-7 Estimated Position

The conventional correlation metric isn’t work in this platform due to bad correlation property. And the propose correlation metric would improve the performance but isn’t good enough and we could get much better performance to achieve less than 0.1% at SNR=6. Fig. 4-8 shows the boundary error rate in the CFO range of ±400 ppm. The results indicate that the synchronization performances degrade insignificantly if CFO is less than ±200 ppm. The high CFO resistance also means the proposed synchronizer being well-suited to most wireless standards without pre-compensation of frequency errors

Fig. 4-8 CFO tolerance of Boundary detection

Chapter 5

Conclusion and Future Work

5.1 Conclusion

In this thesis, we introduce automatic gain control and frame synchronization algorithm for 802.15.3c systems. The path loss and dynamic shadowing effects could be solved by AGC with several schemes to prevent saturation or suffer high quantization noise from ADC and get only 0.8dB loss compare with ideal case. And the propose frame synchronizer could work well on 802.15.3c system by combine cross-correlation and ML method.

5.2 Future work

The performance of AGC still get relative loss of SNR under dynamic shadowing effects get worse, so it must need more complex calculation to approach the behavior of shadowing effects.

The trend of wireless broadband communications had created the need of frequency-domain front-end receivers that can relax the analog-to-digital requirements and benefit the suppression of narrow band interference. The concepts of this work would try to translate from time domain to frequency domain.

Bibliography

[1] V.P.G. Jimenez , M.J.F.-G. Garcia , F.J.G. Serrano and A.G. Armada, “Design and implementation of synchronization and AGC for OFDM-based WLAN receivers”, IEEE Trans. Consum. Electron, vol. 50, no 4, pp 1016–1025, Nov 2004.

[2] A. Fort , W. Eberle, “Synchronization and AGC proposal for IEEE 802.11a burst OFDM systems” Global Telecommunications Conference, 2003. GLOBECOM '03.

IEEE, pp 1335–1338, Dec 2003 .

[3] J. V. D. Beek, M. Sandell, and P. O. Borjesson, “ML estimation of timing and frequency offset in OFDM Systems” IEEE Tran.on Signal Processing, vol. 45, no 7, pp. 1800-1805, July 1997.

[4] K.Wang, M.Faulkner, J. Singh and I.Tolochko, “Timing synchronization for 802.11a WLANs under multipath channels” ATNAC, Melbourne, Dec 2003

[5] T. M. Schmidl and D. C. Cox,“ Robust Frequency and Timing Synchronization for OFDM” IEEE Trans. on Communications, vol. 45, no. 12, pp. 1613-1621, Dec. 1997.

[6] S. H. Muller-Weinfurtner, “On The Optimality of Metrics for Coarse Frame Synchronization in OFDM: A Comparison” PIMRC 98, pp533- 537, Sept. 1998, Boston, MA.

[7] F. Tufvesson, O. Edfors, and M. Faulkner, “Time and frequency synchronization for OFDM using PN-sequence preambles” in Proc. Vehicular Technology Conf. (VTC), Amsterdam, The Netherlands, 1999, vol. 4, pp 2203–2207.

[8] B. Yang, K. B. Letaief, R. S. Cheng, and Z. Cao, “Timing recovery for OFDM transmission” IEEE J. Sel. Areas Commun., vol. 18, no. 11, pp. 2278–2291, Nov.

2000.

[9] S Nandula, K Giridhar, “Robust timing synchronization for OFDM based wireless LAN System,” Proc. IEEE International Conference on Convergent Technologies for Asia-Pacific Region, TENCON 2003, vol 4C, pp. 1558-1561, Bangalore, India, 2003.

[10] S. Yong, “TG3c Channel Modeling Sub-committee Final Report”, Samsung Advanced Institute of Technology, March 2007.

[11] A. Mathew and Z. Lai, “Observations of the UMass Measurements,” IEEE 802.15.06-0137-00-003c, Denver, Mar 2006.

[12] A. F. Molisch, D. Cassioli, C. –C. Chong, S. Emami, A. Fort, B. Kannan, J.

Karedal, J. Kunisch, H. Schantz, K. Siwiak, and M. Z. Win, “A comprehensive standardized model for ultrawideband propagation channels,” IEEE Trans. Antennas and Propagation, to appear.

[13] C. -C. Chong Y. E. Kim, S. K. Yong and S. S. Lee., “Statistical characterization of the UWB propagation channel in indoor residential environment,” Wiley J. Wireless Commun. Mobile Comput. (Special Issue on UWB Communications), vol. 5 no. 5, pp.

503-512, Aug. 2005.

[12] J. Lago-Fernández. and. J. Salter J. Lago-Fernandez and J. Salter, “Modelling impulsive interference in DVB-T: statistical analysis, test waveforms & receiver performance”, R&D white Paper, WHP080, April 2004.

[13] M.C. Jeruchim, P. Balaban, K.S. Shanmugan, Simulation of Communication Systems: Modelling, Methodology, and Techniques, 2^nd Ed., Kluwer Academic / Plenum Publishers, Aug 2000.

[14] K. L. Blackard, T.S. Rappaport, and C.W. Bostian, “Measurements and Models of Radio Frequency Impulsive Noise for Indoor Wireless Communications”, IEEE Journal on Selected Areas in Comms., Vol. 11, No. 7, Sep 1993.

[15] Yahya, Mazlaini,” Practical Packet Detection and Symbol Timing Synchronization Scheme for Packet OFDM System” RF and Microwave Conference, 2006. RFM 2006. International, pp. 421 – 425, 12-14 Sep. 2006

[16] T. Liang, X. Li, R. Irmer, G. Fettweis, “Synchronization in OFDM-based WLAN with transmit and receive diversities” Personal, Indoor and Mobile Radio Communications, 2005. PIMRC 2005. IEEE 16th International Symposium on, Vol.

2, pp. 740-744, Sep 2005

[17] B. Kim ; C. Shin ; S. Choi; “Packet detection scheme using cross correlation and complex multiplication in MB-OFDM UWB system”Information, Communications

& Signal Processing, 2007 6th International conference on, pp. 1-5 10-13 Dec. 2007