Chapter 4 Synchronization Techniques for MIMO OFDM Systems
4.4 Sampling Clock Offset Synchronization
4.4.1 Sampling Clock Offset Estimation
4.4.2.3 Farrow Structure
where cm,n are real-valued coefficients of those approximating polynomials. Then the resulting interpolator will be able to produce continuous delay. In addition, the well-known Farrow structure can be applied to the approximating polynomials for low-complexity realization, which will be shown in the next section.
4.4.2.3 Farrow Structure [34,35,42]
Increasing filter length of an interpolator results in better phase and magnitude responses. However, the filter length of an interpolator cannot be arbitrarily long. Here are two reasons: First, the length of composite channel, including the transmission channel and the interpolator of the receiver, must be shorter than the guard interval to avoid ISI. Second, longer interpolator length means higher computational and hardware
53
complexities. After some trials, we found that a 4-tap interpolator is sufficient. To further reduce the complexity, Farrow structure is applied to implement the interpolator.
Since the fractional delay to be compensated varies over time. The design of high-quality FD filter is difficult. Farrow [35] suggested that every filter coefficient of the FIR FD filter could be expressed as a Pth-order polynomial in the variable delay parameter D.
Design a set of filters approximating a fractional delay in the desired range, 1
0≤ d ≤ , and then approximate each coefficient as a P-order polynomial of fractional delay. The transfer function of the filter becomes
∑
This is the well-known Farrow structure, which is illustrated in Figure 4.13.
(.)
Figure 4.13 Farrow structure of an interpolator.
54
An interpolator with Farrow polynomial approximation coefficients is able to produce continuous delays. The delay accuracy is affected by the filter length L and the Farrow polynomial order P. After some trials, we found that it is sufficient for an interpolator with L= 4 and P=3. Note that polynomial-based interpolator, such as Lagrange interpolation and B-spline interpolation, can be directly realized by the Farrow structure without further approximation.
55
Chapter 5
Simulation Results and Comparisons
In this chapter, we will evaluate the performance of the discussed and proposed synchronization techniques, by applying them to IEEE 802.11n system, and compare the performances among various methods.
5.1 Simulation Environment
As for the simulation environment, AWGN channel and multi-path channel are assumed. Since IEEE 802.11 uses 5GHz band as the major carrier, we utilize the power delay profile measured in indoor environment at 5.3 GHz by using a wideband sounder
56
for simulations. Table 5.1 shows the model parameters.
Table 5.1 Channel Model Parameters [37] for simulations.
Tap No.
Delay (ns)
Power (dB)
Amplitude
Distribution Doppler Spectrum
1 0 0 Rayleigh Classical / Flat
2 36 -5 Rayleigh Classical / Flat
3 84 -13 Rayleigh Classical / Flat
4 127 -19 Rayleigh Classical / Flat
We assume the total transmit power from the multiple transmit antennas is the same as the transmit power from the single transmit antenna. It is also assumed the fading amplitudes from each transmit antenna to each receive antenna are mutually uncorrelated Rayleigh fading, and the averaged signal power at each receive antenna from each transmit antenna are the same.
Table 5.2 shows the simulated MIMO system parameters. Low mobility is considered in our simulations. Therefore, the Doppler shift frequency is set to 150Hz which corresponds to a mobility of 32 km/hr. We simulate some carrier frequency offset cases from 0.6 to 1.9 carrier spacing, and find the results are almost the same. For the reason, the carrier frequency offset is assumed as 1.35 carrier spacing in the following simulation environment. As for sampling clock offset, we simulate the clock offset by Lagrange interpolator with 50 interpolation taps, and try 50, 100, and 200 ppm cases, and find the results are almost the same. Therefore, the sampling clock offset is set to 100 ppm in the following simulations.
57
Table 5.2 Simulated MIMO system parameters.
Sample period 50 ns
Total number of carriers 64
The number of pilot carriers 4
The number of data carriers 48
Symbol period 4µs
Guard interval 0.8µs
Modulation QPSK
Sampling frequency 20 MHz
Carrier spacing 312.5 kHz
Doppler shift frequency 150 Hz
Carrier frequency offset 1.35 carrier spacing
Sampling clock offset 100 ppm
Max. no. of Tx/Rx antennas 4/3
5.2 Performance of Frame Detection
Figure 5.1 shows the frame timing error probability due to frame detections. When the estimated frame timing is over 32 samples away from the exact frame start, we define it is a failed frame detection. The probability of failed frame detections is called the frame timing error probability. As the number of transmitter antennas is increased, the cyclical shift will also increase the difficulty of detecting the frame start. Even in
58
this condition, we can see that the probability is close to zero when the SNR is higher than 5 db.
Figure 5.1 The frame timing error probability vs. SNR due to the frame detection for various numbers of Tx antennas.
Figure 5.2 shows the estimated frame timing distribution due to the frame detection when the SNR is 10 db. The numbers of receiver antennas are all one. When the number of receiver antennas is more than one, the receiver antennas perform the frame detections independently. We can detect the frame start successfully, even if the number of spatial data streams is up to four.
59
Figure 5.2 The estimated frame timing distribution due to the frame detection, SNR = 10 db, (a) NT=1. (b) NT=2. (c) NT=3. (d) NT=4.
60
Figure 5.3 The frame timing error probability vs. SNR due to the frame detection.
5.3 Performances of Symbol Timing Synchronization
For the reason mentioned above, the performance decreases slightly when the number of transmitter antenna increases. Figure 5.4 shows the probability of timing errors when there are more than 5 samples estimated error. We can find that the method we used for the coarse symbol timing estimation still works well even if the number of the spatial data stream is up to four.
Figure 5.5 shows the comparison among the three methods discussed in chapter 4 for the fine symbol timing estimation. The DTDFS method achieves the similar performance with the conventional CFDFS method. Its major drawback is the high computation complexity compared with the conventional CFDFS method. However,
61
the STDFS method has a smaller complexity than the previous two methods. Since the search range of fine symbol synchronization can be reduced to +/- 5 samples by the coarse symbol timing estimation, we can reduce the computation complexity significantly. The performance of the simplified time-domain method is also similar to the other two methods mentioned above as shown in Figure 5.5.
In Figure 5.7 and 5.8, it is assumed that the number of receiver antennas is one and the SNR is 10db. Figure 5.6 shows the MSE comparison between the coarse and fine symbol timing estimations by using the double-sliding-window method and the STDFS method, respectively. In this figure, the numbers of the transmit antennas and receive antennas are set to two and three, respectively. In these figures, we can find that the fine symbol timing estimation can achieve a significant improvement of the timing estimation accuracy. Table 5.3 shows the error probability comparison between the coarse and fine symbol timing estimations.
62
Figure 5.4 The symbol timing error probability vs. SNR due to the coarse symbol timing estimation with the double-sliding-window method for various Tx antenna
numbers.
Figure 5.5 BER performance vs. SNR comparison of the discussed methods for fine symbol timing estimation.
63
Figure 5.6 MSE performance vs. SNR comparison between the coarse symbol timing estimation and the combined coarse and fine symbol timing estimation, NT=2,
NR=3.
64
Figure 5.7 The estimated symbol timing distribution due to the coarse symbol timing synchronization, SNR = 10 db, (a) NT=1. (b) NT=2. (c) NT=3. (d) NT=4.
Figure 5.8 The estimated symbol timing distribution due to the fine symbol timing synchronization with STDFS method, SNR = 10 db, (a) NT=1. (b) NT=2. (c) NT=3. (d)
NT=4.
65
Table 5.3 The error probability of the symbol timing estimation.
(a) The error is within +/-3 samples
1×1 2×3 4×3
NT×NR
SNR Coarse Fine Coarse Fine Coarse Fine
0 0.5787 0.4260 0.3413 0.1720 0.4633 0.2480
5 0.2013 0.0847 0.1100 0.0127 0.1840 0.0213
10 0.0133 0.0047 0.0180 0.0020 0.0220 0.0027
15 0 0 0.0027 0 0 0
20 0 0 0 0 0 0
25 0 0 0 0 0 0
(b) The error is within +/-1 samples
1×1 2×3 4×3
NT×NR
SNR Coarse Fine Coarse Fine Coarse Fine
0 0.7407 0.4553 0.6847 0.1987 0.6987 0.2773
5 0.4513 0.0933 0.5020 0.0193 0.4380 0.0340
10 0.1433 0.0053 0.3987 0.0027 0.2500 0.0087
15 0.0073 0 0.3407 0.0013 0.0733 0.0020
20 0 0 0.2713 0.0007 0.0053 0
25 0 0 0.1480 0 0 0
66
5.4 Performance of Carrier Frequency Offset Synchronization
Here, we test the three discussed methods. We can see the improvement of the proposed smoothed method clearly in Figure 5.9. Since the other two methods use only one point to estimate the frequency offset, they have high noise level. The new smoothed method can significantly reduce the noise effect. However, the performance improvement comes at extra hardware cost.
Figure 5.9 MSE performances vs. SNR comparison of the proposed new method and other conventional methods for the carrier frequency offset estimation.
67
Figure 5.10 shows the performance of the coarse frequency offset estimation and the overall combined coarse and fine carrier frequency offset estimation, using the proposed smoothed method.
Figure 5.10 MSE performances vs. SNR comparison of the coarse frequency offset estimation and the overall combined coarse and fine carrier frequency offset estimation,
using the proposed smoothed method.
Figure 5.11 shows the performance of the coarse carrier frequency offset estimations. Figure 5.12 shows the performance of the coarse and fine carrier frequency offset estimations. In Figures 5.11, 5.12, we can find that the performance will be better when the number of the receiver antenna increases. However, there is no improvement when the number of the spatial data streams increases.
68
Figure 5.11 MSE performances vs. SNR of the coarse carrier frequency offset estimation, using the proposed smoothed method.
Figure 5.12 MSE performances vs. SNR of the overall combined coarse and fine carrier frequency offset estimation, using the proposed smoothed method.
69
5.5 Performance of Sampling Clock Offset Synchronization
5.5.1 Performance of Sampling Clock Offset Estimation
In Section 4.4.1, we discussed three feasible methods for the sampling clock offset estimation. The fist one directly averages all the possible cases to estimate the clock offset. For lower complexity considerations, the second method separates the pilot carrier in two groups first, then finds each group’s averaged phase and finally obtains the offset estimation from the phase difference. The proposed third method reduces the computational complexity by using the most apart pilot carriers to estimate the sampling clock offset.
Figure 5.13 shows the comparison between the three methods. It shows that the new method achieves the similar performance compared to the other two methods, with less computational complexity.
70
Figure 5.13 MSE performance vs. SNR comparison of the new and two conventional methods for sampling clock offset estimation.
5.5.2 Performance of Sampling Clock Offset Compensation
In Figure 5.14 – 5.17, we can find the performances of various interpolators are similar when NT≦2. However, the performance of the Cubic B-spline interpolator is poor when NT=3 or 4, because of serious magnitude distortions at the high frequency band. Hence, the Cubic B-spline interpolator is less suitable for IEEE 802.11n systems.
Although the Cubic B-spline is not suitable for IEEE 802.11n system, it has good performance in some other systems, which adopt bit loading process, because of coherent magnitude responses.
71
Furthermore, the performances of windowed-sinc interpolator with rectangular window, least-square interpolator, and equiripple interpolator are slightly better than the other interpolators. Table 5.4 shows the computational complexity comparison of various interpolator designs [43]. One can find that the computational complexities of polynomial-based interpolators, Lagrange and Cubic B-spline, are slightly lower than the other interpolators. Unfortunately, the Cubic B-spline interpolator performance is poor when applied to IEEE 802.11n system. However, the Lagrange interpolator has similar performance compared to the three interpolators. For the reason, we suggest that Largange interpolator design is more suitable when applied to IEEE 802.11n standard.
Table 5.4 The computational complexity comparison of various interpolator designs for sampling clock offset compensation. L=4, P=3. [43]
Interpolator type + /− ×constant << or>> ×
Lagrange 11 2 4 3
Cubic B-spline 11 4 3 3
Equiripple General LS.
Windowed- Sinc
15 16 0 3
72
(a)
(b)
Figure 5.14 BER performance vs. SNR comparison of the major resampling interpolators for sampling clock offset compensation. NT=1, NR=1.
(a) polynomial-based interpolators. (b) windowed sinc interpolators.
73
(a)
(b)
Figure 5.15 BER performance vs. SNR comparison of the major resampling interpolators for sampling clock offset compensation. NT=2, NR=1.
(a) polynomial-based interpolators. (b) windowed sinc interpolators.
74
(a)
(b)
Figure 5.16 BER performance vs. SNR comparison of the major resampling interpolators for sampling clock offset compensation. NT=3, NR=1.
(a) polynomial-based interpolators. (b) windowed sinc interpolators.
75
(a)
(b)
Figure 5.17 BER performance vs. SNR comparison of the major resampling interpolators for sampling clock offset compensation. NT=4, NR=1.
(a) polynomial-based interpolators. (b) windowed sinc interpolators.
76
Chapter 6 Conclusion
In this thesis, we investigate all the required synchronization operations and related design techniques that jointly achieve frame, symbol, carrier, and sampling clock synchronizations for MIMO OFDM systems. Practical designs are applied to IEEE 802.11n receiver. Performances are measured under the multi-path fading channels. From simulation results, the proposed synchronization schemes work well in those conditions.
In the frame detection, we use the received signal power to set the threshold, and detect the beginning of a frame by comparing the auto-correlation outputs to the threshold [44]. In the symbol timing synchronization, we perform the coarse symbol timing estimation first with the double-sliding-window method [45], then adjust the
77
symbol timing by the proposed STDFS method to get the more accurate symbol timing estimation than the current techniques. Owing to the features of the IEEE 802.11n preambles which are composed of ten repeat short training symbols in the short training field, two repeat long training symbols, and the guard interval in the long training filed, we utilize the features to enhance the carrier frequency offset estimation by averaging the available auto-correlation outputs, and take advantage of the multi channel diversity of MIMO for better synchronization. In the sampling clock offset estimation, we reduce the computation complexity by only computing the most apart pilots, and take advantage of the multi channel diversity of MIMO for better synchronization. As for the sampling clock compensation, we find that Lagrange interpolation is suitable for IEEE 802.11n standard.
In the future, we will further reduce the computational complexity of the overall synchronization schemes. In the frame synchronization, we will try to reduce the computational complexity by only comparing the real part of the auto-correlation outputs, or by averaging the squares of the auto-correlation real part and the auto-correlation imaginary part. Furthermore, we will try to max-ratio combine the possible pilot pairs to obtain more accurate clock offset estimation, and max-ratio combine the estimated MIMO multi channel parameter samples for better parameter estimation. Up to now, the simulations are conducted by floating-point operations. We will also conduct fixed-point simulations so that we can reflect practical software and hardware realization and implementation designs.
78
References
[1] R. W. Chang, “Synthesis of band limited orthogonal signals for multichannel data transmission,” Bell Syst. Tech. J., vol. 45, pp. 1775-1796, Dec. 1966.
[2] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Pers. Commun., vol. 6, no. 3, pp. 311–335, Mar. 1998.
[3] WWiSE, “WWiSE proposal” http://www.wwise.org/
[4] TGnSync, “TGnSync proposal” http://www.tgnsync.org/home
[5] IEEE Std. 802.11, Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, 1999 edition.
[6] IEEE Std. 802.11a-1999, Wireless LAN Medium Access Control and Physical Layer specifications: High-speed physical layer in the 5 GHz band.
[7] R. V. Nee and R. Prasad, OFDM for Wireless Multimedia Communications. Boston:
Artech House, 2000.
[8] H. Nogami, and T. Nagashima, “A frequency and timing period acquisition technique for OFDM System,” Proc. IEEE Personal, Indoor, Mobile Radio Commun., pp. 1010-1015, 1995.
[9] T. Pollet, M. V. Bladel, and M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency and weiner phase noise,” IEEE Trans. Commun., vol. 43, pt. 1, pp.
191-193, Feb.- Apr. 1995.
[10] A. Palin and J. Rinne, “Symbol synchronization in OFDM system for time selective channel conditions,” Proc. Electronics, Circuits and Systems, 1999, Proceedings of ICECS '99, The 6th IEEE International Conference on, vol. 3, pp.
1581 – 1584, Sept. 1999.
[11] B. Yang, K. B. Letaief, R. S. Cheng, and Z. Cao, “Timing recovery for OFDM
79
transmission,” Selected Areas in Communications, IEEE Journal on, vol. 18, pp.
2278 - 2291, 2000.
[12] F. Classen and H. Meyr, “Frequency synchronization algorithms for OFDM systems suitable for communication over frequency selective fading channels,”
Vehicular Technology Conference, 1994 IEEE 44th, vol.3, pp. 1655 - 1659, June 1994.
[13] M. Speth, D. Daecke and H. Meyr, “Minimum overhead burst synchronization for OFDM based broadband transmission,” Global Telecommunications Conference, 1998, GLOBECOM 98, The Bridge to Global Integration, IEEE, Volume: 5 , pp.
2777 – 2782, Nov. 1998.
[14] E. Kuusmik, “Wireless Lan integration into mobile phone,” Master’s Thesis, Department of Signals and Systems, Chalmers University of Technology, Finland, September 2004.
[15] ANSI/IEEE Standard 802.11b, 1999 Edition.
[16] ANSI/IEEE Standard 802.11g, 2003 Edition.
[17] Y. Asai, S. Kurosaki, T. Sugiyama, and M. Umehira, “Precise AFC scheme for performance improvement of SDM-COFDM,” Proc. Vehicular Technology Conference, 2002. Proceedings. VTC 2002-Fall. 2002 IEEE 56th, vol. 3, pp.
1408 – 1412, Sept. 2002.
[18] T. C. W. Schenk and A. van Zelst, “Frequency synchronization for MIMO OFDM wireless LAN systems,” Proc. Vehicular Technology Conference, 2003. VTC 2003-Fall, 2003 IEEE 58th, vol. 2, pp. 781 – 785, Oct. 2003.
[19] S. Johansson, M. Nilsson, and P. Nilsson, “An OFDM timing synchronization ASIC,” Proc. Electronics, Circuits and Systems, 2000. ICECS 2000. The 7th IEEE International Conference on, vol.1, pp. 324 – 327, Dec. 2000.
80
[20] J. Liu and J. Li, “Parameter estimation and error reduction for OFDM-based WLANs,” Mobile Computing, IEEE Transactions on, vol. 3, pp. 152-163, 2004.
[21] A. Fort, J.-W. Weijers, V. Derudder, W. Eberle, and A. Bourdoux, “A performance and complexity comparison of auto-correlation and cross-correlation for OFDM burst synchronization,” Proc. Acoustics, Speech, and Signal Processing, 2003.
Proceedings. (ICASSP '03). 2003 IEEE International Conference on, vol. 2, pp.
341-344, April 2003.
[22] A. N. Mody and G. L. Stuber, “Receiver implementation for a MIMO OFDM system,” Proc. Global Telecommunications Conference, 2002. GLOBECOM '02.
IEEE, vol. 1, pp. 716 – 720, Nov. 2002.
[23] A. N. Mody and G. L. Stuber, “Synchronization for MIMO OFDM systems,” Proc.
Global Telecommunications Conference, 2001. GLOBECOM '01. IEEE, vol. 1, pp. 509 - 513, Nov. 2001.
[24] G. L. Stuber, J. R. Barry, S. W. McLaughlin, Y. Li, M. A. Ingram, and T. G. Pratt,
“Broadband MIMO-OFDM wireless communications,” Proceedings of the IEEE, vol. 92, pp. 271-294, 2004.
[25] K. Taura, M. Tsujishita, M. Takeda, H. Kato, M. Ishida, and Y. Ishida, “A digital audio broadcasting (DAB) receiver,” Consumer Electronics, IEEE Transactions on, vol. 42, pp. 322-327, 1996.
[26] E. Zhou, X. Zhang, H. Zhao, and W. Wang, “Synchronization algorithms for MIMO OFDM systems,” Proc. Wireless Communications and Networking Conference, 2005 IEEE, vol. 1, pp. 18 – 22, March 2005.
[27] N. P. Sands and K. S. Jacobsen, “Pilotless timing recovery for baseband multicarrier modulation,” IEEE Journal on Selected Areas in Communications, Volume: 20, Issue: 5, pp. 1047 – 1054, June 2002.
81
[28] M. Speth, S. Fechtel, G. Fock, and H. Meyr, “Optimum receiver design for OFDM-based broadband transmission .II. A case study,” Communications, IEEE Transactions on, vol. 49, pp. 571-578, 2001.
[29] T. Pollet, P. Spruyt and M. Moeneclaey, “The BER performance of OFDM systems using non-synchronized sampling,” Proc. IEEE Global Telecommunications Conference, pp. 253-257, 1994.
[30] T. Pollet and M. Peeters, “Synchronization with DMT modulation,” IEEE Communications Magazine, Volume: 37 Issue: 4, pp. 80 -86, April 1999
[31] F. M. Gardner, “Interpolation in digital modems-part I: fundamentals,” IEEE Transactions on Communication, vol. 41, pp. 502-508, Mar 1993.
[32] L. Erup, F. M. Gardner, R. A. Harris, “Interpolation in digital modems-part II:
implementation and performance,” IEEE Transactions on Communications, vol.
41, pp. 502-508, Jun 1993.
[33] E. Martos-Naya, J. Lopez-Fernandez, L. D. del Rio, M.C. Aguayo-Torres and J. T.
E. Munoz, “Optimized interpolator filters for timing error correction in DMT systems for xDSL applications,” IEEE Journal on Selected Areas in Communications, Volume: 19, Issue: 12, pp. 2477 –2485, Dec. 2001.
[34] T. I. Laakso, V. Valimaki, Matti Karjalanen and U. K. Laine, “Splitting the unit delay,” IEEE Signal Processing Magazine, pp. 30-60, Jan 1996.
[35] C. W. Farrow, “A continuously variable digital delay element,” Proc. IEEE Int.
Symp. Circuit and System, pp. 2641-2645, Jun 1988.
[36] N. J. Fliege, Multirate Digital Signal Processing: Multirate Systems, Filter banks, Wavelets, Chichester, John Wiley, 1994.
[37] X. Zhao, J. Kivinen, and P. Vainnikainen, “Tapped delay line channel models at 5.3 GHz in indoor environments,” Proc. Vehicular Technology Conference, 2000.
82
IEEE VTS-Fall VTC 2000. 52nd, vol. 1, pp. 1 – 5, Sept. 2000.
[38] Y. Li, N. Seshadri, and S. Ariyavisitakul, “Channel estimation for OFDM systems with transmitter diversity in mobile wireless channels,” Selected Areas in Communications, IEEE Journal on, vol. 17, pp. 461-471, 1999.
[39] Y. Li, “Simplified channel estimation for OFDM systems with multiple transmit antennas,” Wireless Communications, IEEE Transactions on, vol. 1, pp. 67-75, 2002.
[40] S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” Selected Areas in Communications, IEEE Journal on, vol. 16, pp. 1451-1458, 1998.
[41] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time block coding for wireless communications: performance results,” Selected Areas in Communications, IEEE Journal on, vol. 17, pp. 451-460, 1999.
[42] V. Valimaki and T. I. Laakso, “Principles of fractional delay filters,” IEEE International Conference on Acoustics, Speech, and Signal Processing, 2000.
[42] V. Valimaki and T. I. Laakso, “Principles of fractional delay filters,” IEEE International Conference on Acoustics, Speech, and Signal Processing, 2000.