Boundary Variation Distribution

In this section, we simulate the boundary variation of FFT window detection in both AWGN channel and multi-path channel specified by the 802.15.3a channel modeling sub-committee report [22] for low SNR condition (SNR=2dB) and high SNR condition (SNR=20dB) with CFO=400KHz. In the following figures, “matched-filter off” represents only turning on dynamic searching window (coarse band detection) without matched-filter (FFT window detection) to find boundary; “matched-filter 128 taps” represents conventional matched-filter using all 128 compared taps to find boundary; and “matched-filter 32 taps” represents proposed matched-filter using 32 compared taps to find boundary.

In AWGN channel environment, as long as the estimated FFT window boundary is located during pre guard intervals (32 sample indexes), circular convolution property can be obtained for FFT transforming received data into frequency domain. FIG 5.20 and FIG 5.21 are the boundary variation in AWGN channel. It shows that only using dynamic window is sufficient to converge FFT window boundary in 16 variation samples (-8 to 7) with FER<1%, and boundary variation of dynamic window will be greatly improved by increasing SNR as shown in FIG.5.21.

But in multi-path channel environment, FFT window boundary will not always locate at the estimated index of dynamic window because of multi-path interference. Moreover, boundary variation effects the switching time of received time-interleaved OFDM symbols, degrading

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circular convolution property of received OFDM symbols and reducing the ability to resist multi-path interference. The loss of multi-path energy not captured in cyclic prefix (CP) will results in ICI effect. To find the correct FFT window boundary as possible, matched-filter is needed for FFT window detection. Since the 802.15.3a channel modeling sub-committee report specified four multi-path channel characteristics and corresponding measured model parameters from CM1 to CM4, and TI has proposed using 90th percentile channel realization (the best 90%

channel model) of CM1~CM4 environment for performance evaluation [7]. We measure the boundary variation of CM1~CM4 for original and the 90th percentile channel realization from FIG 5.22 to FIG 5.37.

CM1 channel model is based on a 0~4m line of sight (LOS) channel environment with an RMS delay spread of 5ns. From FIG 5.22 to FIG 5.25, it shows that only turn on dynamic window detection has boundary variation of 12 indexes in 90th percentile CM1 channel, and the residual effective CP length in worst variation case becomes only 62.5% from the original CP length (60.6ns). But by adding matched-filter for FFT window detection, residual effective CP can increase to 93.75% from the original CP for conventional 128-tap matched-filter and 87.5% for proposed 32-tap matched-filter in SNR=2dB.

CM2 channel model is based on a 0~4m non line of sight (NLOS) channel environment with an RMS delay spread of 8ns. It is usually seen as the typical environment for UWB channel model.

FIG 5.26 to FIG 5.29 shows the boundary variation of 90th percentile CM2 channel. The residual effective CP of dynamic window in worst variation case becomes only 50% from the original CP

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and distorts circular convolution property seriously. Conventional 128-tap matched-filter still maintain effective CP of 93.75% from the original CP, and for proposed 32-tap matched-filter, effective CP is 81.25% from the original CP which has a little degradation from CM1 channel.

CM3 channel model is based on a 4~10m NLOS channel environment with an RMS delay spread of 14ns and boundary variation distribution shows in FIG 5.30 to FIG 5.33. Boundary variation of dynamic window extends to 19 indexes. Thus in worst variation case residual effective CP is less than 40% from the original CP. Conventional 128-tap matched-filter has effective CP of over than 90% from the original CP; and proposed 32-tap matched-filter has effective CP of 78.125% from the original CP.

CM4 channel model is generated to fit a 25 ns RMS delay spread to represent an extreme NLOS channel environment and is the worst case of UWB channel model. FIG 5.34 to FIG 5.37 shows the boundary variation distribution. The serious multi-path interference makes dynamic window varies 25 sample indexes (from –10 to +15) in 90th percentile CM4 channel. Thus we must use matched-filer researching FFT window boundary of ±16 sample indexes from the estimated boundary of dynamic window. Conventional 128-tap matched-filter converges boundary variation to 4 sample indexes, still maintaining effective CP of 87.5% from the original CP. On the other hand, proposed 32-tap matched-filter has effective CP of 71.125% from the original CP. But it still can resolve CM4 channel model with acceptable SNR loss in PER simulation compared with perfect synchronization.

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FIG. 5.20 Boundary variation in AWGN channel with CFO=400KHz, SNR=2dB

FIG. 5.21 Boundary variation in AWGN channel with CFO=400KHz, SNR=20dB

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FIG. 5.22 Boundary variation in original CM1 channel, CFO=400KHz, SNR=2dB

FIG. 5.23 Boundary variation in best 90% CM1 channel, CFO=400KHz, SNR=2dB

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FIG. 5.24 Boundary variation in original CM1 channel, CFO=400KHz, SNR=20dB

FIG. 5.25 Boundary variation in best 90% CM1 channel CFO=400KHz, SNR=20dB

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FIG. 5.26 Boundary variation in original CM2 channel, CFO=400KHz, SNR=2dB

FIG. 5.27 Boundary variation in best 90% CM2 channel, CFO=400KHz, SNR=2dB

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FIG. 5.28 Boundary variation in original CM2 channel, CFO=400KHz, SNR=20dB

FIG. 5.29 Boundary variation in best 90% CM2 channel, CFO=400KHz, SNR=20dB

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FIG. 5.30 Boundary variation in original CM3 channel, CFO=400KHz, SNR=2dB

FIG. 5.31 Boundary variation in best 90% CM3 channel, CFO=400KHz, SNR=2dB

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FIG. 5.32 Boundary variation in original CM3 channel, CFO=400KHz, SNR=20dB

FIG. 5.33 Boundary variation in best 90% CM3 channel, CFO=400KHz, SNR=20dB

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FIG. 5.34 Boundary variation in original CM4 channel, CFO=400KHz, SNR=2dB

FIG. 5.35 Boundary variation in best 90% CM4 channel, CFO=400KHz, SNR=2dB

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FIG. 5.36 Boundary variation in original CM4 channel, CFO=400KHz, SNR=20dB

FIG. 5.37 Boundary variation in best 90% CM4 channel, CFO=400KHz, SNR=20dB

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