Sampling Clock Synchronization

Sampling clock synchronization consists of three blocks: Resampler, SCO estimator and loop filter. These three blocks constitute a timing recovery loop which tracks out the SCO and

adjusts the timing error. In our receiver design, we propose the fully digital sampling clock synchronization. The relative simulations of each block are illustrated in the following section.

(1) Resampler

As mentioned previously, the resampler exploits FIR filter to interpolate the intermediate points between two consecutive samples. Since the number of taps in FIR filter plays an important role in power consumption, we should reduce the taps of FIR filter as far as possible. However, the truncated sinc function raises the side-lobe amplitude in frequency domain so that the interpolated signals are not as perfect as ideal interpolated signals. In order to improve the finite-tap FIR filter, a Kaiser window is applied as truncation window. The simulations of different numbers of taps with direct truncated sinc function or sinc function truncated by Kaiser window are shown in Fig 3.24.

0 50 100 150 200 250 300 350

10^-7 10^-6 10^-5 10^-4

SCO (ppm)

MSE

Mean square error of FIR interpolation

sinc & kaiser 8-tap sinc & kaiser 6-tap sinc & kaiser 4-tap sinc 8-tap sinc 6-tap sinc 4-tap

Fig 3.24 MSE of FIR interpolation

For evaluating the performance of interpolated signals, mean square error (MSE) is used to measure the error between transmitted signals and interpolated signals. In this figure, the shape parameter value β of Kaiser window is decided as 4 by simulation. As we can see, the performance is apparently improved after applying Kaiser window. Comparing the sinc function and sinc function truncated by Kaiser with the same taps, we can find a large amount of MSE improvement. Considering the number of taps, the more taps yield the more accurate signals in the case of sinc function. However, the MSE curve tends to saturate at 8-tap in the case of sinc function with Kaiser window. As a result, we can keep the number of taps to 6-tap or 8-tap for the least interpolation error.

(2) Sampling clock offset estimation

There are many SCO estimation algorithms in relative researches, and most of them estimate the CFO jointly. We exploit the LLS (linear least square) algorithm to find the regression line so that the SCO and CFO can be jointly obtained. As mentioned in Chapter 2, reference [14] proposed a “CFD/SFD algorithm” to do joint CFO and SCO tracking. And reference [13] mentioned a “1-D LLS algorithm” which is also based on linear least square method. Table 3.3 lists the one-shot simulation results of the above two algorithms and our proposed algorithm. Three channels are simulated which are Gaussian channel, Ricean channel with Doppler spread 70Hz and Rayleigh channel with Doppler spread 70Hz. We assume the initial SCO is 20 ppm, the residual fractional CFO is 0.02 (subcarrier spacing) and AWGN is 15db.

Initial SCO = 20ppm, residual CFO = 0.02 (subcarrier spacing)

Table 3.3 Joint SCO and CFO estimation (one shot)

In order to evaluate the estimation error, we compute the mean of one-shot estimation SCO and its standard deviation. As we can see, the CFD/SFD algorithm [14] will generate a negative mean error due to the unequally distributed continual pilots. In contrast to CFD/SFD algorithm, the 1-D LLS algorithm [13] has a larger positive mean error with respect to other two algorithms. Our proposed algorithm has the most accurate mean estimation value but the worse standard deviation than CFD/SFD algorithm. The joint CFO estimation is also listed in

! for reference. It is apparently that our proposed algorithm has the best performance in terms of mean value.

For observing the tracking error, we simulate these three algorithms in 648 OFDM symbols. The simulation result is depicted as Fig 3.25. The mean square errors of residual SCO are 0.1487, 0.2133, and 0.1275 respectively. Our proposed algorithm gets the best

performance, and the next is CFD/SFD algorithm.

Fig 3.25 SCO tracking

(3) Loop filter

How to choose the parameters of loop filter is a tradeoff between convergence speed and steady-state standard deviation of estimation result. Fig 3.26 shows the convergence speed and corresponding steady-state standard deviation in the different values of K . _p

0 50 100 150 200 250 300 350

-5 0 5 10 15 20

Symbol index

Residual SCO

SCO tracking (Kp=1/4)

0 50 100 150 200 250 300 350

-5 0 5 10 15 20

Symbol index

Residual SCO

SCO tracking (Kp=1/32)

(a) 1

p 4

K = (b) 1

p 32

K =

Fig 3.26 SCO tracking with different parameter

In above simulation, we assume initial SCO=20 ppm and AWGN=15db. As Fig 3.26(a) is depicted, large K_p yields fast convergence speed of less than 50 samples. However, a

huge steady-state mean square error of 0.6714 ppm is also produced which reduce system performance much. And Fig 3.26(b) shows the small K causes slow fast convergence _p speed of more than 200 samples as well as a small mean square error of 0.1287 ppm. As mentioned, the convergence speed requests to be less than one TPS frame which contains 68 OFDM symbols. In order to look after both sides, a multi-stage SCO tracking is adopted as shown in Fig 3.27.

(a) Two-stage (b) Three-stage Fig 3.27 Multi-stage SCO tracking

Fig 3.27(a) shows two-stage SCO tracking. The initial tracking period uses a large K_p

like 1/4 for fast convergence. Afterward, we switch to a small K_p like 1/32 for decreasing steady-state standard deviation. The convergence can be achieved during less than 68 symbols and small mean square error in steady-state can be obtained. In general, the multi-stage SCO tracking is feasible if we do not concern the hardware cost. Multi-stage operation will yield more robust tracking system. Three-stage SCO tracking is depicted in Fig 3.27(b). The third

stage applies a very small K_p 1/256 so that the steady-state standard deviation can be further reduced. In the mobile reception, the multi-stage tracking is needed because of Doppler frequency shift.