# OQPSK Synchronization Parameter Estimation Based on Burst Signal Detection
## 3 Performance Evaluation
### Performance Simulation of Synchronization Parameter Estimation
#### 3.2.3 Performance Simulation of Timing Error Estimation  
Figure 6 shows the estimation accuracy of QQPSK signals under different timing estimation algorithms. Simulation conditions: the roll-off factor is set to 0.35, \(N=108\); \(L=12\); and the frequency offset is zero. It can be seen from the figure that the [PERSON], [PERSON], and AVN [15; 16; 17] algorithms are completely invalid at this time, and only the suggested algorithm and the Ye algorithm [18] can be used. We note that to make the system suitable for the proposed algorithm and the Ye algorithm, we especially emphasize the up-sampling of local \(UW\) and staggering the in-phase component and quadrature component by half a symbol period in Section 2.1.  
Figure 5: Accuracy of the phase offset estimation algorithm under different \(UW\) lengths.  
Figure 6: Timing error estimation algorithm used on QQPSK.  
Since [PERSON], [PERSON], and AVN do not work for OQPSK, in order to carry out a fair comparison, we also test OPSK signals in the following. Figure 7 shows the accuracy of the timing error estimation algorithms under different roll-off factors. Simulation conditions: adopt the QPSK signal; \(N=108\); \(L=12\); the frequency offset is zero. It can be seen from the figure that the performance of the [PERSON], [PERSON], and AVN algorithms is greatly affected by the roll-off factor, while the proposed algorithm and Ye algorithm are not sensitive to the roll-off factor. In addition, we can also see that the MSE performance of the proposed algorithm is slightly better than that of Ye and much better than that of [PERSON], [PERSON], and AVN.  
If the roll-off factor is set to 0.35, a normalized frequency offset of 0.05 is added, and the other conditions remain the same as those in Figure 7, then we can get the simulation in Figure 8. Figure 8 implies that with the existence of frequency offset, the Ye algorithm fails, while other algorithms are not affected.  
From the above comparison, we can draw a conclusion: firstly, for the traditional [PERSON], [PERSON], and AVN algorithms, the performance is not only greatly affected by the roll-off factor, but also, they cannot be used on OQPSK signals. Secondly, although Ye solved these problems, it lost the ability of anti-frequency offset.  
As we mentioned in Section 3.2.1, the anti-frequency offset ability in practical applications must be at least within the range of \((-0.1\text{:}0.1)\). Figure 9 shows the anti-frequency offset ability of the algorithm in this article when it is used on OQPSK signals. Simulation conditions: \(N=108\); \(M=9\); \(L=12\); the roll-off factor is 0.35; the added normalized frequency offsets is \([-0.1\text{:}0.1]\) in steps of 0.025. It can be seen from the figure that as the frequency offset becomes larger, the estimation accuracy will slightly decrease, but  
Figure 7: Simulation of the timing error estimation algorithm under different roll-off factors.  
overall, the difference is not large. Therefore, the timing algorithm in this article has good anti-frequency offset ability, and its range can fully meet the needs of the actual situation.  
All in all, the timing estimation algorithm in this article not only has high accuracy, but also, its performance is not affected by the roll-off factor; it also has a good ability of anti-frequency offset. In addition, the value used in the interpolation of the timing estimation algorithm is generated during burst signal detection. According to Equation (29), it can be seen that the result can be achieved with only a very simple calculation.