# Effective Blind Frequency Offset Estimation Scheme for BST-OFDM Based HDTV Broadcast Systems
## 5 Simulation Results and Discussion  
The performance of an OFDM system is evaluated with the ISDB-T transmission parameters summarized in Table 1 and the following parameter settings: a common carrier frequency of \(f_{c}=800\) MHz, a sampling time of \(T_{s}=63/512\)\(\upmu\)s, and GI ratio of \(1/8\) for all transmission modes [4]. The channel profile is the 6-tap Typical Urban defined in [27], where the amplitude of each tap is Rayleigh distributed such that a non-line-of-sight (NLOS) scenario is considered. In our simulations, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Complex Multiplication** & **Real Multiplication** & **Real Addition** \\ \hline Conventional & \(N_{a}N_{f}\) & \(4N_{a}N_{f}+N_{f}+2\) & \(2(N_{f}-1)\) \\ Proposed & \(N_{a}(2N_{p}-1)\) & \(N_{p}+1\) & \(2(N_{p}-1)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The complexity of the joint estimation schemes. Doppler effects due to mobility are not considered for the purpose of verifying the accuracy of MSE analysis. For fair comparison, we consider that \(N_{f}=N_{p}\) for the conventional and proposed methods. Figure 2 shows the MSE of the proposed joint LS estimator versus the number of averaging in the ISDB-T 2k mode. The probability of Rayleigh distributed random variable \(|H_{l}(k)|\) exceeding a minimum level \(p_{min}\) is \(e^{-p_{min}/\sigma_{l}^{2}}\) such that the 99.9% level of Rayleigh fading could be achieved when \(p_{min}/\sigma_{H}^{2}=-30\)dB, which is used to calculate the MSE in (35) and (37). It is observed that theoretical results closely match to the simulation results regardless of \(N_{a}\) and frequency offsets. There is a small gap between the simulated and analytical curves at low SNR because of the approximation used in (23). As expected, one can see that the averaging strategy is an attractive solution to improve the estimation accuracy at the expense of computational complexity and processing delay. Nevertheless, the increase of frequency offsets leads to a severe irreducible error floor as the SNR grows. Figures 3 and 4 illustrate the MSE of the proposed joint LS estimator versus \(N_{a}\) in the ISDB-T 4k and 8k modes, respectively, under the same simulation scenarios to Figure 2. In these examples, \(N_{p}=26\) for 4k mode and \(N_{p}=52\) for 8k mode. Here, we can see a similar trend to that of Figure 2 where \(N_{p}=13\) is used in 2k mode. It is evident that the large number of TMCC signals tends to give a more accurate match between the simulated and analytical curves. The more TMCC signals available in one OFDM symbol that can take part in the joint estimation of CFO and SFO, the better the ICI can be mitigated, as the ICI is similarly treated as AWGN. Figure 5 presents the MSE comparison between the conventional and proposed LS estimators when \(N_{a}=1\), \(\Delta_{c}=0.02\), and \(\Delta_{s}=20\)ppm. The CRBs using (38) and (39) are also presented as a baseline reference. It can be seen that the MSE performance is the same for both schemes and all algorithms suffer from an error floor for higher SNR values, regardless of the transmission mode. In practice, the conventional joint LS estimation scheme cannot be directly applied to the ISDB-T system because of an unknown phase of TMCC signals, whereas the proposed estimation scheme resolves this problem using the repeated property of TMCC signals as done in (17). The performance difference between 2k and 4k modes becomes more visible in the case of SFO estimation. This is because the performance of the SFO estimation scheme relies on both the number and location of TMCC subcarriers as in (37), whereas the CFO estimation performance is dependent on only \(N_{p}\). In order to examine the effect of bias caused by the use of non-uniformly distributed pilot, we also consider the scenario that there is no ICI. In this case, one can see that the bias of the proposed scheme is more significant than that of the conventional scheme at the high SNR.