# Signal Detection for GSTFIM Systems with Carrier Frequency Offset +
## 6 Simulation Results  
In this section, the BERs of the proposed SC-MMSE, BC-MMSE, SC-MP, and BC-MP detectors are simulated. The maximum likelihood detector without the CFO (\"ML-IDEAL\") and the ML detector with the CFO (\"ML-WORST\") are given as two baselines. Moreover, QPSK modulation and the Extended Vehicular A (EVA) channel model [31] are employed in the GSTFIM system. Figure 3 compares the BERs of the proposed SC-MMSE and SC-MP detectors for the GSTFIM system with different numbers of iterations, while Figure 3 compares the BERs of the proposed BC-MMSE and BC-MP detectors. The specific GSFTIM system parameters in Figures 3 and 4 are as follows: \(N_{t}=2\), \(N_{r}=2\), \(N=128,K=64\), \(N_{b}=2\), \(N_{a}=1\), \(L=2\), \(G=31\), and \(T=2\). The CFOs \(e_{m}\) and \(f_{n}\) are independent and random from frame to frame following a uniform distribution over the range \(-0.2\) to \(0.2\), and the length of the CP is 32. As can be observed from Figures 3 and 4, the performances of the proposed four detectors are converged in three iterations. Moreover, the convergence behaviors of the proposed SC-MP and BC-MP detectors are similar to that of the ML-IDEAL detector. Meanwhile, Figure 5 compares the BERs of the proposed SC-MMSE detectors for the GSTFIM system with four iterations under different Gaussian noise types, i.e., Gaussian noise and non-Gaussian noise. The specific GSFTIM system parameters in Figure 5 are same as those in Figure 3. As can be seen from Figure 5, under non-Gaussian noise, the proposed MMSE-criterion-based detector exhibits worse performance. In this situation, the maximum-correntropy-based detector can slightly improve the BER performance. However, the performance is still much worse than that under Gaussian noise. This is mainly because there is a deviation in the calculation of the mean and variance of \(\mathbf{X}_{l}\) under non-Gaussian noise, resulting in the inaccurate calculation of the posterior probability. Figure 6 compares the BERs of the proposed SC-MMSE and SC-MP detectors for the GSTFIM systems with different numbers of effective subcarriers \(G\) in three iterations, while Figure 7 depicts the BERs of the proposed BC-MMSE and BC-MP detectors. The other system parameters in Figures 6 and 7 are same as those in Figure 3. Figures 8 and 9 show the complexities of Figures 6 and 7, respectively. As can be seen in Figures 6 and 7, the performances of the proposed four detectors become better with the increase in the number of effective subcarriers \(G\). However, according to the complexity comparisons in Figures 8 and 9, it can be observed that the complexities of the proposed MMSE-based detectors do not increase much with the increase in the number of effective subcarriers, while that of the proposed MP-based detectors increases significantly when the number of effective subcarriers increases. In order to balance between performance and complexity, we choose the number of effective subcarriers to be \(G=15\) as an example. Then, the BERs of the proposed SC-MMSE, BC-MMSE, SC-MP, and BC-MP detectors with \(N_{t}=2\), \(N_{r}=2\), \(G=15\) are compared in Figure 10, which shows that the MP-based detectors offer a better performance than their MMSE-based counterparts. Moreover, the detector based on block carriers offers a better performance than the one based on the single carrier due to the fact that the detector based on block carriers is able to maintain the integrity of the system symbols. Finally, the BERs of the proposed four detectors for GSTFIM systems are compared in Figure 11. The specific GSFTIM system parameters of Figure 10 are \(N_{t}=2\), \(N_{r}=4\), \(N=64\), \(K=32\), \(N_{b}=2\), \(N_{a}=1\), \(L=1\), \(G=15\), and \(T=2\). The CFOs \(e_{m}\) and \(f_{n}\) are independent and random from frame to frame following a uniform distribution over the range \(-0.3\) to \(0.3\), and the length of the CP is 16.