## 4 Simulation Results  
In this section, simulation results are presented to compare the performance between convention LS, OMP, CoSaMP, SAMP and the proposed algorithm. The evaluations are mainly based on bit error rate (BER) and mean square error (MSE). The MSE is plotted with respect to the signal to noise ratio (SNR). The estimation of multipath delay profile and percentage recovered of the algorithms are also given. We take modulation as 4 OQAM, the number of subcarriers in FBMC/OQAM systems is \(N=2048\). The square root raise cosine filter is employed in FBMC/OQAM, the roll off factor of the filter is one, and length of the filter is \(4T_{0}\) We adopt the IEEE 802.22 channel with sampling frequency 6.86 MHz as a simulation channel. The channel profile is shown in Table 1. The channel sparse \(K\) is 6. The channel coding adopts convolutional code (\(k=7\) with \(g_{1}=(133)_{o^{\prime}}\)\(g_{2}=(171)_{o}\) and code rate = 1/2). Figure 3 is a snapshot of the original and estimated delay profiles of IEEE 802.22 channel. It shows that the proposed ARCoSaMP for FBMC/OQAM successfully detect the channel with sixmultipaths and SNR = 8 dB. The proposed scheme not only precisely estimates the multipath delay values but also exactly estimates the relative power of the multipath. We also investigate the probability of recovery for a fixed signal sparsity \(K=6\) among the above-mentioned algorithms. Figure 4 depicts the probability curves of Gaussian sparse signal. It can be seen that ARCoSaMP outperforms the other three algorithms in the range of \(M=15\) to \(M=35\). ARCoSaMP also requires the least measurements for exact recovery. When the measurements \(M\succ 35\), CoSaMP provides better recovery probability than SAMP. With the measurement increasing, ARCoSaMP provides recovery probability approximate to that in CoSaMP without prior knowledge of sparsity. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Multi-Paths** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Delay(\(\mathrm{\mu s}\)) & 0 & 3 & 8 & 11 & 13 & 21 \\ Power(dB) & 0 & \(-7\) & \(-15\) & \(-22\) & \(-24\) & \(-19\) \\ \hline \end{tabular}
\end{table} 
Table 1: IEEE 802.22 channel profile. Figure 3: IEEE 802.22 channel delay profile and estimated channel delay profile. Figure 5a,b shows the BER and MSE performance comparisons when IAM preamble structure is adopted in FBMC/QOAM systems. In Figure 5a, it is obvious that CS based channel estimation methods can obtain significantly BER improvement compared with conventional least squares (LS) method. Careful observation shows that CoSaMP outperforms other algorithms in the whole SNR range considered. CoSaMP can obtain about 4.2 dB gain compared with LS when BER of \(10^{-2}\) is considered. ARCoSaMP performs slightly better than OMP, and has a gain of 0.3 dB compared with SAMP, when the BER of about \(10^{-4}\) is considered. Figure 5b plots the MSE performance comparisons. We can see that CoSaMP still performs the best MSE performance in the five schemes. It enjoys a significant SNR gain compared to those of LS, when at the same MSE level. ARCoSaMP is slightly worse performing than CoSaMP, but well performing than OMP and SAMP. It should be noted that ARCoSaMP provides BER performance comparable to CoSaMP algorithm without the prior known of sparsity and exceeds the conventional SAMP algorithm. In addition, we compare simulation time of SAMP and ARCoSaMP, where both of the two algorithms do not need to know the prior knowledge of sparsity. The result shows that ARCoSaMP needs less simulation time than SAMP, with ARCoSaMP simulation time is 30.1824 s and SAMP simulation time is 32.8995 s.  
Figure 6a,b depict the BER and MSE performance comparisons when ICM preamble structure is adopted in FBMC/QOAM systems. We can find that the trends of both BER and MSE curves are the same as that in Figure 5. Preamble structure ICM based channel estimation outperforms the IAM scheme. ICM-LS provides significant BER improvement compared with IAM-LS.