# Low-Complexity Channel Estimation in 5G Massive MIMO-OFDM Systems
## 5 Simulation Results
### Channel Estimation Comparison with SNR Variation  
In addition to the influence of the number of pilot variation simulated in Section 5.3 on the performance of the estimation algorithm, there is also a parameter that has a great influence on the performance of the estimation algorithm, that is, the SNR. In order to further verify the relationship between the performance of the algorithm and the change of SNR, this section experiments with the  
Figure 6: Normalized mean square error (NMSE) performance comparison of algorithms under a different number of pilots.  
performance simulation of the channel estimation algorithm with SNR. Figure 7 is an NMSE simulation of the channel estimation algorithm as a function of SNR. When the number of pilots is 650, 750, and 850, the experimental results are clearer and more accurate.  
It can be seen from Figure 7a that when the number of pilots is 650, the performance of the SSA-CoSaMP algorithm is much better than that of the S-CoSaMP algorithm. However, the CoSaMP algorithm does not change significantly with the increase of SNR, and it is in a state in which efficient operation cannot be performed. The experimental results show that the improved algorithm can still estimate the channel state well under low pilot conditions. In other words, when lower pilot overhead is required, only the SSA-CoSaMP algorithm can better estimate the channel state. From Figure 7b, when the number of pilots is increased to 750, the SSA-CoSaMP algorithm is slightly better than S-CoSaMP. However, for the CoSaMP algorithm, increasing the number of pilots to 750 still does not allow it to perform efficient operations. Figure 7c is a simulation when the number of pilots is up to 850. When the SNR is below 15 dB, the proposed SSA-CoSaMP algorithm is still superior to the S-CoSaMP algorithm; when the SNR is higher than 15 dB, the estimated performance of the SSA-CoSaMP and S-CoSaMP algorithms are basically the same.  
Figure 7: _Cont._  
Combining the simulation data in this section, in any case, the performance of the CoSaMP algorithm is far less than those of the S-CoSaMP algorithm and the SSA-CoSaMP algorithm. When the number of pilots is less than 750, the performance of the SSA-CoSaMP algorithm is better than that of the S-CoSaMP algorithm, and the SSA-CoSaMP algorithm is adaptive to sparsity and is more suitable for real environments where sparsity is unknown. The experimental results show that the SSA-CoSaMP algorithm is more robust than the SSA-CoSaMP algorithm.  
Figure 7: NMSE performance comparison under different SNR and pilots.  
SSA-CoSaMP algorithm enhances the sparsity. Under the same estimation performance conditions, the pilot overhead is reduced and the spectrum resources are saved. In the case of low pilot overhead, SSA-CoSaMP has advantages.  
Figure 8 compares the bit error rate (BER) of the proposed algorithm with the other state-of-the-art algorithms [9; 14; 15] for the system configured parameters of Table 1. As can be seen from Figure 8, the proposed SSA-CoSaMP algorithm gives better overall BER performance than the other competing alternatives for different SNR levels which makes it superior for utilization in massive MIMO channel estimation. On the other hand, the traditional CoSaMP of [14] has poor BER performance compared to all the rest of competing alternatives and its channel estimation performance gets worse for increasing SNR values which makes it impractical to be deployed in such systems. The structured turbo-CS algorithm in [15] has better performance than S-CoSaMP [9] but is less efficient than the proposed algorithm for low and high SNR levels. Therefore, the proposed scheme is more effective than the other existing algorithms.