# Compressive Sensing-Based Sparsity Adaptive Channel Estimation for 5G Massive MIMO Systems
## 4 Simulation Results
Furthermore, the rate gap between the proposed BSAMP algorithm and the literature [32; 33] algorithms increases as the SNR increases, which makes the BSAMP algorithm superior in low and high SNR communication environments. The throughput levels of literature [32; 33] are more closely related and show approximately same characteristics for different levels of SNR. Figure 5 shows the MSE performance of each channel estimation algorithm under a different number of pilots when SNR is 30 dB. As can be seen from the Figure, as the number of pilots increases,  
Figure 4: Throughput comparison of each algorithm with increasing SNR. Figure 3: Throughput comparison of each algorithm with increasing number of antennas. the performance of each recovery algorithm is improved. Under the same number of pilots, the ASSP algorithm is significantly better than other channel estimation algorithms due to the joint sparseness of MIMO channels. At the same time, BSAMP does not need to rely on the iterative steps to achieve the sparsity adaptive process. The BSAMP algorithm effectively eliminates the influence on the estimation accuracy due to improper step selection in the iterative process, which has better performance than the ASSP algorithm. When the number of pilots is 16, the performance of the BSAMP algorithm is equivalent to that of ASSP with 18 pilots. On the other hand, the LS shows the worst channel estimation performance while the SP and OMP have approximately similar MSE. The SAMP algorithm indicates better performance than the OMP, SP, and LS but is less effective than the ASSP and BSAMP algorithms as the MSE gap among them increases with increasing number of pilots. In summary, it is concluded from Figure 3 that, to obtain the required MSE and better channel estimation performance, the LS, SP, OMP, SAMP and  
Figure 7 shows the systematic BER of each channel estimation algorithm under different pilots when SNR is 30 dB. As can be seen from the Figure, under the same pilot number, the BSAMP algorithm performance is far superior to that of other algorithms. When the pilot number is 24, the system BER reaches 1.066 \(\times\) 10\({}^{-5}\). Table 2 shows the different sparse channel recovery algorithms. It can be seen that the BSAMP algorithm is comparable in computational complexity to the LS algorithm but much lower than other compression aware algorithms. Due to the larger channel vector dimension and unknown channel sparsity, too many iterations result in higher computational complexity for OMP and SP algorithms. The SAMP algorithm does not take advantage of the joint sparseness of the MIMO channel and gradually approximates the channel sparsity by a fixed step, which takes a lot of time. The ASSP algorithm also has the problem of increasing the iterative step length steadily, but it takes advantage of the joint sparseness of the channel and reduces the computation time compared with SAMP. The BSAMP algorithm proposed in this paper can achieve the sparsity adaptive process without setting the step size and greatly reduces the number of iterations of the algorithm. It takes full advantage of the joint sparseness of the channel and can recover the information of multiple antennas simultaneously in each iteration, thus having lower computational complexity. \begin{table}
\begin{tabular}{c c} \hline \hline
**Sparse Channel Recovery Algorithm** & **Average Runtime (s)** \\ \hline LS & 0.02328 \\ OMP & 2.28870 \\ SP & 1.10690 \\ SAMP & 93.3930 \\ ASSP & 15.3610 \\ BSAMP & 0.01284 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of average running time of different sparse signal recovery algorithms. LS: least-square; OMP: orthogonal matching pursuit; SP: subspace pursuit; SAMP: sparsity adaptive matching pursuit; ASSP: adaptive and structured subspace pursuit; BSAMP: block sparsity adaptive matching pursuit. Figure 7: Comparison of BER of each algorithm under a different number of pilots.