# Compressive Sensing-Based Sparsity Adaptive Channel Estimation for 5G Massive MIMO Systems
## 4 Simulation Results  
The MATLAB (2017a, MathWorks, Natick, MA, USA, 2017) simulator is used for the analysis. Table 1 mentioned the main simulation setup parameters for the proposed system. In the simulation, the system has 500 transmit antennas, using 64 QAM modulation and low-density parity-check (LDPC) coding (coding efficiency 5/8). Each transmit antenna sends an OFDM signal with a signal length \(N\) of 256, with a cyclic prefix length of 64. The OFDM signals transmitted by each transmitting antenna have 16 pilot symbols, and all the algorithms use the same pilot distribution method. The pilot positions are randomly distributed and the pilots of different antennas are orthogonal to each other. The channel length \(L\) is 60, and the number of channel multipath is a random integer [5; 8]. The multipath amplitude follows the Rayleigh distribution, and the multipath positions follow a random distribution. Figure 1 shows the mean square error (MSE) performance of each channel estimation algorithm at different signal-to-noise ratios when the pilot number is 16. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value/Type** \\ \hline Number of transmit antennas & 500 \\ Modulation & 64 QAM \\ Encoding Scheme & LDPC \\ Coding Efficiency & \(5/8\) \\ Signal length (\(N\)) & 256 \\ Cyclic Prefix & 64 \\ OFDM Pilot Symbols & 16 \\ Channel Length (\(L\)) & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Parameters. LDPC: low-density parity-check; OFDM: orthogonal frequency-division multiplexing. As can be seen from the Figure 1, the performance of BSAMP algorithm proposed in this paper is superior to other algorithms. This is because the LS algorithm fails when the pilot number is less than the channel length, while the OMP and SP algorithms need to set their iteration times to half the number of pilots when the channel sparsity is unknown, reducing the accuracy of the algorithm. SAMP algorithm and ASSP algorithm do not need prior information such as the sparsity of the channel. However, the SAMP algorithm and the ASSP algorithm realize the adaptive process by using a fixed increment step, which easily causes over-estimation and under-estimation, which is slightly less than the estimation accuracy. The proposed BSAMP algorithm not only considers the effect of Gaussian white noise on the system performance but also considers the energy dispersion caused by the non-orthogonality of the observed matrix, which has better performance than the above algorithm. Figure 2 shows the systematic bit error rate (BER) for each channel estimation algorithm at different signal-to-noise ratios when the number of pilots is 16. As can be seen from the Figure, the BSAMP algorithm using the system BER has the best performance. When the SNR is 30 dB, the system BER reaches \(4.187\times 10^{-5}\). Figure 1: Comparison of mean square error of each algorithm under different signal to noise ratios (SNRs). MSE: mean square error; LS: least-square; SP: subspace pursuit; OMP: orthogonal matching pursuit; SAMP: sparsity adaptive matching pursuit; ASSP: adaptive and structured subspace pursuit; BSAMP: block sparsity adaptive matching pursuit. Figure 2: Bit error rate (BER) comparison of each algorithm under different SNRs. Figure 3 compares the throughput between the proposed BSAMP algorithm with literature [32; 33] algorithms versus the number of antennas. It is clear from the Figure 3 that, as the number of antennas (\(M\)) increases, the throughput of all the algorithms improves. Moreover, the proposed BSAMP algorithm outperforms the other algorithms and the rate gap between them increases with increasing number of antennas. Figure 4 compares the throughput of the proposed BSAMP algorithm with literature [32; 33] algorithms versus the SNR. It is clear from the Figure 4 that, as the SNR increases, the throughput of each algorithm increases. Moreover, the proposed BSAMP algorithm shows overall better throughput as compared with the reference [32; 33] algorithms.