# Implementation of a Cross-Layer Sensing Medium-Access Control Scheme
## 4 The Experimental Results
### Identification of Active Nodes  
To identify active nodes correctly, in this experiment, active nodes sent 2000 binary bit streams to the destination. At the destination, after acquiring the measurement matrix by the training sequence, we sampled the modulated complex symbol to reconstruct the original signal. By comparing the original binary bit and the reconstructed binary bit, we can get the exact recovery binary bit rate.  
Figures 4-6 show the exact recovery bit rate of the experiments with different parameters. The exact recovery bit rate with sparse degrees versus the transmitted SNR of the sensor nodes is shown in Figure 4. The exact recovery bit rate of transmission will increase as the SNR increases.  
Figure 5 shows the results of the exact recovery bit rate with different total transmission node (\(N\)) values. As \(N\) increases, the system becomes sparser. It can be seen that the sparser the system is, the higher the exact recovery bit rate will appear to be. The performance improves when there are more inactive nodes.  
We show the relationship between the number of receiving antennas \(M\) and the exact recovery bit rate in Figure 6. The four lines in Figure 6 indicate the exact recovery bit rate with different receiving antennas \(M\). We found that the largest \(M\) system has the highest exact recovery bit rate, which means that a large number of receiving antennas will be beneficial for the correct transmission of the system. This is because the more receiving antennas there are, the more measured values will be received.  
Figure 3: The symbol constellation diagram. (**a**) Original symbol constellation. (**b**) Recovery symbol constellation (signal/noise ratio (SNR) = 16 dB). (**c**) Recovery symbol constellation (SNR = 28 dB).  
compressive sensing is utilized to avoid the collision, and the concurrent signal can be departed by compressive sensing. However, CS-MAC only deals with the random binary matrix as the measurement matrix and cannot accurately match the measurement process, especially with low sparsity and low SNR. This results in high decision error in exact active node identification. Therefore, collisions cannot be efficiently avoided.  
Figure 7 shows the comparison of the exact recovery rate of the CL CS-MAC and CS-MAC with the transmission node number and the SNR. It can be seen that the exact recovery rate of CL CS-MAC is higher than that of CS-MAC with the same transmission nodes and SNR. The same trend is also shown in Figure 8, where the exact recovery rate of CL CS-MAC is higher than that of CS-MAC with the same SNR. This means that the CL CS-MAC scheme can identify the exact active node more accurately than the CS-MAC scheme.  
Figure 8 shows the throughput of different schemes versus the number of active nodes. For the CSMA scheme, as the number of active node increases, the channel becomes more congested and collision occurs more frequently, so the throughput of the CSMA scheme declines. For CS-MAC and CL CS-MAC, the throughput can rise steeply as the number of active node increase. However, as the active node continues to grow, the throughput will slightly decline. The critical point of the number of active nodes of CL CS-MAC is much larger than that of CS-MAC. Further, the throughput ratio of CL  
Figure 8: Software simulation result of throughput. (**a**) The throughput of different schemes; (**b**) The throughput ratio of different schemes.  
Figure 7: Software simulation of exact recovery rate. (**a**) Exact recovery rate of transmission nodes; (**b**) Exact recovery rate of different SNR.  
CS-MAC is better than that of CS-MAC. The reason is that the CL CS-MAC scheme can identify the exact active node more accurately than can the CS-MAC scheme.