## 5 Performance Evaluation and Analysis  
To evaluate the effectiveness of CS-DDSG, we ran simulations in MATLAB 2012b. The simulation parameters were set as shown in Table 1. Furthermore, we adopted the FFT orthonormal basis and the orthogonal matching pursuit (OMP) method for the reconstruction algorithm. We used the real sensor readings extracted from the GreenOrbs [29] system. In this paper, we present the performance comparations of CS-DDSG, Compressive Sensing Data storage (CStorage) [20], Improved Cstorage (ICStorage) [21], Compressed Network Coding based Distributed data Storage (CNCDS) [21] and Direct Cluster-Based Compressive Sensing Data Collection (DCCS) [15] on unreliable links. These first four schemes all combine DDS and CS to gather data. Cstorage, ICStorage and CNCDS are concerned with reducing the number of transmission and fusions. In Cstorage, intermediate nodes receive the broadcasting packets when they first receive, and then, they forward the received packet with a given probability. The intermediate nodes in ICStorage forward their own readings rather than the received source nodes readings. In the CNCDS scheme, the intermediate nodes receive broadcast packets only if the receiving node does not share any node IDs with the corresponding transmitting node. We also analyze the numbers of transmissions, receptions and fusions involved in the first four algorithms. DCCS combines CS and cluster topology to reduce the total power consumption with no consideration of packet loss rate. All member nodes gather data and transmit to cluster heads, where the CS measurements and measurement matrices are generated and send to sink directly. Additionally, we discuss the impact of packet loss rate, the number of measurements and the proportion of source nodes on the performance of CS-DDSG. The simulation results shown are the average values from 1000 runs. First, we evaluate the performance on unreliable links when \(\mathbf{p1=0.3,M=50}\), as shown in Figure 9. It can be seen that: (1) As \(\mathbf{p}\) increases, the reconstruction accuracy of all the algorithms decreases in Figure 9a. When \(\mathbf{p\leq 0.6}\), the NMAEs of the four algorithms are stable and increase gradually, which indicates that CS-DDSG is effective at resisting the packet loss. Although the packet loss rate impacts the nodes receiving broadcasting packets, the sink still gathers enough packets to recover the data. In addition, the sink constructs the measurement matrix based on received packets, which avoids the need to measure the lost nodes and reduces the impact of unreliable links on measurement vector \(\mathbf{Y}\). However, the performance of DCCS is poor with an increase in \(\mathbf{p}\). Sink cannot find the lossy nodes and still reconstructs data based on the original measurement matrices. Thus, DCCS is sensitive to \(\mathbf{p}\). (2) CS-DDSG outperforms the other algorithms. This improved performance occurs because in CS-DDSG, nodes receive only one packet which is broadcasted by its neighbor nodes in CS-DDSG. Thus, the measurement vectors have the characteristic of strong spatial correlation, which is utilized by CS to recover the data. However, in the other algorithms, nodes would fuse packets from distant nodes as long as the receipt condition is satisfied, which leads to a weak spatial correlation of measurement vectors. Thus, CS-DDSG outperforms the other algorithms. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Parameters** & **Value** \\ \hline \(\mathbf{N}\) & The total number of sensors & 400 \\ \(\mathbf{a}\) & Boundary length & 1 \\ \(\mathbf{p_{2}}\) & The probability of forwarding in Stage 3 & 0.32 \\ \(\mathbf{r_{t}}\) & Communication radius & 0.075 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Default Simulation Parameters. We present the total number of transmissions, receptions and fusions of the four algorithms in Figure 10 when \(\mathbf{p=0.3}\) and \(\mathbf{p_{1}=0.15}\). CS-DDSG requires fewer transmissions, receptions and fusions than do the CNCDS, CStorage and ICStorage schemes.