# Bayesian Compressive Sensing Based Optimized Node Selection Scheme in Underwater Sensor Networks
## 4 Simulation Results and Discussion  
In this section, simulation results are provided for comparing our proposed optimized sensor nodes selection scheme with conventional compressed sensing scheme [31]. In [31], each sensor node sends data randomly with a probability or the fusion center deciding the nodes to send data randomly. The selection of nodes with a random scheme doesn't consider the state and correlation of each node. OMP is an efficient algorithm that is usually used to reconstruct a signal [36]. This algorithm is also compared with our proposed algorithm in the simulation. We consider a sink node in the center of a circular region with the radius \(r=500\) m. The sensor nodes are uniformly distributed in this region. For decreasing the computation complexity, the number of the sensor nodes is set as 64. The minimum distance between sink node and sensor node is 50 m. The minimum distance among sensor nodes is 40 m. Each sensor node acquires information and transmits it to sink node. The sink node collects all the information and requires that the minimum received power is \(P_{0}=50\) mW. The discrete Fourier basis is applied in the evaluation. Assume that the energy of each sensor node is the same and is set as 600 J. The carrier frequency is assumed as 10 kHz. The constant \(C\) is set as \(\frac{M}{N}\). The simulation shows mainly the performance of the reconstruction error and the lifetime of the sensor network. The reconstruction error is defined as follows:  
\[R_{e}=\frac{\|\mathbf{\mathrm{x}}-\mathbf{\mathrm{\hat{x}}}\|_{2}}{\|\mathbf{\mathrm{x}}\| _{2}}, \tag{23}\]where \(\mathbf{x}\) is the original signal and \(\hat{\mathbf{x}}\) is the reconstructed signal. If the residual energy of one sensor node is full, the sensor network is regarded as invalid. The lifetime of the sensor network is defined as the times that the sensor network can collect the information until the first sensor node died. In Figure 1, the performance of reconstruction error is evaluated with the number of selected sensor nodes. It can be seen that the reconstruction error is decreasing when the number of selected sensor nodes increases. The proposed optimized sensor nodes selection scheme is superior to the conventional compressed sensing scheme. The performance of reconstruction scheme by using optimized Bayesian estimation outperforms the scheme with conventional Bayesian estimation. The reconstruction scheme by using optimized Bayesian estimation is better than the OMP algorithm and the optimized OMP algorithm when the number of selected sensor nodes is more than 30. When the number of selected sensor nodes is less than 30, the optimized OMP algorithm has better performance than the OMP algorithm and the optimized Bayesian estimation scheme. It is reasonable because the prior information is little when the number of selected sensor nodes is few. It is not suitable to use a Bayesian estimation scheme. Figure 2 shows the network lifetime versus the number of selected sensor nodes. When the number of selected sensor nodes grows, the network lifetime decreases. This is because the feasible selection schemes are less as the number of selected sensor nodes grows larger. It is obvious that the optimized sensor nodes selection scheme has a significant improvement than the conventional sensor nodes' selection scheme. For example, when the number of selected sensor nodes is 25, the network lifetime with optimized sensor nodes selection scheme is 5.6 times more than conventional sensor nodes selection scheme. This paper proposed an optimized sensor nodes selection scheme for compressed information acquisition based on Bayesian estimation. The proposed scheme is not limited to reconstructing the signal. In practice, the sink node can select different schemes to reconstruct the signal according to different performance requirements.