## 5 Successive Approximation Using CS-WSNs
### Simulation Results
#### 5.3.2. Energy Consumption Evaluation: Case Studies  
We now empirically evaluate the possible energy savings derived from the use of the proposed successive approximation scheme at sensor nodes. In the experiment, we evaluate the energy consumed when a sensor node traverses its operational curve, moving on a sequence of operational points \((M_{j},B_{j})\). We compare the energy expenditure when the proposed successive approximation mechanism is employed against simply transmitting the whole data using one encoder with the operational set-up leading to the same total.  
In this experiment (Scenario 1) we consider the same set-up used in Section 4.3. Table 3 presents the results. The first column shows the operational points traveled by the sensor (the first encoder configuration (RD operational point) is \((M_{0},B_{0})=(8,4)\). At each operational point, the following one is obtained considering \(c_{n}=10\) and \(d_{R}=0.1\).). The second column presents the energy required to transmit the \(M_{j}\) CS measurements using \(B_{j}\) bits without using the proposed scheme. The third column presents the energy consumed when the successive approximation scheme is employed. The last column in Table 3 shows the percentage reduction in energy consumption gained by using the proposed scheme. The reduction comes from having to transmit only extra measurements and refinement bits. This energy economy behavior is steadily observed for all operational points.  
Now we consider another operational curve to be traversed by sensor nodes. The same fifteen-node WSN used in simulations of the previous scenario are also considered for Scenario 2, but in this case all sensor nodes traverse their operational curve transmitting to the sink \(M_{j}\) CS coefficients, each one with \(B_{j}\) bits, using the proposed successive approximation scheme. Results are shown in Table 4, presenting the average MSEs and the average energy consumptions for all network nodes. One observes the same energy economy behavior as in Scenario 1, for all operational points.  
A disadvantage of the proposed successive approximation scheme is the fact that sensor nodes are unable to perform an on-line construction of their operational curves (successive approximation tables). This is so because of the extensive required computations to generate the operational points. Thus, sensor nodes must be aware of the table or the sink must inform the new operational point. However, results presented in Figure 8, and Tables 3 and 4 show that the proposed scheme provides a rate-distortion performance that closely matches the convex hull, while sensor nodes save their energy.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \((M_{j},B_{j})\) & **NMSE (dB)** & **E. Cons. (J)** & **E. Cons. (J)—App. suc.** & **Energy Reduction (\%)** \\ \hline \((10,4)\) & \(-10.27\) & \(0.54\) & \(0.54\) & - \\ \((16,6)\) & \(-13.97\) & \(1.12\) & \(1.07\) & \(4.46\) \\ \((32,8)\) & \(-16.11\) & \(1.73\) & \(1.56\) & \(9.83\) \\ \((64,10)\) & \(-17.72\) & \(2.48\) & \(2.07\) & \(16.53\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Evaluation of the proposed successive approximation scheme capability to save sensor nodes energy—Scenario 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \((M_{j},B_{j})\) & **E. Cons. (J)** & **E. Cons. (J)—App. suc.** & **Energy Reduction (\%)** \\ \hline \((8,4)\) & \(0.53\) & \(0.53\) & - \\ \((12,6)\) & \(1.08\) & \(1.03\) & \(4.60\) \\ \((16,8)\) & \(1.64\) & \(1.44\) & \(12.19\) \\ \((32,10)\) & \(2.44\) & \(1.88\) & \(22.95\) \\ \((60,11)\) & \(3.41\) & \(2.37\) & \(30.49\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Evaluation of the proposed successive approximation scheme capability to save sensor nodes energy—Scenario 1.