## 2 Related Work  
Information acquisition consists of data transmission and signal recovery. The most frequently-used approach for providing reliable data transmission over lossy links is to use the acknowledgment-based retransmission mechanism, at the cost of extra energy consumption and latency. Specifically, the energy cost to successfully transmit a packet over a lossy link is proportional to the number of transmissions (including the first transmission and subsequent retransmissions if necessary) for that packet. Furthermore, traditionally, transmission power is adjusted dynamically to overcome unreliability over lossy links in energy-constrained WSNs. The network node increases its transmission power to achieve immunity against link errors. Nevertheless, besides the extra energy consumed, [13] illuminatesthat it adversely affects the channel contention, network throughput and energy consumption at the network scale. Other approaches try to study the link behavior for better understanding of the wireless communication characteristics and transmit data packets based on this to achieve better performance. The works in [5, 6, 14] utilize link burstiness to achieve better communication performance. The work in [5] presents a metric denoted \(\beta\) to measure this link burstiness. Measuring \(\beta\) allows one to reason about how long a protocol should pause after encountering a packet failure to reduce its transmission cost. The works in [6, 14] characterize links by their maximum burst length and then adaptively allocate slots for reliable data transmission. However, link-aware methods always induce large transmission delay and extra energy cost, because of waiting for a good link; besides they are all data-centric methods, which must transmit almost all of the data sampled to sink node to get information detected. Once the data packet has been received, the conventional interpolation technique is used for signal recovery. Despite much progress in the area of data interpolation, existing methods are suitable for only a few data loss condition, but cannot scale when the rate of data loss is high [15]. Furthermore, data fusion algorithms have always been adopted for denoising, overcoming environmental effects, _etc_. [16]. \begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Explanation** \\ \hline \(\mathbf{x}\) & sampled signal, \(\mathbf{x}=[x_{1},...,x_{n}]^{T}\) \\ \(\hat{x}\) & reconstruction signal, \(\hat{x}=(\hat{x}_{1},\hat{x}_{2}...\hat{x}_{N})\) \\ \(\varepsilon\) & reconstruction error, \(\varepsilon=||\mathbf{x}-\mathbf{\hat{x}}||_{2}/||\mathbf{x}||_{2}\) \\ \(N\) & dimension of sampled signal \\ \(M\) & dimension of projection (measurement) vector \\ \(\mathbf{\Psi}\) & fast Fourier transform matrix, \(\mathbf{\Psi}\in R^{N\times N}\) \\ \(\mathbf{\Phi}\) & projection matrix,\(\mathbf{\Phi}\in R^{M\times N}\) \\ \(\alpha\) & coefficients that represent \(\mathbf{x}\) on the basis \(\Psi\), \(\alpha=[\alpha_{\mathbf{1}},...,\alpha_{\mathbf{N}}]^{\mathbf{T}}\) \\ \(K\) & nonzero coefficients in \(\alpha\) \\ \(\mathbf{A}\) & equivalent matrix, \(\mathbf{A}=\mathbf{\Phi}\mathbf{\Psi}\) \\ \(\mathbf{y}\) & measurement vector, \(\mathbf{y}=\mathbf{\Phi}\mathbf{x}\) \\ \(\mu(\mathbf{A})\) & mutual coherence \\ \(\mathbf{\tilde{A}}\) & column-normalized version of \(\mathbf{A}\) \\ \(\mathbf{G}\) & \(\mathbf{G}=\mathbf{\tilde{A}}^{\mathbf{T}}\mathbf{\tilde{A}}\) \\ \(P_{prr}\) & packet reception rate (PRR) \\ \(P_{e}\) & bit error rate (BER) \\ \(L\) & packet length \\ \(L_{overhead}\) & overhead length \\ \(L_{payload}\) & payload length \\ \(n\) & packet number \(n=\frac{N}{L_{payload}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Symbols and notations. In practical WSNs applications, multi-sensor data fusion can also be applied at the fusion center for performance promotion. Advances in compressive sensing [9,10] offer a promising approach for signal acquisition and recovery.