## 7 Conclusions and Open Problems  
Wireless sensor networks can be applied to a variety of applications, and most of these applications require synchronization among the sensor nodes. Based on the two-way message exchange system model described in Section 2.2, this paper surveyed the most representative pairwise and fully-distributed clock synchronization algorithms from a statistical signal processing viewpoint. The interested reader is referred to [59; 60; 61; 62; 63] for references based on other system models. Specifically, similar to Equation (2), [59] adopted a two-way message exchange mechanism where no random delay is considered and the fixed portion of delays is different for the uplink and downlink (_i.e._, replace \(d\) in Equation (2) by \(d_{\text{AB}}\) and \(d_{\text{BA}}\)). The main result is that while estimating the clock skew between two nodes is possible, it is impossible to determine the clock offset for pairwise synchronization, unless the delays in two-way message communication are symmetric, _i.e._, \(d_{\text{AB}}=d_{\text{BA}}\). The same result was later extended in [60] for the network case. Recently, timestamp-free synchronization algorithms were reported in [61; 62] to avoid the overhead brought by timestamp exchanges. The approach employed in [61] is based on conveying implicit timing information in the physical layer via the timing responses from the receiver to the transmitter. The work in [62] avoids timestamp exchanges using the round-trip-time data, which can be measured by a time-to-digital converter in the master node. The clock parameters, such as the offset and skew, as well as the unknown range between the master and slave nodes were experimentally estimated and verified with an accuracy in the order of a nano-second. Without considering the random delays, a fully-distributed network-wide synchronization algorithm was presented in [63] by assuming the constraint that the relative clock offsets in any network loop sum to zero. Recently, [PERSON] [64] developed a statistical process control (SPC) algorithm that can be used in the context of the two-way message exchange mechanism to detect translations in the delay distribution.  
In reflecting on the research problems which have been addressed, we have observed several open research topics that need further investigation. On the one hand, the algorithms presented in this article all assume a line-of-sight transmission. The fixed portion of delays \(d\) herein is actually related to the propagation delay between the transmitter and the receiver nodes. It may occur that some obstacles exist in the signal path, and they might reflect or simply absorb the signal. In this case, the received signal strength and the propagation delay may be significantly affected, and thus, the mathematical system model proposed in this article might not be plausible. To our best knowledge, the clock synchronization problem under non-line-of-sight transmissions is still open. In addition, even though many references that exploit the statistical system model from Section 2.2 have been reported in the literature, more convincing experimental results based on large-scale WSN testbeds are necessary for a more accurate clock synchronization system model. Other possible future research topics lie in the investigation of the convergence rate and computational complexity of the proposed distributed synchronization algorithms. Due to the limited energy of sensors in WSNs, designing new distributed synchronization schemes with reduced energy consumption, low implementation complexity and a fast convergence rate represents another fruitful research direction.  
This work was supported by NSF Award CCF-1318338.