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practical terms, one may distinguish among synchronism mediated by the operating system of the sensor node as compared to synchronism for physical layer communications. Very different types of algorithms are required; and in practice, multiple layers of synchronism are often present in sensor networks. Explicit synchronism algorithms are required because clocks that are initially aligned will not stay that way. Even if they are physically identical, small temperature differences will be manifested as frequency offsets, and thermal noise will cause jitter. Radios typically present the most stringent synchronism requirements in sensor networks since the carrier frequency and phase must usually be aligned, using some combination of frequency and phase-locked loops [106], wherein the receiver locks to the reference of the transmitter. Motion of either the communicating parties or strong re ecting media will also affect timing loops; in general, high channel dynamics are also problematic in that it is dif cult to achieve high-precision estimates before the situation changes. The data bearing signals themselves are used to establish symbol synchronism, while preambles of packets or frames can be used to establish frame synchronism. It is this level of alignment that usually forms the basis of more coarse levels of network synchronism, as may be required for time stamping data, duty-cycling nodes to conserve energy, or performing coherent combining of low frequency signals such as acoustic or seismic waves. Synchronism within the communications range of a single master clock is relatively straightforward, with the clocks of all the subordinate nodes slaved to it, offset by some delay. The propagation delay is important only for applications such as coherent combining of radio signals; for other applications it will be a negligible fraction of the total timing offset produced by lower-cost procedures. Chief among the delays are (a) the time taken to interrupt a processor to record a timing event and (b) delays experienced when there is queuing of packets over congested links. These delays will then accumulate in a multihop network as timing references propagate outward from the master clock. In the NTP protocol used in wired networks [107], queuing delays are mitigated by sending large numbers of packets and taking the early arrivals and returns as being more reliably indicative of the actual delay than other statistical quantities. The RBS protocol [108] shares this feature and additionally is designed to reduce software delays that are typical when a processor controls a radio. In small networks it produces suf cient accuracy to enable acoustic beamforming [109], but in larger networks it suffers from the problem of accumulation of random error as more links are traversed. This error can be mitigated to some extent through explicit estimation of clock skews; but even so, the error variance will generally grow linearly with the number of hops since the problem is well-modeled as a random walk. Interestingly, this growth in synchronization error with network size is not fundamental but rather an algorithmic artifact. It has been shown that there exist distributed algorithms for which the synchronization error variance is O(1) as network size grows [110]. Quite a number of protocols have been proposed to establish synchronism in networks with resource-constrained nodes including TPSN [91], LTS [111], Mini/Tiny Sync [112], and RATS [113]. If there is GPS at every node, synchronism to a high level is quite easy, but there are many physical situations in which GPS is either unavailable (indoors, mountainous
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terrain, heavy tree cover, etc.) or simply too expensive in cost or energy consumption. Nonetheless, if timing beacons are available, they can greatly simplify network synchronism, and to achieve phase alignment of radios there is no practical alternative. Just as a set of nodes with known locations can anchor network location algorithms, a network of nodes slaved to a common timing base can similarly stabilize network synchronism. Thus, even if not all nodes have GPS or lock with some other timing beacon, the remaining nodes can bene t through limitation of the number of hops over which clock synchronism is propagated. Again as in the calibration and position location problems, provision must be made for misbehaving nodes, with explicit estimation of outliers. This is only possible with redundant sources of timing information (e.g., communication of time by multiple neighbors), or the presence of trusted elements such as timing beacons [114]. The RANSAC [115] and LMS [116] algorithms have been proposed for detection of outliers, whether due to node failures or malicious attack. One may additionally exploit certain physical facts concerning propagation time, which can be exploited to detect inconsistencies in timing for individual links [96]. Secure routing protocols may then be used as the basis for secure multihop synchronism. 14.4.4 Key Distribution in Sensor Networks Another component of data integrity is some security in the communications system. Many solutions that apply to MANETs also apply to sensor networks, with the caveat that some of the nodes in the network may have low computational and storage capabilities. Since the nodes are potentially deployed for long periods of time, they may be captured and subverted. This can result in insertion of bad data, interception of good data, and failure to forward information. While it is unrealistic to expect that full recovery from some events is possible, what is desired is that the damage should be detectable and limited in scope in its effects on the network. Since the managers of the network may be in a position to add new nodes to the network over time (e.g., to recover from regions of failures/subversion), it is desirable therefore for the security protocol to be able to accommodate variable numbers of nodes, added at different times. A basic requirement for any security protocol is some mechanism for distribution of cryptographic keys. An ideal protocol would provide strong encryption, scalability, low vulnerability to the capture of small numbers of nodes, adaptability to adding new nodes, low computational cost, and low communications overhead. Obviously, these are dif cult to all satisfy, and so protocols have been proposed using a variety of approaches. TinySec, among its various security features, provides symmetric keys and is designed speci cally for resource constrained motes [117]. Keys may be deterministically preassigned, as in the SPINS [118] and LEAP [119] protocols. This has the virtue of perfect security in that capture of one node does not impact the security of other links, but relies upon sharing of keys with one secure base station and requires considerable work prior to deployment. Such strategies are thus suitable for modest-sized stable deployments, but are not well-suited to large-scale systems or rapidly changing topologies. Random key distribution schemes [120 122] yield more
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