Quickest detection is an important technique to detect the change of probability distribution in a random process being monitored. It is widely used in problems like financial decision making, environmental monitoring and industrial quality control. With the rapid development of networking techniques, there exist pressing demands to carry out quickest detection based on observations from many nodes and make decision at more than one node. Motivated by this demand, this research studies collaborative quickest detection in ad hoc networks, in which nodes exchange observation statistics and make local decisions about distribution change. In contrast to existing theory of decentralized quickest detection, the collaborative quickest detection does not need a data processing center, thus avoiding the round-trip time overhead and possible data congestion. Moreover, collaboration can enhance the agility and robustness of the detection of change. The research involves aspects of statistical signal processing (e.g. detection rule), information theory (e.g. source coding) and networking (e.g. scheduling or broadcast). An important application of collaborative quickest detection is spectrum sensing in cognitive radio systems. In such a system, secondary nodes need to monitor the activity of primary users and should quit the frequency band once primary users emerge. It is essentially a problem of quickest detection since the secondary nodes need to detect the change as quickly as possible. Therefore, this research also involves the design of collaborative quickest detection in cognitive radio networks. Inter-disciplinary essence of the research also lends itself to cross-disciplinary education. A one-semester graduate level course will be devised, which introduces quickest detection, cooperative communication and cognitive radio. This project also expects to attract traditionally underrepresented groups.
This project is focused on the distributed quickest detection, as well as the application in cognitive radio systems. Quickest detection means how to detect a sudden change in a random process. For example, there could be an abrupt change in stock price; or, the edges in an image can also be considered as changes of pixels. It is important to detect such changes as quickly as possible. However, there could be random noise in the data; e.g., stock price experiences small oscillations. If the detection is too sensitive, it may consider a small random noise as an abrupt change, thus resulting in a false alarm. Another requirement is that the detection should be as quickly as possible (e.g., if you can only realize the sudden change in stock market after three days, you lose money). Hence, quickest detection can be used to detect the change as quickly as possible, but incurring fewer false alarms. In this project, we consider multiple observers / decision makers. They observe different replicas of the random process. Then, they can communicate with each other, exchange their observations and figure out whether a change has happened. For example, they can have a vote on two options: ‘changed’ or ‘not changed’. The decision will be the majority of the votes. A finer decision can be made if the observers can exchange raw observation data. A challenge is that the information exchange must be very quick since we want to detect the change as quickly as possible. However, the communication capability of these observers is usually small. Hence, the quickest detection must take the limited communication capability into account. We proposed an algorithm, in which observers broadcast their observations. Since the communication capability is limited, the observers need to censor their observations before transmission. If they feel that the change has not occurred, according to their own observations and received messages, they broadcast the messages with less probability. However, if they decide that a change has happened with a large probability, they broadcast with higher probability. We have derived the mathematical framework for designing the algorithm and have demonstrated the validity of the algorithm using numerical simulations. We applied the distributed quickest detection in cognitive radio. In cognitive radio, users without license (called secondary users) to licensed spectrum, which usually require expensive access fee, are allowed to access the spectrum if there is no licensed user (called primary user) in the corresponding channel. However, when primary user emerges, secondary users must quit. Hence, the secondary users must be able to detect whether the primary user exists, or equivalently the change in the spectrum occupancies. We allowed the secondary users to collaborate with each other, in order to detect the spectrum change quickly and reliably. Our numerical simulation shows that the distributed quickest detection, which collects the intelligence of all collaborators, can significantly improve the performance of spectrum sensing.
