Multi-alternative online change detection with applications in wireless communications

Statistical decision tools for detecting and isolating abrupt changes in the properties of stochastic signals are used in many applications such as quality control, automatic segmentation of signals in biomedical, seismic and speech data processing, on-line fault diagnosis in dynamical systems, edge detection in images, and detection of signals with unknown arrival time in geophysics, radar and sonar array processing. The main objective in all these applications is the design of an algorithm that detects a change as quickly as possible when a change does occur, and has tolerably few false alarms otherwise. For example, in industrial processes, early on-line fault diagnosis is useful in preventing the system from more catastrophic failures, and also in saving costs related to systematic maintenance policies, therefore increasing product availability.; This thesis investigates the multi-alternative on-line change detection problem, a relatively new field that is an extension of the classical (binary) change detection theory. Two applications of this theory in the field of wireless communications are also presented: user activity detection in a multiuser environment, and target detection and location estimation using a radar array. The thesis consists of two parts, one addressing theoretical issues, and the other addressing applications. In the first part, after reviewing the classical change detection theory, the problem of multi-alternative change detection is addressed and a new recursive approach, the matrix cumulative-sum (CUSUM) algorithm, is introduced. This method is computationally very efficient, simple to implement and is shown to achieve certain optimality criteria. In the second part, this new scheme is applied to the problem of detecting a new user entering a direct-sequence code-division multiple access (DS-CDMA) communications channel. Finally, a second algorithm, the parallel CUSUM test, a method based on simultaneously operating CUSUM tests, is developed and applied in detecting targets appearing against background noise in sensor arrays.