# Statistical signal detection with multi-sensor and sparsity

## Abstract/Contents

- Abstract
- The objective of many signal processing problems is to detect signals buried in a noisy background. Many of these signal detection problems have sparsity structure that can be exploited to reduce noise or reduce complexity. This dissertation will focus on two such problems: multi-sensor sequential change-point detection and multiuser detection, and it will present new methods to exploit sparsity: the mixture sequential detection procedure and reduced-dimension multi-user detection (RD-MUD). In multi-sensor change-point detection, sensors are deployed to monitor the abrupt emergence of a change-point. The change-point is an event that affects the observations of a subset of sensors simultaneously. Typically the subset of sensors that are affected is unknown, and the level-of-affectedness of each affected sensor is also unknown. The goal is to detect the change-point as soon as possible once it occurs, and rarely make false detections if it does not occur. An empirical observation is that the number of affected sensors is usually small compared to the total number of sensors. This is a form of sparsity. For this problem, traditional methods have not exploited the sparsity structure: they either assume all sensors are affected by the change-point and use observations from all sensors and, hence, include too much noise from the observations of the unaffected sensors, or assume only one sensor is affected, use only observations from the affected sensor with the highest level-of-affectedness, and ignore observations from other affected sensors. We develop a mixture procedure that exploits this sparsity. In particular, we model this sparsity by assuming that each sensor has a small probability $p_0$ to be affected by the change-point. The value of $p_0$ is a guess for $p$. Based on this model, we form a mixture log generalized likelihood ratio (GLR) statistic and present a mixture detection procedure. The mixture statistic essentially applies a non-linear weighting function, which is parameterized by $p_0$, on the log GLR statistic of each sensor before combining them. This nonlinear weighting function automatically emphasizes the statistics from the sensors that are affected by the change-point and suppresses those from the sensors that are not affected. We derive a theoretical approximation for the false alarm rate, which is captured by the average-run-length (ARL), and a theoretical approximation for the expected detection delay. The accuracy of these approximations is verified by numerical studies. We also demonstrate that the mixture procedure is robust against the lack of knowledge of $p$. Numerical studies compare the new mixture procedure with other proposed procedures. The multiuser detection (MUD) problem arises in multiuser communication systems, where multiple users communicate simultaneously with a receiver. The receiver receives a signal consisting of a set of known waveforms modulated by the information symbols of the users that is contaminated by noise. The receiver has to determine which users are active and their information symbols. The conventional solutions to the MUD problem all consist of a matched-filter bank (MF-bank) front-end, followed by digital signal processing. The MF-bank front-end uses a set of correlators, where each one correlates the received signal with a signature waveform. Hence the number of correlators used in the conventional matched-filter bank is equal to the number of users in the system. We present a reduced-dimension multiuser detector (RD-MUD) structure that significantly decreases the number of required correlation branches in the receiver front-end, while still achieving performance similar to that of the conventional matched-filter (MF) bank. RD-MUD exploits the fact that the number of active users is typically small relative to the total number of users in the system and relies on ideas of analog compressed sensing to reduce the number of correlators. The correlating signals used by each correlator are chosen as an appropriate linear combination of the users' spreading waveforms, which in turn are chosen from a large class of spreading codes. We derive the probability-of-error when using two methods for recovery of active users and their transmitted symbols: the reduced-dimension decorrelating (RDD) detector, which combines subspace projection and thresholding to determine active users and sign detection for data recovery; and the reduced-dimension decision-feedback (RDDF) detector, which combines decision-feedback orthogonal matching pursuit for active user detection and sign detection for data recovery. We identify conditions such that error is dominated by active user detection. We then show that the number of correlators needed to achieve a small probability-of-error under these conditions is on the order of the logarithm of the number of users in the system for a given projection method based on random discrete Fourier transform (DFT) matrices. Thus, RD-MUD has significantly fewer correlators than the number of correlators required by MUD using the conventional MF-bank. Our theoretical results take into consideration the effects of correlated signature waveforms as well as near-far issues. The theoretical performance results for both detectors are validated with numerical simulations.

## Description

Type of resource | text |
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Form | electronic; electronic resource; remote |

Extent | 1 online resource. |

Publication date | 2011 |

Issuance | monographic |

Language | English |

## Creators/Contributors

Associated with | Xie, Yao | |
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Associated with | Stanford University, Department of Electrical Engineering | |

Primary advisor | Siegmund, David, 1941- | |

Thesis advisor | Siegmund, David, 1941- | |

Thesis advisor | Goldsmith, Andrea, 1964- | |

Thesis advisor | Ye, Yinyu | |

Advisor | Goldsmith, Andrea, 1964- | |

Advisor | Ye, Yinyu |

## Subjects

Genre | Theses |
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## Bibliographic information

Statement of responsibility | Yao Xie. |
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Note | Submitted to the Department of Electrical Engineering. |

Thesis | Ph.D. Stanford University 2011 |

Location | electronic resource |

## Access conditions

- Copyright
- © 2011 by Yao Xie
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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