#### Title

New Combined Machine Learning and Estimation/Detection Approaches for IEEE 1588 and Passive Radar

#### Date

1-1-2020

#### Document Type

Dissertation

#### Degree

Doctor of Philosophy

#### Department

Electrical Engineering

#### First Adviser

Rick S. Blum

#### Abstract

Signal detection and estimation theory attempts to recover useful information from data corrupted by random perturbations. On the other hand, unsupervised learning theory tries to find unknown patterns in a data set without any preexisting labels. The presented research investigates the application of signal detection, estimation and unsupervised learning theory to two problems of significant practical interest: robust time synchronization over packet-switched networks, and passive multiple-input-multiple-output (MIMO) radar networks. Under the first topic, we describe new robust clock synchronization algorithms for IEEE 1588, a widely used time synchronization protocol for packet-switched networks. In the second topic, we present new target detection algorithms for passive MIMO radar networks.

The IEEE 1588 Precision Time Protocol (PTP) is a popular time synchronization protocol used in various packet-switched networks. PTP is built upon the classical two-way message exchange scheme in which a slave node exchanges a series of time synchronization packets with a master node. {\color{black} The slave node then} uses the timestamps {\color{black} from} these exchanged packets to estimate its clock skew and offset relative to the clock of the master. The messages traveling between the master and slave nodes can encounter several intermediate switches and routers, accumulating delays at each node. The main factors contributing to the overall delay are the fixed propagation and processing delays at the intermediate nodes and the random queuing delays at each such node. Due to the stochastic nature of the end-to-end delays, the joint recovery of clock skew and offset from the timestamps of the exchanged packets can be treated as a statistical estimation problem.

In most practical implementations of PTP, it is assumed that the fixed propagation delays in the forward and reverse paths are identical. The presence of an unknown asymmetry between the fixed path delays can significantly degrade the performance of clock skew and offset estimation schemes. In the first part of this dissertation, we employ concepts from estimation theory and unsupervised learning theory to develop new clock skew and offset estimation schemes for PTP that are robust against unknown path asymmetries.

We first consider the problem of clock offset estimation when complete information on the clock skew is available, possibly from synchronous ethernet. We assume the availability of multiple master-slave communication paths, each with a possibly unknown asymmetry between the fixed path delays in the two directions. Under this scenario, we describe new lower bounds on the mean square estimation error for a clock offset estimation scheme and present a robust clock offset estimation scheme that exhibits performance close to these bounds. The robust scheme employs the expectation-maximization (EM) algorithm and unsupervised learning to identify the asymmetric paths while simultaneously providing an estimate of the clock offset.

Next, we consider the problem of the joint estimation of clock skew and offset, assuming synchronous ethernet is unavailable. We describe new optimum clock skew and offset estimators when the fixed path delays in the two directions are identical. These optimum estimators achieve the smallest mean square estimation error among the class of invariant estimators and exhibit significant performance gains over conventional estimators. Further, the optimum estimators are useful in developing lower bounds on the mean square estimation error for clock skew and offset estimation schemes when we have multiple master-slave communication paths, and there is possibly unknown asymmetry between the fixed path delays.

Finally, for the case of unknown path asymmetries, we present a robust iterative clock skew and offset estimation scheme that exhibits a mean square estimation error close to the lower bounds when asymmetry is present. The robust scheme approximates the statistical distribution of the random queuing delays using a Gaussian mixture model and employs the space-alternating-generalized-expectation-maximization (SAGE) algorithm, an unsupervised learning algorithm and a variant of the EM algorithm, for learning all the unknown parameters, including clock skew and offset. The robust iterative scheme provides impressive run times since the SAGE algorithm allows us to obtain closed-form update equations for all unknown parameters, eliminating the need for a numerical solver.

The second topic of this dissertation investigates the problem of target detection in passive MIMO radar. Passive radar differs from conventional active radar in that it relies on preexisting signals from non-cooperative transmitters instead of transmitting a known signal. Although we do not control the transmitters, we usually have prior information regarding the modulation scheme employed at the non-cooperative transmit stations. The transmitted signal, however, is not fully known as it still contains unknown information symbols. By employing concepts from detection and learning theories, we developed new target detection algorithms for passive MIMO radar that can exploit the available information regarding the modulation format of the transmitted signal.

We introduce a relaxation, where we assume the information symbols to be any complex real numbers as opposed to an actual modulation symbol from a defined finite set. Assuming the modulation format of the transmitted signal is known, we present new explicit closed-form expressions for the generalized likelihood ratio tests for target detection in passive MIMO radar networks. The performance of the generalized likelihood ratio test in the known modulation format case is often significantly more favorable when compared to the case that does not exploit this information. Further, the performance improves with an increasing number of samples per symbol and, for a sufficiently large number of samples per symbol, the performance closely approximates that of an active radar with a known transmitted signal. Finally, numerical results indicate that the relaxation causes little loss at reasonable signal-to-noise ratios.

#### Recommended Citation

Nagarajan, Anantha Krishna Karthik, "New Combined Machine Learning and Estimation/Detection Approaches for IEEE 1588 and Passive Radar" (2020). *Theses and Dissertations*. 5689.

https://preserve.lehigh.edu/etd/5689