# Adaptive constant-false-alarm-rate (CFAR) processors utilizing structured covariance matrices

#### Abstract

In radar systems and signal processing, it is common to detect a signal in a background of non-homogeneous noise. Radar detection algorithms are usually implemented by taking a snapshot of one or more range gates adjacent to the cell under test, forming an analysis window, and calculating the noise statistics within this window. The spatial statistics of the noise vary with time, but for a finite size analysis window, the background can be assumed homogeneous. Several variants of detection processor exist, the two primary categories being scalar and vector. Both types of processor are dependent on the statistics of the background noise when setting the detection threshold. In the scalar case, the true variance of the background, $\sigma\sbsp{n}{2}$, is unknown. In the vector case, this unknown variance is incorporated within the noise sample covariance matrix. Scalar processors perform well, but do not incorporate all of the known information related to the detection process, such as the a priori knowledge of the signal to be detected. The result is a loss in detection efficiency. Vector processors can incorporate this a priori known signal and thus, are capable of improved performance. However, an additional increase in the performance of vector processors can be achieved if the various unknown parameters such as the noise covariance matrix are replaced by their maximum likelihood estimate. For techniques utilizing the generalized likelihood ratio test (GLRT) involving exponentially distributed noise, the maximum likelihood estimator for the unknown actual noise correlation matrix, given no prior constraints, is the sample covariance matrix. It is known that some random processes have an underlying structure associated with their unknown true correlation matrices. Generally the sample covariance matrix obtained from the data will not exhibit this structure. This structure can be accomplished if one derives a maximum likelihood structured matrix from the available sample matrix, which is constrained to be of the correct form. It can be reasoned that algorithms relying on such matrix estimates will perform better. In this work characteristics of structured matrices will be analyzed. Various scalar and vector CFAR detection algorithms will be examined. A vector CFAR detection processor will then be implemented which incorporates structured matrices. The performance of this structured matrix based processor will then be compared to vector processors based on the standard sample covariance matrix. Currently, there is no closed form solution for the processor detection statistic. However, the processor performance will be examined in terms of its eigen-decomposition and its resulting receiver operating characteristics (ROC).

#### Recommended Citation

Whitney, James Edward, "Adaptive constant-false-alarm-rate (CFAR) processors utilizing structured covariance matrices" (1995). *Dissertations (1962 - 2010) Access via Proquest Digital Dissertations*. AAI9600866.

https://epublications.marquette.edu/dissertations/AAI9600866