We investigate methods of co-existence between radar and communications systems. Each system typically considers the other system a source of interference. Consequently, the traditional solution is to isolate the two systems spectrally or spatially. By considering a cooperative radar and communications signaling scheme, we derive achievable bounds on performance for a receiver that observes communications and radar return in the same frequency allocation. We assume the radar and communications operations to be a single joint system. Bounds on performance of the joint system are measured in terms of data information rate for communications and a novel radar estimation information rate for the radar.Index Terms-Performance bounds, radar-communications co-existence. I. INTRODUCTIONT HERE is an ever increasing demand for spectrum and given the limit on resources, communications and radar systems are increasingly encouraged to share bandwidth. This can cause inter-system interference that degrades the performance of both systems. The standard solution is to separate (temporally, spatially or spectrally) the radar and communications systems. In this paper, we do not require this separation, and we explore the fundamental radar and communications co-existence performance bounds. An important contribution that enables this exploration is the novel parameterization of estimation information rate. The estimation information rate incorporates the insights of rate distortion theory but emphasizes the symmetry with the communications bound. In this paper, we refine and extend the performance bounds introduced in [1], as well as the additional bounds discussed in [2]. We also expand the results in [1] in greater detail. The two new inner bounds on performance discussed in this paper are the isolated sub-band inner bound and the optimal Fisher information inner bound.

Finding the best decision boundary for a classification problem involves covariance structures, distance measures, and eigenvectors. This article considers how eigenstructures are an inherent part of the support vector machine (SVM) functional basis that encodes the geometric features of a separating hyperplane. SVM learning capacity involves an eigenvector set that spans the parameter space being learned. The linear SVM has been shown to have insufficient learning capacity when the number of training examples exceeds the dimension of the feature space. For this case, an incomplete eigenvector set spans the observation space. SVM architectures based on insufficient eigenstructures lack sufficient learning capacity for good separating hyperplanes. However, proper regularization ensures that two essential types of 'biases' are encoded within SVM functional mappings: an appropriate set of algebraic (and thus geometric) relationships and a sufficient eigenstructure set.

This paper presents a high-level overview of the Fundamental Limits studies for the DARPA SSPARC program. It focuses on the key techniques and insights that have resulted from this effort and presents possible future research directions that have been suggested by these studies 1 .

This analysis was completed as part of a larger Modeling and Simulation effort to estimate algorithm-level Measures of Performance (MOP), such as the probability of detection (PD) and the probability of identification (PID) of a vehicle or person transiting through an area of interest. The present work focuses on MOPs for Unattended Ground Magnetometer Sensors, which may be used to detect passing vehicles and estimate their bearing relative to the magnetometer position. In the first phase of the analysis, we concentrate on the probability of detection as a function of vehicle speed and distance (i.e., point of closest approach (CPA)) from the sensor. In the second phase, we try to localize the vehicle by extracting its relative bearing with respect to the magnetometer from the two orthogonal induced magnetic field measurements. The derivations are based on the assumption that a road vehicle may be approximated as a prolate homogeneous ellipsoid, as well as the assumption of uniform linear motion. Results show that, for speeds below 30 MPH, the maximum detection ranges (for PD = 0.5) are on the order of 40 meters for two-axis fluxgate magnetometers and for the operational parameters used in this analysis. 1

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