A simple and robust sequential detector commonly used in remote sensing applications declares a signal is present the first time M successes are observed in any N consecutive measurements. In scenarios where N is fixed by stationarity restrictions, the sliding M-of-N detector is designed by varying M. This provides coarse control of the false alarm rate (FAR), which decreases as M is increased from one to N. In this report, the value of M is randomized to allow precise control of the FAR, which can reduce the average delay before detection (i.e., latency) compared to using the smallest fixed value of M that meets or exceeds the FAR specification. The cost of using a randomized sliding M-of-N detector is an increase in the standard deviation of the number of measurements required to make a decision relative to its mean. Approximations to the detection performance measures for standard sliding M-of-N detectors are reviewed and employed to design and analyze the randomized sliding M-of-N detector. Precise control of the false alarm performance is then exploited to compare approaches for controlling FAR in a two-stage detection algorithm when the first-stage background is dominated by false-alarm-inducing clutter and the second stage employs a sliding M-of-N detector. Throttling the first stage to maintain a constant single-measurement probability of false alarm was seen to have a minor advantage in detection latency at very high signal-to-noise power ratio (SNR), compared with passing the clutter-induced false alarms to a randomized sliding M-of-N detector in the second stage. At moderate SNR with heavy clutter or at low SNR, however, throttling reduces the single-measurement probability of detection to the point where there is a significant increase in latency relative to using the randomized sliding M-of-N detector to control FAR. This analysis supports the commonly encountered engineering design approach where the first-stage single-measurement detector is run "hot" and the second-stage multiple-measurement detector cleans up the excessive false alarms, while providing a means for precise control of the FAR and adding the nuance of the high-SNR result.

Beamforming algorithms are typically designed to maximize their output signal-to-interference-and-noise power ratio (SINR), under the assumption that doing so will optimize the probability of detection (P_d), given a design probability of false alarm (P_f ), in the ensuing detection algorithm. An alternative performance metric, the J-divergence detection currency (JDC), is employed here to represent performance before and after beamforming. Building on early use of the J-divergence in modeling array processing performance, the basic analysis is extended to account for correlated multipath signals and shaded conventional beamforming. The reduction in performance observed in practical adaptive beamforming algorithms that must estimate the array covariance matrix (ACM) or its eigen-structure is then assessed for processors having a beta-distributed SINR loss factor, representing a number of popular processors. Simple approximations to the JDC in this scenario that are accurate at low SINR, as well as more involved ones for higher SINR, are presented along with the tools required to evaluate them. The analysis presented in this report allows assessing the potential gain in performance from combining multipath signals and the losses incurred by ACM estimation in a metric that is easily combined across multiple measurements, is more closely related to the (P_d, P_f ) detection metrics than SINR, and can be evaluated throughout the signal and information processing chain.