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.

Estimation of the location and motion of an object of interest is one of the primary inferential objectives in underwater acoustical remote sensing. In active sensing systems, this often begins with estimation of range through time delay and radial velocity by exploiting the Doppler effect. In systems that project a sequence of pulses, radial velocity can also be estimated from multiple time-delay measurements using waveforms insensitive to Doppler. The focus of this report is on performance bounds for estimation of time delay and radial velocity when using multiple frequency-modulated pulses that are not restricted to being narrowband. An emphasis is placed on the case of estimating radial velocity when time delay is also unknown while using combinations of the basic sonar waveforms: continuous-wave (CW), linear-frequency-modulated (LFM), and hyperbolic-frequency-modulated (HFM) pulses. A review of single-pulse bounds on the variance of unbiased estimators (i.e., Cramér–Rao lower bounds) is presented to facilitate development of bounds when combining echoes from multiple pulses. The pulse characteristic time-frequency properties comprising the single-pulse bounds are employed to provide multiple-pulse bounds that are straightforward to evaluate. As might be expected, the case of coherent echoes (i.e., echoes having a common bulk phase) generally leads to a lower bound on estimation performance than when the echoes are incoherent (i.e., they have different bulk phases). A number of examples are used to demonstrate multiple-pulse estimation performance. An important theme seen throughout the examples is that diversity across multiple pulses can have an outsize effect on parameter estimation (i.e., the bound decreases by a factor greater than the number of pulses). For similar types of pulses, spectral diversity improves time-delay estimation and temporal diversity aids estimation of radial velocity. Independent of this, diversity in the time-frequency character of the pulses (e.g., combining up- and down-sweeping LFM or HFM pulses) can provide a similarly significant improvement over the performance of any of the pulses alone.