| Modern radar and sonar systems operate in complex environments that require separation of targets of interest from undesired clutter, reverberation, and multipath. Estimation of the channel multipath response is critical in algorithms employed for equalization, advanced detection, classification, and improved parameter estimation in multipath environments. For time-varying channels, the problem is further confounded by the fundamental rank deficiency inherent in the estimation of a two-dimensional channel using a one-dimensional received signal.; This dissertation covers topics related to estimating deterministic time-varying linear channels for active sensors. The intent is not only to address channel estimation, but also to address signal design and the signal-sensitive aspects of performance. The flexibility to choose a transmit waveform is important to consider.; Projection onto Convex Sets (POCS) and Method of Generalized Projections (MGP) algorithms are presented for simultaneously estimating delay and Doppler of multipath components. These algorithms have the ability to apply constraints to reduce the dimensionality of the channel space being estimated, improving performance where the general problem is ill-posed with significant rank deficiency. Applying a priori knowledge using constraints mitigates the fundamental lack of information available to estimate the time-varying channel.; Signal-dependent error for least squares delay-Doppler specular multipath estimation is developed. The results are also applicable to POCS and MGP constraint sets that use square error. Error results are presented versus transmit pulse width and bandwidth.; The trajectory diagram, a graphical view of a time-varying channel, is used and extended to consider general time-varying channels. A sampling channel estimation method is extended for operation with any pulsed signal using sampling, reconstruction, and deconvolution.; Trajectory ambiguity, a representation of signal ambiguity as a family of target trajectories that yield nearly identical receive signals, is introduced. The trajectory ambiguity representation preserves information about target and channel behavior that is typically lost in other ambiguity representations. A novel approach for trajectory insensitive signal design is developed by applying the relationship between signal instantaneous frequency and trajectory ambiguity, which can be used to select a signal that is insensitive to channel components not of interest to the sensor. |
