We consider Signal Waveform's Optimal-under-Restriction Design (SWORD) for active sensing. In the presence of colored interference and noise with known statistical properties, waveform optimization for active sensors such as radar can significantly increase the signal-to-interference-plus-noise ratio needed for much improved target detection. However, the so-obtained optimal waveforms can result in significant modulus variation, poor range resolution, and/or high peak sidelobe levels. To mitigate these problems, we can constrain the waveform optimization problem by restricting the sought-after waveform to be similar to a desired waveform, which is known to have, for example, constant modulus as well as reasonable range resolution and peak sidelobe level. One example of the desired waveform is the widely used linear frequency modulated waveform or chirp. We will provide a detailed solution to the constrained optimization problem and explain how it is related with the existing waveform optimization methods

Optimal detection of a target return contaminated by signal-dependent interference, as well as additive channel noise, requires the design of a transmit pulse f(t) and a receiver impulse response h(t) jointly maximizing the output signal to interference plus noise ratio (SINR). Despite the highly nonlinear nature of this problem, it has been possible to show that f(t) may always be chosen minimum-phase. A full analysis concludes with the construction of an effective numerical procedure for the determination of optimal pairs (f,h) that appears to converge satisfactorily for most values of input SINR. Extensive simulation reveals that the shape of f(t) can be a critical factor. In particular, the performance of a chirp-like pulse is often unacceptable, especially when clutter and channel noise are low-pass dominant and comparable.

A new generalized statistical signal processing framework is introduced for optimal signal representation and compression. Previous work is extended by considering the multiple signal case, where a desired signal is observed only in the presence of other non-white signals. The solution to this multi-signal representation problem yields a generalization of the Karhunen-Loeve transform and generates a basis selection which is optimal for multiple signals and colored-noise random processes under the minimum mean-square error criterion. The important applications for which this model is valid include detection, prediction, estimation, compression, classification and recognition.

A major issue in space-time adaptive processing (STAP) for airborne moving target indicator (MTI) radar is the so-called sample support problem. Often, the available sample support for estimating the interference covariance matrix leads to severe rank deficiency, thereby precluding STAP beamforming based on the direct sample matrix inversion (SMI) method. The intrinsic interference subspace removal (ISR) technique, which is a computationally and analytically useful form of diagonally loaded SMI method, is derived here. It covers from Hung-Turner (1983) projection (HTP) algorithm to the matched filter according to the loading factor. Also the optimum loading factor which gives the maximum signal-to-interference-plus-noise ratio (SINR) is derived from the viewpoint of singular value decomposition of the covariance matrix. The simulation results with synthetic data show that the maximum SINR indeed coincides with the proposed optimum loading factor in various data sample situations.

A major issue in space-time adaptive processing (STAP) for airborne moving target indicator (MTI) radar is the so-called sample support problem. Often, the available sample support for estimating the interference covariance matrix leads to severe rank deficiency, thereby precluding STAP beamforming based on the direct sample matrix inversion (SMI) method. The intrinsic interference subspace removal (ISR) technique, which is a computationally useful form of diagonally loaded SMI method, can handle this case, although the performance is poor in low sample situations. In this context, new subarray-subpulse schemes using forward and backward data vectors are introduced to overcome the data deficiency problem. It is shown that a multiplicative improvement in data samples can be obtained at the expense of negligible loss in space-time aperture of the steering vector.

Space-time adaptive array processing has emerged as a key technology thrust area for the next generation of airborne radar systems due to its inherent potential for vastly improving moving target indicator (MTI) performance. Unfortunately, these performance gains come with a commensurate increase in on-line computational complexity if full degree-of-freedom (DOF) space time adaptive processing (STAP) processors are employed. In this paper we introduce a class of efficient STAP processors which exploit the fact that the full DOF space-time clutter covariance matrix is rank deficient with respect to a coherent processing interval.