Robust Design of Transmit Waveform and Receive Filter For Colocated MIMO Radar

We consider the problem of angle-robust joint transmit waveform and receive filter design for colocated Multiple-Input Multiple-Output (MIMO) radar, in the presence of signal-dependent interferences. The design problem is cast as a max-min optimization problem to maximize the worst-case output signal-to-interference-plus-noise-ratio (SINR) with respect to the unknown angle of the target of interest. Based on rank-one relaxation and semi-definite programming (SDP) representation of a nonnegative trigonometric polynomial, a cyclic optimization algorithm is proposed to tackle this problem. The effectiveness of the proposed method is illustrated via numerical examples.Comment: 6 pages, 13 figures, part of this work was submitted to IEEE Signal Processing Letters; (short introduction; typos corrected; revised statement in section III-B and IV; revised figure labels

Characterizing Real-Valued Multivariate Complex Polynomials and Their Symmetric Tensor Representations

In this paper we study multivariate polynomial functions in complex variables and the corresponding associated symmetric tensor representations. The focus is on finding conditions under which such complex polynomials/tensors always take real values. We introduce the notion of symmetric conjugate forms and general conjugate forms, and present characteristic conditions for such complex polynomials to be real-valued. As applications of our results, we discuss the relation between nonnegative polynomials and sums of squares in the context of complex polynomials. Moreover, new notions of eigenvalues/eigenvectors for complex tensors are introduced, extending properties from the Hermitian matrices. Finally, we discuss an important property for symmetric tensors, which states that the largest absolute value of eigenvalue of a symmetric real tensor is equal to its largest singular value; the result is known as Banach's theorem. We show that a similar result holds in the complex case as well

Mathematical optimization techniques for cognitive radar networks

This thesis discusses mathematical optimization techniques for waveform design in cognitive radars. These techniques have been designed with an increasing level of sophistication, starting from a bistatic model (i.e. two transmitters and a single receiver) and ending with a cognitive network (i.e. multiple transmitting and multiple receiving radars). The environment under investigation always features strong signal-dependent clutter and noise. All algorithms are based on an iterative waveform-filter optimization. The waveform optimization is based on convex optimization techniques and the exploitation of initial radar waveforms characterized by desired auto and cross-correlation properties. Finally, robust optimization techniques are introduced to account for the assumptions made by cognitive radars on certain second order statistics such as the covariance matrix of the clutter. More specifically, initial optimization techniques were proposed for the case of bistatic radars. By maximizing the signal to interference and noise ratio (SINR) under certain constraints on the transmitted signals, it was possible to iteratively optimize both the orthogonal transmission waveforms and the receiver filter. Subsequently, the above work was extended to a convex optimization framework for a waveform design technique for bistatic radars where both radars transmit and receive to detect targets. The method exploited prior knowledge of the environment to maximize the accumulated target return signal power while keeping the disturbance power to unity at both radar receivers. The thesis further proposes convex optimization based waveform designs for multiple input multiple output (MIMO) based cognitive radars. All radars within the system are able to both transmit and receive signals for detecting targets. The proposed model investigated two complementary optimization techniques. The first one aims at optimizing the signal to interference and noise ratio (SINR) of a specific radar while keeping the SINR of the remaining radars at desired levels. The second approach optimizes the SINR of all radars using a max-min optimization criterion. To account for possible mismatches between actual parameters and estimated ones, this thesis includes robust optimization techniques. Initially, the multistatic, signal-dependent model was tested against existing worst-case and probabilistic methods. These methods appeared to be over conservative and generic for the considered signal-dependent clutter scenario. Therefore a new approach was derived where uncertainty was assumed directly on the radar cross-section and Doppler parameters of the clutters. Approximations based on Taylor series were invoked to make the optimization problem convex and {subsequently} determine robust waveforms with specific SINR outage constraints. Finally, this thesis introduces robust optimization techniques for through-the-wall radars. These are also cognitive but rely on different optimization techniques than the ones previously discussed. By noticing the similarities between the minimum variance distortionless response (MVDR) problem and the matched-illumination one, this thesis introduces robust optimization techniques that consider uncertainty on environment-related parameters. Various performance analyses demonstrate the effectiveness of all the above algorithms in providing a significant increase in SINR in an environment affected by very strong clutter and noise