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To enhance maneuvering target tracking in modern battlefield, cognitive radar could adjust its waveforms and information processing manner. In this paper, a novel adaptive waveform design method based on multiple model interaction and measurement information fusion is developed. First, some latest measurements and virtual ones are collected to exploit more robust information. Second, the unknown target state is formulated via the multi-model idea, and the tracking framework is highlighted by the matrix-weighted multi-model fusion (MMF) in lieu of the probability-weighted way. Finally, the MMF output covariance matrix is selected as the ellipse metric, and ellipse parameters can be obtained by using the eigenvalue decomposition. Given these parameters, fractional Fourier transform is used to rotate the measurement error-ellipse to make them orthogonal, and further obtain the desirable rotating orientations for the cognitive transmitting waveform. Simulations show that compared with several algorithms, e.g., MIMM and IMM, our algorithm could further improve tracking performance and robustness.

The unimodular LFM-Syn waveform is formulated by a combination of random noise waveform and conventional LFM, where the phase-scaling factor makes it come true.To achieve low range sidelobes and high Doppler tolerance, a novel template-optimizing function is established with constraints on quadratic phase and random phase.Relaxed Alternating Projection Phase Control method, incorporating spectrum approximation and quadratic phase amendment, is proposed.The LFM-Syn waveform optimized by RAPPC has Doppler tolerance, LPI capability and low range sidelobes. This paper considers the unimodular Linear-FM Synthesized (LFM-Syn) waveform design for cognitive radar.Firstly, the synthesized waveform is formulated by a given phase-scaling factor which combines the random noise waveform and the conventional LFM waveform. Secondly, to achieve low range sidelobes and high Doppler tolerance of LFM-Syn waveforms, a novel template-optimizing objective function is established and then transformed into a two-variable non-convex optimization case with constraints on quadratic phase and random phase. Meanwhile, a Relaxed Alternating Projection Phase Control method (RAPPC) incorporating spectrum approximation relaxed alternating projection and quadratic phase amendment is proposed via an iterative way. RAPPC not only enhances local exploiting for desired waveforms but also keeps high Doppler tolerance and low range sidelobes. Lastly, simulations have provided evidences that the LFM-Syn waveform optimized by RAPPC 1) has high Doppler tolerance similar to conventional LFM, 2) has Low Probability of Intercept (LPI) similar to random noise waveform, and 3) has low range sidelobe levels for prescribed requirement. Additionally, simulations also highlight the superior performance of our proposed algorithms over several existing techniques.

This paper tries to design waveform with low probability of intercept and high doppler tolerance for cognitive radar. Firstly, the novel waveform is formulated by the chaotic-noise waveform and conventional LFM one, where a given phase scaling factor combines them. Then, the template-optimizing function is established with constraints on quadratic phase and chaotic phase, to achieve low range sidelobes. Finally, an approach incorporating spectrum approximation alternating projection and quadratic phase amendment, named Phase-based Alternating Projection Optimized Method (PAPOM), is proposed. Simulations have demonstrated its superior performance. Additionally, results from the matched filter output provide evidence that the novel waveform optimized by PAPOM 1) has range-Doppler resolution similar to conventional LFM one and 2) has Low Probability of Intercept (LPI) similar to random noise-one, as well as 3) has low range sidelobe in specified units.

We propose an approach to design locally orthogonal waveform pairs (LOWP). The approach is based on alternating projection, in which an algorithm framework called alternating projections to synthesize LOWP (APLOWP) is derived. Two specialized versions of APLOWP, namely, APLOWP dynamic ideal autocorrelation construction (DIAC) and APLOWP inner product constraint (IPC), are developed. APLOWP-DIAC is used to synthesize waveform pairs for instantaneous polarization radar, because its designed waveforms have very low auto- and cross-correlation magnitudes in specified lag intervals. APLOWP-IPC is used for joint transmit-receive optimization. The IPC of APLOWP-IPC guarantees that the signal-to-noise ratio (SNR) loss is below the specified bound even though a mismatched filter leads to SNR loss. The effectiveness of the proposed algorithms is demonstrated by using numerical simulations.

A two-stage design approach is proposed to address the sparse antenna array design for multiple-input multiple-output radar. In the first stage, the cyclic algorithm (CA) is used to establish a covariance matrix that satisfies the beam pattern approximation for a full array. In the second stage, a sparse antenna array with a beam pattern is designed to approximate the desired beam pattern. This paper focuses on the second stage. The optimization problem for the sparse antenna array design aimed at beam pattern synthesis is formulated, where the peak side lobe (PSL) is weakly constrained by the mean squared error. To solve this optimization problem, the differential evolution (DE) algorithm with multistrategy is introduced and PSL suppression is treated as an inequality constraint. However, in doing so, a new multiobjective optimization problem is created. To address this new problem, a multiobjective differential evolution algorithm based on Pareto technique is proposed. Numerical examples are provided to demonstrate the advantages of the proposed approach over state-of-the-art methods, including DE and genetic algorithm.

We propose a beamforming algorithm based on waveform diversity for hyperthermia treatment of breast cancer using an ultrasonic array. The introduced array has a structure with a network connecting the feeding nodes and the array elements, and the objective of the algorithm is to train the weight matrix of the network to minimize the difference between the generated beam pattern and the ideal one. The training procedure of the algorithm, which is inspired by the idea of machine learning, comprises three parts: forward calculation, comparison, and backward calculation. The forward calculation maps the weight matrix to the beam pattern, and in the comparison step, the generated beam pattern is modified based on the error, and finally, the backward calculation maps the modified beam pattern to a refined weight matrix which performs better than the original one. An optimal weight matrix is obtained by iterative training. The effectiveness of the algorithm is demonstrated by using numerical simulations.

This paper mainly considers the unimodular Linear-FM synthesized (LFM-Syn) waveform design for cognitive radar. To achieve its low range sidelobes and high Doppler tolerance together, a novel template-based objective function is formulated with constraint on both the quadratic phase and random phase of the waveform. In addition, a novel Alternating Projection Phase Control method (APPC) is proposed to optimize this function. Simulations show some performance of APPC over several existing techniques, and also our waveforms optimized by APPC 1) has Doppler tolerance similar to conventional LFM one and 2) has Low Probability of Intercept (LPI) similar to the random noise one, as well as 3) has low range sidelobes.

We propose an approach to design waveform sets with good auto- and cross-correlation properties. The designed waveform sets can be used for multiple-input multiple-output radars to minimize the cross-interference, and consequently improve the radar performance. Firstly, we transform the original correlation optimization problem into a spectral approximation problem. Secondly, we define the objective function based on the square error between the designed waveform matrix and the ideal one. Finally, the problem is solved by using an algorithm based on alternating projection and phase retrieval. We further improve the proposed method, and derive an extended version to design waveforms with sparse spectrum and good correlation property for combating electronic jamming. The algorithms are computationally efficient because their main steps are based on fast Fourier transform. The effectiveness of the proposed approach is demonstrated by numerical simulations.

We propose an approach for designing unimodular waveforms with low correlation sidelobes in one or more lag intervals. The approach includes an iterative spectral approximation algorithm (ISAA) and derivative-based non-linear optimization algorithms. ISAA is based on power spectral density fitting, phase retrieval, and alternating projection. Phase-only versions of the derivative-based optimization algorithms are also derived. These algorithms eliminate the unimodular constraint by expanding the objective function with respect to the phase vector and by replacing the normal line search with the phase-only line search. The effectiveness of the approach is demonstrated by numerical simulations.