This paper deals with the joint design of Multiple-Input Multiple-Output (MIMO) radar transmit waveform and receive filter to enhance multiple targets detectability in the presence of signal-dependent clutter and noise. The worst-case Signal-to-Interference-Noise-Ratio (SINR) over multiple targets is explicitly maximized. To ensure hardware compatibility and coexistence between MIMO radar and other wireless systems, constant modulus and spectral restrictions on the waveform are incorporated in our design. A max-min non-convex optimization problem emerges as a function of the transmit waveform, which we solve via a novel polynomial-time iterative procedure that involves solving a sequence of convex problems with constraints that evolve with every iteration. The overall algorithm follows an alternate optimization over the receive filter and transmit waveform. For the problem of waveform optimization (which is our central contribution), we provide analytical guarantees of monotonic cost function improvement with proof of convergence to a solution that satisfies the KarushKuhnTucker (KKT) conditions. We also develop extensions that address the well-known waveform similarity constraint. By simulating challenging practical scenarios, we evaluate the proposed algorithm against the state-of-the-art methods in terms of the achieved SINR value and the computational complexity. Overall, we show that our proposal outperforms state of the art competing methods while providing the most favorable performance-complexity balance.

This paper deals with the joint design of Multiple-Input Multiple-Output (MIMO) Space-Time Transmit Code (STTC) and Space-Time Receive Filter (STRF) to improve the detectability of a moving target embedded in signal-dependent clutter in the presence of uncertainties on the target azimuth angle and Doppler frequency. The Signal to Interference plus Noise Ratio (SINR) is considered as a figure of merit to maximize and multiple restrictions on STTC are forced at the design stage, i.e., similarity and modulus constraints as well as a uniform power requirement among the transmit antennas. To deal with the resulting non-convex design problem, a novel polynomial-time iterative procedure based on Successive Greedy Optimization (SGO) framework ensuring that SINR monotonically increases and converges to a finite value, is developed. Each iteration of the proposed algorithm involves the generalized eigenvalue decomposition to design STRF and a nested iterative technique involving Dinkelbach's procedure and an Alternating Direction Penalty Method (ADPM) to obtain STTC. Numerical results are provided to assess the performance of the proposed algorithm against some counterparts in terms of the optimized SINR value and computational complexity.

This paper considers the integrated waveform design to simultaneously achieve a desired radar beampattern and multi-users communication for a dual-function Multiple-Input Multiple-Output (MIMO) system. To this end, a spatio-spectral modulation strategy via shaping the spatial waveform Energy Spectral Density (ESD) in directions of communication is proposed for the communication function, while beampattern Integrated Sidelobe Level (ISL) is minimized to enhance radar detectability. Meanwhile, Peak-to-Average Ratio (PAR) and power restrictions to comply with the current hardware technique and the mainlobe width constraint to cohere the beampattern main energy on the spatial region of interest are forced, respectively. Exploiting an equivalent reformulation of the original non-convex optimization problem, a Sequential Block Enhancement (SBE) framework that alternately updates each waveform in each emitting antenna is developed to monotonically decrease ISL. Each block involves the Dinkelbach’s procedure, sequential convex approximation and Alternating Direction Method of Multipliers (ADMM) to obtain single waveform, while the analytic proof with the converged block being a Karush-Kuhn-Tucker (KKT) point is provided. Finally, numerical results highlight the effectiveness of both the proposed dual function scheme and the waveform synthesis technique in comparison with some counterparts.

We consider the design of wideband Multiple-Input Multiple-Output (MIMO) radar waveforms to approximate a desired beampattern and achieve prescribed space-frequency nulling in a space-frequency region of interest. A general design model involving modulus, power and energy constraints on the probing waveforms is introduced. To deal with the resulting non- convex design, a novel iterative algorithm with low computational complexity is proposed. In each iteration, the non-convex design is approximated successively through a series of convex subproblems. Then, each convex subproblem is reformulated in a new Alternating Direction Method of Multipliers (ADMM) form, with small-sized subproblems solved in parallel with closed- form solutions via utilizing the Karush-Kuhn-Tucker (KKT) conditions. Numerical results are provided to demonstrate the effectiveness of the proposed algorithm.

This article deals with the multiple-input–multiple-output (MIMO) radar beampattern design in an effort to the coexistence with multiple communication systems. A waveform optimization model accounting for the minimization of the beampattern integrated sidelobe level (ISL) along with the mainlobe width, peak-to-average power ratio, and energy constraints, as well as multispectral requirements where the interference energy injected by the MIMO radar in each shared frequency band in a particular direction, is precisely controlled to ensure the desired quality of service at each communication system. Through an equivalent reformulation of the original nonconvex problem, a polynomial-time sequential convex approximation (SCA) procedure that involves the tackling of a series of constrained convex problems is proposed to monotonically decrease the ISL with the convergence guaranteed to a Karush–Kuhn–Tucker point. Herein, to speed up the convergence, a fast iterative algorithm based on the alternating-direction-method-of-multipliers framework is introduced to globally solve the convex problems during each iteration of the SCA procedure. Numerical results are provided to assess the proposed algorithm in terms of the computational complexity, the achieved beampattern, and spectral compatibility with some competitive counterparts available in the open literatures.

This paper deals with the NP-hard quadratic optimization problem under similarity and constant modulus constraints. A computationally efficient iterative algorithm based on the Alternating Direction Penalty Method (ADPM) framework is proposed for continuous and discrete phase cases. In each iteration, it converts the considered problem into two subproblems with closed-form solutions via an introduced auxiliary variable, while locally increasing the penalty factor involved in the ADPM framework. The proposed algorithm is proven to converge for any initialization under some mild conditions and avoids the non-convergence problem of the Alternating Direction Method of Multipliers (ADMM) when handling the NP-hard problems. It ensures that the obtained solution fulfills the Karush-Kuhn-Tucker (KKT) conditions for the continuous phase case. To further refine the ADPM solution, a joint approach involving both the ADPM and the coordinate descent frameworks is introduced. The extension that solves the quadratic optimization problem incorporating more complicated constraints is also developed. Finally, two radar waveform design examples are presented to demonstrate that the proposed algorithms can outperform their counterparts by providing better objective values with relatively low polynomial computational complexities.