This paper aims to design a set of transmit waveforms in cognitive colocated Multi-Input Multi-Output (MIMO) radar systems considering the simultaneous minimization of spatial- and the range- Integrated Sidelobe Level Ratio (ISLR). The design problem is formulated as a bi-objective Pareto optimization under practical constraints on the waveforms, namely total transmit power, peak-to-average-power ratio (PAR), constant modulus, and discrete phase alphabet. A Coordinate Descent (CD) based approach, called UNIQUE, is proposed in which at every single variable update of the algorithm we obtain the solution of the uni-variable optimization problems. The novelty of the paper comes from deriving a flexible waveform design problem applicable for the emerging 4D imaging MIMO radars with application to automotive radar systems. The simultaneous optimization leads to a trade-off between the two ISLRs and the simulation results illustrate significantly improved trade-off offered by the proposed methodologies.

Spatial- and Range- ISLR Trade-Off in MIMO Radar Via Waveform Correlation Optimization

This paper deals with constant modulus waveform design in spectrally dense environments assuming a discrete phase code alphabet. The goal is to optimize the radar detection performance while rigorously controlling the injected interference energy within each shared band and enforcing a similarity constraint to manage some relevant signal features. To tackle the resulting NP-hard optimization problem, an iterative procedure characterized by a polynomial computational complexity, is introduced leveraging the coordinate descent method. Numerical results are provided to show the effectiveness of the technique in terms of detection performance, spectral shape and autocorrelation features.

Design of Constant Modulus Discrete Phase Radar Waveforms Subject to Multi-Spectral Constraints

In this article, we propose a new algorithm that designs a transmit beampattern for multiple-input multiple-output (MIMO) radar considering coexistence with other wireless systems This design process is conducted by minimizing the deviation of the generated beampattern (which in turn is a function of the transmit waveform) against an idealized one while enforcing the waveform elements to be constant modulus and in the presence of spectral restrictions This leads to a hard nonconvex optimization problem primarily due to the presence of the constant modulus constraint (CMC) In this article, we exploit the geometrical structure of CMC, ie, we redefine this constraint as an intersection of two sets (one convex and other nonconvex) This new perspective allows us to solve the nonconvex design problem via a tractable method called iterative beampattern with spectral design (IBS) In particular, the proposed IBS algorithm develops and solves a sequence of convex problems such that constant modulus is achieved at convergence Crucially, we show that at convergence the obtained solution satisfies the Karush–Kuhn–Tucker conditions of the aforementioned nonconvex problem Finally, we evaluate the proposed algorithm over challenging simulated scenarios, and show that it outperforms the state-of-the-art competing methods

Spectrally Compatible MIMO Radar Beampattern Design Under Constant Modulus Constraints

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.

Multispectrally Constrained MIMO Radar Beampattern Design via Sequential Convex Approximation

Range profiling refers to the measurement of target response along the radar slant range. It plays an important role in automatic target recognition. In this paper, we consider the design of transmit waveform to improve the range profiling performance of radar systems. Two design metrics are adopted for the waveform optimization problem: one is to maximize the mutual information between the received signal and the target impulse response (TIR); the other is to minimize the minimum mean-square error for estimating the TIR. In addition, practical constraints on the waveforms are considered, including an energy constraint, a peak-to-average-power-ratio constraint, and a spectral constraint. Based on minorization-maximization, we propose a unified optimization framework to tackle the constrained waveform design problem. Numerical examples show the superiority of the waveforms synthesized by the proposed algorithms.

Constrained Radar Waveform Design for Range Profiling

This paper deals with the synthesis of constant modulus waveforms that optimize radar performance while satisfying multiple spectral compatibility constraints. For each shared band, a precise control is imposed on the injected interference energy. Furthermore, the compliance with amplifiers operating in saturation is ensured at the design stage where phase-only waveforms are considered. To tackle the resulting NP-hard optimization problem, an iterative procedure based on the coordinate descent method is introduced. The overall computational burden of the algorithm is linear with respect to the code length as well as the number of iterations and less then cubic with reference to the number of spectral constraints. Hence, some case studies are reported to highlight the effectiveness of the technique.

On the Design of Multi-Spectrally Constrained Constant Modulus Radar Signals

This paper deals with the synthesis of waveforms that optimize radar performance while satisfying multiple spectral compatibility constraints. For each shared band, precise control is imposed on the injected interference energy. Furthermore, compliance with amplifiers operating in saturation is ensured at the design stage where phase-only waveforms are considered. To tackle the resulting NP-hard optimization problem, an iterative procedure based on the coordinate descent method is introduced. Hence, some case studies are reported to highlight the effectiveness of the technique.

Lorenzo Martino

Papers

On the Design of Multi-Spectrally Constrained Constant Modulus Radar Signals

Phase-Only Radar Waveform Design for Spectrally Dense Environments