Constant modulus waveforms with restraining spectral interferences for cognitive MIMO radar

This paper proposes a novel method of unimodular transmitting waveforms design for multiple-input multiple-output (MIMO) radar to strengthen the detection performance in the presence of clutter and white Gaussian noise. An improved iterative algorithm is put forward to maximize the signal-to-clutter-plus-noise ratio (SCNR) under the constant modulus constraint. During iterations, the optimization of unimodular waveforms with filters fixed is a nonconvex fractional quadratically constrained quadratic program problem, which is NP-hard and not able to be solved in polynomial time. An algorithm based on semidefinite programming relaxation combined with bisection and Gaussian randomization is introduced to provide the high-quality suboptimal solutions with a polynomial time computational complexity. The analysis on the approximation bound is given to prove the tightness of the semidefinite programming relaxation and so the correctness of the proposed algorithm. The simulation results show that the improved method is efficient in designing unimodular waveforms for MIMO radar to achieve a better SCNR performance.

We consider the problem of waveform design for Multiple-Input Multiple-Output (MIMO) radar in the presence of signal-dependent interference embedded in white Gaussian disturbance. We present two sequential optimization procedures to maximize the Signal to Interference plus Noise Ratio (SINR), accounting for a constant modulus constraint as well as a similarity constraint involving a known radar waveform with some desired properties (e.g., in terms of pulse compression and ambiguity). The presented sequential optimization algorithms, based on a relaxation method, yield solutions with good accuracy. Their computational complexity is linear in the number of iterations and trials in the randomized procedure and polynomial in the receive filter length. Finally, we evaluate the proposed techniques, by considering their SINR performance, beam pattern as well as pulse compression property, via numerical simulations.

A multiple-input multiple-output (MIMO) radar system that transmits orthogonal waveforms via its antennas can achieve a greatly increased virtual aperture compared with its phased-array counterpart. This increased virtual aperture enables many of the MIMO radar advantages, including enhanced parameter identifiability and improved resolution. Practical radar requirements such as unit peak-to-average power ratio and range compression dictate that we use MIMO radar waveforms that have constant modulus and good auto- and cross-correlation properties. We present in this paper new computationally efficient cyclic algorithms for MIMO radar waveform synthesis. These algorithms can be used for the design of unimodular MIMO sequences that have very low auto- and cross-correlation sidelobes in a specified lag interval, and of very long sequences that could hardly be handled by other algorithms previously suggested in the literature. A number of examples are provided to demonstrate the performances of the new waveform synthesis algorithms.

In this paper, a novel radar waveform phase function design is presented that constructs a radar waveform that spectrally manuevers around in-band co-channel interference (CCI) from active communications users that are co-channel with the radar system. The design approach treats the CCI problem as the physical interpretable problem of optical refraction where the time-frequency (TF) signature of the radar waveform is made to be analogous to a light ray propagating from a start time and position (frequency) to an end time and position (frequency) and will naturally accelerate through the CCI as if the equivalent light ray accelerated in through different mediums (with an index of refraction related to CCI power spectral density (PSD)). Using the Euler-Lagrange equations, we design the radar phase function that is used to modulate a constant modulus (CM) waveform. The radar waveform design will generally result in a nonlinear-frequency modulated (NLFM) waveform that provides improved signal-to-interference-plus-noise-ratio (SINR) on a potential target in the presence of CCI leading to improved probability of detection performance. We provide theoretical analysis and simulation results for the proposed waveform design.

To avoid mutual interferences and detection confusion, orthogonal waveforms are usually employed for multiple-input multiple-output (MIMO) radar. In this paper, we apply chaos to design orthogonal waveforms for MIMO radar. Chaotic phase coded waveforms are generated, which are further optimised for obtaining good correlation performance of low sidelobe level. A sidelobe suppression method with complementary transmitting is introduced. The clonal selection algorithm is imposed to obtain the corresponding complementary coding waveforms. Correlation performance are compared with transmitting single chaotic phase coded signals and shown to be superior. Simulations based on biphase coded signals verify this method. (4 pages)

This study investigates the problem of low probability of intercept (LPI)-based distributed multiple-input multiple-output (MIMO) radar waveform design against barrage jamming in signal-dependent clutter and coloured noise. Given the priori knowledge of the extended target impulse response, signal-dependent clutter, barrage jamming signals and coloured noise, the LPI-based scheme for optimal radar waveform design is proposed to minimise the total power consumption of the MIMO radar system by optimising the transmitted waveforms of different transmitters with a predetermined mutual information (MI) constraint for target characterisation performance. Firstly, the MI between the received echoes from the target at each receiver and the target impulse response is derived as a practical metric to characterise the parameter estimation performance of a target. Then, the LPI-based distributed MIMO radar waveform design strategy is developed. The resulting radar waveform optimisation problem is convex and solved analytically, whose solutions represent the optimum power allocation for each transmitter in the MIMO radar system. With the aid of numerical simulations, it is illustrated that to minimise the total transmission power, the optimal waveform should match with the target, clutter, jamming and coloured noise. In addition, it is also demonstrated that the LPI performance of the MIMO radar system can be significantly improved by employing the proposed radar waveform design scheme.

In multiple-input multiple-output (MIMO) radar, the efficiency of target detection in clutter that is distributed over a certain range bin-Doppler frequency region depends on the sidelobe level of the waveformspsila auto- and cross-ambiguity functions within this region. We introduce the MIMO ambiguity function as the sum of all auto- and cross-ambiguity functions of the K MIMO radar waveforms, with the integral of this function over some range-Doppler region serving as a measure of the orthogonality (separability) of the waveforms within this region of interest. We derive an upper bound on the attainable ldquoclear areardquo for the MIMO ambiguity function, and show that, with respect to the conventional single-waveform ambiguity function, the maximum clear area is K times smaller for the MIMO system.

Multiple-input multiple-output (MIMO) radar equipped with a frequency diverse array (FDA) can produce a range-dependent beampattern and increase the degrees-of-freedom of the antenna array. In this paper, a new method of designing the MIMO radar beampattern with sparse frequency waveforms is proposed for the FDA, which randomly samples multiple distance points such that the MIMO radar beampattern with the both sparse frequency spectrum and constant modulus constraints are realized by the proposed beampattern design framework. The main steps are as follows. We first obtain the covariance matrix of the transmitted signal by a given ideal beampattern, and formulate the problem of designing the realizable beampattern as a nonconvex optimization problem, which includes the constraints of the both constant modulus of transmitted signals and sparse frequency spectrum. Then, a cyclic optimization algorithm is proposed, which guarantees the monotonic decrease of the objective function as the algorithm proceeds. The simulation results illustrate that the proposed method can achieve smaller errors than the traditional method, which does not consider the frequency diversity.

Beampattern synthesis with nulling for sub-arrayed MIMO radar under constant modulus constraints

In this paper, an optimal waveform design method for target recognition is proposed based on the relative entropy. Since the target recognition can be considered as a hypothesis test procedure, the detection probability could be the cost function to characterize the recognition performance. Then the cost function associated with the relative entropy is maximized to optimize the waveform for improving the recognition performance. The most proposed optimal waveform design methods just only consider the energy constraint. However, only the energy constraint is impractical. In this paper, we do not only consider the total energy limit, but also add the constant modulus constraint from the practice side to design the optimal waveform, since the radar systems commonly require constant modulus waveforms in order to utilize nonlinear power amplifiers. Finally, the simulation results show the effectiveness of the proposed algorithm.

In this paper, the Multiple-input Multiple-output(MIMO) radar waveform design under constant modulus constraint is considered. The process of current transmit beampattern design is conducted by approximating the desired transmit beampattern and minimizing the cross-correlation sidelobes. This leads to hard optimization problem due to the nonconvexity of the objective function and constant modulus constraint. In this work, an efficient method is proposed to address those problem based on Majorization-Minimization(MM) method. Finally, we evaluate the performance of the proposed MM-based algorithm via numerical simulations.

This study investigates the problem of designing unimodular waveform with spectral compatibility for multiple-input multiple-output radar in the presence of multiple targets and the signal-dependent interferences. A new approach is proposed to optimise the spectrally compatible radar waveform subject to not only the constant modulus constraint and the similarity constraint but also the signal-to-interference-plus-noise ratio (SINR) requirements for targets, aiming at suppressing the radar energy in some space-frequency areas occupied by other cooperative communication systems. However, the formulated optimisation problem is NP-hard because of the existence of the non-convex constraints. Based on the dual ascent framework, the authors develop an iterative algorithm to solve this challenging problem. The receive filter is obtained at the beginning of each iteration with the off-the-shelf technique and an innovative method termed phase-only dual ascent method is proposed to get the desired waveform. Additionally, they analyse the performance of the waveforms designed under the global SINR constraint and the local SINR constraint, respectively. Moreover, the convergence of the proposed algorithm is discussed concretely. Finally, the numerical simulations are provided to show the validity of the proposed approach.

Joint radar communication systems have been recently proposed for radar and communication sharing spectrum and hardware, to reduce the resource cost of platforms. In this paper, we consider the waveform design problem for a joint multiuser MIMO communication and MIMO radar system. We propose an optimization problem for waveform design, in which the signal-to-interference-plus-noise ratio (SINR) at users and the transmit beam pattern of radar are jointly optimized. To guarantee the efficiency of power amplifiers, the transmit waveform is constrained to be constant modulus. To deal with the non-convex constant modulus constraint, we propose an alternating descend method to solve the problem. The simulation results indicate that under high transmit signal-to-noise ratio (SNR), the communication quality can be guaranteed, along with a reasonable performance loss of radar. Moreover, the performance gap between the constant modulus constraint and the more relaxed per-antenna power constraint, is not significant.

The Multiple-Input Multiple-Output (MIMO) radar transmit beampattern matching under the Constant Modulus Constraint (CMC) is a key technology. Most existing approaches address this problem by relaxation, which result in performance degradation. Different from these methods, we notice that the CMC is the product of complex circles. Based on this characterisic, a Riemannian Complex Circle Manifold (RCCM) method without relaxation is developed. More precisely, the aforementioned problem is firstly reformulated as an unconstraint quartic function over the RCCM. After that, an efficient Riemannian conjugate gradient algorithm is developed to solve it. Compared with the existing methods, the proposed method obtains better performance with lower computational cost.

Multiple-input and multiple-output (MIMO) synthetic aperture radar (SAR) should use the waveforms that have a big product of time-width and frequency-width and a constant modulus. In this case, the Barker code-based waveforms are not suitable. In this paper, a kind of orthogonal frequency diversion multiplexing (OFDM) chirp diverse waveform is presented for MIMO SAR imaging. The waveform performance is evaluated by the radar ambiguity function. Numerical results show that the waveform has the superiorities of high range resolution, constant modulus, large time-banwidth product, implementation simplicity, and low ambiguity function sidelobes.