A two-step optimal waveform design for detection in signal-dependent interference

In this study, the authors address the design of optimal waveform for detecting extended target in signal-dependent interference, using the probability of detection as a cost function. The authors model the received signal in frequency domain and derive the optimum Neyman-Pearson (NP) detector. Considering the distribution of test statistic is rather complicated, the authors use a mathematically tractable form to approximate and derive an analytical expression for the probability of detection with regard to the transmitted waveform. This lays the foundation for the subsequent waveform optimisation. Finally, the authors focus on rank-one target, and propose methods for designing optimal, suboptimal and asymptotic optimal waveforms for detecting rank-one target.

This study addresses the challenge of cognitive waveform design for multiple-input–multiple-output (MIMO) radar systems operating in cluttered environments. It focuses on the key practical requirements for transmitting time-domain waveforms and proposes a novel approach. This method first determines the optimal frequency-domain waveform and then designs a time-domain waveform that closely approximates the frequency-domain solution. The primary objective is to enable MIMO radar systems to transmit orthogonal waveforms while accommodating various constraints. A frequency-domain waveform optimization model was initially developed using the principle of maximizing dual mutual information (DMI), and the energy spectral density (ESD) of the optimal waveform was derived using the water-filling method. Next, a time-domain waveform approximation model is constructed based on the minimum mean square error (MMSE) criterion, which incorporates constant modulus and peak-to-average power ratio (PAPR) constraints. To minimize the performance degradation of the waveform, an improved adaptive gradient descent genetic algorithm (GD-AGA) was proposed to synthesize multichannel orthogonal time-domain waveforms for MIMO radars. The simulation results demonstrate the effectiveness of the proposed model for enhancing the performance of MIMO radar. Compared with traditional genetic algorithms (GA) and two enhanced GA alternatives, the proposed algorithm achieves a lower ESD loss and better orthogonal performance.

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.

Radar Phase-Modulated Waveform Design for Extended Target Detection

Suppression of stimulated Brillouin scattering effect in 2 μm narrow linewidth Tm3+-doped fiber amplifier based on phase-modulated waveform design

In this article, we introduce a frequency-based waveform design to maximize binary target classification. The optimization problems can be solved via optimal solvers available in the literature. The presented formulation is applicable to the classification scenarios where the extended target frequency responses (TFRs) are complex, random, and normally distributed with unequal mean vectors. However, their covariance matrices are either identical or different. For the former, i.e., identical covariance matrices, the optimization problem consists of a cost function that has been obtained by deriving a closed-form expression of the probability of misclassification. For the latter, i.e., different covariance matrices, we present an optimization problem where the cost function has been obtained via the Fisher separation function. For this, we also present a closed-form expression for an approximate solution to the optimization problem. We show that the proposed solution achieves performance levels comparable to the exact solution of the optimization problem obtained via state-of-the-art optimization solvers while incurring low computational complexity. We expand on the two main scenarios by introducing clutter (i.e., signal-dependent interference) in the signal model and studying possible closed-form designs in extreme waveform energy levels. Simulations are conducted using synthetically generated data in addition to the civilian vehicle data from the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset, in order to validate the proposed method.

In this paper, the problem of adaptive waveform design for cognitive radar (CR) in signal-dependent interference, as well as additive channel noise is investigated. With constraints on waveform energy and bandwidth, a flexible waveform optimization method taking both detection and range resolution into account is proposed. Unlike existing optimal waveforms designed by a single design criterion, waveform designed by the proposed method can be updated according to the environment information fed back by receiver and radar performance demands simultaneously at each cycle of CR. Simulations are conducted to illustrate that CR with the proposed waveform performs better than traditional radar system with fixed waveform, and offers more practical and flexible.

In the past decades, there has been an extensive research interest in the areas of both waveform diversity/design and advanced signal processing algorithms departing from the more classical solutions based on Linear Frequency Modulated (LFM) pulses and Matched Filters (MF). In the waveform diversity community, especially within the context of spectrum sharing, MIMO and cognitive radars, several waveform optimization and design methodologies have been studied, see [1], [2] and references therein. In parallel to waveform design, several signal processing techniques have also been proposed which exploit some kind of prior knowledge and/or iterative algorithms to improve the performance of the more classical MF, such as the Adaptive Pulse Compression(APC) [3], MUSIC [4], CLEAN [5] and Sparse Signal Processing (SSP) [6], [7]. In this paper we present some results and examples to show how the combination of waveform design with SSP can lead to improved performance in radar compared to the more classical approach.

The design of optimal waveform for enhanced detection of rank-one targets is addressed. Rather than simultaneous design of waveform and matched filter maximizing the clutter-plus-noise ratio (SCNR), we design the optimal waveform maximizing the probability of detection under the Neyman-Pearson (NP) criterion.

A simple scheme to generate a dual-band complementary linearly chirped microwave waveform using a Mach–Zehnder modulator (MZM) paralleled with a phase modulator (PM) is proposed. In the scheme, a five-line optical frequency comb, generated by MZM, is combined with a phase modulated optical chirp waveform by a baseband parabolic signal or a single-chirp signal as two beams with inverse relative phases via a 2 × 2 optical coupler. After balanced detection with heterodyne beating, the dual-band complementary linearly chirped microwave waveform is generated for the two driving cases, and they demonstrate different enhanced performances. The dual-band complementary linearly chirped microwave waveforms with center frequency of 20 and 40 GHz are generated simultaneously for both cases by simulation. The generated two complementary linearly chirped waveforms with a baseband parabolic driving signal have a larger bandwidth of 7.6 GHz, corresponding to larger pulse compression ratios (PCRs) of 1462.86 and 1365.33, which could effectively improve the range Doppler resolution in modern radar systems, although their peak-to-sidelobe ratios (PSRs) are only 12.98 and 12.97 dB. Although for the case with a single-chirp driving signal, the PSRs of the two waveforms with a bandwidth of 4 GHz are higher, 13.66 and 13.67 dB, respectively, but with the PCRs of only 787.69 and 758.52, which is of practical significance for radar detection in weak targets and multitargets.

With recent advances in both algorithm and component technologies, through-the-wall radar imaging (TWRI) is emerging as an affordable sensor technology in civil and military settings. Design of appropriate waveforms is important for improving the performance of TWRI systems. We present optimal waveforms, based on the matched illumination concept, for detection of targets inside enclosed structures using a monostatic multi-antenna radar system. We evaluate the effect of these optimal detection waveforms on the performance of through-the-wall radar imaging. The design flexibility for transmit signal duration and its role in the ultimate range resolution of the TWRI system is investigated. Supporting examples based on numerical electromagnetic modeling are also provided.

Animals that navigate and hunt by echolocation, such as some bats and marine mammals, have been observed to change their sonar pulse depending on the environment, as well as during hunting. It has become of interest to incorporate these strategies into man-made sonar waveform and receiver design. We examine the benefits of optimal waveform design versus transmitting a linear FM waveform for detecting elastic objects. Performance loss suffered by assuming a point target is also examined. Our approach utilizes a method recently proposed by Kay to design the optimal power spectrum of the transmit waveform. Because there is an unlimited number of waveforms with the same power spectrum, we further impose a time domain constraint, in terms of the signal duration, to obtain a unique optimal waveform. [Work supported by ONR 321US.]

Optimal control theory concepts are thought to be useful in understanding the problem of determining safe deceleration characteristics for a crashing vehicle. These deceleration waveforms are to be computed such that passenger belt forces are minimized. Using both a linear one-degree-of-freedom model and a nonlinear two-degree-of-freedom model for a frontal collision, this problem is shown to be equivalent to the minimization of a performance or cost function when the terminal time is not fixed a priori, but is determined by terminal constraints. While the maximum principle is applied directly to find the optimal deceleration waveform for the linear problem, the steepest ascent method is used to optimize iteratively the nonlinear problem. Passenger seatbelt forces which resulted from using these optimal waveforms were compared with those forces which resulted from using step and ramp functions. Results showed that the seat belt forces resulting from the optimally derived deceleration signals were considerably smaller than those using step and ramp functions. With further effort, these results could possibly be used as design guides.

To improve the target recognition and classification performance of integrated radar and communications system in signal-dependent interference, we propose an innovative robust adaptive orthogonal frequency division multiplexing integrated radar and communications waveform design taking into account the clutter. We set the uncertainty class for clutter and other prior information to solve the problem of system performance degradation caused by inaccurate information in actual environments. Then, we formulate the optimization function to maximize the normalized weighted sum of mutual information and data information rate subject to the constraint of the total transmitted energy. To solve the optimization problem, we propose a maximum marginal allocation algorithm that transforms the original problem into a multi-stage energy distribution problem, and performs optimal energy distribution in each stage according to the optimization criteria. Moreover, by considering a more practical scenario of multiple downlink communication users, a joint scheme for channel allocation and waveform design is presented to ensure the fairness of multiple communication users. Simulation results show the effectiveness and feasibility of the designed waveform and channel allocation method.

The problems of multiple-input multiple-output (MIMO) radar adaptive waveform design in additive white Gaussian noise channels and multitarget recognition based on sequential likelihood ratio test are jointly addressed in this paper. Two information-theoretic waveform design strategies, namely, the optimal waveform for maximizing the mutual information (MI) between the extended target impulse response and the target echoes and the optimal waveform for maximizing the Kullback-Leibler (KL) divergence (or relative entropy), are applied in the multitarget recognition application. For multitarget case, two adaptive waveform design methods for all possible targets based on the current knowledge of each hypothesis are proposed. Method 1 is the probability weighted waveform method. Method 2 is the probability weighted target signature method. The optimal waveform is transmitted and adaptively changed such that a decision is made based on the likelihood ratio after several illuminations. Numerical results demonstrate that the best waveform is the KL divergence-based optimal waveform using Method 1 as it has the lowest average illumination number and the highest correct decision rate for target recognition. By optimally designing and adaptively changing the transmitted waveform, the average number of illuminations required for multitarget recognition can be much reduced.