Performance Bound for Joint Multiple Parameter Target Estimation in Sparse Stepped-Frequency Radar: A Comparison Analysis

Abstract

A performance bound—Cramér-Rao lower bound (CRLB) for target estimation and detection in sparse stepped frequency radars is presented. The vector formulation of this CRLB is used to obtain a lower bound on the estimation error. The estimation performance can be transformed into different types of CRLB structures. Therefore, the expressions of bounds under three equivalent models are derived separately: time delay and Doppler stretch estimator, joint multiple parameter estimator, and sparse-based estimator. The variables to be estimated include the variances of unknown noise, range, velocity, and the real and imaginary parts of the amplitude. A general performance expression is proposed by considering the echo of the target in the line-of-sight. When the relationship between CRLB and various parameters are discussed in detail, the specific effect of waveform parameters on a single CRLB is compared and analyzed. Numerical simulations demonstrated that the resulting CRLB exhibits considerable theoretical and practical significance for the selection of optimal waveform parameters.

Waveform Selection For Multi-Band Multistatic Radar Networks

“…given by [28] for OFDM signals in (16), the last element of the modified FIM for an OFDM waveform consisting of L OFDM symbols can be given by (17). The other two elements of FIM for OFDM signals are given as…”

“…Cramér-Rao lower bounds (CRLBs) have been widely used in radar studies to evaluate the detection performance of various radar systems and waveforms and also used as a benchmark for parameter estimation algorithms as it defines the lower bounds of mean squared error (MSE) of the estimation, i.e., achievable best estimation accuracy, for unbiased estimators. [16,17]. Efficient unbiased estimators can attain CRLBs, for instance, maximum likelihood estimator (MLE) was shown to reach the CRLBs when the received radar returns have sufficient SNR [18].…”

“…Efficient unbiased estimators can attain CRLBs, for instance, maximum likelihood estimator (MLE) was shown to reach the CRLBs when the received radar returns have sufficient SNR [18]. Furthermore, the CRLB can be calculated for different parameter estimations such as velocity, range, angle, location estimations, and this makes the CRLB a commonly used benchmark for estimator studies [16,19,17,20,21]. blueFor example, it was shown that efficient target tracking and localisation algorithms can achieve the minimum variance, as defined by the CRLBs [22,23].…”

Advancing Stepped-Waveform Radar Jamming Techniques for Robust False-Target Generation against LFM-CFAR Systems

“…However, their objective did not involve deceiving the radar through false targets. Chen et al [ 26 ] developed a filtering method based on the Cramer-Rao Lower Bound (CRLB) to suppress the stepped-chirp jamming of LFM signals. Therefore, although these studies have contributed to the understanding and implementation of stepped frequency waveforms for radar jamming, the specific aspect of false target impacts has not been extensively addressed.…”

Range and velocity estimations in multi-band hybrid multistatic radar networks

“…Cramér-Rao lower bounds (CRLBs) have been widely used in radar studies to evaluate the performance of various radar systems and waveforms, and also used as a benchmark for estimation algorithms as it defines the lower bounds of mean squared error (MSE) of the estimation for unbiased estimators. [6]. Efficient unbiased estimators can attain CRLBs, for instance, the maximum likelihood estimator (MLE) was shown to reach the CRLBs when the received radar returns have sufficient SNR [7].…”