AI summaryⓘ
The authors address the problem of estimating both the frequency and change in frequency (chirp rate) of noisy chirp signals, which are important in radar, sonar, and satellite communications. They develop a two-step deterministic method that avoids common accuracy problems usually seen near cell edges and at low signal-to-noise ratios. Their approach uses a time-centered, zero-padded Fourier transform combined with iterative interpolation to improve estimation precision uniformly across the entire signal range. They provide mathematical analysis showing low error and robustness, confirmed by simulations, and note that their method runs efficiently with fixed computation time. This work offers a reliable way to estimate chirp parameters more consistently than traditional methods.
Chirp signalFrequency estimationChirp rateSignal-to-noise ratio (SNR)DechirpFFT (Fast Fourier Transform)Discrete-time Fourier transform (DTFT)Fisher informationInterpolationMonte Carlo simulation
Authors
Miaomiao Wei, Jianjun Li, Yang Wang, Huaiyuan Chen, Lulu Gao, Hang Liu
Abstract
Joint estimation of the frequency and chirp rate of a noisy chirp signal arises in radar, sonar, and burst satellite communications. Conventional estimators combine a coarse grid search with fine interpolation; accuracy degrades at the edges of the residual cell (the edge effect) and below the breakdown SNR (the threshold effect). This paper presents a deterministic two-stage estimator that controls both failure modes uniformly over the entire residual cell. The estimator combines a time-centered, zero-padded dechirp-FFT acquisition bank with alternating selectable-$p$ amplitude-interpolation refinements on fractional-bin DTFT samples; in the centered frame, the frequency-chirp-rate cross-term of the Fisher information vanishes. The paper derives a mean-squared-error and threshold characterization across the full SNR range, in closed form except for one calibrated scalar (an effective cell count), to our knowledge the first for the joint problem: the breakdown threshold is governed by the cell count, and its cell-position dependence is dominated by the straddle loss of the coarse FFT, which the padding bounds at 0.4 dB. An asymptotic uniformity analysis over the whole cell, including the corners, gives closed-form fixed-point variance ratios of $1.003$ and $0.998$, analytically free of the residual. A closed-form bias analysis under unmodeled jerk shows the centered chirp-rate estimate is first-order immune. Monte Carlo experiments at $N=256$ (validated at $N=32$-$512$) measure frequency- and chirp-rate-axis efficiencies with median $1.03$ and worst case $1.07$ over $144$ cell positions at $-5$ dB. Threshold predictions hold within $1.0$ dB on four held-out configurations. The dechirp-FFT bank is fully parallel, and each of the four refinement iterations evaluates three DTFT samples per axis; under fixed operating conditions, per-estimate latency is constant at $O(N\log N)$ cost.