AI 中文总结
本文提出一种确定性两阶段联合频率与调频率估计器，结合去调频-FFT采集组与DTFT插值细化，在全信噪比范围实现均匀性能，实验验证其效率高、阈值预测准确且延迟恒定。
AI 中文摘要
在雷达、声呐及突发卫星通信场景中，含噪线性调频信号的频率与调频率联合估计是核心问题。传统估计方法结合粗网格搜索与精细插值，但其精度在残差单元边缘会出现边缘效应，且在低于破信噪比（阈值）时会退化。本文提出一种确定性两阶段估计器，可在整个残差单元内均匀控制两种失效模式：该估计器结合以时间为中心、补零的去调频-FFT采集组，以及对分数频点DTFT样本的交替可选p值幅度插值细化；在中心帧中，频率-调频率的费希尔信息交叉项会消失。本文推导了全信噪比范围内的均方误差与阈值特性，除一个经校准的标量（有效单元数）外均为闭式表达，据本文所知，这是该联合问题的首次闭式分析：破阈值由单元数决定，其单元位置依赖性主要由粗FFT的跨距损耗主导，补零可将该损耗限制在0.4 dB以内。对包含角点的整个单元的渐近均匀性分析，得到闭式定点方差比为1.003和0.998，解析上不含残差。对未建模加加速度的闭式偏差分析显示，中心调频率估计具有一阶免疫性。N=256的蒙特卡洛实验（在N=32~512上验证）测量了频率轴与调频率轴的效率，在-5 dB下144个单元位置的中位数效率为1.03，最坏情况为1.07。阈值预测在四个预留配置上的误差在1.0 dB以内。该去调频-FFT组完全并行，四次细化迭代中每次沿各轴评估3个DTFT样本；在固定工作条件下，每次估计的延迟为恒定的O(N log N)复杂度。
英文摘要
Joint frequency and chirp-rate estimation for 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). We present a deterministic two-stage estimator that controls both failure modes uniformly over the residual cell. The estimator combines a time-centered, zero-padded dechirp-FFT acquisition bank with alternating selectable-$p$ amplitude-interpolation refinements on DTFT samples at fractional bins; 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 over 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 scalloping loss of the coarse FFT, which the padding bounds at 0.4 dB. An asymptotic uniformity analysis over the cell, including its corners, gives fixed-point variance ratios of $1.003$ and $0.998$, analytically free of the residual. A closed-form bias analysis under a cubic phase mismatch shows the centered chirp-rate estimate is insensitive to first order. 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 configurations not used in the calibration. 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.
Comments18 pages, 11 figures (13-page main text plus supplementary material). Submitted to the IEEE Transactions on Signal Processing. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible
