CLEAN-Based Sidelobe Suppression in Radar

• The paper introduces CT-CFAR, a CLEAN-based algorithm that integrates truncated-statistic noise-target separation, iterative sidelobe subtraction, and learnable penalty maps to suppress sidelobes in radar signal processing.
• It employs methods such as 2D-FFT, noncoherent accumulation, and least-squares fitting to achieve a high detection probability (P_d > 0.9) at low SNR and maintain low false alarm rates.
• The algorithm dynamically adapts to nonhomogeneous conditions, reducing computational complexity while enhancing target reconstruction accuracy and multi-target robustness.

CLEAN-based sidelobe suppression refers to a class of target detection algorithms in radar signal processing that leverage the CLEAN concept—originating in radio astronomy—for iterative subtraction of estimated sidelobe contributions, thereby mitigating false alarms and preserving the constant false alarm rate (CFAR) in environments with strong sidelobe contamination. The CT-CFAR (CLEAN + Truncated-statistics CFAR) algorithm exemplifies this paradigm, integrating robust noise estimation, dynamic sidelobe mapping, and precise target reconstructions to address non-homogeneity in spectrally dense, multichannel radar data (Zhu et al., 23 Nov 2025).

1. Truncated-Statistic Noise–Target Separation

The foundational step in the CT-CFAR framework is robust estimation of the noise floor in the presence of multiple targets and sidelobe artifacts. Following 2D-FFT and noncoherent accumulation (NCA) across $L$ receive channels, the detection matrix cell power is given by

$$PNCA[p,q] = \sum_{\ell=1}^L |X_\ell[p,q] + W_\ell[p,q]|^2 \simeq P_X[p,q] + P_W[p,q] + P_{XW}[p,q]$$

With moderate-to-high SNR, the cross-term $P_{XW}$ is negligible, so high values are dominated by target and sidelobe energy, while the underlying noise-only distribution remains Gamma$(L,\theta)$ (scale $\theta = \mu_W/L$, mean $\mu_W$).

This motivates a truncation-based approach: all matrix cells $z_i$ are vectorized, and those beneath a truncation threshold $T$ are retained as $\{x_i\} = \{z_i \mid z_i \leq T\}$. The noise mean $\mu_W$ is iteratively estimated through a fixed-point update: \begin{align*} &\text{(1) Set initial } \mu_W^{(0)} \ &\text{(2) At each } t: T^{(t)} = L^{-1} u_g \mu_W^{(t)} \ &\quad \text{Compute mean of } {x_i}, \ \bar x^{(t)} \ &\quad \mu_W^{(t+1)} = \frac{\bar x^{(t)}}{g(\alpha, u_g)} \ &\text{(3) Iterate until convergence} \end{align*} The converged $\mu_W$ is adopted as the per-cell noise estimate $N_G[p,q]$. This decouples target/sidelobe influence and restores the statistical homogeneity assumed by classic CFAR processing.

2. Learnable Historical Sidelobe Information Model

CT-CFAR introduces a learnable sidelobe “penalty” map $N_S[p,q]$ to dispositionally track regions contaminated by previously detected targets’ sidelobes. Each time a cell $(i_0, j_0)$ is declared a target, its sidelobe footprint $P_{OUT}$—obtained by CLEAN-style reconstruction (see Section 3)—is added to $N_S$:

$N_S \leftarrow N_S + P_{OUT}$

In subsequent thresholding operations, the CFAR threshold is augmented:

$$T_{\text{CFAR}}(i,j) = a \cdot \frac{1}{(2r+1)^2} \sum_{p=i-r}^{i+r} \sum_{q=j-r}^{j+r} [N_G(p,q) + N_S(p,q)]$$

where $a$ adjusts the global $P_{FA}$ and $r$ is the window half-span. This mechanism dynamically increases detection thresholds for contaminated regions, suppressing sidelobe-originated false alarms without sacrificing sensitivity elsewhere.

3. Target Reconstruction and CLEAN Iteration

When the cell with the highest residual power $XCUT(i_0, j_0)$ exceeds its local threshold, CT-CFAR reconstructs the full target’s mainlobe and sidelobe pattern using a combination of the Candan algorithm and least-squares (LS) fitting:

• Candan fractional bin refinement: DFT slices $y[n-1]$, $y[n]$, $y[n+1]$ are used to compute fractional offsets $\epsilon$ in frequency indices for precise beat/frequency estimates.
• Multi-antenna template LS fitting: An $r\times r$ patch centered about $(f_{\text{ind}}, v_{\text{ind}})$ from each channel forms $Y \in \mathbb{C}^{(r^2) \times L}$, fit by

$Y = g a^T + N$

where $g$ is the template, and $a$ captures the per-channel complex gains. The LS solution is

$\hat a = (g^H g + \epsilon I)^{-1} g^H Y$

This yields $\hat G = g \hat a^T$ and $P_{OUT} = |\hat G|^2$ summed over channels.

• CLEAN update: The estimated $P_{OUT}$ is subtracted from $PNCA$ and simultaneously added to $N_S$. This iterative process “cleans” both the mainlobe and sidelobe contributions of detected targets, refining the joint detection and suppression in subsequent rounds.

4. Algorithmic Flow

The integrated workflow of CT-CFAR is summarized as follows:

1. Compute $PNCA$ using 2D-FFT and NCA.
2. Estimate $\mu_W$ via the truncated-statistics iterative method to form the $N_G$ noise matrix.
3. Initialize the sidelobe penalty map $N_S \leftarrow 0$.
4. Iteratively:
   • For each $(i,j)$, compute $T(i,j) = a \cdot \text{mean}[N_G + N_S]$ over the local window.
   • Identify $CUT = \arg\max PNCA$; if $PNCA(CUT) \le T(CUT)$, terminate.
   • Apply Candan refinement to obtain precise target indices.
   • Reconstruct and subtract $P_{OUT}$ via LS fitting.
   • Update $PNCA \leftarrow PNCA - P_{OUT}$, $N_S \leftarrow N_S + P_{OUT}$.
   • Record the detected target.
5. Continue until no cell exceeds its threshold.

This closed-loop interleaving of noise modeling, adaptive sidelobe mapping, and CLEAN-based subtraction is central to CT-CFAR’s sidelobe suppression efficacy.

5. Key Performance Metrics and Comparative Analysis

Extensive Monte Carlo simulation and real-data experiments establish the following empirical outcomes:

• Probability of Detection ($P_d$) vs SNR (fixed $P_{FA}=10^{-3}$): CT-CFAR attains $P_d > 0.9$ at SNR ≈ –10 dB, in contrast to the next-best SS-CFAR needing SNR = –7 dB for the same detection probability.
• False Alarm Rate ($P_f$) stability: CT-CFAR maintains $P_f \approx 10^{-4}$ across SNR range –20…0 dB. Competitor algorithms exhibit $P_f$ escalation by up to two orders of magnitude in the same regime.
• ROC characteristics at SNR = 0 dB: Area-under-curve (AUC) for CT-CFAR is approximately 0.985, exceeding those of SS-CFAR (0.973) and TS-CFAR (0.960).
• Multi-target robustness: For up to 100 simultaneous returns, CT-CFAR $P_d$ decreases by less than 5%, compared with >15% loss in alternative approaches.
• Qualitative results: Human posture point cloud reconstructions with CT-CFAR show clearly delineated features and negligible sidelobe fuzz.

• Computational complexity (MATLAB on 2.8 GHz CPU):

  Algorithm	Runtime per Frame (s)
  CT-CFAR	0.015
  SS-CFAR	0.030
  TS-CFAR	0.025
  OS-CFAR, TM-CFAR	0.030

This metric suite demonstrates that CT-CFAR achieves improved detection accuracy, maintains stringent false alarm control, sustains performance in dense target environments, and incurs lower computational burden relative to comparably robust methods (Zhu et al., 23 Nov 2025).

6. Context and Implications

The integration of CLEAN-based subtraction with truncated-statistics estimation and learnable sidelobe penalty mapping enables CT-CFAR to break the limitations of fixed-window CFAR in nonhomogeneous, sidelobe-contaminated scenarios. This approach obviates the need for prior knowledge of outlier statistics, offering a practical, adaptive framework for both simulation and real-data regimes. A plausible implication is that similar iterative sidelobe suppression schemes could be generalized to other sensor array and spectral estimation contexts with severe interference nonstationarity.

The performance improvements and computational efficiency position CLEAN-based CFAR detectors as state-of-the-art for detection tasks where clutter, sidelobe, or mutual target interference degrade the efficacy of classical or order-statistics-based CFAR solutions.