# Resource-Efficient FPGA Architecture for Real-Time RFI Mitigation in Interferometric Radiometers
## 4 Validation and Testing  
The validation of RFI detection and mitigation implementations requires a systematic approach to verify both functional correctness and performance under various operating conditions. The testing strategy consists of multiple stages, from synthetic data validation to full system integration testing, ensuring the implementation meets its design specifications while maintaining real-time performance. The simulation was performed either by \begin{table}
\begin{tabular}{|l|c|c|c|c|c|} \hline  & **LUT Logic** & **LUT Memory** & **Latch** & **BRAM** & **DSP** \\ \hline ObsGen STFT & 3838 & 785 & 7388 & 7 & 16 \\ \hline ObsGen EqTrunc & 625 & 0 & 743 & 6.5 & 12 \\ \hline RFI Det & 9260 & 99 & 5782 & 30 & 48 \\ \hline PMS Blank & 2755 & 84 & 2631 & 3 & 0 \\ \hline Total & 16,478 & 968 & 16,544 & 46.5 & 76 \\ \hline KU040 & & 242,400 & 484,800 & 1200 & 1920 \\ \hline Percent & & 6.80 \% & 3.41 \% & 3.88 \% & 3.96 \% \\ \hline \end{tabular}
\end{table} 
Table 1: Resource utilization compared with the available resources in the Xilinx KU040 architecture. MATLAB R2022a HDL Coder or MATLAB R2022a Simulink (MathWorks), and the results were compared numerically to the outputs of the original MATLAB algorithm, which uses floating-point double-precision data types. Initial validation employs synthetic datasets designed to test specific aspects of the implementation. Test vectors include:  
* Clean radiometric signals with known statistical properties;
* Simulated RFI patterns of varying intensity and temporal characteristics;
* Corner cases designed to stress the fixed-point arithmetic implementation. The RFI detection performance was evaluated using simulated impulsive interference with varying occurrence probabilities. The RFI was modeled as pulses with amplitude \(10\times\) higher than the background thermal noise (modeled as Gaussian white noise), added to both I/Q components of dual-polarization channels. We tested different false alarm probabilities (PFA = \(1\times 10^{-2}\), \(1\times 10^{-3}\), and \(1\times 10^{-4}\)) by adjusting the RFI occurrence rate accordingly, allowing assessment of the detection algorithm under different interference scenarios. Results from hardware simulation are compared against high-precision floating-point MATLAB implementations. The Observable Generation subblock implements signal processing operations that require careful validation to ensure robust RFI detection. The two algorithms in it require special considerations in the implementation phase. The first operation comprises the time-frequency transform operations. The windowing procedure using Hamming window shapes the temporal response and affects spectral leakage characteristics of the subsequent analysis. This windowing stage works in conjunction with the STFT operation, which establishes the time-frequency resolution tradeoff of the system. These operations must maintain numerical stability when processing signals with high dynamic range, even though in this case, the input is 1-bit. To validate the numerical accuracy of the windowing and STFT operations, we compared the output between the full-precision MATLAB implementation and the hardware-oriented Simulink model. Figure 7 shows the error distribution and scatter plot between both implementations, both for the windowing and STFT operations. The close alignment along the diagonal in the scatter plot confirms that the fixed-point implementation maintains adequate numerical precision through the transform stages. For the windowing operation, the implementation achieves a Root Mean Square Error (RMSE) of \(1.28\times 10^{-5}\) with maximum errors of \(2.15\times 10^{-5}\). The subsequent FFT operation shows slightly higher but still acceptable errors, with RMSE values around \(3.97\times 10^{-4}\) and maximum errors below \(7.48\times 10^{-4}\). The second operation is the Calibration and Equalization stage.