# Resource-Efficient FPGA Architecture for Real-Time RFI Mitigation in Interferometric Radiometers
## 4 Validation and Testing
The numerical precision in this stage becomes particularly critical when processing strong RFI signals, as they can push the arithmetic operations near their dynamic range limits. Fixed-point implementation considerations directly affect the accuracy of the equalization coefficients. Furthermore, the accumulation of quantization errors through the spectrum integration must be carefully managed to maintain the detection sensitivity required for weak interference signals. The final stage involves bit-width reduction, where the signal is truncated to 3 bits (Equations (2)-(5)). The configuration parameters for this truncation stage (as  
Figure 7: Main sources of precision loss in the Observable Generation block. (**a**) Comparison of the full-precision and fixed-point values after windowing. (**b**) Comparison of the full-precision and fixed-point values after FFT. explained in Section 2.2.2) must be thoroughly validated across the expected range of signal dynamics to ensure reliable operation under all observing conditions. Because these parameters are not fixed, the loss of precision will depend on the final values, and is not included in the validation. To validate the numerical precision of the kurtosis implementation, the hardware fixed-point results are compared against full-precision computations for both RFI and RFI-free scenarios. Tables 2 and 3 present the RMSE for the kurtosis of the different Stokes parameters. In the RFI scenario (Table 2), the time-domain kurtosis shows RMSE values of \(2.72\times 10^{-4}\) and \(2.81\times 10^{-4}\) for KX and KY, respectively, while K3 and K4 exhibit slightly lower errors of \(2.31\times 10^{-4}\) and \(2.34\times 10^{-4}\). The frequency-domain implementation shows marginally higher errors, with RMSE values ranging from \(7.39\times 10^{-4}\) to \(1.10\times 10^{-3}\). Similar error patterns are observed in the RFI-free scenario (Table 3), where time-domain errors remain around \(2.56\times 10^{-4}\), confirming that the chosen fixed-point representation maintains consistent precision across different signal conditions. Following the kurtosis computation, detection is performed through thresholding operations (Equation (6)) on each kurtosis estimator (\(K_{X}\), \(K_{Y}\), \(K_{3}\), \(K_{4}\)). The threshold values are computed following the methodology described in Threshold Calculation Section. Since the thresholding operation is inherently a binary decision, the numerical precision requirements are less stringent than in previous stages. To validate this final stage, we compare the resulting detection masks (AND/OR combinations) between the hardware implementation and the full-precision reference, as seen in Figures 8 and 9. Given the binary nature of these masks, the comparison is performed using Bit Error Rate (BER) measurements rather than Mean Square Error (MSE). This metric directly quantifies the detection performance impact of the complete fixed-point implementation chain, from the initial signal processing through the final detection decision. The BER results (Table 4) provide a practical assessment of the detection reliability, as they represent actual mismatches in RFI identification between both implementations. The PMS blanking stage maintains measurement accuracy through careful fixed-point design. The process relies primarily on binary operations for sample selection, minimizing computational complexity and precision loss. The gamma coefficients, implemented in 16 bits, derive from temporal and frequency averages of 7-bit values (resulting from squaring and adding the truncated 3-bit values), providing sufficient precision for the blanking masks. This bit width selection ensures negligible precision loss in the coefficient calculation stages. The critical averaging operation of valid PMS samples employs 32-bit arithmetic to preserve precision during the COordinate Rotation DIgital Computer (CORDIC)-based division by the non-constant number of retained samples.