## 6 Discussion  
Although we have shown the effectiveness of integrating our proposed module into a radar system, it is crucial to acknowledge a few limitations and highlight several key points.  
* While this paper primarily focuses on simulation results and a proof-of-concept implementation using SDR, experimental validation using real-world radar data presents practical difficulties due to the need for diverse targets, controlled conditions, and logistical considerations. Future research and collaboration with radar operators or institutions may be necessary to overcome these challenges and gather empirical evidence for the performance of the proposed module under real-world scenarios.
* The proposed module employs an iterative approach to estimate and correct the Doppler frequency. While iterations enhance accuracy, they can introduce computational complexity, potentially affecting real-time performance in practical applications. However, our simulation results showed that our module achieves efficient Doppler estimation with just one iteration at low and medium speeds and with two iterations at high and very high speeds, minimizing the computational burden while maintaining accurate results.
* The proposed module was specifically designed for signals with bi- and poly-phase modulation in mind, and it might require advanced nonlinear transformations for other modulation schemes. With that being said, by leveraging the capability of estimating the Doppler effect from a single pulse, a bi-phase signal can be used as a marker signal to compensate for the Doppler effect in other modulation schemes. This flexibility allows our algorithm to be used in MIMO systems, enabling accurate Doppler estimation and compensation across multiple antennas.
* Since there are no papers on radar systems that specifically address the estimation of the Doppler effect in the time domain and the subsequent recovery of the radar waveform, a direct comparison with other systems is not possible. Our proposed module fills this research gap by introducing a novel approach that enables Doppler estimation and radar waveform recovery. By leveraging this unique capability, our module offers distinct advantages in terms of accuracy and performance compared to existing methods in the literature.
* In practical scenarios, filtering is seldom perfect due to factors such as imperfect filter design, hardware limitations, environmental noise, and computational constraints. These non-ideal filtering conditions can introduce residual noise and interference into the signal, potentially affecting the performance of subsequent processing stages. In our experiments, we used two USRP SDR devices, one for transmission and the other for reception. Despite these non-ideal conditions, our results show that the system effectively handles such imperfections, maintaining robust performance and achieving promising results. Utilizing a software-defined platform allows for flexible adaptation to non-ideal filter conditions. This adaptability ensures that the system can be dynamically reconfigured to mitigate the effects of non-ideal filtering, thereby preserving the integrity of the signal-processing pipeline.
* The proposed radar system was not tested under jamming conditions, and it might experience degradation with some jamming techniques. It is important to note, however, that this degradation is not specific to our system alone; any radar system subjected to jamming attacks will inevitably experience performance degradation based on the jamming techniques employed. While recognizing the impact of jamming on radar systems, the primary focus of this paper is to present the novelty of the proposed module and its effectiveness in non-jammed scenarios. The investigation of the proposed module under jamming conditions has been deferred to a separate manuscript, as it requires a comprehensive analysis that would contribute valuable insights to the field of radar signal processing and anti-jamming techniques.