###### Abstract  
This paper presents a novel, cost-effective technique for estimating the Doppler effect in the time domain using a single pulse and subsequently leveraging the precise Doppler value to recover the radar waveform. The proposed system offers several key advantages over existing techniques, including the ability to calculate the target speed without any frequency ambiguity and the ability to detect a wide range of target speeds. These two features are not available in any existing techniques, including the conventional moving target detection (MTD) processor. To ensure improved accuracy and robust estimation, the system employs ensemble and iterative techniques by recursively and efficiently reducing the Doppler residues from the signal. Furthermore, the proposed system demonstrates effective signal recovery of a well-known bi-phase code shape at low signal-to-noise ratios in just a few iterations. The performance evaluation of the new algorithm demonstrates its practicability and its superiority over traditional radar systems. Implementation on software-defined radio (SDR) reveals that the proposed system excels in Doppler estimation and signal recovery at low SNRs, demonstrating promising results. radar systems; Doppler estimation; signal recovery; bi-phase signal; signal-to-noise ratio; software-defined radar 2  
In [9], the authors proposed a decision-directed Doppler estimation method based on the frequency average for phase-shift keying (PSK) signals for underwater acoustic communications. This estimation is achieved by averaging the frequency estimates from a bank of correlators. A robust estimate can be further computed by increasing the observation intervals at the expense of the computational cost. This method, however, is limited to underwater targets with very slow speeds. Doppler estimation is achieved in [10] using the dual alternating-direction method (ADM) with standard statistical tools and a multiple-hypothesis testing procedure using a few pulses and without any frequency or phase modulation. Although the method introduced a good range and Doppler estimation, it gave only approximate values due to cell accuracy. In [11], the authors attempted to estimate the real-time Doppler effect using up-down and up-mute-down hyperbolic frequency modulation methods. The estimation is based on finding the relationship between the Doppler scaling factor (the rate of change in the delay of a signal in a time-varying channel) and the time delay of the signal at the receiver. Unfortunately, the method was found inadequate for low-speed targets. The authors of [12] managed to compensate for the Doppler effect on complementary phase modulation signals. By creating a new complementary code of length \(N\) and multiplying each sample at index \(n\) by the conjugate of the adjacent sample at \(n+1\) in the new code, the method is able to produce the desired compensated code. Although this approach is straightforward for short codes, it becomes increasingly complex and computationally intensive as the code length increases. Additionally, this method was only tested on targets moving at moderate speeds. Furthermore, after compensation, the Doppler information is lost, preventing the determination of the target velocity. Another method for Doppler estimation was proposed in [13], and it relied on a combination of hyperbolic frequency modulation and speed spectrum scanning. Although the method reduces interference in speed spectrum peak detection and improves the accuracy of the estimation, the success of this method requires high sampling rates. In addition, the signal suffers from high time sidelobes, which can affect nearby targets. Yet another Doppler estimation method can be found in [14], and it was primarily developed for non-terrestrial networks. The method involves using reference signals at different frequency positions in an OFDM carrier to estimate the Doppler shift for high-speed targets.