## 1 Introduction
### Motivation  
The relationships described in Section 1.1 indicate some important radar design criteria in the context of the extraction of velocity information from radar data:  
1. Precise Doppler measurements require long coherent integration intervals, see (2)
2. The higher the center frequency of the radar emission, the higher is the Doppler shift for a given radial velocity \(v_{r}\), see (1)The higher the center frequency, the shorter is the required coherent integration interval for a given precision \(\Delta v_{r}\) of the velocity measurement  
For these considerations, many Doppler radars operate at center frequencies of 10 GHz and above. As an example, the commercial Doppler radars of the company Blighter, used for ground surveillance and drone detection, operate in the Ku-band around 16 GHz [15]. These high frequencies are usually applicable for short-range and medium-range applications. Common long-range radars, instead, operate in lower frequency bands such as marine navigation radars that transmit mostly S-band signals.  
The following example illustrates the problems of accurate Doppler measurements with such a navigation radar set. The aimed velocity estimation shall be set to an accuracy of 1 knots, that is, \(\Delta v_{r}=0.514\) m/s, for a hypothetical S-band radar operating at a center frequency of \(f_{0}=3\) GHz. From (1) results that the Doppler precision should not exceed a value of \(\Delta f_{D}=\frac{2\Delta v_{r}f_{0}}{c}=10.28\) Hz. This increment, according to (2), defines the minimum coherent processing interval to \(T_{CPI}=\frac{1}{\Delta f_{D}}\approx 100\) ms. But a strong discrepancy occurs when the minimum required value of \(T_{CPI}\) is compared to the typical design of long-range navigation radars such as the JMR-5472-S [16]. With a typical beam width of \(\theta=2\) degrees and a rotation of the antenna at \(\omega=24\) revolutions per minute, a maximum _time-on-target_ of about 14 ms is achieved by such a radar set. This interval is much shorter than the minimum coherent processing interval required for the respective Doppler analysis. But the method presented later in this paper might solve this issue. The duration of the experimental data of Section 4, deliberately limited to 12 ms, was chosen in agreement with the just made considerations.  
Moreover, the Doppler extraction method presented in this paper is also considered as beneficial for modern agile multi-role radars that perform different tasks, enabled by a sophisticated resource management. One important resource is the illumination time, that is, the interval at which the antenna (which usually is a phased array antenna) of the multi-role radar is locked to a specific direction. The Doppler extraction procedure presented in this paper reduces the required time-on-target by a waveform-specific signal processing algorithm making use of the characteristic Doppler tolerance of a continuous emission noise radar. This is particularly important for phased array radar tracking applications [17] which involve rapidly switched beam positions and demand for an efficient management of the revisit time and the time-on-target. The resource management becomes even harder when it comes to multi-function RF systems (MFRFS) that combine radar, electronic warfare and communication tasks by a single sensor [18]. A general concept, of how these MFRFS might further benefit from the use of noise radar technology was presented in [19].