## 1 Introduction  
Spectral-Doppler-based ultrasound medical devices have the potential to be used for pre-screening various vascular diseases such as diabetes, vascular stenosis, arterial stiffness, and so on. There are various study results showing the pre-diagnosis of vascular diseases by monitoring hemodynamics via ultrasound [1, 2, 3, 4, 5, 6, 7, 8]. These diagnosis modalities have a common feature, that is, a spectrogram or a wavelet transform spectrum is utilized to assess hemodynamics status, which can reflect structural and functional changes in a vessel. A spectral Doppler mode, one of the essential imaging modes of commercial medical ultrasound imaging devices, provides a real-time spectrogram of blood flow, so various studies on the pre-diagnosis of vascular diseases can be done by using a commercial imaging device. Even though a multi-channel ultrasound system can provide various clinical results, it usually requires considerable hardware overhead in terms of hardware size, power consumption, cost, and so on [9; 10; 11; 12]. Most of the aforementioned overhead stems from implementation of the multi-channel probe, along with front-end circuitry, beamforming, and back-end signal processing. However, in the case of portable or wearable ultrasound blood-flow monitors for early diagnosis, a hardware-efficient system implementation to intensively support a spectral Doppler mode is required. There are several approaches to implementing an ultrasound blood-flow monitor by using a single transducer [13; 14; 15; 16]. A single-transducer-based ultrasound blood-flow monitor basically needs only single-channel interface circuitry and a digital signal processor with fewer computation requirements. Accordingly, the system can be compact, and its complexity can be remarkably decreased compared to a multi-channel system. One of primary issues of single-transducer-based ultrasound blood-flow monitoring is positioning of a range gate on a scanline to acquire sample volumes from the vessel region without an ultrasound image. The work of [13] developed a continuous-wave Doppler scheme. This means the echo signal does not include depth information. In principle, a continuous-wave Doppler cannot distinguish the focal position of an echo signal, so it has a potential limitation if a spectral analysis from a specific vessel position is necessary. The work of [14] is based on pulsed-wave Doppler scheme. It allocates a range-gate position by manually adjusting an RC delay. However, an RC delay is vulnerable to voltage and temperature variations of the system. The work of [15] adopts a pulsed-wave Doppler to acquire Doppler signals from the carotid artery. It manually adjusts the location of the range gate on a scanline. Even though the work of [15] suggests a possible method to automatically adjust the range-gate position by monitoring pulsatile indices from pre-partitioned sparse regions, the amount of computation and the resources required can be burdensome for a general portable device. The work of [16] tracks the position of the artery wall to evaluate the pulse wave velocity. Automatic vessel-wall identification has been accomplished by using an amplitude (A)-mode signal analysis; that is, a vessel wall is detected by recognizing two consecutive echo signals with distinctive amplitude which satisfy a pre-determined time-difference range. The wall-detection algorithm of [16] is relatively simple and efficient to be implemented. However, the wall-detection algorithm of [16] uses the hypothesis that the ultrasound device is applied to interrogate specific arteries, such as the carotid or femoral artery, because a specific echo pattern should be guaranteed. Thus, the wall-detection algorithm of [16] has potential limitations when it is applied for general vessels. In addition, the work of [16] requires a relatively higher center frequency of ultrasound to avoid aliasing of echo signals in the time domain. Correspondingly, the center frequency along with the system-clock frequency of the hardware should be increased.