## 1 Introduction  
Vehicle detection applications have been playing crucial roles in traffic management of an intelligent transport system (ITS). For those transportation operations, the inductive-loop detector and non-intrusive wired sensors are widely used [1] despite the emergence of wireless traffic sensors in [2; 3]. In practice, non-intrusive traffic detectors are much preferred [1; 4; 5; 6; 7; 8] owing to apparatus durability, functional diversity, and minimum adverse effect on road conditions when installed and maintained. The detection accuracies of non-intrusive sensors using video imaging, ultrasound, infrared, and microwave radar technologies have been evaluated under various conditions for vehicle classification and monitoring (e.g., [5; 6; 7; 8]). It is noted that among non-intrusive sensors, the traffic microwave radar detectors (TMRDs) are highly likely to prevail as an integral part of an ITS. This is due to the advantages that the detection accuracy of the TMRD is unaffected by weather, air turbulence, temperature and light conditions, and the TMRD in sideway-looking mode can perform multi-lane traffic detection. Besides, the TMRD using the frequency modulated continuous waveform (FMCW) technique in [9; 10] can have lower peak-to-average power ratio in transmission, and more advantages such as small size, light weight, and low cost. Technical applications of the FMCW TMRD include vehicle tracking [11], car classification [12; 13], automobile detection [14], vehicle velocity estimation [12; 14; 15], and vehicle distance estimation [15], etc. Unlike the aforementioned works [11; 12; 13; 14; 15], this paper is focused on traffic flow detection of the FMCW TMRD. In this aspect, the TMRD acquires the round-trip travel time of the FMCW from the TMRD to a vehicle within a lane. The time information can then be converted into an estimated distance between the TMRD and the fast Fourier transform (FFT) main lobe of the vehicle signal. We utilize the FFTs of vehicle signals, and develop several smart schemes for vehicle flow detection. The resulting methods aim to yield highly accurate real-time traffic information of highways, roads and bridges in urban areas. Satisfactory outcomes can help make appropriate policies and strategies (e.g., road construction, deployment and control of traffic lights) for increasing transportation efficiency (e.g., reduction of traffic congestions). For vehicle flow estimation in a multiple-lane environment, the conventional approach first sets the same threshold for each lane to filter out noise (e.g., motorcycles and bicycles) from the FFTs of received signals. The resulting FFTs of vehicle signals and those of clutter (e.g., buildings) are distinguishable. This is because the latter are comparably large and constantly appear at fixed positions outside of road lanes. Next, the number of the resulting vehicle FFTs within a lane is assigned as the number of vehicles within the lane. However, the conventional method usually yields highly inaccurate traffic statistics caused by three undesirable situations. One is that the actual traffic within a lane can be wrongly estimated because of the inclusion of lane-crossing FFT side lobes from adjacent lanes. Another is that a vehicle may be counted twice for its previous and current lane if the vehicle makes and completes a lane change when it passes the detection zone. The other is that the reflected signal of a vehicle moving within a lane is missing due to the obstruction of a large bus moving within adjacent lanes. Accordingly, it is apparent that the first unfavorable situation is improvable while the second and the third situations seem too difficult to be rectified. In this paper, the development of our smart schemes emphasizes how to ameliorate adverse effects of lane-crossing FFT side lobes from adjacent lanes. We first adjust and select an adequate threshold for each lane not only to remove noise but also to sensibly reduce edged FFT side lobes within each lane.