As the third step the azimuth angle of the objects can be retrieved by applying digital beam forming (DBF) to the range-Doppler arrays across the multiple receive channels. A simple yet efficient way of DBF is the addition of pre-defined phase shift values to the range-Doppler array elements to compensate for the propagation delays n*τ, as depicted in Figure 3.
The phase-shift values are dependent on the characteristics and dimensions of the physical antenna patches, the receive channel and the targeted angle. This is also called static DBF and can be simply realized by complex multiplications of the individual range-Doppler array elements with the predefined phase-shift values, followed by the summation across all receive channels. The abovementioned procedure has to be repeated per digital beam. This results in a three dimensional complex range-Doppler-beam/azimuth array as shown in the diagram of Figure 2(d).
Before continuing with the final radar signal processing step, the complex array has to be converted into an array with absolute values, which represent absolute power figures. The array elements are superimposed by clutter from multi-path reflections, background noise and interference from other sources in close proximity. The clutter can greatly vary in spatial and time domain.
Therefore an adaptive filter is required that can cope with the varying conditions while finding the most probable targets. A reliable filter is the OS-CFAR detector (see step (e) in Figure 2). OS-CFAR means “Order Statistic Constant False Alarm Rate”. So as to maintain the constant false alarm rate the threshold in a CFAR detector is set on an element by element basis according to the estimated noise/clutter power, which is determined by processing a group of reference elements surrounding the element under investigation (EUI). The surrounding elements are first sorted by their absolute values. Secondly, the value of the sorted element at rank R is the reference element that is compared with the EUI. When the element under investigation is lower than the reference element the EUI is set to 0. Otherwise EUI becomes a target. By selecting a higher rank R the filter becomes more restrictive in detecting targets. In addition, an offset value can be added to the reference element at rank R to make the detector more robust.