Principles of Modern Radar - Volume 2 1891121537

720 CHAPTER 16 Human Detection With Radar: Dismount DetectionCPI. Each fast-time matrix entry is also known as a range bin, because of the relationshipbetween sampling interval and range: R = cT/2, where T is time interval betweentransmitted pulses. Slow-time refers to samples taken from each CPI corresponding to thesame range bin. Slow-time matrix entries are also known as Doppler bins, as taking afast Fourier transform (FFT) across slow-time yields Doppler frequency. Once the slowtime,fast-time data matrix is formed, pulse compression across the fast-time dimensionis performed so that a peak occurs at the range bin in which the target is present.The pulse compression matched filter function is defined as the time-reversed replicaof the transmitted signal, h (t) = e − jπγt 2 . Thus, for a single body partx (t) ==The peak occurs when t = t d :∫ ∞−∞t∫d +τs r (u) h (t − u) dut da t e j(−2π f ct d +πγ(u−t d ) 2 ) e− jπγ(t−s) 2 du (16.21)x peak = x (t d )t∫d +τ= a t e j[−2π f ct d +πγ(u−t d ) 2 ] e− jπγ(t d −u) 2 du=t d∫t d +τa t e − j2π f ct ddut d= a t τe − j2π f ct d(16.22)To find the pulse compressed output for the entire human return, it is only necessary to sum(16.22) for each body part and substitute the expression for time delay in terms of range∑12x p [n] = a t,i τei=14π fc− j R i [n]c(16.23)The spectrogram is then found by simply stacking the FFTs of short, overlapping timesegments taken from the slow-time slice in (16.23). An example of the simulated spectrogramfor a human target is shown in Figure 16-6. The strongest component of the return iscaused by reflections from the torso, with its low-frequency, small-amplitude sinusoidaloscillatory motion. The larger amplitude oscillations are caused by reflections from theappendages, with the largest amplitude oscillation corresponding to the response from thefeet—that is, the appendages that travel the farthest during the walking cycle.It is important to note that the structure of the periodicities within the human spectrogramis unique to humans. Even the spectrograms of other animals are differentiablefrom human spectrograms. Consider the spectrograms for a human and a dog measuredby Otero [85], which are shown in Figure 16-7. While the measured human spectrogramis similar to the simulated spectrogram in Figure 16-6, the spectrogram for a dog appearsmore noise-like as a result of the quadrupedal nature of the animal and equal-sized appendages.Indeed, Otero proposed a quantified approach to exploit these differences in