Principles of Modern Radar - Volume 2 1891121537

16.2 Characterizing the Human Radar Return 711transforms to characterize the gait signature; however, since then, most researchers haveused spectrogram analysis as a means of visualizing micro-Doppler.The modeling, simulation, and understanding human spectrograms is important in thedevelopment of dismount detection algorithms for radar. Model-based approaches [51–53]exploit mathematical models of human kinematics to analytically derive the spectrogram ofhuman radar returns. Alternatively, computer models derived from virtual reality animationdata have been successfully used to simulate human micro-Doppler [54–57]. One widelyused3-D human motion data library is that compiled by the Carnegie Mellon University(CMU) Motion Research Laboratory, which is available online at [58]. The CMU library isbased on data captured from video camera coverage of real human motion. Using this data,a 3-D motion model for a human body comprised of 30 bones is created and animated.Thus, the motion is not modeled or approximated, but instead directly measured and stored.Motion-capture based models have been successfully used in simulations that enablethe assessment of ground reflections and multipath [59], multiple interactions betweendifferent body parts, as well as through-the-wall propagation [60] on human micro-Dopplersignatures. In comparison, model-based approaches are limited in modeling such effects;however, they are computationally fast and reasonably accurate, while also providinginsight into the underlying physical process that makes human spectrograms unique. Inthe remainder of this section, a mathematical formulation of the expected human radarreturn is derived. This model will be used later in Section 16.3 to derive and analyze thespectrograms of human targets.16.2.1 Expected Radar Return from a Human TargetConsider a radar antenna transmitting a series of chirped pulses at constant intervals intime and space while moving along a straight path. In general, the received radar signal isa time-delayed version of the transmitted chirp signal (Figure 16-1). The received radarsignal for a point target may be expressed as( ) ˆt − t ds r (n, t) = a t rect e j[−2π f ct d +πγ(ˆt−t d ) 2 ](16.1)τwhere n is the pulse number; t is the total time elapsed since transmission of the first pulseand may be defined in terms of the pulse repetition interval (PRI), T , and the time relativethe start of each PRI, ˆt,ast = T (n − 1) + ˆt; τ is the pulse width; c is the speed of light; γis the chirp slope; f c is the transmitted center frequency; and t d is the round-trip time delaybetween antenna and target, defined in terms of the target slant range, R, ast d = 2R/c.The signal amplitude, a t , is given by the radar range equation asa t = Gλ√ P t σ(4π) 1.5 R 2 (16.2)where G is the antenna gain, λ is the signal wavelength, P t is the transmit power, σ is thetarget RCS, and R is the range from the radar to the target. Here, it is also assumed thatthere are no losses due to atmospheric attenuation or system noise.Human targets, of course, are not point targets but may be viewed as the collection ofa large number of point targets residing upon the surface of the human body. An importantresult is that the spectrogram from the entire human body can be well approximated bythe sum of the spectrograms from the constituent body parts [61], which implies that for