Radar based detection of human targets behind walls or in dense urban environments is an important technical challenge with many practical applications in security, defense, and disaster recovery. Radar reflections from a human can be orders of magnitude weaker than those from objects encountered in urban settings such as walls, cars, or possibly rubble after a disaster. Furthermore, these objects can act as secondary reflectors and produce multipath returns from a person. To mitigate these issues, processing of radar return data needs to be optimized for recognizing human motion features such as walking, running, or breathing. This paper presents a theoretical analysis on the modulation effects human motion has on the radar waveform and how high levels of multipath can distort these motion effects. From this analysis, an algorithm is designed and optimized for tracking human motion in heavily clutter environments. The tracking results will be used as the fundamental detection/classification tool to discriminate human targets from others by identifying human motion traits such as predictable walking patterns and periodicity in breathing rates. The theoretical formulations will be tested against simulation and measured data collected using a low power, portable see-through-the-wall radar system that could be practically deployed in real-world scenarios. Lastly, the performance of the algorithm is evaluated in a series of experiments where both a single person and multiple people are moving in an indoor, cluttered environment.