This paper presents a novel blind signal separation method for the measurement of pulse waves at multiple body positions using an array radar system. The proposed method is based on a mathematical model of pulse wave propagation. The model relies on three factors: (1) a small displacement approximation, (2) beam pattern orthogonality, and (3) an impulse response model of pulse waves. The separation of radar echoes is formulated as an optimization problem, and the associated objective function is established using the mathematical model. We evaluate the performance of the proposed method using measured radar data from participants lying in a prone position. The accuracy of the proposed method, in terms of estimating the body displacements, is measured using reference data taken from laser displacement sensors. The average estimation errors are found to be 10-21% smaller than those of conventional methods. These results indicate the effectiveness of the proposed method for achieving noncontact measurements of the displacements of multiple body positions.