  Reflection of radio waves off the short-lived plasma produced by the
high-energy shower particles in the air is simulated, considering various radar
setups and shower geometries. We show that the plasma produced by air showers
has to be treated always as underdense. Therefore, we use the Thomson
cross-section for scattering of radio waves corrected for molecular quenching
and we sum coherently contributions of the reflected radio wave over the volume
of the plasma disk to obtain the time evolution of the signal arriving at the
receiver antenna. The received power and the spectral power density of the
radar echo are analyzed. Based on the obtained results, we discuss possible
modes of radar detection of extensive air showers. We conclude that the
scattered signal is too weak for the radar method to provide an efficient and
inexpensive method of air shower detection.
