The problem of UAV radar monitoring by its acoustic radiation is considered. It is shown that in a number of practical cases such an approach is preferable to observation by radar methods directly from the UAV airframe. It is noted that the radio signals scattered by acoustic packets from the UAV are characterized by an unknown in advance complex envelope, which does not allow the use of optimal filtering methods for their detection and estimation. It is shown that to solve these problems, it is advisable to use the principle of accumulation over the observation interval of the energy of a narrow-band random process reduced to the noise dispersion, using the statistical differences between noise fluctuations and the additive "signal-plus-noise" mixture. It is shown that the energy estimate reduced to noise has either a central or an off-center "chi-square" distribution with a certain number of degrees of freedom and an off-center parameter greater than or equal to zero. As a result of comparing the current value of the no centrality parameter with the threshold value, a decision is made on the presence or absence of a useful signal in the observation interval with minimal a priori information about its parameters. It is noted that the well-known expressions for the differential probability densities of the central and non-central chi-square distributions allow one to obtain qualitative estimates of the synthesized detector. A practical structural diagram of a detector using processing of received oscillations in quadrature channels is proposed.