The work in this area was started by V.I. Gomozov and V.I. Zamyatin in 1978. Similar papers of foreign authors were published for the first time in 1988-1991. It is shown that in comparison with traditional spatial-phase modulation the proposed reciprocally matched spatial-frequency-phase-time modulation of radio pulses in the channels of transmitting Phased Array Antennas (PAA) has the following principal merits: duration of microwave radiation Focused Radio Pulse (FRP) is determined by the carrier frequency spacing (range) of signals of the channels of transmitting PAA. It does not depend upon its aperture, and its limit minimum length by distance is equal to the average wave length λ_aver. FRP duration is constant irrespective of the distance to the point of focusing. Within the limits of the Fresnel zone only the domain of its existence changes (the domain of scanning by distance), that is substantially restricted by the selection of matched pulse-time-modulation. FRP formed in the 2-nd half of the Fresnel zone keeps the shape even after a further propagation in the Fraunghofer zone. At a distances of more than 2 lengths of the domain of microwave radiation focusing, at the level of 0.5P_max, the spectrum of the signal transforms into a noise-like one, and the level of power flow density decreases to (m-n)^–1P_max, where m and n are the numbers of radiators and channels with different carrier frequencies in the transmitting PAA, respectively. Spatial phase front of FRP wave in the Fresnel zone differs from the normal plane to the direction of energy propagation the more the closer it is to PAA and a false varying phase centre of PAA appears outside its aperture.

The results of a detailed mathematical modelling confirming the above mentioned statements are given. The spectrums of formed spatial signals and requirements to acceptable reciprocal instabilities of the frequency and phase modulation parameters of radio pulses in transmitting PAA modules are also considered.