The troposcatter channel fading and diffusion modeling for multi-beamforming in receiving antennas

The tropospheric scatter mechanism is potentially valuable for over-the-horizon (OTH) target detection, in which a fatal limitation is the large propagation loss caused by the long path length and the scattering. High antenna gain is indispensable to compensate the high propagation loss, which results in narrow beamwidth and small spatial coverage by time-consuming mechanical scanning. Array antenna is promising to handle this contradiction between real-time wide spatial coverage and high antenna gain, owning to its multiple beamforming techniques, which is able to cover the whole interest area simultaneously. However, the beamforming performance is severely degraded by the troposcatter channel fading correlation between multiple beams, and the diffusion phases among array antennas. According to the latest Recommendation of International Telecommunication Union (ITU-R), and two recent troposcatter fading correlation researches, i.e., ‘ring-scatter model’ and ‘scatter transfer function model’, this paper firstly derives the correlation with adjacent azimuth angle, which describes the correlation coefficients along multiple beams with respect to receiving/transmitting beam angles, beam width, the target distanceetc. Then the phase diffusion in each antenna is derived by substituting its relative distance from the common volume into the scatter transfer function, and the phase diffusion can be written in closed-form with respect to the array interval and other parameters as beamwidth, target distance etc. Based on the above two results, a modified Linear Constrained Minimum Variance (LCMV) multi-beamforming method is proposed, wherein the beam directions and the constrained vector are designed to reach a compromise between the independence and the interval of the multiple beams according to their mutual correlations. Besides, the array manifold matrix of the multi-beam directions is compensated with the diffusion phases to accommodate the common volume scattering source. The simulation results show that the desired multi-beam pattern can be effectively arranged with the given parameters under OTH troposcatter propagating scenarios, and the pattern distortion caused by the troposcatter diffusion is significantly relieved.