Over-the-horizon radar signal-to-external noise ratio improvement in over-sampled uniform 2D antenna arrays: Theoretical analysis of superdirective SNR gains

We present the results of theoretical signal-to-noise (SNR) performance assessment for optimal (adaptive) and conventionally beamformed uniform rectangular antenna arrays with inter-element spacing smaller than the half-wavelength. We provide theoretical analysis of SNR in such arrays, exposed to strong night-time external noise arriving from all azimuth (Az) and elevation (El) angles. In addition to uniform (in Az and El) noise distribution, we also consider two distributions uniform in Az but “tapered” in elevation. This elevation “tapering” accounts for more realistic external noise propagation mechanisms. For uniform external noise, the definitions of the output signal-to-external noise ratio (SENR) coincides with directivity; and therefore, any SINR gains delivered by the optimum (vs. conventional) beamforming are exclusively associated with the superdirectivity of these arrays. We analyze these superdirective SNR gains for uniform and “tapered” in El external noise distributions with respect to different limiting factors, including mutual coupling, calibration accuracy, and internal noise. We demonstrate that within the frequency range such that d/λ=[1/5, 1], the optimum (adaptive) beamforming may secure practically constant SNR gains, equal to 10log₁₀N, where N is the number of antenna elements in an array.