Principles of Modern Radar - Volume 2 1891121537

518 CHAPTER 11 Space-Time Coding for Active Antenna Systems4 sub-arrays, 4 elements per sub-array:Aim: 0ç Aim: 0ç Aim: 0ç000−10−20−30−40−50−60−70−80−80−80 −60 −40 −20 0 20 40 60 80 −80 −60 −40 −20 0 20 40 60 80−10−20−30−40−50−60−70−10−20−30−40−50−60−70−80−80 −60 −40 −20 0 20 40 60 80Suppressed GratingLobeFIGURE 11-25 Sub-arrays and grating lobes (left: ideal full array diagram; center:sub-array diagram; right: array factor with grating lobes, sub-array diagram, and finalresulting diagram superposed) Sub-arrays and aiming oriented towards broadside direction.11.4.2 Space domain: sub-arrays and grating lobesIn the space domain, the main difficulty is to minimize the number of channels – hencethe number of sub-arrays – while still keeping the benefits of wide angle coverage. It willbe seen that sub-arrays are a good solution for pencil beams observations, but are difficultto use for wide beam applications.The phenomenon is best explained on an example, as shown in Figure 11-25, with alinear array of 4 sub-arrays, each constituted with 4 elementary radiating elements, 0.5 λapart from each other.In Figure 11-25, are successively shown (from left to right):• The diagram of the global array, each source being processed independently;• The diagram of each sub-array of 4 radiating elements (with 0 ◦ phase shift on eachradiating element);• The resulting diagram (in red), when the array is obtained as the result of the 4 subarraycoherent summation, and when the phase shifts imposed on the 4 sub-array outputscorrespond to an aiming direction equal 0 ◦ .It can be seen that the resulting diagram, which is the product of the sub-array diagram(in green) by the diagram (in blue), of the under-sampled antenna made of the 4 phasecenters of the 4 sub-arrays, is correct because the sub-array has a minimum exactly in thedirection (30 ◦ ) of the grating lobe of the under-sampled antenna (array factor constitutedof the 4 phase centers of the 4 sub-arrays: blue curve).However, looking in the direction 5 ◦ , for instance, as in Figure 11-26, then the phaseshifts imposed on the outputs of the sub-arrays are changed: the result is that the gratinglobes of the array factor (blue curve) do not correspond to the minimum of the subarraydiagram anymore (green curve), and there is a residual grating lobe, in red inFigure 11-26.The way to mitigate this problem is of course to aim the sub-arrays in the aimingdirection 5 ◦ , as shown in Figure 11-27: the grating lobe is now suppressed, as in the 0 ◦aiming case.