Proceedings with Extended Abstracts (single PDF file) - Radio ...

SNR Gain[dB]0-0.1-0.2-0.3-0.4-0.5-0.6α=-1α=0α=1-0.70 0.02 0.04 0.06 0.08 0.1 0.12 0.14UFigure 5: SNR loss as a function of constrained norm value Í.element is multiplied by Í before addition, and it may not be in phase with the main array. Inthis case, Eq. (13) becomes ËÆÊ ´ÔÅ· « Ô × Íµ ¾½·Í (14)where « takes a value between -1 and 1, and is 1 for the case where two signals are in phase, 0for the orthogonal phase, and -1 for the opposite phase. This situation corresponds to the worstpossible case of the proposed algorithm with norm constraint value of Í. Although we haveexamined only the case of one antenna element, Eq. (14) can also be applied to a sub-arrayconsisting of multiple antenna elements, because the norm constraint Í limits the sum of theweight of sub-array elements.In the case shown in Fig. 4, × ½ (0dB) and Í ¼, which gives ËÆÊ of -1.5dB.However, the actual loss is much less than this value as is clear from the figure, because Eq. (14)gives the worst case. Fig. 5 shows ËÆÊ versus Í for the case of Å , assuming the MUradar, and × Í.Apparently, a small constraint is desirable in order to assure a small loss in SNR. If weallow a loss of up to 0.5dB, the norm constraint Í should be set to 0.135, 0.120, and 0.105for the in-phase, orthogonal, and the out-of-phase cases, respectively. As we assumed that theantenna element used for the sub-array has a gain of × Í relative to that for the main-arrayelement, it means that the sub-array element should have a relative gain of -9.2dB in the mainlobe direction for Í ¼½¾. In the case of the MU radar, as a typical example of VHF MSTradars, 3-element Yagi antenna elements with an isotropic gain of 7.2dB are pointed to thezenith, and the main lobe is steered in an angular region of 30 Æ from the zenith. An isotropicgain of less than -2dB is easily achieved in this angular region by pointing the same elementto the horizontal direction, for example. If a specially designed antenna element which hasless sensitivity to the main lobe region is used for the sub-array element, a larger value of Íbecomes acceptable.If we apply the proposed DCMP-CN algorithm, the sub-array elements should always bekept in phase with the main antenna because of the directional constraint. The orthogonal andthe out-of-phase cases examined above correspond to situations where this constraint is notapplied. Fig. 5 shows that if we remove the directional constraint from the algorithm withÍ ¼½¾, we further loose about 0.13dB, or 3%, of the sensitivity. The advantage of not442