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This paper discusses the antenna phase center trajectory (APCT) design for the "one-active" linear-array 3D imaging SAR (LASAR). First, we discuss the principle of the one-active LASAR and demonstrate its feasibility by experiment. To describe the 3D spatial resolution of the one-active LASAR, the relationship between the 3D ambiguity function (AF) of the one-active LASAR and the system parameters is discussed in detail. Based on the analysis, we divide the APCT design into three topics: the direction of the linear array, the length of the linear array, and the switching mode of the active element [named as antenna phase center function (APCF)]. On the first topic, we conclude that, when the range, along-track, and cross-track directions are orthogonal to each other, the ambiguity region of the one-active LASAR attains minimum, and the 3D spatial resolution can be separated into the range, along-track, and cross-track resolutions. On the second topic, we find that the cross-track resolution is determined by the length of the linear array and the frequency of the carrier. To ensure that the length of the linear array is acceptable, the carrier should be W-band wave or millimeter wave. On the third topic, the effect of APCF is researched, and we find that both the periodic APCF and the pseudorandom APCF can produce 3D resolution, except for the periodic rectangle APCF. For the pseudorandom APCF and the periodic APCF with short period, the cross-range 2D AF is or can be approximated as the product of two 1D AFs in the along- and cross-track directions. Finally, the distribution of the pseudorandom APCF is optimized by the Lagrange multiplier method under the minimum variance criterion, and we find that, when the pseudorandom APCF obeys the parabolic distribution, the cross-range 2D AF is optimal.