This paper presents a novel design approach for movable antenna (MA)-enabled wireless sensing systems by jointly minimizing the Cramér-Rao bound (CRB) and the maximum sidelobe level (MSL) of the ambiguity function via antenna position optimization. In particular, the mean squared error (MSE) of angle-of-arrival (AoA) estimation is decomposed into a local estimation error within the mainlobe of the ambiguity function (i.e., CRB) and an additional ambiguity error caused by its sidelobes. Since the MSE is dominated by the CRB in the high-signal-to-noise ratio (SNR) regime but by the sidelobes of the ambiguity function in the low-SNR regime, our analysis reveals a fundamental trade-off between CRB minimization and MSL minimization in the moderate-SNR regime. Specifically, minimizing the CRB prefers a narrower mainlobe, where antennas are concentrated near the two edges of the one-dimensional (1-D) movement region; whereas minimizing the MSL favors a wider mainlobe, where antennas are distributed more densely near the center of the movement region. Inspired by this and to ensure robust sensing performance across different SNR regimes, we formulate an optimization problem to minimize the CRB subject to a prescribed MSL constraint via antenna position optimization. An efficient successive convex approximation (SCA) algorithm is developed to optimize the antenna position vector (APV), and a 1-D linear search method is proposed to determine the optimal MSL threshold that minimizes the actual MSE for any given SNR. Numerical results demonstrate that the proposed scheme effectively balances the trade-off between MSL and CRB minimization, thus achieving a significantly lower AoA estimation MSE across the entire SNR range compared to conventional uniform and non-uniform fixed-position antenna (FPA) arrays.

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