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This paper addresses the problem of joint time-delay and frequency synchronization in the CDMA receiver STAR. We observe that its space/time structural approach enables us to decouple time and frequency offsets. We thus introduce a new procedure based on space/time separation that implements a simple linear regression approach for both time-delay and frequency synchronization. We analyze the performance of this procedure in an unknown time-varying channel with multipath and carrier offset. Simulations show that the modified STAR provides significant performance gain over its previous version. The link-level gain is more than 3 dB for BPSK (128 kbit/s) when the frequency offset equals 0.1 ppm (i.e., 200 Hz). This gain increases at higher frequency offsets and small-constellation modulations.