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The capacity of a satellite DS-CDMA system with a conventional matched filter receiver is limited by the forward link due to interference from adjacent beams, and possibly overlapping beams from multiple satellites. In this paper, we study the performance of the linear minimum mean squared error (MMSE) receiver for the satellite forward link. We consider a "one-step" power adjustment algorithm which attempts to compensate for random shadowing and path loss, and compare the associated performance of the MMSE and matched filter receivers. Dual-satellite diversity is also considered. The effect of the code rate on performance is studied through the use of punctured convolutional codes. Our results indicate that linear MMSE interference suppression can improve the quality of service and increase system capacity significantly.