In this paper, we consider overlaying a secondary-user signal over a satellite communication channel occupied by a primary user. The objective is to find the jointly optimal transmitter and receiver pair of a secondary system to minimize the mean squared error (MSE) at the output of the secondary receiver, subject to zero interference induced at the output samples of the primary receiver. It is assumed that both the primary and the secondary transmitters employ linear modulation and the receivers employ linear filter front-ends. Unlike prior work, the secondary user is allowed to transmit data symbols at a fraction of the primary user's symbol rate. This rate reduction technique enables the secondary user to achieve the additive white Gaussian noise (AWGN) bound or the performance close to the AWGN bound even when the excess bandwidth of the primary user is very small but positive. Numerical results show that the proposed scheme significantly improves the spectral efficiency by exploiting the cyclostationarity of the primary-user signal.