To improve the bandwidth efficiency of free-space optical (FSO) systems and at the same time to reduce the impact of the background noise, we propose a differential M-ary pulse-amplitude modulation (M-PAM) signaling scheme that uses two laser transmitters. We first consider the condition that the receiver perfectly knows the instantaneous channel coefficient and compare the performance of the proposed differential PAM with the conventional PAM signaling and show the improved performance when the background noise level is relatively high. Second, we consider the practical situation where the receiver has to estimate the channel for signal detection. We propose an estimation scheme based on the characteristics of the differential PAM signaling while requiring no pilot symbol transmission. The proposed data-aided channel estimation is performed on a sequence of received PAM symbols. We show that for a sufficiently large observation window, the proposed estimation method allows achieving a performance close to the perfect channel knowledge.