Abstract-Interference alignment (IA) is an emerging technique which can suppress the interference effectually and provides a means to approach the channel capacity in the multiple-input and multiple-output (MIMO) networks. However, little work has concentrated on the bandwidth efficiency of IA systems, which is undoubtedly important especially in the current situations of spectrum scarcity. In this paper, a novel IA scheme is proposed, which leverages the advanced continuous phase modulation (CPM) to increase the bandwidth efficiency. Due to the continuity of the information-bearing phase, the proposed CPM-IA scheme exhibits low sidelobe and rapid spectrum rolloff. Moreover, a low-complexity pulse amplitude modulated (PAM) decomposition algorithm is applied to CPM-IA scheme, which can reduce the number of matched filters without much performance degradation. In addition, a novel spatial-frequency domain (SFD)-CPM-IA scheme is proposed to mitigate the interference that the traditional IA cannot handle when the IA feasibility condition cannot be satisfied. The proposed SFD-CPM-IA scheme inherits the high bandwidth efficiency of CPM-IA, and can accommodate many more users to communicate simultaneously.Index Terms-Interference alignment, bandwidth efficiency, continuous phase modulation, pulse amplitude modulated (PAM) decomposition, spatial-frequency domain, bit error rate (BER)