## 1 Introduction  
Using relays in multi-user wireless communication systems can effectively extend the coverage area and improve the throughput of a network [1]. However, with the structure becoming complicated, the interference in such a network will be more severe. There are some methods to manage the interference in the relay network. Interference alignment (IA) is thought to be a promising technique to mitigate interference [2]. There are some methods to achieve IA. Reference [3] studied IA based on the orthogonalization of matrices, which needs a large amount of antennas when the number of interference increased. In References [4; 5; 6], closed-form IA schemes were investigated to reduce the computational complexity and offload the backhaul overhead. A retrospective interference alignment method was proposed in Reference [7], where it is shown that even under delay channel state information (CSI) the capacity also scales with the number of users. A cognitive IA (CIA) scheme was proposed in Reference [8] to deal with the interference and improve the spectral efficiency for the case of several self-organizing small cells serving one user in a heterogeneous network (HetNet). In Reference [9], IA precoding was combined with iterative decision feedback equalization to design efficient small-cell transmitters and macro-receivers for single-carrier frequency-division multiple access(SC-FDMA) based HetNets. However, all the algorithms above are only adopted in homogeneous networks or two-tiered HetNets (macro cells coexisting with small cells), which may not be able to achieve the desired performance in a relay-aided transmission scenario, since the two-hop links constructed by relay were not considered. Some studies concentrate on relay-aided networks, i.e., References [10; 11; 12; 13; 14; 15; 16; 17; 18]. Reference [10] proposed an alternate transmission method for the two-cell relay network and obtained \(2M/3\) (\(M\) is the number of transmit antennas) degrees of freedom (DoF) by complementing the two-hop transmission in three sub-time slots. The authors of Reference [11] viewed the two-hop relay interference channel as a cascade of two interference channels, and \(4/3\) DoF was achieved by applying an IA scheme. Reference [12] combined the idea of IA and interference neutralization to show that the outer bound of 2 DoF can be achieved in the \(2\times 2\times 2\) relay network. However, the algorithms above are only applicable to the decode-and-forward (DF) modal relay network. There are also some investigations directed at the amplify-and-forward (AF) relay network. For example in References [13; 14; 15], different transmission strategies with IA were studied to achieve a higher sum DoF (SDoF). For the two-cell case (e.g., \(2\times 2\times 2\)), it can be derived that the maximum of 2 SDoF can be achieved. Authors of Reference [16] orthogonalized different transmissions and introduced a relay protocol based on distributed zero-forcing algorithm to recover the half-duplex loss and improve the sum-rate performance. In Reference [17], interference was aligned by the relay in the \(K\)-cell network to offload the burden of mobile users, through which the maximum sum-rate performance and optimal number of \(K\) DoF was achieved. It is noteworthy that all the transmit links in the above references are two-hop end-to-end channels. For the relay-aided HetNet where direct links coexist with two-hop links, the mitigation of various types of interference has not been deeply investigated. Hence, it is necessary to propose an IA scheme to manage both the inter-cell and intra-cell interference. In this paper, we focus on the scenario mentioned above where the cell-center user (CCU) directly served by base station (BS) coexists with the cell-edge user (CEU) served through a two-hop link constructed by an AF modal relay. In particalular, we propose a cross time slot partial interference alignment (TPIA) scheme to deal with different kinds of interference.