  For a K-user interference channel, the degree of freedom (DoF) which can be
achieved through interference alignment (IA) is constrained to signal space
dimension governed by the number of Tx/Rx antennas. To overcome this problem,
IA can be combined with interference cancellation (IC), involving a new
receiver architecture associated with signaling over backhaul links among the
different users, as another interference mitigation scheme which is referred to
as interference alignment and cancellation (IAC). In our earlier work, by
proposing an IAC graph, we have derived the necessary and sufficient conditions
for the existence of closed-form solutions for IAC subject to the given DoF
requirement for individual user. Furthermore, we have also shown that it can
achieve the theoretically maximum possible DoF, which is 2M for MIMO system
with M Tx/Rx antennas. Following our previous works on IAC, we aim to
investigate the design criteria to obtain such closed-form transceivers when
they exist. We first develop a general closed-form IAC transceiver design for
any given DoF requirement of individual user and then, we specify how the
optimal IAC transceiver can be designed to achieve the theoretically maximum
DoF of 2M, beating the performance of conventional IA with much less
computational complexity.
