Degrees of freedom in a three-user cognitive interference channel

We study the degrees of freedom of the three-user Gaussian interference channel under the circumstance where one or more transmitters are non-causally cognitive, meaning they are aware of the messages of one or more transmitters in a non-causal manner. Our focus is on the total degrees of freedom of the three-user cognitive interference channel. Our first case is when only one of the transmitters is fully cognitive and knows the messages of the other users. We prove that using interference alignment and interference cancellation, the achievable total degrees of freedom is 116 and does not coincide with the calculated total degrees of freedom upper bound which is 2. In the second and third cases, while one transmitter is fully cognitive, another one is partially cognitive and only knows the message of one other user and one user is non-cognitive. We prove that the achievable total degrees of freedom in both of these channels is 2, using a linear combination of messages in the transmitters, which results in interference alignment and interference cancellation in the receivers. In the second case, our calculated upper bound for total degrees of freedom coincides with the achievable total degrees of freedom but in the third case the upper bound is 3.