In modern wireless communication systems, the per-user data rate demand is constantly growing. To sustain the heavy user data rate demand, network operators try to deploy cellular system with more cells and applying more efficient spectrum reuse techniques. One possible solution to increase system throughput is to get the user closer to the transmitting base station and hence deploy very dense network infrastructure. In this setup strong interference situations will result. Interference has been commonly identified as the main bottleneck of the modern wireless cellular communications systems. With small dense cells this is more the case. This consideration has led to intense research activities that has recently pushed network operators and manufacturers to include more proactive and efficient way to suppress/control interference. From an information theoretic point of view this problem can be mathematically studied as, what is called, an interference channel.
In the first part of this thesis, we focus our attention on the beamforming design for the interference channel with particular focus on the MIMO case. There we propose the joint optimization of linear transmitter and receiver according to two criteria: Interference Alignment and weighted sum rate maximization. The second part of the thesis is devoted to the beamforming design problem in cognitive radio settings. We start considering an underlay scenario where the secondary network is modeled as a MISO interference channel. Then we move to the interweave cognitive radio setting where now all the devices are multi-antenna terminals. There the objective is to design the transmitters and receivers, at the secondary network, such that the interference, generated at each primary receiver, is zero.