Transmit Beamforming Design with Received-Interference Power Constraints: The Zero-Forcing Relaxation

The use of multi-antenna transmitters is emerging as an essential technology of the future wireless communication systems. While Zero-Forcing Beamforming (ZFB) has become the most popular low-complexity transmit beamforming design, it has some drawbacks basically related to the effort of "trying" to invert the channel coefficients towards the interfered users. In particular, ZFB performs poorly in the low Signal-to-Noise Ratio (SNR) regime and does not work when the interfered users outnumber the transmit antennas. In this paper, we study in detail an alternative transmit beamforming design framework, where we allow some residual received-interference power instead of trying to null it completely out. Subsequently, we provide a close-form non-iterative optimal solution that avoids the use of sophisticated convex optimization techniques that compromise its applicability onto practical systems. Supporting results based on numerical simulations show that the proposed transmit beamforming is able to perform close to the optimal with much lower computational complexity.