Optimization of interference alignment beamforming vectors

Interference alignment, while optimum in its achievement of the maximum degrees of freedom for the K user interference channel, does so only at high SNR and for large numbers of dimensions over which to align the interference, n. A sizable SNR penalty is paid in order to approach the theoretical outerbound and only grows increasingly higher for larger n. For the single antenna, K = 3 interference channel, an efficient means of drastically reducing the required power to approach the outerbound of 3/2 is presented. By no longer using a vector of all ones in the creation of the transmit beamforming vectors as originally proposed, a new weighted vector w is designed in order to distribute the power across the precoding vectors more evenly. Furthermore, we introduce a new structure of beamforming vectors that also provides significant savings in SNR independently of vector w. By doing so, our proposed designs achieve the same degrees of freedom of the original scheme at only a fraction of the SNR.