This letter proposes an optimal precoder design using a generalized inverse structure for downlink crosstier interference suppression between macro base station (MBS) and femtocell access point (FAP) transmission in heterogeneous networks. Using Tikhonov regularization, we derive a closed form relationship between given MBS transmit power or interference constraints and the regularization parameter.

Determining a Pareto optimal regularization parameter requires extensive computation. As an alternative, we propose an algorithm to find a suitable regularization parameter to achieve fairness in the system, i.e., equal FAP and MBS user rates. Simulation results show that the proposed precoder greatly improves FAP user rates at the expense of a small yet tolerable decrease in average MBS user rate.