Robust power allocation for two-tier heterogeneous networks under channel uncertainties

In this paper, the trade-off among system sum energy consumption and robustness is studied. In this regard, a robust power allocation problem is formulated for a two-tier heterogeneous network with uplink transmission mode and consideration of imperfect channel state information. The objective is to minimize the total transmit power of femtocell users (FUs), while the interference to macrocell user receiver is limited to a predefined interference level, the transmit power of each FU transmitter is kept within their power budgets, and the actual signal-to-interference-plus-noise ratio of each femtocell receiver is above a minimum threshold. Considering the uncertainties of the interference links from FUs to macrocell base stations and forward transmission links of each FU, the robust power allocation problem is formulated as a semi-infinite programming problem (SIPP). By the worst-case approach, the SIPP is transformed into a convex optimization problem solved by the Lagrange dual decomposition method. Moreover, the feasible regions of constraints, computational complexity, and sensitivity degree of the proposed robust algorithm are also analyzed. Simulation results investigate the impact of channel uncertainties and the superiority of the proposed algorithm by comparing with non-robust algorithm.