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In this paper, the nonlinear distortion effects of power amplifiers are studied, in particular from uplink subcarrier and power allocation perspectives in multiuser multicarrier cognitive networks. The out‐of‐band emissions of a nonlinear power amplifier create interference to the other users. The target is then to maximize the achievable uplink rate in a multiuser multicarrier cognitive network where a cognitive user should not introduce interference to the other users more than a specified threshold level, called interference power constraint. This task is formulated as a convex optimization problem with interference power constraints. Obtaining a closed‐form solution for this problem is, however, not feasible due to its nonlinear nature. Accordingly, the problem is solved numerically, and extensive simulations are conducted to obtain performance results. The obtained results are also compared with a more simple heuristic approach. The results show that the proposed scheme provides a maximum rate while at the same time also guaranteeing that the interference levels are lower than the specified interference power constraint. The results also indicate that the maximum rate can be closely approximated by using the assisted or optimization‐directed heuristic approach.