Peak to average power ratio (PAPR) constrained power allocation in single carrier multiuser (MU) single-input multiple-output (SIMO) systems with iterative frequency domain (FD) soft cancelation (SC) minimum mean squared error (MMSE) equalization is considered in this paper. To obtain full benefit of the iterative receiver, its convergence properties need to be taken into account also at the transmitter side. In this paper, we extend the existing results on the area of convergence constrained power allocation (CCPA) to consider the instantaneous PAPR at the transmit antenna of each user. In other words, we will introduce a constraint that PAPR cannot exceed a predetermined threshold. By adding the aforementioned constraint into the CCPA optimization framework, the power efficiency of a power amplifier (PA) can be significantly enhanced by enabling it to operate on its linear operation range. Hence, PAPR constraint is especially beneficial for power limited cell-edge users. In this paper, we will derive the instantaneous PAPR constraint as a function of transmit power allocation. Furthermore, successive convex approximation is derived for the PAPR constrained problem. Numerical results show that the proposed method can achieve the objectives described above.