This paper considers interference-aware optimum transmission power control for the maximization of the aggregate communication rate of a desired tier in a multi-tier network under channel state information feedback constraints. The users of the desired tier form a non-orthogonal multiple access channel with their base station while causing interference to other tiers. In our previous works, it was assumed that the channel state information of the interference channels is perfectly known at the desired tier base station. For real-time systems, this assumption becomes rather unpractical. In order to avoid this, the problem is handled under quantized interference channel power coefficients. The optimum power allocation policy is found by maximizing aggregate data rate of the desired tier users under a total interference power constraint at the first tier and also under interference channel state information feedback constraints. It is shown that the optimum power allocation scheme accepts a binary form, i.e., the users are either "on" or "off" up to at most one user with power in-between. (C) 2019 Elsevier B.V. All rights reserved.