In this paper, we present a novel method for a base station (BS) to estimate the total downlink interference power received by any given mobile receiver, without information feedback from the user or information exchange between neighbouring BSs. The prediction method is deterministic and can be computed rapidly. This is achieved by first abstracting the cellular network into a mathematical model, and then inferring the interference power received at any location based on the power spectrum measurements taken at the observing BS. The analysis expands the methodology to a K-tier heterogeneous network and demonstrates the accuracy of the technique for a variety of sampling densities. The paper demonstrates the methodology by applying it to an opportunistic transmission technique that avoids transmissions to channels which are overwhelmed by interference. The simulation results show that the proposed technique performs closely or better than existing interference avoidance techniques that require information exchange, and yields a 30% throughput improvement over baseline configurations.