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Broadcast in radio-based wireless networks has been a difficult problem. When a node broadcasts, all nodes within its radio coverage will attempt to relay the message by rebroadcasting, causing excessive radio communication in the region that leads to the broadcast storm problem. Most previous solutions assumed a perfect radio condition with a static, circular coverage. However, in real situations, radio signals are very dynamic and irregular in their coverage. This is especially true for wireless sensor networks, which usually employ low quality radio modules to reduce the cost. Assuming no location information is available, we approach the problem in this paper from two aspects: space and time. To solve the irregularity in space in radio coverage, we propose a scheme that is able to find the neighbors on the rim of the irregular radio coverage region to narrow down the choices of the forwarders. To solve the dynamic in radio coverage, we consider an on-demand, stateless strategy to reduce the overhead of maintaining the state information. Through simulation, we compare the resultant algorithm, called RIM, with Double-Covered Broadcast (DCB) , one of the best algorithms proposed so far. The results show that under dense deployment and irregular and dynamic radio coverage, our algorithm performs better.