Cooperative broadcast, in which receivers are allowed to combine received packet from different senders to combat transmission errors, has gained increasing attention. Previous studies showed that broadcast optimization solutions are sufficient in non-fading environments but may suffer a low delivery ratio under wireless channel fading. Though previous work analyzed the tradeoff between energy and delay in cooperative broadcast, no works investigated the tradeoff in a fading environment. Thus, in this paper, we study this tradeoff with the consideration of fading. We formulate this problem as a Fading-resistant Delay-constrained Minimum Energy Cooperative Broadcast (FDMECB) problem, and prove that it is NP-complete. We then propose an approximation algorithm for theoretical interests. We further propose a heuristic algorithm that makes approximately optimal local decision to achieve global optimization. Our experimental results show that our algorithms outperform a previous non-fading resistant algorithm.