Current cellular systems use pilot-aided statistical-channel state information (S-CSI) estimation and limited feedback schemes to aid in link adaptation and scheduling decisions. However, in the presence of pulsed radar signals, pilot-aided S-CSI is inaccurate since interference statistics on pilot and non-pilot resources can be different. Moreover, the channel will be bimodal as a result of the periodic interference. In this paper, we propose a max-min heuristic to estimate the post-equalizer SINR in the case of non-pilot pulsed radar interference, and characterize its distribution as a function of noise variance and interference power. We observe that the proposed heuristic incurs low computational complexity, and is robust beyond a certain SINR threshold for different modulation schemes, especially for QPSK. This enables us to develop a comprehensive semi-blind framework to estimate the wideband SINR metric that is commonly used for S-CSI quantization in 3GPP Long-Term Evolution (LTE) and New Radio (NR) networks. Finally, we propose dual CSI feedback for practical radar-cellular spectrum sharing, to enable accurate CSI acquisition in the bimodal channel. We demonstrate significant improvements in throughput, block error rate and retransmission-induced latency for LTE-Advanced Pro when compared to conventional pilot-aided S-CSI estimation and limited feedback schemes.