This paper addresses the use of channel state information (CSI) for Long Term Evolution (LTE) signal fingerprinting localization. In particular, the paper proposes a novel CSI-based signal fingerprinting approach, where fingerprints are descriptors of the "shape" of the channel frequency response (CFR) calculated on CSI vectors, rather than direct CSI vectors. Experiments have been carried out to prove the feasibility and the effectiveness of the proposed method and to study the impact on the localization performance of (i) the bandwidth of the available LTE signal and (ii) the availability of more LTE signals transmitted by different eNodeB (cell diversity). Comparisons with other signal fingerprinting approaches, such as the ones based on received signal strength indicator or reference signal received power, clearly show that using LTE CSI, and in particular, descriptors as fingerprints, can bring relevant performance improvement.