The low complexity quantization of channel state information (CSI) and the utilization of vertical freedom of three dimension (3D) channels are two critical issues in the limited feedback design of the \emph{full dimension multi-input-multi-output} (FD-MIMO) systems. In this paper, we propose an effective limited feedback scheme. We first employ Kronecker product based codebook (KPC) to explore the vertical freedom of 3D channels, extending the limited feedback from two dimension (2D) to 3D. Fruthermore, we use noncoherent sequence detection (NCSD) to quantify the CSI which includes both the vertical and horizontal channel information. This quantization method exploits the duality between codebook searching and NCSD to transform the CSI quntization on KPC to two parallel NCSD. The complexity is reduced from exponential to linear with the number of antennas. We also show the proposed scheme does not affect the diversity gain of the system by demonstrating the full diversity order. Monte Carlo simulation results show that the proposed scheme provides at least 1.2dB coding gain compared with traditional 2D limited feedback schemes. Moreover, the proposed scheme outperforms other FD/3D CSI quantization schemes by 0.8dB coding gain with moderate complexity when the channel is highly spatially correlated.