Massive multiple-input multiple-output (MIMO) is believed to be a key technology to get 1000x data rates in wireless communication systems. Massive MIMO occupies a large number of antennas at the base station (BS) to serve multiple users at the same time. It has appeared as a promising technique to realize high-throughput green wireless communications. Massive MIMO exploits the higher degree of spatial freedom, to extensively improve the capacity and energy efficiency of the system. Thus, massive MIMO systems have been broadly accepted as an important enabling technology for 5th Generation (5G) systems. In massive MIMO systems, a precise acquisition of the channel state information (CSI) is needed for beamforming, signal detection, resource allocation, etc. Yet, having large antennas at the BS, users have to estimate channels linked with hundreds of transmit antennas. Consequently, pilot overhead gets prohibitively high. Hence, realizing the correct channel estimation with the reasonable pilot overhead has become a challenging issue, particularly for frequency division duplex (FDD) in massive MIMO systems. In this paper, by taking advantage of spatial and temporal common sparsity of massive MIMO channels in delay domain, nonorthogonal pilot design and channel estimation schemes are proposed under the frame work of structured compressive sensing (SCS) theory that considerably reduces the pilot overheads for massive MIMO FDD systems. The proposed pilot design is fundamentally different from conventional orthogonal pilot designs based on Nyquist sampling theorem. Finally, simulations have been performed to verify the performance of the proposed schemes. Compared to its conventional counterparts with fewer pilots overhead, the proposed schemes improve the performance of the system.