systems.

In this paper, we propose adjustable phase shift pilots (APSPs) for massive MIMO-OFDM to reduce the pilot overhead. For APSPs, one sequence along with different adjustable phase shifted versions of itself in the frequency domain are adopted as pilots for different UTs. The proposed APSPs are different from conventional PSOPs [@Li02Simplified; @Barhumi03Optimal; @Chi11Training], in which phase shifts for different pilots are fixed, and phase shift differences between different pilots are no less than the maximum channel delay (divided by the system sampling duration) of all the UTs. Since in our approach the phase shifts for different pilots are adjustable, more pilots are available compared with conventional PSOPs, which leads to significantly reduced pilot overhead.

The proposed APSPs exploit the following two channel properties: First, wireless channels are sparse in many typical propagation scenarios; most channel power is concentrated in a finite region of delays and/or angles due to limited scattering [@Tse05Fundamentals; @Clerckx13MIMO; @win2chanmod; @Bajwa10Compressed]. Such channel sparsity can be resolved in the angle domain in massive MIMO due to the relatively large antenna array apertures, which has been observed in recent massive MIMO channel measurement results [@Payami12Channel; @Gao13Massive]. Second, channel sparsity patterns, i.e., channel power distributions in the angle-delay 