In modern wireless communication systems, orthogonal pilot signals has been generally employed in estimation of the channel state information. However, orthogonal pilot signals are inadequate for supporting the rapidly increasing requirements of communication throughput for 5G-and-beyond wireless environments, owing to the pilot contamination and short coherence times in high-mobility situations. To address these concerns, we present a new strategy for making use of non-orthogonal pilot sequences in channel estimation for multi-cell massive multiple-input multiple-output systems. First, we extend prior pilot assignment strategies based on the orthogonality of pilots to the general case of non-orthogonal pilot signals. Based on the proposed non-orthogonal pilot assignment strategy, we establish the minimal pilot length that fulfills a requirement for the channel estimate error, under a given degree of non-orthogonality. Then, we demonstrate validity of the pilot assignment strategy with the minimal length, which maximizes the entire network throughput. Simulation results show that our proposed method gives a significantly enhanced performance in terms of the net throughput compared to that with orthogonal pilot sequences. The performance gain becomes particularly significant with a higher density of users or shorter coherence time intervals.