How Many Signals Can Be Sent in a Multi-Cell Massive MIMO System

In this letter, we study how large the signal constellation can be under pilot contamination in a multi-cell massive multiple-input multiple-output uplink system. Specifically, based on an equivalent transmit-receive signal model, we observe that the transmitted signals by all users in different cells are compacted into a low-dimensional space when they arrive at the target base station. Then, the equivalent model reveals that the size of constellations used by all users is limited by a parameter, which is related to the large-scale fading factors only. We find that when the size of the signal constellation is smaller than the parameter, the error probability goes to zero. Otherwise, an error floor occurs regardless of the number of antennas and the pilot signal to noise ratio. Our simulations results validate the proposed analytical results.