  In this paper, we propose an efficient optimal joint channel estimation and
data detection algorithm for massive MIMO wireless systems. Our algorithm is
optimal in terms of the generalized likelihood ratio test (GLRT). For massive
MIMO systems, we show that the expected complexity of our algorithm grows
polynomially in the channel coherence time. Simulation results demonstrate
significant performance gains of our algorithm compared with suboptimal
non-coherent detection algorithms. To the best of our knowledge, this is the
first algorithm which efficiently achieves GLRT-optimal non-coherent detections
for massive MIMO systems with general constellations.
