We address the problem of downlink channel estimation in frequency division duplex (FDD) Massive MIMO system when downlink training duration is limited. Leveraging the concept of Compressive Sensing (CS), downlink channel could be estimated with limited training duration if channel can be sparsely represented. In this paper, we develop a better dictionary under which the downlink channel can be more sparsely represented, thus improving the performance of recovery in the compressive sensing process. We develop a method for learning such a dictionary from channel measurements, which capture information about communication environment as well as the property of antennas. We develop methods to learn the dictionary that best models the data, thus adapting to the environment and antenna property, while simultaneously inducing sparsity. Also we compare different dictionaries and provide insights into reasons why a learned dictionary outperforms others.
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