Leveraging sparsity into massive MIMO channel estimation with the adaptive-LASSO

Recent results have revealed that massive multiple-input-multiple-output (MIMO) channels exhibit a sparse structure. In this paper, we leverage this feature into the development of a novel channel estimation algorithm, namely, the Adaptive-Least Absolute Shrinkage and Selection Operator (A-LASSO), in which the sparsifying matrix (dictionary) and the sparse vector are jointly optimized. The key ingredients of our approach are: a continuous model of the dictionary and a randomized dictionary optimization which alternates with a classic basis-pursuit denoising to find a very sparse representation of the channel. A comparison with a Fourier-based sparse channel estimation method is provided and it is shown that the proposed A-LASSO can achieve over 20dB improvements on the estimation error. Also, it allows a significant reduction of the number of pilots.