Dictionary Learning for Channel Estimation in Hybrid Frequency-Selective mmWave MIMO Systems

Exploiting channel sparsity at millimeter wave (mmWave) frequencies reduces the high training overhead associated with the channel estimation stage. Compressive sensing (CS) channel estimation techniques usually adopt the (overcomplete) Fourier transform matrix as sparsifying dictionary. This may not be the best choice when considering hardware impairments in practical arrays. We propose two dictionary learning (DL) algorithms to learn the best sparsifying dictionaries for channel matrices from observations obtained with practical hybrid frequency-selective mmWave multiple-input-multiple-output (MIMO) systems. First, we optimize the combined dictionary, i.e., the Kronecker product of transmit and receive dictionaries, as it is used in practice to sparsify the channel matrix. This stage operates as a calibration phase, since all the hardware imperfections are embedded into the learnt dictionaries. Second, considering the different array structures at the transmitter and receiver, we exploit separable DL to find the best transmit and receive dictionaries. Once the channel is expressed in terms of the optimized dictionaries, various CS-based sparse recovery techniques can be applied for low overhead channel estimation. The effectiveness of the proposed DL algorithms under low SNR conditions has been corroborated via numerical simulations with different system configurations, array geometries and hardware impairments.