Channel estimation and precoder design for millimeter-wave communications: The sparse way

We propose strategies for mmWave communications that exploit the inherent sparsity of mmWave channels in the angle and delay domains. In particular, we propose the use of aperture shaping to ensure a sparse virtual-domain MIMO channel representation; fast FFT-based modulation and demodulation schemes to expose the virtual-channel coefficients; a pilot design that facilitates fast LASSO-based sparse-channel estimation; and spectrally efficient precoding and decoding, via the Lanczos algorithm and waterfilling over both frequency and angle. Numerical experiments suggest that our approach comes close to achieving the perfect-CSI capacity of the mmWave channel.