Two-stage compressed sensing for millimeter wave channel estimation

In millimeter wave (mmWave) communication systems, large antenna arrays are used to compensate high path loss. While the large array provides high beamforming gain, it also poses a challenge in channel estimation. Since mmWave channels are likely to be sparse in angular domain, the channel estimation can be converted into a sparse recovery problem, and compressed sensing (CS) can be leveraged for the channel estimation. However, conventional non-adaptive CS algorithms show poor recovery performance with low signal-to-noise ratio (SNR), which is common before beamforming in mmWave channels. Although recently developed adaptive CS schemes perform better in a low SNR regime, their excessive feedback requirement hinders practical usage. In this paper, we propose a two-stage CS scheme that requires one-time feedback and is robust to noise, which can be regarded as a compromise between the two approaches. Sufficient conditions for the support recovery with the proposed scheme are characterized, and its effectiveness is also shown numerically.