On the design of low-resolution sensing matrices for noncoherent compressive channel estimation

Low-overhead channel estimation is a crucial prerequisite for mmWave massive MIMO communication. Compressive sensing techniques are well suited to this task, as they exploit the angular domain sparsity of multipath channels to accurately recover all significant paths in the channel with a small number of beacon measurements. In practice, however, frontend limitations such as loss of phase coherence across beacons and heavy quantization of beamforming weights necessitate the modification of conventional compressive sensing algorithms for agile channel estimation on practical frontends. In this paper, we propose a novel procedure for noncoherent compressive channel estimation on low-resolution arrays that relies on careful design of the projection weight vectors from a finite dictionary to facilitate iterative recovery of the measurement phases. In the noiseless case, the proposed method can match the performance of coherent compressive channel estimation with a factor of 3 increase in measurement complexity. Numerical results show that this factor should be increased to 4 in order to provide robustness to measurement noise.