  We develop a broadband channel estimation algorithm for millimeter wave
(mmWave) multiple input multiple output (MIMO) systems with few-bit
analog-to-digital converters (ADCs). Our methodology exploits the joint
sparsity of the mmWave MIMO channel in the angle and delay domains. We
formulate the estimation problem as a noisy quantized compressed-sensing
problem and solve it using efficient approximate message passing (AMP)
algorithms. In particular, we model the angle-delay coefficients using a
Bernoulli-Gaussian-mixture distribution with unknown parameters and use the
expectation-maximization (EM) forms of the generalized AMP (GAMP) and vector
AMP (VAMP) algorithms to simultaneously learn the distributional parameters and
compute approximately minimum mean-squared error (MSE) estimates of the channel
coefficients. We design a training sequence that allows fast, FFT-based
implementation of these algorithms while minimizing peak-to-average power ratio
at the transmitter, making our methods scale efficiently to large numbers of
antenna elements and delays. We present the results of a detailed simulation
study that compares our algorithms to several benchmarks. Our study
investigates the effect of SNR, training length, training type, ADC resolution,
and runtime on channel estimation MSE, mutual information, and achievable rate.
It shows that our methods allow one-bit ADCs to perform comparably to
infinite-bit ADCs at low SNR, and 4-bit ADCs to perform comparably to
infinite-bit ADCs at medium SNR.
