A method for decoding a symbol transmitted over a millimeter wave (mmWave) channel from a transmitter to a receiver, comprising: receiving, using a set of antennas of the receiver, time-domain signals transmitted over the mmWave channel from the transmitter to the receiver; converting, using a front end of the receiver, a format of the received time-domain signals and transforming the format converted time-domain signals into at least a test symbol suitable for a probabilistic channel estimator of the receiver and a data symbol suitable for a decoder of the receiver; estimating, using the probabilistic channel estimator of the receiver, channel state information of the mmWave channel using a Bayesian inference on the test symbol according to a probabilistic model of the mmWave channel including statistics on paths and spread of mmWaves propagating in the mm Wave channel, wherein the probabilistic channel estimator is implemented using a processor executing software instructions estimating the CSI using the Bayesian inference; wherein the mmWaves propagating in the mmWave channel are spread upon arrivals and departures, such that the mmWaves are detected as clusters of the mmWaves at the receiver, wherein the statistics of the paths of mmWaves include statistics on locations of the clusters in a space of propagation of the mmWaves, and wherein the statistics on the spread of mmWaves include statistics on a spread density of the cluster, and wherein the probabilistic model of the mmWave channel includes statistics on power profile of the clusters, and wherein the space of propagation of the mmWaves is a Cartesian product of a set of angles of directions of departure (DoD) of the mmWaves and angles of directions of arrivals (DoA) of the mmWaves; and decoding, using the decoder of the receiver, the data symbol using the CSI, wherein steps of the method are performed by a processor of a receiver. receiving, using a set of antennas of the receiver, time-domain signals transmitted over the mmWave channel from the transmitter to the receiver; converting, using a front end of the receiver, a format of the received time-domain signals and transforming the format converted time-domain signals into at least a test symbol suitable for a probabilistic channel estimator of the receiver and a data symbol suitable for a decoder of the receiver; estimating, using the probabilistic channel estimator of the receiver, channel state information of the mmWave channel using a Bayesian inference on the test symbol according to a probabilistic model of the mmWave channel including statistics on paths and spread of mmWaves propagating in the mm Wave channel, wherein the probabilistic channel estimator is implemented using a processor executing software instructions estimating the CSI using the Bayesian inference; wherein the mmWaves propagating in the mmWave channel are spread upon arrivals and departures, such that the mmWaves are detected as clusters of the mmWaves at the receiver, wherein the statistics of the paths of mmWaves include statistics on locations of the clusters in a space of propagation of the mmWaves, and wherein the statistics on the spread of mmWaves include statistics on a spread density of the cluster, and wherein the probabilistic model of the mmWave channel includes statistics on power profile of the clusters, and wherein the space of propagation of the mmWaves is a Cartesian product of a set of angles of directions of departure (DoD) of the mmWaves and angles of directions of arrivals (DoA) of the mmWaves; and decoding, using the decoder of the receiver, the data symbol using the CSI, wherein steps of the method are performed by a processor of a receiver.