Channel estimation based on structural prior information is a crucial topic in future millimeter wave communication systems. This is in contrast to current systems where channel estimation is model-free because of rich scattering. Of particular interest are conditionally normal channel models. In these models, the channel vector is assumed to be Gaussian distributed with a covariance matrix that depends on a hidden variable, which cannot be observed. The channel matrix is assumed to be approximately low rank. Thus, the coefficients of the channel vector have a very strong correlation structure and this can be exploited to improve channel estimation.
Recently, we proposed a neural network based approach that approximates the minimum mean squared error (MMSE) estimator of the channel vector . This estimator was designed as a proof-of-concept for a very simple flat-fading uplink scenario. In more realistic scenarios, not all receive antennas are equipped with their own analog-digital converters. Instead, an analog network of phase shifters and combiners is employed to reduce power consumption. The goal of this thesis is to derive the MMSE estimator for this particular model and design an appropriate neural network that can be used as an efficient alternative to the MMSE estimator.
 D. Neumann, T. Wiese, and W. Utschick, "Learning the MMSE Channel Estimator," IEEE Trans. Signal Processing, vol. 66, no. 11, pp. 2905-2917, June 1, 2018.
- familiarity with numerical linear algebra, statistical signal processing, and Bayesian estimation
- some programming experience