Effect of Gaussian Correlated Channel on Uplink Channel Estimation for Massive MIMO with Nested Array at the Base Station

mmWave massive MIMO can support high data rate on account of enhanced spectral efficiency. Uplink channel estimation is an important intermediate problem. Usually channels between the base station and the user equipment is assumed IID, Rayleigh and flat fading. However, the antennas are closely packed together in a massive MIMO and local scatterers are present around the user equipment. This means that a correlated channel model is more realistic. In this paper, a Gaussian one ring scattering model for the channel is used. The uplink Linear Minimum Mean Square Error (LMMSE) channel estimator performance is analyzed, with a pilot reuse factor of L > 1. The upper limit of the estimation performance for varying degrees of correlation and pilot length is derived and verified by numerical experiments. In place of usual dense uniform linear array, a sparse nested array is employed at the base station. It is verified experimentally that the sparse array performs better when the channels are highly correlated. However, both arrays showed similar performance for the usual IID case when the correlation is small ((σφ>> 0.5).