Reduced Dimension Beamspace Design Incorporating Nested Array For Mmwave Channel Estimation

Millimeter wave systems often have very few number of RF chains as compared to the number of antenna elements in order to reduce power consumption and complexity. In this work, we study the design of the mapping function QN×r from the antenna element space of size N to the reduced beamspace dimension r. In the first part of this paper, we restrict the mapping function to antenna selection matrix that chooses antenna elements in a large ULA to form a nested array. For $r \leq 2\sqrt N - 1$, we can identify such nested arrays using appropriate selection matrices. For $r > 2\sqrt N - 1$, we select elements associated with each additional RF chain to maximally improve CRLB for a limited scattering environment, modeled using a single angle of arrival. The above design of the mapping function lacks beamforming (BF) gain, which is crucial for the channel estimation (CE) phase in mmWave communications. In the second part of the paper, we design a mapping function QN × r that provides BF gain while forming an approximate nested array, when focused in an appropriately narrow angular space.