Lattice parameter estimation from multivariate sparse, noisy measurements

In current standards for MIMO wireless communication, considerable energy is expended in providing training from the transmitter so that the channel matrix can be estimated with sufficient accuracy at the receiver. What if this training could be significantly reduced or, in some cases, eliminated? If the communication system uses QAM as its underlying modulation technique, the received signals can be modelled as points on a lattice translate, displaced by noise. Estimation of the lattice basis is closely related to estimation of the channel matrix. We propose a statistical model - MIMO signal transmission being an important example - in which lattice points are observed with noise. The aim is to accurately estimate the lattice basis. We examine a generalisation of the Bartlett point-process periodogram for this purpose. Under appropriate conditions, we show that the estimated basis vectors converge almost surely to the true ones and we derive a central-limit theorem. We demonstrate excellent agreement with the theoretical results through simulation studies.