Massive MIMO Pilot Decontamination and Channel Interpolation via Wideband Sparse Channel Estimation

We consider a massive MIMO system based on time division duplexing (TDD) and channel reciprocity, where the base stations (BSs) learn the channel vectors of their users via the pilots transmitted by the users in the uplink (UL). It is well-known that, in the limit of very large number of BS antennas, the system performance is limited by pilot contamination, due to the fact that the same set of orthogonal pilots is reused in multiple cells. In the regime of moderately large number of antennas, another source of degradation is channel interpolation because the pilot signal of each user probes only a limited number of orthogonal frequency division multiplexing (OFDM) subcarriers, and the channel must be interpolated over the other subcarriers, where no pilot symbol is transmitted. In this paper, we propose a low-complexity algorithm that uses the received UL wideband pilot snapshots in an observation window comprising several coherence blocks (CBs) to obtain an estimate of the angle-delay power spread function (PSF) of the received signal. This is generally given by the sum of the angle-delay PSF of the desired user and the angle-delay PSFs of the copilot users, i.e., the users re-using the same pilot dimensions in other cells/sectors. We propose supervised and unsupervised clustering algorithms to decompose the estimated PSF and isolate the part corresponding to the desired user only. We use this decomposition to obtain an estimate of the covariance matrix of the user wideband channel vector, which we exploit to decontaminate the desired user channel estimate by applying minimum mean squared error (MMSE) smoothing filter, i.e., the optimal channel interpolator in the MMSE sense. We also propose an effective low-complexity approximation/implementation of this smoothing filter. We use numerical simulations to assess the performance of our proposed method, and compare it with other recently proposed schemes that use the same idea of separability of users in the angle-delay domain.