Generally, In large/Massive MIMO systems, the transmit/receive antenna no. are in 100's. In these systems, Channel State Information available at the receiver is much helpful for data detection. However, pilot sequence requirements becomes very high for large antenna systems, which in turn creates scarcity of orthogonal pilot sequences and hence reuse of the avail pilot sequences. This reuse of same sequence when done in nearby cell can lead to pilot contamination. for ex. a user situated at the cell boundary is receiving the same reused pilot sequence from two different base station. This in turn causes wrong estimation of the desired channel(whether the estimated channel coefficient is for channel from cell 1(desired, where user stands) or cell 2(nearby cell reusing same pilot sequence)). This effect of pilot contamination on channel estimation can be soothed by using asymptotic orthogonality property of channel vectors in large MIMO systems. Further, The eigen decomposition of the covariance matrix of received contaminated pilot/data is utilized for channel estimation.
Here, a sample code is attached which utilizes the above property to estimate the channel requiring a very small training sequence(utilizes eigenvalues and eigenvector property of a matrix). The given code shows that for data length of 50, 100 are enough for channel estimation in such contaminated scenario.