Study of a fast channel estimation technique for LTE Downlink systems based on fast linear Toeplitz system solver with displacement structure

Abstract

The traditional Linear Minimum Mean Square Error (LMMSE) channel estimation technique costs O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) floating operations and O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) memory locations where N represents the channel autocorrelation matrix order. In this paper, we propose to study a fast LMMSE channel estimation technique for LTE Downlink systems based on a fast solver for linear system with displacement structure which is based on the application of the Generalized Schur Algorithm (GSA) which costs only O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) floating operations and O(N) memory locations. We propose two fast LMMSE channel estimators. The first algorithm is without pivoting which requires the LU factorization. In order to avoid this requirement and for stability issues, we propose a second fast algorithm with partial pivoting technique and without changing the algorithm complexity. The performances of proposed fast algorithms in terms of Bit Error Rate (BER) and Mean Square Error (MSE) are verified via Monte-Carlo MATLAB simulations.