Avoiding Matrix Inversion in DD SAGE Channel Estimation in MIMO-OFDM with M-QAM

A decision directed (DD) channel estimation is considered for a multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system to improve the spectral efficiency. Unlike in the pilot based channel estimation, the least-squares (LS) channel estimator operating in the DD mode for MIMO-OFDM requires a matrix inversion. The size of the matrix to be inverted depends on the number of transmit antennas and the length of the channel impulse response. The frequency domain (FD) space-alternating generalized expectation-maximization (SAGE) channel estimator calculates the LS estimate iteratively avoiding the matrix inversion with a constant envelope modulation. The drawback with the FDSAGE channel estimator is the required matrix inversion with a non-constant envelope modulation. The size of the matrix to be inverted depends on the length of the channel impulse response. However, it is considerably less complex than the LS channel estimator in the DD mode. In this paper, a time domain (TD) SAGE channel estimator is derived to avoid the matrix inversion in DD channel estimation for MIMO-OFDM systems when using non-constant envelope modulation. The derived TDSAGE channel estimator is shown to offer the same performance as the FD-SAGE channel estimator with reduced complexity.