Minimum mean‐square‐error expression of LMMSE channel estimation in SISO OFDM systems

Abstract

International audienceAn expression of the minimum mean square error (MMSE) of the linear MMSE channel estimation is given in the case of a non-invertible channel covariance matrix, as in single-input single-output (SISO) OFDM system. A matrix expression, already proposed for a multi-input multi-output OFDM system in a previous article, is not valid in SISO. A new proof is then proposed, by deriving a scalar expression of the MMSE, which leads to solve an optimisation problem. Furthermore, we show that the proposed solution is the global minimum. Simulations validate the proposed development

Mean square error analysis and linear minimum mean square error application for preamble‐based channel estimation in orthogonal frequency division multiplexing/offset quadrature amplitude modulation systems

“…at SNR = 18 dB MSE ICM = 0.0549 and MSE IAM = 0.0251). The ratio between MSE IAM = 0.0251 and MSE ICM = 0.0549 exactly corresponds in (13) to the energy ratio between |D m,n | 2 = 1 for ICM method and |D m,n | 2 = 2.186 for IAM method. We conclude from Fig.…”

“…5b by considering the AWGN, TU, and HT channels. Obtained results are compared with the theoretical MSE expression in (13). To improve the observation, a zoom from SNR = 15 to 20 dB has been added on both figures.…”

“…A small difference between the theoretical MSE values and those obtained by simulation considering the HT channel at SNR > 10 dB can be observed. This can be explained by the fact that the approximation E{H m−1,n H * m+1,n } = s 2 H is made in order to derive the theoretical MSE expression in (13). This approximation proves to be accurate for weakly frequency selective channels as AWGN and TU models, but is less appropriate for high selective channels as HT.…”

“…Without loss of generality, the proof is made by assuming C m,n = 1 with an even m value, the final results remaining valid for C m,n = −1 and m odd. The MSE expression in (13) shows that MSE I should inevitably reach an error floor, even if σ 2 = 0. This is the main difference with performance analyses in OFDM, which show that the MSE converges to zero in noise-free conditions [8,9], whereas the term s 2 I ′ in (13) reflects the presence of residual interferences.…”

“…Nevertheless, in [2,4], the POP method is always derived under very optimistic conditions in which the noise is considered to be negligible. Pilot allocation and channel estimation techniques have been widely analysed in the scientific literature for OFDM scheme [8,9,[11][12][13][14][15]. However, still open challenges exist for the OFDM/OQAM scheme because of its dependence on the used prototype filter [2,4,6] that has a direct impact on the channel estimation, as it generates intrinsic interferences on the transmitted data.…”