Noniterative Joint Frequency Offset and Channel Estimation for MIMO OFDM Systems Using Cascaded Orthogonal Pilots

In this paper, we reconsider the issues of frequency offset and channel estimation in multiple-input-multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems. We first design “cascaded orthogonal” pilot symbols and adopt the properties of Fourier transform and Hadamard product to deliver a closed-form estimate of frequency offset; meanwhile, another closed-form estimate of channel under minimum mean square error (MSE) criterion is presented. A tight lower bound for the MSE of the channel is also derived. The proposed channel estimator is robust to the residual frequency offset, whereas the frequency offset estimator is nearly independent of the unknown channel vector and is also robust to channel variations. Simulation results show that the proposed method greatly reduces the MSE of the channel in the moderate-to-high value of signal-to-noise ratio (SNR), even at a large normalized (by subcarrier spacing) frequency offset |ν| = 0.5. Compared with the optimal pilot design without frequency offset, our solution performs only slightly worse for low values of frequency offset (|ν| ≤ 0.01), but the difference is insignificant. The computational complexity of the proposed scheme is also much lower than that of the conventional iterative means.