Optimal training signals for MIMO OFDM channel estimation in the presence of frequency offset and phase noise

We develop robust mean-square error (MSE)-optimal training signal designs for multiple-input multiple-output orthogonal frequency-division multiplexing channel estimation with frequency offset and phase noise (PN), and present analytical and simulation results for the frequency-offset and PN effects on channel estimation. The proposed designs are more advantageous for moderate-to-high values of signal-to-noise ratio (SNR), residual frequency offset, and PN level. At SNR = 10 dB, the normalized MSE reductions of our proposed training signals at normalized frequency offset |v|=0.1,0.5 are about 9 and 19 dB, respectively, for one transmit antenna, and 6 and 11 dB for two transmit antennas