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

I. Introduction

Training-signal design for channel estimation is a well-studied problem for single-input single-output (SISO) single-carrier systems, but a relatively new one for multiple-input multiple-output (MIMO) systems [1]–[9]. To the best of our knowledge, all existing training-signal designs for channel estimation assume no frequency offset and phase noise (PN). In practice, frequency offset and PN are unavoidable due to nonideal oscillators. They cause a loss of orthogonality among the subcarriers which, in turn, seriously degrades the performance of orthogonal frequency-division multiplexing (OFDM) systems [10], [11]. Hence, frequency offset and PN estimation and compensation techniques are typically applied at the receiver. However, in practice, there will still be a nonzero residual frequency offset. In addition, PN compensation techniques (e.g., [12]) require channel estimates, and hence, obtaining robust channel estimates in the presence of PN is important. It is unclear how the existing optimal training signals behave in the presence of (residual) frequency offset and PN.