Abstract
In this paper, we investigate the optimality of training signals for linear minimum mean square error (LMMSE) channel estimation in multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) with frequency-selective fading channels. This is a very challenging problem due to its mathematical intractability and has not been analytically solved in the literature. Using the Lagrange multiplier method, we derive the optimality conditions for training signal design. Important findings revealed on optimal training signals are twofold: (i) the energies of the training signals on each subcarrier are equal, and (ii) on each subcarrier, the training signals transmitted from the different antennas are orthogonal and of equal energy. We verify that our results are in line with the design principles that have been derived in single-carrier MIMO systems. Two types of optimal training signal examples that satisfy the optimality conditions are presented for practical implementations in MIMO-OFDM systems. Simulation results show that the training signals based on the optimality conditions outperform other non-optimal training signals in terms of channel estimation performance.
Highlights
Increasing interest has been concentrated on multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) for broadband wireless communication
In MIMO-OFDM systems where a sequence of a training signal is transmitted at the transmitter through Q transmit antennas, N subcarriers, M OFDM symbols with the total transmit power of Etotal, and linear minimum mean square error (LMMSE) channel estimation is performed at the receiver upon the reception of M OFDM symbols from P received antennas, the training signal is ‘optimal’ in terms of minimizing channel estimation errors if the training signal satisfies the following conditions:
7 Conclusions In this paper, optimality conditions are analytically derived and design guidelines for the optimal training signals are provided for LMMSE channel estimation for MIMO-OFDM
Summary
Increasing interest has been concentrated on multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) for broadband wireless communication. We directly tackle a multi-carrier system model and solve the optimality conditions of training signals for LMMSE estimator in MIMO-OFDM systems. This is quite challenging because simultaneous considerations on all MIMO dimensions, channel statistics, multicarriers, and multisymbols lead to an extremely complex modeling and mathematically intractable problem. In MIMO-OFDM systems where a sequence of a training signal is transmitted at the transmitter through Q transmit antennas, N subcarriers, M OFDM symbols with the total transmit power of Etotal, and LMMSE channel estimation is performed at the receiver upon the reception of M OFDM symbols from P received antennas, the training signal is ‘optimal’ in terms of minimizing channel estimation errors if the training signal satisfies the following conditions:.
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