The lattice-reduction （LR） has been developed to im- prove the performance of the zero-forcing （ZF） precoder in multiple input multiple output （MIMO） systems. Under the assumptions of uncorrelated flat fading channel model and perfect channel state information at the transmitter （CSIT）, an LR-aided ZF precoder is able to collect the full transmit diversity. With the complex Lenstra- Lenstra-Lov^sz （LLL） algorithm and limited feedforward structure, an LR-aided linear minimum-mean-square-error （LMMSE） pre- coder for spatial correlated MIMO channels and imperfect CSIT is proposed to achieve lower bit error rate （BER）. Assuming a time division duplexing （TDD） MIMO system, correlated block flat fad- ing channel and LMMSE uplink channel estimator, it is proved that the proposed LR-aided LMMSE precoder can also obtain the full transmit diversity through an analytical approach. Furthermore, the simulation results show that with the quadrature phase shift keying （QPSK） modulation at the transmitter, the uncoded and coded BERs of the LR-aided LMMSE precoder are lower than that of the traditional LMMSE precoder respectively when Eb-No is greater than 10 dB and 12 dB at all correlation coefficients.
A hybrid pilots assisted channel estimation algorithm for multiple input multiple output（MIMO） orthogonal frequency division multiplexing（OFDM） systems under low signal-to-noise ratio（SNR） and arbitrary Doppler spread scenarios is proposed.Motivated by the dissatisfactory performance of the optimal pilots（OPs） designed under static channels over multiple OFDM symbols imposed by fast fading channels,the proposed scheme first assumes that the virtual pilot tones superimposed at data locations over specific subcarriers are transmitted from all antennas,then the virtual received pilot signals at the corresponding locations can be obtained by making full use of the time and frequency domain correlations of the frequency responses of the time varying dispersive fading channels and the received signals at pilot subcarriers,finally the channel parameters are derived from the combination of the real and virtual received pilot signals over one OFDM symbol based on least square（LS） criterion.Simulation results illustrate that the proposed method is insensitive to Doppler spread and can effectively ameliorate the mean square error（MSE） floor inherent to the previous method,meanwhile its performance outmatches that of OPs at low SNR region under static channels.
