  In this paper, we propose a scheme called "beam-nulling" for MIMO adaptation.
In the beam-nulling scheme, the eigenvector of the weakest subchannel is fed
back and then signals are sent over a generated subspace orthogonal to the
weakest subchannel. Theoretical analysis and numerical results show that the
capacity of beam-nulling is closed to the optimal water-filling at medium SNR.
Additionally, signal-to-interference-plus-noise ratio (SINR) of MMSE receiver
is derived for beam-nulling. Then the paper presents the associated average
bit-error rate (BER) of beam-nulling numerically which is verified by
simulation. Simulation results are also provided to compare beam-nulling with
beamforming. To improve performance further, beam-nulling is concatenated with
linear dispersion code. Simulation results are also provided to compare the
concatenated beam-nulling scheme with the beamforming scheme at the same data
rate. Additionally, the existing beamforming and new proposed beam-nulling can
be extended if more than one eigenvector is available at the transmitter. The
new extended schemes are called multi-dimensional (MD) beamforming and MD
beam-nulling. Theoretical analysis and numerical results in terms of capacity
are also provided to evaluate the new extended schemes. Simulation results show
that the MD scheme with LDC can outperform the MD scheme with STBC
significantly when the data rate is high.
