23 MIMO transmission example.
where H is an M N channel matrix and Im is the identity matrix of size M M. This can be rewritten
below assuming K min (M, N)
(Bps/Hz) (9.29)
where are the K nonzero eigenvalues of the matrix formed by given the number
of receive antennas is less than the number of transmit antennas. Note this matrix is a Wishart matrix.
It is well known that the MIMO capacity grows linearly with K. We have provided some statistical
properties of the eigenvalues in the earlier chapters when STE receivers were discussed. There we
noticed the eigenvalues decreased rapidly. Applying that observation to the present topic, we notice
the linear gain can also decrease rapidly on the distribution of ??™s [41].
If we can take a temporary step backward to one earlier comment made about the channel resembling
a matrix, then the following can be said. The rank of the MIMO channel is equal to the rank of
the M N channel matrix. Based on linear algebra, the rank is less than the number of transmit and
receiver antennas. The significance of this rank is that it defines the number of independent streams
that can be transmitted through the MIMO channel. As we will soon see MIMO transmission has similarities
to what was presented earlier for OFDM regarding the transmission of parallel channels.
Pages:
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827