Assume I have a MIMO system with $M=8$ transmit antennas, and an arbitrary number of receive antennas.
This MIMO systems uses space-time coding. the block codes (matrices) transmitted are part of a set $S$. $S$ contains 110592 unitary matrices having complex elements belonging to an M-PSK moduolation.
And let $T$ be the normalized coherence interval, which is the duration in which the channel remains constant.
The maximum spectral efficiency achievable by such a system is: $$R_{max}=\frac{1}{T}\left\lfloor \log_2 |S| \right\rfloor$$ where $\left\lfloor \log_2 |S| \right\rfloor$ is the cardinality of the set $S$, which is 110592. This leads to a maximum spectral efficiency of $2\text{ bps/Hz}$.
The number of matrices needed to attain $2\text{ bps/Hz}$ or $\text{bpcu}$ (bits per channel use) is $2^{RT}$ which amounts to a set $C\subset S$ of 65536 matrix.
In my work, these 65536 matrix are not chosen randomly from the set $S$, rather they follow a criterion which is to choose the matrices having the largest distance among each other in order to improve system performance. The distance between two matrices is measured using the Frobenius Norm as follows $D_{MaMb}=||M_a-M_b||_F$
My problem is that it is not feasible to run my search algorithm on all 65536 matrices. Is there a sub-optimal method that i could use to select these matrices without running through the whole Set?