In the previous two experiments, we have learned about spatial diversity and multiplexing techniques separately. It is understood that the diversity improves the received SNR which helps to reduce the bit error rate (BER), whereas the spatial multiplexing enables the transmission of parallel data streams so that the transmission capacity can me improved.

In multiplexing, we decompose the MIMO channel into parallel SISO channels. The SNRs associated with these parallel streams depend on the eigenvalues of channel covariance matrix. Thus, there is a possibility that the SNR of a particular stream is poor which may result in poor its BER performance. To overcome this, the spatial degree of freedom offered by the channel can be partially used for diversity gain with some reduction in the multiplexing gain. This will improve SNR performance at the cost of the reduced number of parallel streams, which leads essentially to {\em diversity vs. multiplexing trade-off}. The choice of diversity and multiplexing orders will depend on the application. For instance, a higher multiplexing order will provide a high transmission rate but with poor BER performance. Whereas, setting a high diversity order will improve BER performance but at the cost of reduced data rate. Therefore, such diversity vs. multiplexing trade-off can be also viewed as the trade-off between transmission rate and BER.

Consider the following scenario: We have 4 transmit antennas, and 4 receive antennas. If we want a multiplexing gain of 2, we can have the following visualization

If the multiplexing gain of the system is m, then the optimal diversity gain that can be achieved is given as $d = (N_t - m)(N_r - m)$ and can be observed in the following plot