Analysis of channel correlation and channel capacity for indoor MIMO visible light communication systems

In indoor multi-input–multi-output (MIMO) visible light communication (VLC) systems, spatial multiplexing (SMP) is employed to improve spectral efficiency. However, the performance of SMP in an indoor VLC system depends on a low channel correlation. In this paper, a receiver model with angular diversity detectors is considered. The objective is to reduce the channel correlation and hence the system performance in terms of bit error rate (BER) and channel capacity compared to vertically oriented detectors under no-line-of-sight (NLOS) channel conditions. For a vertical detector setup, the results show that the channel correlation cannot be further reduced by varying the transmitter separation, transmitter semi-angle, or field of view of the receiver in NLOS conditions due to the design of receiver separation being very small in small mobile devices. In comparison to vertical detector setups, by varying the detector axis of each photodetector (PD) detector axis in angular diversity detector setups, the channel matrix rank is improved under LOS conditions, and the channel correlation is effectively reduced under NLOS conditions without requiring any implementation complexity at the receiver. Therefore, it is found that the angular diversity detector setup can substantially improve the BER performance of SMP, since it makes each PD more spatially separated to improve channel conditions. Notably, we deduce the channel capacity expression to approximate the capacity of the indoor highly correlated MIMO channel and verify the theoretical analysis by numerical simulations. The results show that the angular diversity detector setup provides capacity improvement when compared with the vertical detector setup. Even though it diminishes the received power when the elevation angle exceeds the optimal elevation angle, it outweighs this degradation by providing reduced channel correlation.