  Linear minimum mean square error (LMMSE) receivers are often applied in
practical communication scenarios for single-input-multiple-output (SIMO)
systems owing to their low computational complexity and competitive
performance. However, their performance is only the best among all the linear
receivers, as they minimize the bit mean square error (MSE) alone in linear
space. To overcome this limitation, in this study, we propose an LMMSE receiver
based on the measurements augmented by their nonlinear conversion for a
photon-counting receiver, a photomultiplier tube, and an avalanche
photodetector. The performance of the proposed LMMSE receiver is studied for
different nonlinear conversions, numbers of receivers, and receiver types. The
simulation results indicate that the Monte Carlo results are consistent with
the analytical results and that the proposed LMMSE receiver outperforms the
conventional one in terms of bit MSE and bit error rate. Accordingly, it can be
concluded that to achieve a desired bit MSE, the proposed LMMSE-based nonlinear
receiver not only reduces the need to increase the number of receivers but also
reduces the bandwidth requirements.
