of SIMO systems. However, the complexity of SMX increases linearly with the number of transmit antennas.

Thus, the reduction of SM–ML receiver complexity relative to the complexity of the SMX–ML decoder for the same spectral efficiency is given by,

$$\mathcal{C}^{\text{ML}}_{\text{rel}} = 100 \times \left( 1 - \frac{2}{N_t+1} \right). \label{Eq:RelComp}$$

From , the reduction in complexity offered by SM increases with the increase in the number of transmit antennas. For example for $N_t=4$ SM offers a $60\%$ reduction in complexity compared to SMX, and as the number of transmit antennas increases the reduction increases.

SM–Rx
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The complexity of the SM–Rx receiver is given by:

$$\label{Eq:Rxcomp} \mathcal{C}_{{\rm{Rx-SD}}} = 3\sum\limits_{\ell = 1}^{N_t } {\sum\limits_{s = 1}^M {\tilde N_r \left( {\ell,s} \right)} }$$

It is easy to show that $\mathcal{C}_{{\rm{Rx-SD}}}$ lies in the interval $3 \times 2^m  \le \mathcal{C}_{{\rm{Rx-SD}}} \le 6N_r2^m$, where the lower bound corresponds to the scenario where $\tilde N_r \left( {\ell,s} \right) = 1$, and the upper bound corresponds to the scenario where $\tilde N_r \left( {\ell,s} \right) = 2N_r$ for $\ell \in \left\{ {1,2, \ldots N_t } \right\}$ and $s \in \left\{ {s_1 ,s_2 , \ldots s_M } \right\}$. An interesting observation is that SM–Rx offers a reduction in 