of transmit antennas, the computational complexity of SM is the same as the computational complexity of SIMO systems.

-   The number of RF chains needed by SM is significantly less than the number of RF chains needed by SMX. In fact, only one RF chain is required for SM.

For these reasons we believe that SM is a strong candidate for large scale MIMO systems, which strongly motivates this work.

Channel Model
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The modulated vector, ${\bf{x}}_{\ell_t ,s_t }$, in is transmitted through a frequency–flat $N_r\times N_t$ MIMO fading channel with transfer function $\mathbf{H}$, where $N_r$ is the number of receive antennas. In this paper, a Rayleigh fading channel model is assumed. Thus, the entries of $\mathbf{H}$ are modelled as complex independent and identically distributed (i.i.d.) entries according to $\mathcal{CN}(0, 1)$. Moreover, a perfect channel state information (CSI) at the receiver is assumed, with no CSI at the transmitter.

Thus, the $N_r \times 1$ received vector can be written as follows:

$$\begin{aligned}
{\bf{y}} &=& {\bf{Hx}}_{\ell_t ,s_t }  + {\bf{n }} \nonumber \\
         &=& {\bf{h}}_{\ell_t}s_t + \bf{n} \label{Eq:Comp_Mod}\end{aligned}$$

where ${\bf{n }}$ is the $N_r$–dimensional Additive White Gaussian Noise (AWGN) with zero–mean and variance $\sigma^2$ per dimension at the receiver input, and 