Spatial modulation was proposed few years back to achieve a higher data rate and solving the major problems in multiple-input multiple-output (MIMO).
This was made possible just by using spatial dimension to convey information together with the transmitted signal. However, the spatial dimension of the constellation dimension
is also used to select the active antenna per transmission instant. This made the use of single antenna per transmission instant possible. Resulting in the use of single radio frequecy chain.
This eliminate the need for antenna synchronization since only one antenna is active at a time so the antennas don’t need to synchronize before transmission. Also this eliminate inter-channel interference and
inter-symbol interference since only one symbol is transmitted at each time slot.
The announcement of SM actually made more development in MIMO scheme as seen in Space-Time Block Code (STBC SM). I will talk about this in details in another article.
The data rate of a spatial modulation system is
Where M is the quadrature amplitude modulation used and Tx is the total number of the transmit antennas in the system.
Assuming a signal x is transmitted over a Rayleigh fading channel H in the presence of additive white Gaussian noise n. The signal x is modulated by log2M and the remaining log2 Tx is used to select the active transmit antenna to be used for transmission at every instant. Thus, the received signal vector y will become:
Y =sqrt(p)*hj*x+n -----------------------------------(1)
Let’s consider an example of 4-QAM 2Tx and 4Rx system. In this case the data rate will be a bit of length 4 bits such as . The first 2 bits [1 0] which is the log2(M)
modulate the transmitted symbol and the remaining bit  selects the antenna to be used for transmission in this case out of the 4 antennas the second one will be selected
at this time slot. Then, this is transmitted across an i.i.d channel H in the presence of AWGN n noise given raise to Y in equation (1) above.
This can be detected at the receiver optimal with Maximum Likelihood detector or with a sub-optimal detector. In this article will focus on an optimal detector.
The estimate of the transmit antenna index and the estimate of the transmitted symbol can be evaluated by finding the minimum argument of the forbenius norm of Y-hx.
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