SIMO channel configuration is characterized by 1 transmit antenna and multiple receiver antennas (Figure 1). SIMO configuration is used to provide receive diversity, where the same information is received across independent fading channels to combat fading. When multiple copies of the same data are received across independently fading channels, the amount of fade suffered by each copy of the data will be different. This guarantees that at-least one of the copy will suffer less fading compared to rest of the copies. Thus, the chance of properly receiving the transmitted data increases. In effect, this improves the reliability of the entire system.
The channels are independent and identically distributed (i.i.d) and hence the error event across those independent channels are also independent. The signal to noise ratios (SNR) of the channels are also i.i.d and the every channel has the same average SNR. The is the fundamental assumption of the SIMO model incorporating receive diversity.
For the case of 
receive antennas, 
independent received signal copies are
Writing in compact form, the received signal
where, ![\mathbf{h} = [ h_1, h_2, \cdots, h_N ]^T](https://s0.wp.com/latex.php?latex=%5Cmathbf%7Bh%7D+%3D+%5B+h_1%2C+h_2%2C+%5Ccdots%2C+h_N+%5D%5ET&bg=ffffff&fg=000&s=0&c=20201002)
The receiver, takes in these received copies, applies weights according to the chosen receive diversity technique (see below) and outputs a single copy (Figure 2). The combined output signal is given by
where, the weight vector is ![\mathbf{w} = [w_1, w_2, \cdots, w_N]^T](https://s0.wp.com/latex.php?latex=%5Cmathbf%7Bw%7D+%3D+%5Bw_1%2C+w_2%2C+%5Ccdots%2C+w_N%5D%5ET+&bg=ffffff&fg=000&s=0&c=20201002)
How are the weights chosen ? The weights are chosen based on the following receive diversity techniques.
Selection Combining (SC)
In selection combining, the received signal from the antenna that experiences the highest SNR is chosen for further processing. That is, the path that has the highest 
is chosen.
This is the simplest of all the receive diversity techniques. It simply chooses one branch that experiences the highest SNR. It seems to waste the remaining branches in the selection processes. Also, channel phase information is not needed for this technique.
This technique provides SNR gain in the order of 
.
Maximum Ratio Combining (MRC)
As we saw earlier, the selection combining is the simplest algorithm but it wastes 
receive elements in the computations. Maximum ratio combining technique uses all the received signals in order to maximize the output SNR. It represents maximum likelihood estimation. The output signal is the weighted sum of all the received branches. The weights for MRC technique is chosen as
Therefore, it requires the knowledge of the channel at the receiver and matching of both magnitude and phase. The output signal, with weight set as 
, is given by
The SNR gain achieved by this technique is .
Equal Gain Combining (EGC):
The MRC technique requires matching of both magnitude and the phase of the channel. The magnitudes can fluctuate significantly. In equal gain combining, only the phase of the channel is cancelled out. The weights are chosen as
where 
is the channel phase information. The output signal is given by
The technique suffers small SNR loss compared to MRC, but it is a good alternative for implementation.
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References
[1] Andrea Goldsmith, “Wireless Communications”, ISBN: 978-0521837163, Cambridge University Press, 1 edition.↗
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