Here is my question regarding SNR of a SIMO model (one transmitter antenna and K receiver antennas):

$$\vec{y}_{K\times 1}=\vec{h}_{K\times 1}x+\vec{n}_{K\times 1} $$

In a Matlab simulation, if say, I want to simulate the system performance under SNR=10 dB and noise is (0,\$\sigma^2\$), the general process would be: assign a power, say 1, to \$x\$, then use given SNR=10dB to assign corresponding value to \$\sigma\$.

The code of \$\vec{n}\$ should be: Noise=sigma*randn(K,1).

Here is my confusion: when we say SNR=10dB, does it mean:

1) On each receiving antenna, \$SNR= h^2_i/\sigma^2 =10dB\$?

2) Or, totally for all receiving antennas, \$SNR= ||\vec{h}||^2/\sigma^2 =10dB\$?

3) Or, since every antenna has a copy of noise, \$SNR= ||\vec{h}||^2/(K\sigma^2) =10dB\$ ?

So which understanding is correct? If none of them is right, could someone explain to me about the correct way to do the simulation?


Each antenna/LNA pair has noise independent of the other antenna/LNA pairs.

You have to define what the SNR means: output of a combiner is 10dB SNR, or input to each LNA is 10dB.


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