# The theoretical formula of error probability and the data rate in MIMO,and the relation between $G^T$ and $G^R$ and $M$

I want to use Matlab to plot these two figures,fig(a) is the error probability,and as we can see,the higher M is,the lower error probability it has in the same SNR . The fig(b) is data rate,the higher M is,the higher data rate it has.M is the antennas number

(a) error probability

(b) date rate

I believe there are some theoretical formula of error probability and the data rate in MIMO.However,i can't find the theoretical formula for error probability in MIMO,so can anyone give me some information about this?

I have found some formula about the data rate in MIMO

$$1.C=log_2(1+G^T \rho_0 G^R)$$,

$$\rho_0$$ is SNR,and $$G^T$$ and $$G^R$$ are the gain of the transmitting and receiving antennas.However,i can't find the relation between the $$G^T$$ and $$G^R$$ and $$M$$,so i can't plot the figure like the (b) shown.Does anyone know about their relation or know how to write the code to plot these two figures

• where did you find that formula? That place will definitely at least in words define what $G$ and $G^R$ are. – Marcus Müller May 1 at 11:54