Three signals that overlap

Idea. The setting is symmetric, so all three signals get the same weight $b$. One normal equation gives $b$, and then $R^2$ follows.

Step 1: the coefficient. The normal equation for the first signal reads $b+0.5b+0.5b=0.3$, so $2b=0.3$ and $b=0.15$.

Step 2: $R^2$. $$R^2=3\times 0.15\times 0.3=0.135=\frac{27}{200}.$$

Compare. If the three signals were uncorrelated, the $R^2$ would be $3\times 0.3^2=0.27$. Because they overlap, they carry much of the same information, and the joint $R^2$ is only half of that.

In general. With $k$ signals, each correlated $r$ with the target and $\rho$ with each other, $$R^2=\frac{k{r}^2}{1+(k-1)\rho },$$ which tends to $\frac{r^2}{\rho }=0.18$ as $k$ grows: adding more of the same kind of signal hits a ceiling.