About discrete time model for wireless channel
The mathematical notation for the formula uses \$-\infty...\infty\$ as its domain and, as such, it can afford a theoretical non-causal response. Similarly, \$\text{sinc}(x)\$ is also defined with the same limits, yet in practice \$x\$ is shifted by a certain amount.
The same thing happens here: the formula may have its roots in the mathematical, ideal formulation, but in practice the shifting (that you can already see in the equations) makes the response perfectly causal, so you don't have to worry about free energy.