All tech manuals and Blue prints have always showed that the Enterprise-D had a large (heavy) Antimatter generator on board. It was always suggested that this wasnt the primary source of antimatter though. More of an emergency thing.
Problem is STILL, we have really no way to contain a large quantity of antimatter. And it has to be a certain type of antimatter (Anti-Hydrogen). Then theres the process of combining it wit the right normal matter (Deuterium aka heavy Hydrogen). Also, you have to find something that can cool a matter/anti-matter reaction, and something that can contain the reaction itself, and a material that can with stand the high heat of high energy produced (aka Plasma conduits). But even then, the faster you go, the more you have to worry about time dilation.
Be a hopeful good way power reactors. IF I recall, matter/antimatter reactions (especially the 1:1 ratio ) doesnt produce any radiation. Everything is annihilated . Even the subatomic particles are all turned into useful energy.