In quite a few threads, it's been pointed out that our clone soldiers lack some of the abilities and equipment that are considered standard-issue to real-life armed forces, and there are good reasons that they are standard.
Most soldiers today are trained in some kind of martial art (US trains a style too, it just didn't come from Asia), which is really just a disciplined way to fight effectively in hand-to-hand combat.
In DUST, martial arts in one form or another have likely survived the Dark Age, possibly with the Caldari's honor-and-tradition culture as it is more likely to pass down such concepts.
Gameplay-wise, an ideal hand-to-hand fighting style would be attacks focused on staggering or knocking down an opponent so that you can get your gun back up first, as this still pertains to a shooter gameplay.

As for appearance, either the Four Empires each developed/saved their own martial art, or the other three adopted the Caldari style. If they are different:
>Amarrians don't want to get their hands physically dirty while they're killing. If they're forced, they would be more likely to use their in-hand weapon as a bludgeoning tool, just with a little more finesse than currently. Medium damage medium speed.
>Minmatar would be brutal in a melee. Do not let a Matari get the first hit in, or you will be staggered continually until the Matari kills you with either a final punch or Flaylock blast. Slow, but brutal.
>Caldari culture is mostly based on the feudal Asian cultures of honor, tradition and respect. This race will be the most likely to have the kung-fu fighting style that above posters likely think of when they see this thread. "Fast as lightning", but low per-strike damage.
>Gallente draw most inspiration from the Greco-Roman ideology and myth, most apparent in their ship and vehicle names. This means they will likely have a style similar to that used by Alexander and the Roman elite soldiers. This type of combat style is designed to disable an opponent rather than kill, which will set them up for a follow-up shotgun blast to the face. Attacks have a chance to knock down the opponent, increasing with consecutive hits. Medium damage, slow speed.

As for how to control all this, CCP can either make it a flourished R3 melee, or have same-time melees engage a freeflow QTE, with the player able to choose between multiple attacks with different button presses. R2 would always swap back to your weapon if you need to finish off the opponent or run away, while the face buttons and L1/R1 command different attacks. Hitting the same button as your opponent would cause a "block", and who attacks and who tries to defend is based on who pressed first.