Cool, first opportunity to help someone out with this game. My basic strategy for that mission was leapfrogging the infantry and Strykers.
For example with the main gate I lined the Strykers up 5 wide across about 100m, 300m from the gate and pounded the mg bunker and the houses with everything I had. Then I deployed the troops and had them each assault a separate building and get on the roof. By the time that is done your reinforcements should have arrived.
There is a big clearing right behind the main gate, with two rows of tall building forming an alley facing the barracks. This area is deadly, and I took most of my casualties here. What I did was use the same sort of tactics you would to expand a bridgehead. I put 4 Strykers from the reinforcements in a box formation in the clearing behind the main gate. I then assaulted the tall buildings to the left and directly behind the gate with all of my infantry.
From here the basic strategy is to move the Stykers into a position to cover the Infantries next assault, always prepping the site with liberal amounts of artillery.
Good luck. I thought it was a very well designed mission.