Direct proof of use
Army University Press reporting on wartime adaptation documents the AN/TPQ-36 Firefinder in Iraq as part of the Counter Rocket, Artillery, and Mortar system. It says an Iraq C-RAM intercept battery using Phalanx 1B, the U.S. Army AN/TPQ-36 Firefinder target-acquisition radar, and Lightweight Counter Mortar Radar achieved its first combat intercept of an incoming mortar round in March 2006.
A September 2008 U.S. Army brigade publication from FOB Hammer gives a more local example. It identifies Task Force 4-27's radar section as operating around the clock with two primary radars, the AN/TPQ-36 and AN/TPQ-37, to protect FOB Hammer and associated combat outposts from mortars, rockets, missiles, and artillery.
Sources: Army University Press C-RAM Adaptation, Striker Torch FOB Hammer Radar Section
Timeline
The Iraq requirement for C-RAM began in June 2004, when the commander of Multi-National Force-Iraq requested support against rocket, artillery, and mortar threats. Army University Press states that a sense-and-warn capability was fielded in Iraq by February 2005.
The same source places the AN/TPQ-36 in the Iraq intercept architecture by March 2006, when a C-RAM intercept battery achieved its first combat intercept of an incoming mortar round. By September 2008, the FOB Hammer radar-section account described the AN/TPQ-36 as one of the radars used for warning, point-of-origin data, impact prediction, and response support against indirect fire.
Sources: Army University Press C-RAM Adaptation, Striker Torch FOB Hammer Radar Section
Operational role
In the Iraq War sources cited here, the AN/TPQ-36 was a U.S. and coalition force-protection sensor rather than a weapon that delivered effects by itself. Its role was to detect incoming indirect fire, support localized warning, identify launch origins, and pass data to a fire-control or tactical operations process for possible response.
The U.S. Army C-RAM foreign-military-sales checklist describes the AN/TPQ-36 as a highly mobile counterfire radar that automatically locates first-round projectile fire, tracks enemy and friendly fire, interfaces target coordinates to tactical fire control, and provides sense-and-warn input for C-RAM. The FOB Hammer account matches that role in Iraq, describing alarms after hostile fire detection and the transfer of point-of-origin, projected-impact, and related information to the Brigade Tactical Operations Center.
Sources: Army C-RAM LOR Checklist, Striker Torch FOB Hammer Radar Section