Public communication campaigns are campaigns that use the media, messaging, and an organized set of communication activities to generate specific outcomes in a large number of individuals and in a specified period of time.
In short, it is 广告. Precisely, there is no corresponding Chinese characters/phrases for communication campaigns. In academic, scholars often create new words/phrases to explain or clarify a new/existing concept... If I didn't look up the definition of Communication campaign, I would have no idea what CC is...
In China(mainland) academia, they categorized advertising into 4 types considering different purpose of advertising: 产品广告(product/services), 企业广告(cooperate image), 品牌广告 (brand), 观念广告(concept). I think the closest one which matches to the definition of CC is 观念广告. It aims at influencing or changing behaviors or beliefs of individuals
Hopefully, it helps.