The conductivity of carbon nanotube (CNT) networks can be improved markedly by doping with nitric acid. In the present work, CNTs and junctions of CNTs functionalized with NO$_3$ molecules are investigated to understand the microscopic mechanism of nitric acid doping. According to our density functional theory band structure calculations, there is charge transfer from the CNT to adsorbed molecules indicating p-type doping. The average doping efficiency of the NO$_3$ molecules is higher if the NO$_3$ molecules form complexes with water molecules. In addition to electron transport along individual CNTs, we have also studied electron transport between different types (metallic, semiconducting) of CNTs. Reflecting the differences in the electronic structures of semiconducting and metallic CNTs, we have found that besides turning semiconducting CNTs metallic, doping further increases electron transport most efficiently along semiconducting CNTs as well as through a junction between them.