Carrier aggregation (CA) was introduced in mobile communication systems in response to the demand for higher network capacity. CA was conceived as a technique to achieve higher data rates by aggregating multiple blocks of spectrum from the same or different frequency bands. This work explores a different point of view, where CA is employed not as a way to increase capacity through using more bandwidth, but as a diversity technique in order to increase the spectral efficiency of the existing spectrum, and therefore, achieve higher capacity without needing additional spectrum. A mathematical model and set of closed-form expressions are provided, which can be used to characterise the performance of CA as a diversity technique (in terms of both ergodic capacity and secrecy capacity) and determine the impact of various relevant configuration parameters. The numerical results obtained by evaluating the mathematical expressions derived in this work are in line with our previous simulation studies and demonstrate that CA can be effectively exploited as a diversity technique to improve the capacity and performance of mobile communication systems compared to the case of single-carrier transmission over the same amount of bandwidth.