## 1 Introduction
PHY-layer diversity receivers are designed based on the fact that the same data symbols at the PHY layer are transmitted in parallel through different physical channel paths and the replicas of the same data symbols are combined coherently at the PHY layer of the receiver. On the other hand, with CA usually a different data stream is transmitted in each CC and all data streams are reorganised at the MAC layer of the receiver in order to recover the original data sequence. Therefore, existing PHY-layer diversity techniques are based on different operating principles and can be employed in conjunction with the method proposed in this work given that CA is fundamentally a MAC-layer technique. The MAC layer can effectively be seen as an additional dimension to exploit the channel frequency diversity through CA with the method proposed in this work and obtain further performance improvements in addition to those achieved through PHY-layer diversity techniques. The performance of CA as a diversity technique was preliminarily evaluated in [22] by means of simulations carried out with the ns-3 simulator, where it was shown that CA can be exploited as a diversity technique to enhance the system performance and increase the network capacity without increasing the total amount of spectrum. While simulations can be valuable to explore the performance of a particular technique, an analytical study is also necessary to provide a comprehensive understanding of the technique being investigated. In this context, this work presents an analytical study that complements the simulation study presented in [22] by developing a mathematical model and a corresponding set of closed-form expressions can characterise the operation of CA as a diversity technique, thus providing a theoretic basis that supports and explains the findings of the simulation study reported in [22]. The following contributions are provided in this work:  
* A novel approach for the use of CA as a diversity technique is proposed. The proposed approach is discussed in detail, including its motivation, relevant design aspects and impact at various layers of the protocol stack. Some example configurations compatible with 3 GPP frequency ranges and channels are presented as well. * In order to investigate the performance of CA as a diversity technique, the concept of _effective SNR_ is introduced, which is defined as the equivalent SNR at which a single channel achieves the same performance as the considered CA scenario with the same total bandwidth. This concept provides a simple yet powerful tool for the mathematical analysis of CA. Two models for the effective SNR are considered (an ideal model and an average model). For both models two scenarios are considered, where the SNR is distributed homogeneously and heterogeneously across the aggregated CCs. Closed-form expressions for the statistical distribution of the effective SNR are then derived for the four possible cases considered in this work. * Capitalising on the model of effective SNR, the ergodic capacity of a system with CA as a diversity technique is analysed and mathematical expressions are derived for both homogeneous and heterogeneous SNR scenarios. * Similarly, the secrecy capacity of a system using CA as a diversity technique is also investigated and mathematical expressions are derived as well for the homogeneous and heterogeneous SNR scenarios. By considering both the ergodic and secrecy capacities, a robust communication system design can be achieved. The remainder of this work is organised as follows. First, Section 2 discusses the concept of CA being used as a diversity technique. The motivation and objectives of this work are then formulated in Section 3. The considered system model is described in Section 4.