Wireless access is becoming the dominant way of connecting to the Internet due to the high data rates that several radio access technologies (RATs) provide. Such success is a result of several advances in wireless communications over the last two decades. A key enabling technique which promises further improvement in data rates is carrier aggregation (CA). Intra-band and inter-band carrier aggregation, in a continuous or a non-continuous fashion, have been proposed within the 3GPP standardization body for LTE-Advanced (LTE-A). Cross-carrier scheduling is also specified through dynamic scheduling on different component carriers. LTE-A has been specified to support all types of CA using several transmission bandwidths for all band combinations. A future enhancement would be the assumption of CA operating over heterogeneous networks (HetNets) and heterogeneous radio access technologies (h-RATs), considering the fact that both HetNets and h-RATs are key aspects of beyond 4G communications. However, CA has not been designed for HetNets and h-RATs so far. Aiming to serve beyond 4G communications, we envisage a spectrum overlay technology that will be able to manage aggregated heterogeneous bands (HetBands) efficiently, which are licensed to HetNets and h-RATs or even based on unlicensed or opportunistic spectrum access, in order to deliver higher data rates to future multi-standard handset devices in a flexible way based on cognitive radio technology. To be specific, we will investigate and design advanced physical and upper layer techniques, such as diversity, link adaptation and radio resource management, which will be able to handle the aggregation of non-continuous and dispersed bands (i.e., HetBands) extending thereby the 3GPP functionality. More specifically, frequency and subcarrier diversity, multi-channel link adaptation and multidimensional radio resource and inter-carrier interference management will be developed and demonstrated over such a new heterogeneous and wideband fading environment. We will also investigate and design radio impairments mitigation techniques, such as reduction of power fluctuation and linearization. To this end, proof of concept prototypes will be developed to demonstrate and validate the soundness of the innovative concepts proposed by SOLDER.