# Cross-Layer Optimization for Heterogeneous MU-MIMO/OFDMA Networks
## 1 Introduction  
Remarkable advances in radio technology over the past few decades have ushered in a new era of wireless communications. IEEE 802.11 ax [1], the newest Wi-Fi standard, is theoretically able to support a link rate of 11 Gbps with 160 MHz bandwidth and eight spatial streams, and 3 GPP has aimed to provide a downlink peak data rate of 20 Gbps and latency of \(<\)1 ms for cellular systems since Release 15 [2]. These achievements can primarily be attributed to the two innovative technologies of OFDMA (Orthogonal Frequency Division Multiple Access) and MU-MIMO (Multiuser-Multiple Input Multiple Output). By dividing a transmission into multiple subchannels, OFDMA can fully use the available radio resources in both the time and frequency domains, and the network capacity can be greatly increased using MU-MIMO without requiring additional bandwidth. Moreover, these technologies enable multiple network entities to communicate simultaneously, which in turn offers great opportunities for enhancing the flexibility of wireless networking. To benefit fully from the potential of these two technologies, researchers have long been interested in their optimal use under conditions of constrained network resources. With MU-MIMO, nodes can transmit or receive as many spatial streams as the number of antennas, and thus the DoF (Degree of Freedom) has been regarded as a key element in optimization [3; 4; 5; 6; 7], while in the field of OFDMA research, the appropriate scheduling of resource blocks (scheduling units consisting of a set of subcarriers) has been investigated for diverse network scenarios and objectives [8; 9; 10; 11]. One valuable tool for optimal resource allocation is _cross-layer optimization_[3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15], as this can take advantage of the collaborative operation among the upper and lower layers of the traditional OSI (Open Systems Interconnection) network model, and thus help reduce the wastage of resources when exchanging information between them. In addition to MIMO/OFDMA networks, cross-layer optimization is actually being used for various network scenarios. For example, a reactive link layer acknowledgement mechanism has been proposed in which the transport layer is considered together to achieve high reliability of data delivery in IEEE 802.15.4/6 LoWPAN networks [16]; an optimal multi-path routing method for wireless sensor networks is taken into account in conjunction with duty-cycle at MAC layer [17]; in network systems allowing for flexible and fine control over network elements, such as SDN (Software Defined Network), cross-layer optimization can be more effective [18; 19]. Although various network scenarios and factors have been considered in previous studies, most of these have several limitations. First, a few studies have considered interactions between OFDMA [8; 9; 10; 11] and MU-MIMO [3; 4; 5; 6; 7]; instead, most have focused on maximizing the performance of only one of these technologies. Several recent studies have addressed the joint use of these within optimization models, but have considered only single-hop networks [12; 13; 14; 15; 20; 21]. In this network model, the effect of interference between nodes is relatively limited, which causes the network performance to be overestimated, and as a result, these approaches may not be applicable to various multi-hop network scenarios. The importance of research on multi-hop networks has been much emphasized thus far. There are a growing number of applications deployed on multi-hop networks, due to the desirable features, such as easy deployment and maintenance, and extended coverage via relay nodes. Above all, the multi-hop network enables a more comprehensive and fundamental understanding of communication technologies, so that the theoretical performance limits and characteristics of the network can be uncovered.