# Cross-Layer Optimization for Heterogeneous MU-MIMO/OFDMA Networks
## 1 Introduction
Secondly, even though the types and capabilities of network devices are becoming more diverse, this heterogeneity has not been sufficiently considered in relation to optimization; the same available bandwidth is assumed [13; 14; 15; 20; 21], or even the same number of antennas of nodes [14], and in particular, the joint use of OFDMA and MU-MIMO is generally assumed to be always available at all the nodes [13; 14; 15; 20; 21]. These assumptions may have the advantage of simplifying the model, but they are somewhat different from the conditions in actual networks; for example, although OFDMA has now been introduced to Wi-Fi systems through IEEE 802.11 ax [1], the joint use of MU-MIMO and OFDMA is not allowed, and most legacy devices, including IoT (Internet of Things) products, are unable to operate with a wide band of 160 MHz and large number of antennas, due to the form factor and the processing power required. Regardless of how quickly high-capacity devices that fully use both technologies can penetrate the market, they will co-exist with low-capacity devices for a long time, and this heterogeneity should therefore be considered to allow for more practical and realistic resource allocation. In this paper, we propose a cross-layer optimization framework that considers both OFDMA and MU-MIMO in heterogeneous wireless networks. Our approach assumes not only that nodes have different capabilities in terms of bandwidth and the number of antennas, but also supports practical use cases in which nodes can operate with either OFDMA or MU-MIMO, or both at the same time. The resultant resource allocation allows these technologies to be appropriately combined and exploited in a given network. In our optimization model, we carefully consider the interactions between the key elements of the physical layer to the network layer. In particular, we consider multi-hop networks,and capture the complicated interference relationships between nodes as well as multi-path routing via multi-user transmissions. We formulate the proposed model as a Mixed Integer Linear Programming (MILP) problem. Since there are a few devices that can support the combined use of OFDMA and MU-MIMO, we first model a case in which each node can selectively use either OFDMA or MU-MIMO. Next, we demonstrate that this model can be easily extended to scenarios where OFDMA and MU-MIMO are jointly used. As reported in many cross-layer optimization studies [9; 10; 12; 13; 14; 15], one challenging issue when designing the model relates to the tightly coupled variables between layers, which are inherently nonlinear. We transform all the constraints of this nonlinear relationship into linear constraints, meaning that integer programming algorithms such as branch-and-bound can be easily applied to our model. In addition, we show that a little extra analysis of the given network can be of great help in reducing the size of the problem and thus making it more feasible. As a case study, we apply the proposed model to sum-rate maximization and max-min fair optimization, and verify through MATLAB numerical evaluations that it can take appropriate advantage of each technology for a given set of network resources. We also analyze how the joint use of MU-MIMO and OFDMA affects the results of resource allocation and the overall performance. From the optimization results, we can observe that when the two technologies are used in combination, more multi-user transmissions are enabled thanks to flexible resource allocation, hence giving better use of the link capacity. The main contributions of this paper can be summarized as follows:  
1. We propose a cross-layer optimization framework for heterogeneous MU-MIMO/OFDMA multi-hop networks. Our model takes into account the heterogeneity in the node capabilities in terms of the bandwidth, the number of antennas, and the modes of transmission. Moreover, the interactions between the key elements of the physical layer to the network layer for multi-hop networks are considered in the model. 2.