# Cross-Layer Optimization for Heterogeneous MU-MIMO/OFDMA Networks
## 2 Related Work  
Numerous studies have investigated ways of fully using the potential of OFDMA and MU-MIMO under a given set of network resources. In the OFDMA system, a resource block (known as a resource unit in Wi-Fi), composed of a set of subcarriers and with a fixed time length, is used as a basic unit for resource allocation. Many resource block allocation schemes have been proposed to satisfy various network requirements and objectives. [PERSON] et al. consider the joint optimization of the subcarrier and modulation rate in the downlink of wireless mesh networks [8]. Power and subcarrier allocation methods for uplink OFDMA networks, based on the user's channel state, are also proposed in many studies in the literature [9; 10], and the QoE (Quality of Experience) in the application layer is taken into account, in conjunction with the power and subcarrier allocation, in a work by [PERSON] et al. [11]. In MU-MIMO, the maximum number of spatial streams that can theoretically be transmitted or received is the same as the number of antennas of a node, and thus the maximization of DoF use has attracted great attention [3; 4; 5; 6; 7]. The optimal link layer models developed by [PERSON] and [PERSON] et al. [3; 4; 7] carefully capture the conditionsrequired for spatial multiplexing and interference cancellation to maximize the number of spatial streams in the network. [PERSON] et al. investigate joint bandwidth allocation and DoF assignment [5], and [PERSON] et al. explore integrated routing and MIMO link scheduling [6]. However, these studies are limited by the fact that they each focus on optimizing the performance of only one of these two technologies, as mentioned earlier. Several recent works have begun to consider OFDMA and MU-MIMO together [12; 13; 14; 15; 20; 21]. [PERSON] et al. examine subcarrier and power allocation as well as stream selection for downlink networks [12]. Along this line, [PERSON] et al. propose an optimal subcarrier allocation algorithm that maximizes the total system capacity subject to the total transmit power minimization [22]. [PERSON] et al. optimize the transmit power in an uplink cooperative MU-MIMO/OFDMA network by taking into account optimal relay selection [13]. In addition, many resource allocation methods have been proposed for various purposes, for example user-fairness [20], QoS (Quality of Service) [21], and PSNR (Peak Signal-to-Noise Ratio) for video communications [14]. Similar to our work, the recent seminal work by [PERSON] et al. models the interaction from the physical data rate to routing in the optimization for MU-MIMO/OFDMA networks, but a different approach is employed: greedy algorithm development from nonlinear optimization formulation [15]. Although these works consider both OFDMA and MU-MIMO, the main drawback is that they are only applicable to single-hop networks. In this scenario, as mentioned before, the effect of interference is limited, and thus the network performance may be overestimated, meaning that these models are impractical. In addition, the heterogeneity of the nodes has not been sufficiently considered in these approaches; they are based on the assumption of equal available bandwidth [13; 14; 15; 20; 21] or the same number of antennas for the nodes [14], and in particular, the joint use of OFDMA and MU-MIMO is assumed to be always available at all the nodes [13; 14; 15; 20; 21]. Optimal resource allocation in MIMO/OFDMA heterogeneous networks in fact has attracted much attention, and various heterogeneity aspects have been investigated in recent studies. A work by [PERSON] et al. is motivated by the fact that concurrent transmission of data of different transmission times could make a big waste of transmission resources [23]. Different channel conditions and queue lengths of the nodes in downlink MIMO/OFDMA networks are taken into account in a work by [PERSON] [24].