# IEEE 802.11 ax OFDMA Resource Allocation with Frequency-Selective Fading
## 1 Introduction  
Wi-Fi networks have become an integral part of modern life. They are used in many scenarios; the number of hotspots is continuously growing [1], which increases the density of the network and the interference. Recently, the IEEE 802 LAN/MAN standardization committee issued the 802.11 ax [2, 3] amendment to the Wi-Fi standard. In contrast to the previous 802.11 ac, 802.11n amendments that mostly featured the increase in the nominal data rates, 802.11 ax focuses on improving the efficiency at the user layer. The 802.11 ax standard [4] describes many innovative solutions designed to improve the user layer efficiency, such as faster modulation and coding schemes (MCSs), overlapping basic service set management, spatial reuse, new power management solutions, uplink multi-user multiple-input multiple-output (MIMO), and orthogonal frequency division multiple access (OFDMA), which is the focus of this paper. OFDMA allows dividing the available channel by frequency between different users and thus enables several stations (STAs) to transmit or receive data simultaneously. OFDMA enables more flexible usage of channel resources in comparison with the legacy non-OFDMA transmissions. Moreover, for uplink transmissions, OFDMA allows concentrating the STAs' transmission power in narrow frequency sub-bands and, consequently, using faster MCSs. Naturally, the benefits of OFDMA for Wi-Fi depend on the method of splitting the channel resources between the STAs, i.e., on the channel resources scheduler. One of the simplest ways--the legacy approach--is to allocate the entire channel to only one STA at a time. Such an approach might be inefficient when many STAs need to transfer small amounts of data because much channel time is wasted by the transmission overhead, so the schedulers that exploit the possibility of simultaneous transmissions by several STAs should be considered. This paper focuses on uplink OFDMA, but most of the obtained results can be generalized for the simpler downlink case. OFDMA schedulers are well studied in the literature for scenarios of a general wireless communication system [5; 6], where the scheduler is designed as a solution of an optimization problem, e.g., to allocate tones and transmission power to the users in order to maximize the total rate while keeping the total power below some threshold. However, most of such research considers idealistic scenarios when the transmitter can be assigned to an arbitrary set of tones, the transmitter and the receiver know the channel state information (CSI) perfectly, and the transmitter power can be arbitrarily distributed among the tones. Such assumptions and simplifications allow us to find exact solutions to optimization problems, and the computation time required to solve the scheduling problem depends linearly on the number of users, tones, and MCSs [6], but real communication systems impose additional restrictions which make the problems more complex and require new solutions. For example, in LTE, the whole channel is split into several resource blocks of the same size. An LTE base station can allocate an arbitrary set of resource blocks to a user equipment for downlink transmission, but for the uplink transmission, the set of resource blocks shall be contiguous because of the usage of Single-Carrier Frequency-Division Multiple Access (SC-FDMA). The uplink scheduling problem becomes NP-hard because of the requirement [7], so the existing research focuses on designing some heuristic algorithms to maximize selected utility functions. At first sight, these schedulers can be easily applied to 802.11 ax, but in reality, in 802.11 ax, the restrictions are more complicated: we cannot allocate an arbitrary range of 26-tone resource units (RUs) as it is done in 3 GPP LTE. Thus, the schedulers designed for cellular OFDMA systems cannot be directly adapted to additional restrictions of 802.11 ax, and we need to solve the scheduling problem taking into account the peculiarities of 802.11 ax uplink OFDMA.