# Low-Computational Extended Orthogonal Matched Filter Structure for Multiuser Detection
## 1 Introduction  
With the advent of the Internet of Things (IoT), industry and people's lives have undergone major changes [1; 2; 3; 4]. The IoT connects various devices, such as sensors, actuators, cars, and unmanned aerial vehicles (UAVs), to the network. In a world where IoT has become the norm, its role as an infrastructure is becoming increasingly important, requiring more reliability and efficiency than ever before. There are also a wide variety of applications that use the IoT. In particular, for applications with limited battery capacity, such as sensors and UAVs, the associated wireless communication systems require low latency, low cost, and low energy consumption [3; 4]. One of the important technologies for realizing an IoT system is a wireless ad hoc network [5; 6; 7; 8; 9]. A wireless ad hoc network is a network consisting of only users who do not need a wireless communication base station. In coming years, vehicle-to-vehicle networks (vehicular ad hoc network: VANET), networks using UAVs and mobile terminals in the event of a disaster, and other networks are expected to be applications of wireless ad hoc networks. To realize a highly reliable wireless ad hoc network, it is essential to introduce a method for cancelling the interference from other usersbecause the network cannot use the transmission power control and interference avoidance techniques of base stations and access points. Our research focuses on a scheme based on code division multiple access (CDMA) [10, 11, 12, 13]. CDMA is well known due to its use in third-generation cellular systems. In it, each user is assigned a different spreading sequence, and the orthogonality of the different sequences is used to identify the user. CDMA also enables simultaneous multiple access and low latency communication [10, 11, 12, 13]. For example, the performances of the CDMA scheme and the orthogonal frequency division multiplexing (OFDM) scheme assuming VANET are evaluated [13]. In addition, it is shown that the CDMA scheme has lower latency communication than the OFDM scheme [13]. However, there are problems with deteriorating performance due to the near-far problem and the increase in the amount of interference as the number of users increases [10, 11, 12, 13]. Another problem is that the spreading sequence of each user is unknown in a wireless ad hoc network [10, 11, 12, 13]. The orthogonal matched filter (OMF) has been applied to solve this problem [14, 15, 16, 17]. The OMF cancels interference by generating and subtracting a replica of the interference signal contained in the received signal [14, 15, 16, 17]. For example, an interference cancellation method using concatenated spreading sequences and a layered OMF to support different period spreading sequences is proposed [14]. A space temporal interference cancellation method for ultra-wideband (UWB) communication systems based on the combination of a tapped delay line array antenna and an OMF is provided since impulse radio UWB does not have a carrier signal [15]. An inter-user and inter-system interference mitigation method using a combination of an orthogonal pulse shape modulation and an OMF detector is proposed [16]. The system aims to detect all signals of users in the same UWB system and to reduce the unknown interference from other UWB systems at the same time. The authors of [17] introduces an interference mitigation method using an OMF based on the modified Hermite polynomials for an impulse radio UWB system, and provides the performance bound and the optimal parameter. An OMF method is suitable for wireless ad hoc networks because it can generate a replica of the interfering signal contained in the received signal, even if the spreading sequence used by the interfering user is unknown. However, if the desired signal-to-interference signal ratio (DIR) is small (i.e., in the case of a near-far problem), the OMF will produce a false replica, resulting in poor performance. Therefore, an extended OMF (EOMF) combining an adaptive array antenna and the OMF are devised [18].