## 1 Introduction  
Beamforming techniques are gaining an increasing research interest in recent years due to the growth of Internet of Things (IoT) applications that require establishing connections for long distances among sensors and a remote base station [1]. The popularity of these applications stems from the demand of increasing throughput accompanied by decreasing size of electronic devices [2]. This requires that all objects or devices in the IoT to be equipped with directional antennas which form a virtual antenna array. Due to a variety of reasons including their small size, low cost, ease of deployment (deterministic or random) and simplified transmission-related protocols in terms of medium access channels and routing [3], it has been found that the antenna array is a key technology for a broad spectrum of future IoT applications ranging from weather forecasting or complex industrial plant monitoring to military surveillance [4]. The next generation of Wireless Sensor Networks (WSNs) target the design of sensors systems that satisfy the requirements of IoT applications taking into consideration recent advancement of beamforming technology in 5G wireless systems, whereby the omnidirectional antenna may either be replaced by directional ones or can work in tandem with the same modes [5]. Although omnidirectional antennas lead to poor network performance due to interference and short transmission range, previous studies investigated network connectivity using omnidirectional antennas [6]. However, directional antennas have become mandatory in future generations of WSNs requiring high network connectivity [7]. Employing a directional antenna model may be very complicated when optimal bounds of network connectivity are sought for specific applications. Such applications may require low-power sensors with simple hardware which are randomly deployed over an area of interest. Furthermore, several IoT applications are required to transmit the acquired data over long distance using multihop transmission resources available only at sensors. Therefore, this can be costly for battery-powered sensors. Hence, one major problem is to obtain optimal bounds of network connectivity between battery-powered sensors and the intended base station which might be allocated far away from the transmission range of sensors. In other words, directional antennas are sensitive in terms of directional alignment and thus every sensor must steer its mainbeam to each other for a successful connectivity [8]. There are several challenges that must be considered when a model is developed in the realm of virtual beamforming in IoT environments. For example, each sensor must connect with others as well as with the wireless devices involved in the IoT environment that may use different technologies for communicating with sensors. Generally, coexistence is a severe challenge in the IoT model, since the devices that are trying to communicate may interfere with each other resulting in data loss, rendering the sensors useless. Meanwhile, there is a substantial work on coexistence for collaborative beamforming; the forecast includes thousands of devices in a narrow range. These applications in IoT also impose challenging requirements on manufacturing as far as creating large-scale deployments is concerned. To overcome this problem, Collaborative Beamforming (CB) can be used for reliable communication over long multihop distance. CB is considered to be a branch of cooperative communication where randomly located sensors cooperate with each other to form a virtual antenna array. This collaboration is presented as a set of sensors operating in half-duplex mode forming an antenna array where their input signals are multiplied with properly selected complex beamforming weights. CB extends the transmission range of collaborative sensors by using sensors which jointly transmit to generate a coherent directive beam for transmission to a given base station.