# Robust Wireless Local Area Networks Based on Compressed Sensing
## 2 Overview of the Related Works  
The conventional sampling approaches have traditionally relied on the SNS procedure. The SNS theory demonstrates that analog and digital signals, images, and videos can be exactly recovered from a set of uniformly spaced samples taken at SNS, which is twice the highest frequency in the signal of interest [9; 10; 11]. Therefore, a signal must be sampled at least twice its bandwidth, in order to be represented without error at the receiver side. The traditional approaches based on SNS have two major drawbacks [12; 13; 14]. First, they generate huge intolerable samples for many applications with a large bandwidth. Second, even for low signal bandwidths, they produce a large amount of redundant digital samples. That is why it is desirable to reduce the number of acquired samples in a WLAN by utilizing sparsity. The main motivation is to replace the conventional sampling and reconstruction operation with a general random linear measurement process and an optimization scheme in order to recover the original signal from a small number of random measurements in a WLAN [15]. The CS states that if a real-world signal has a sparse representation in a certain transform base, then it is possible to recover the signal with significantly fewer random samples or measurements [16]. CS is a new approach for the acquisition and recovery of sparse signals that enables a sampling rate significantly below the classical Nyquist rate. This theory states a small number of random linear measurements of compressible signals in a WLAN contain enough information to recover and process the original signal at each nose of a WLAN. Sensing and processing of the signals in a WLAN has traditionally relied on the Shannon Sampling theorem. This theorem states that, given a signal of bandwidth \(\Omega\), it is sufficient to sample at \(2\Omega\) samples per second to ensure faithful representation and reconstruction. The traditional approach has fallen short lately. First, in many signals, \(\Omega\) is so large that the Nyquist rate is unbearable. Second, even for low signal bandwidths, the traditional approach produces a large amount of redundant digital samples, which are costly for wireless communication and severely limit the WLAN's lifetime. Therefore, traditional approaches have two major drawbacks: they generate a huge and intolerable number of samples for applications with large bandwidth and a large amount of redundant digital samples for low bandwidth signals. Three important advantages of a WLAN are (1) the simplicity of its installation; (2) monitoring and management of the network; (3) applying strong security protocols. Installing a wireless LAN system is easy, and can eliminate the need to pull cables through walls and ceilings [17; 18]. The physical architecture of WLAN is quite simple. Basic components of a WLAN are access points (APs) and Network Interface Cards (NICs)/client adapters, Switches, Routers, Bridges, and Repeaters [19; 20]. The use of WLANs is becoming very widespread, and the variety of usage patterns are increasing. Consequently, the factors that affect the end-to-end QoS of WLANs are becoming much more diverse. These factors are not only due to the different applications of WLANs, but also to other attributes of wireless communications, such as the type of access network (e.g., WPANNs, WMANs, and WANs [20]. Network traffic or data traffic in a WLAN is the amount of network packets moving across a wireless network from each wireless node to another wireless node, which provides the load of sampling in the network [21; 22]. WLAN's network traffic is the main component for network traffic measurement, network traffic control, and simulation [23; 24]. The new RTNTM is presented in this paper. In addition, in this paper, the quality of QoS is improved based on a new tomography method that enables us to identify the cause of QoS degradation when such degradation is detected in a WLAN.