# Fractional Frequency Reuse Optimal SINR Threshold Selection Using NIR and ISODATA
###### Abstract  
A vital part of cellular network evolution has been long-term evolution networks. In these networks, it is important to mitigate inter-cell interference. Fractional frequency re-use has been proposed to address this. The method involves the division of cells into two regions based on a signal-to-interference-plus-noise-ratio threshold value. The inner region adopts a frequency re-use of one (1), while the outer region uses a higher frequency re-use factor. Setting the threshold value is a critical problem addressed in this paper. The proposed approach adapts techniques used in image processing called global-thresholding techniques. The approaches considered are iterative self-organizing data analysis and native integral ratio. Mobile stations in a cell continuously report their signal-to-interference-plus-noise-ratio values to the base station. These reported values are used to determine a threshold which dictates which subscribers fall in the inner and outer regions. The threshold value is periodically updated based on the new reported values over time. Simulations are used to assess the performance using throughput and fairness metrics. By setting the threshold optimally, better throughputs and fairness are then achieved. We concluded that native integral ratio marginally outperformed the iterative self-organizing data analysis method, and it significantly outperformed static fractional frequency reuse techniques.  
f 2  
This popular technique is referred to as global thresholding since a single threshold value is set for the entire image [7]. Global thresholding is desirable for our study since we need to set a single SINR threshold. We adapted pixel values as an input and replaced them with SINR values reported in the cell. The selected threshold value separates the outer and inner region subscribers. Our work considered two methods, i.e., iterative self-organizing data analysis (ISODATA) and native integral ratio (NIR). NIR has been utilized in setting a threshold in handwritten documents that were used for forensic purposes. The pixels forming the handwriting gets categorized into classes of three, i.e., fuzzy, foreground, and background. In between the background and the foreground sits the fuzzy class. The fuzzy pixels are not definitively defined where they exactly fall [8]. ISODATA on the other hand has been used by eye specialists in diagnosing diabetic retinopathy. The process involves segmentation of retinal images of the eye and dividing them into retinal background and blood vessels [9]. Edge throughput and fairness are the performance parameters used to measure the effectiveness of the approaches considered. Poor SINR values are mostly found near the cell edge, and such subscribers tend to suffer dismal throughput. It is important to incorporate fairness as throughput alone can be very misleading. A cellular network might have high throughput; however, the throughput is exclusively enjoyed by just a few subscribers with good SINR values.  
Various frequency allocation schemes have been used widely such as: best channel quality indicator (CQI), proportionally fair (PF), and round robin (RR). Our paper adopted PF scheduler as it forms a great balance between throughput and fairness metric. Round robin would have offered improved fairness. However, equal allocation of resources to subscribers even with poor SINR means that network throughput is reduced. On the other hand, best CQI prioritizes frequency allocation based on signal strength. Only subscribers with the best signal would get the frequency resources at the expense of those with poor signals. This would lead to higher network throughputs but poor fairness.  
The main contribution of this paper is in setting an optimal SINR threshold which is periodically updated. This would yield better throughputs and fairness. The approaches considered were ISODATA and NIR and were compared with static FFR. NIR was found to perform best by achieving better throughput and fairness.