Goodness of Fit Based Non-parametric Spectrum Sensing for Cognitive Radio

Abstract

The opportunistic spectrum access based on cognitive radio (CR) plays an important role to improve spectral efficiency in wireless communications. To utilize the spectrum efficiently, many spectrum sensing schemes have been proposed in the literature of cognitive radio. For a quick detection of primary user (PU), CR should perform the sensing task at lower number of received observations. In addition to this, the detection performance also depends upon channel conditions and transmitted PU signal. Some sensing schemes have assumed that information of PU and channel state information is known a priori. However, in actual practice, it is difficult to have this a priori information. Therefore, detection of null hypothesis (absence of PU), using goodness of fit (GoF) based non-parametric scheme, is of interest wherein no information about PU and channel is required at CR. In this thesis, we focus on GoF based sensing for achieving better detection performance at lower number of received observations, false alarm probability and signal to noise ratio (SNR). In the category of non-parametric sensing, energy detection (ED) based sensing is the simplest one for spectrum sensing due to its low complexity. To improve the performance of ED sensing, antenna diversity is used. However, the assumption of having perfect information about distribution of noise at CR becomes very crucial at the low SNR of the PU signal. In case of having imperfect variance of noise, the performance of the ED degrades drastically and results in SNR wall. Therefore, it is of interest to develop a non-parametric sensing algorithm, which gives better performance at low SNR with less number of observations and false alarm probabilities. Recently, some GoF based sensing schemes have been proposed in the category of non-parametric sensing. In this kind of sensing, empirical cumulative distribution function (ECDF) is determined from the received observations, denoted by Fn. This ECDF is compared with known CDF of noise (F0) or we test the null hypothesis (Fn=F0). The deviation of ECDF from the known CDF of noise (F0) decides presence or absence of PU. The methods based on this concept are called as Goodness of Fit (GoF) based non-parametric sensing methods. The prevailing methods are Anderson Darling (AD) sensing, Kolmogorov-Smirnov (KS) sensing, Student-t sensing and Order statistics (OS) based sensing. These methods have used all observations to determine the ECDF. However, the distance of the CDF and ECDF is higher especially at the right tail, even at null hypothesis, due to less number of observations. This results in degradation of the performance, especially, at low SNR. To alleviate this problem, in this thesis, a concept of Type-II right censoring is used. In this approach, we drop some observations in the right tail and determine the statistics using retained observations. We call it as Censored Anderson Darling (CAD) sensing scheme. This proposed CAD scheme makes receiver simple and also outperforms the ED sensing and OS sensing at lower values of SNR in receiver operating characteristics (ROC). Further, we have assumed imperfect value of variance of noise in CAD sensing, called as Blind-CAD (B-CAD), and shown the performance. The above-mentioned GoF sensing schemes have assumed PU as a constant signal. However, the performance of AD sensing with different PU signals such as independent and identically distributed (i.i.d) Gaussian and single frequency sine signals is degraded. Hence, we propose a Likelihood Ratio Statistics (LRS-G2) sensing based on a likelihood ratio statistic (G2) using robust normality test, which outperforms all the prevailing GoF based sensing along with ED in various scenarios such as different structures of PU, different channel conditions and unknown variance of noise. Till now, the background noise or thermal noise is modelled using Gaussian distribution. However, in radio channel, it may be non-Gaussian noise (NGN) due to a mixture of man-made and natural electromagnetic sources. Unfortunately, sensing schemes, designed for additive Gaussian noise, do not perform well in NGN environment. Therefore, we assume narrow band interference as NGN at CR which is modelled using Middleton Class-A interference model. The proposed LRS-G2 sensing is also used assuming this Middleton Class-A NGN environment and we show that the effect of Gaussian noise in ROC is worst compared to non-Gaussian noise.