Fundamental Limitations in Energy Detection for Spectrum Sensing

Xiao-Li Hu,Pin-Han Ho,Limei Peng

doi:10.3390/jsan7030025

Abstract

A key enabler for Cognitive Radio (CR) is spectrum sensing, which is physically implemented by sensor and actuator networks typically using the popular energy detection method. The threshold of the binary hypothesis for energy detection is generally determined by using the principles of constant false alarm rate (CFAR) or constant detection rate (CDR). The CDR principle guarantees the CR primary users at a designated low level of interferences, which is nonetheless subject to low spectrum usability of secondary users in a given sensing latency. On the other hand, the CFAR principle ensures secondary users’ spectrum utilization at a designated high level, while may nonetheless lead to a high level of interference to the primary users. The paper introduces a novel framework of energy detection for CR spectrum sensing, aiming to initiate a graceful compromise between the two reported principles. The proposed framework takes advantage of the summation of the false alarm probability Pfa from CFAR and the missed detection probability (1−Pd) from CDR, which is further compared with a predetermined confidence level. Optimization presentations for the proposed framework to determine some key parameters are developed and analyzed. We identify two fundamental limitations that appear in spectrum sensing, which further define the relationship among the sample data size for detection, detection time, and signal-to-noise ratio (SNR). We claim that the proposed framework of energy detection yields merits in practical policymaking for detection time and design sample rate on specific channels to achieve better efficiency and less interferences.

Highlights

Cognitive Radio (CR) was first introduced as a promising candidate for dealing with spectrum scarcity in future wireless communications [1]
Under-utilized frequency bands originally allocated to licensed users are freed and become accessible by non-licensed users equipped with CR in an opportunistic manner to maximize the spectrum utilization while minimizing interferences to the primary users
Under the first optimization setting, we show that, with a small signal-to-noise ratio (SNR), the data size M should be larger than a critical value, denoted by Mmin, to guarantee the existence of threshold λ that can satisfy the inequality in Equation (1) under a given confidence level α

Summary

Introduction

Cognitive Radio (CR) was first introduced as a promising candidate for dealing with spectrum scarcity in future wireless communications [1]. Under the first optimization setting, we show that, with a small SNR, the data size M should be larger than a critical value, denoted by Mmin, to guarantee the existence of threshold λ that can satisfy the inequality in Equation (1) under a given confidence level α. Each of the CFAR and CDR principles can general ensure either one of the error probabilities under low level within a limited sensing time, i.e., false alarm probability Pf a for CFAR and missed detection probability (1 − Pd) for CDR, respectively. If it is required to guarantee interference-free to the primary users, the probability of detection should be set high (e.g., Pd = 0.95) and the probability of false alarm should be minimized as much as possible This is called the constant detection rate (CDR) principle [19,22]. It is not surprising to see that some analytic results derived by assuming CFAR based detection can be applied to CDR based detection with minor modifications and vice versa (see, e.g., [19,22])

Thresholds by New Principle

Numerical Experiments

Intuitive Sense of the Solutions for Relevant Optimization Problems

Fundamental Limits of Detection

Conclusions