Unified Approach for Energy Detection of Unknown Deterministic Signal in Cognitive Radio Over Fading Channels

Abstract

Detection of an unknown deterministic signal by using an energy detector is of promising for cognitive radio networks. In this paper, a new approach is proposed to analyze the performance of the energy detector. It is based on the contour integral representation of the Marcum-Q function and the use of the moment generating function (MGF) of the signal-to-noise ratio (SNR). A new decision variable is constructed for the case of maximal ratio combining (MRC) reception. With its help and the MGF based approach, the performance of the MRC energy detector over i.i.d. Rician fading channels is analyzed. This case is intractable with the conventional probability density function (PDF) based approach. Further the detection probability of MRC combined energy detector over Nakagami-m fading branches is derived. The simulation results are presented to support the developed MGF based method, decision variable formulation and derivations. The detector performance is evaluated over different fading and diversity parameters with the help of numerical and simulation examples. I. INTRODUCTION Cognitive radio technology allows unlicensed users (sec- ondary users) to dynamically use unoccupied free spectrum bands of primary users (licensed users), while avoiding in- terference to primary users. Energy detection can be used to explore the presence of primary user transmissions and hence to identify the available spectrum holes. When using this technique, the energy detector of the secondary user treats the received primary user transmission as an unknown deterministic signal. Hence, secondary users do not requires unauthorized, irrelevant details of the primary transmissions. Due to this application, the performance of the energy detector using diversity reception techniques and over various wireless fading environments is of interest. The technique of detecting an unknown deterministic signal by using an energy detector is introduced in (1). It is shown that the detection problem is a test of binary hypotheses and statistics of the decision variable is chi-square distributed, irre- spective of whether the process model is lowpass or bandpass. Kostylev (2) extends the formulation to fading channels. In his work, average detection (Pd) and false alarm (Pf ) probabilities over Rayleigh, Rician and Nakagami-m fading channels are presented. But the Nakagami-m channel result is limited to an integral form expression. In (3) Nakagami-m and Rician fading channels are considered. But the derivation of Nakagami-m is restricted to integer values of the shape parameter (m) while the result of Rician fading channel is limited to unity time bandwidth product (u) in the decision variable. Maximal ratio, selection and switch and stay diversity detectors are analyzed over i.i.d. Rayleigh fading channels in (3). Expressions of Pd over i.i.d. and correlated Rayleigh fading channels with square-law combining is derived in