Performance of energy detection in NLOS frequency-selective fading channels

Abstract

A closed-form solution for the bit error probability for an energy detection receiver using OnOff-Keying in a frequency selective multipath fading channel with zero-mean complex-normal distributed fading amplitudes is introduced. Independent and correlated fading are considered. The presented results are valid for for all kinds of frequency selective fading channels, especially ultra wideband channels, where the Gaussian assumption for the decision statistic and the flat fading assumption do not hold. I. IntroductionAnalysis of the detection performance of energy detectors has been started by Urkowitz in 1967 [1] considering a simple AWGN channel model. More recently, Kostylev [2], Digham [3], [4], Herath [5], [6] and Atapattu [7] concentrate on the flat fading channel.These channel models only fit for narrowband systems, where the transmitted signal bandwidth is much smaller than the channel's coherence bandwidth. A wideband system, for example an ultra-wideband (UWB) receiver, uses an extreme high bandwidth, collects many different reflections and requires a more general model for channel fading: the frequency-selective fading (FSF). The product of integration time and channel bandwidth equals equals the number of signal paths distinguishable by the receiver.An independent decay coefficient is assigned to each signal path. The vector of those decay coefficients, sorted by path arrival time, represents the samples of the channel impulse response.Given free choice of the distribution of each decay coefficient, one fit this channel model to observed systems with arbitrary power spectrum. Thus this fading model is called frequency-selective.Because of the simple design of energy detection receivers, this method has been used in cognitive radio systems to detect spectrum holes [8], [9] and to transmit data for different low and high data rate UWB receivers [10], [11] including location and tracking [12].In this paper we focus on UWB energy detection receivers in FSF channels. We do not use the Gaussian assumption to simplify the decision statistics [13] of the energy detection receiver, because we do not want to limit system parameters in order to fulfil the central limit theorem and we do not limit our result to flat fading channels.

MIRA – Physical Layer Optimisation for the Multiband Impulse Radio UWB Architecture

“…Using the function Θ D (52), the average SEP in a frequency selective fading channel can be expressed in closed form [3]:…”