Second-Order Spectral Statistics for the Power Gain of Wideband Wireless Channels (original) (raw)
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This paper presents a new theory of multipath shape factors that greatly simplifies the description of small-scale fading statistics of a wireless receiver. A method is presented for reducing a multipath channel with arbitrary spatial complexity to three shape factors that have simple intuitive geometrical interpretations. Furthermore, these shape factors are shown to describe the statistics of received signal fluctuations in a fading multipath channel. Analytical expressions for level-crossing rate, average fade duration, envelope autocovariance, and coherence distance are all derived using the new shape factor theory and then applied to several classical examples for comparison. Index Terms-Angle of arrival, diversity, fading channels, mobile communications, multipath channels, propagation, scattering. I. INTRODUCTION T HE motion in space of a wireless receiver operating in a multipath channel results in a communications link that experiences small-scale fading. The term small-scale fading describes the rapid fluctuations of received power level due to small subwavelength changes in receiver position [1]. This effect is due to the constructive and destructive interference of the numerous multipath waves that impinge upon a wireless receiver [2]. The resulting signal strength fluctuations affect, in some way, nearly every aspect of receiver design: dynamic range, equalization, diversity, modulation scheme, and channel and error-correction coding. Due to its random unpredictable nature, small-scale fading is always studied as a stochastic process. Numerous researchers have measured and analyzed the first-order statistics of these processes, which mostly involves the characterization of smallscale fading with a probability density function (PDF) [3]-[5]. The autocorrelation statistics of fading processes or secondorder statistics have also been studied [6], [7]. Second-order statistics include measures of a process such as power spectral density (PSD), level-crossing rate, and average fade duration. Second-order statistics are heavily dependent on the angles-of-arrival of received multipath. Traditionally, most second-order statistics have been studied using an omnidirectional azimuthal propagation model [2]. That is, multipath waves are assumed to arrive at the receiver with equal power