Int. J. Electron. Commun. (AEÜ) 67 (2013) 549–556 Contents lists available at SciVerse ScienceDirect International Journal of Electronics and Communications (AEÜ) jo ur nal ho me page: www.elsevier.com/locate/aeue On the second order statistics of non-isotropic Nakagami Hoyt mobile to mobile fading channel Muhammad I. Akram ∗ , Asrar U.H. Sheikh Electrical Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia a r t i c l e i n f o Article history: Received 13 May 2011 Accepted 5 December 2012 Keywords: Nakagami Hoyt model Average duration of fade Level crossing rate Space time correlation function Power spectral density Simulator a b s t r a c t This paper presents second order statistical properties of the mobile to mobile Nakagami Hoyt channel model under non-isotropic condition. The spatial-time correlation function, the power spectral density (PSD), level crossing rate (LCR) and the average duration of fade (ADF) of the Nakagami Hoyt channel have been derived under the assumption that both the transmitter and receiver are non-stationary having non-omnidirectional antennas. Design of simulator using the Inverse Fast Fourier Transform (IFFT) based computation method has been applied for this model. The simulator and analytical results have been corroborated. © 2012 Elsevier GmbH. All rights reserved. 1. Introduction A thorough knowledge and accurate models of mobile propa- gation channels are essential for a simulator design, which will provide dependable performance results. Over the past many years several mobile channel models have been proposed for links between fixed base station and mobile station. These include short term fading models like the well-known Rayleigh, Rice [1], Hoyt [2], Nakagami [3] and Weibull [4]. For long term fading model log- normal distribution has been used [5,6]. Several composite fading models (Nakagami-lognormal [3], Suzuki [7] and Rice-lognormal [8]) combining the effects of short and long term fading have also been proposed. Recently, the research is focused on mobile to mobile (M2M) communication systems where both the base station (transmitter) and the mobile station (receiver) are in motion. The M2M com- munication finds applications in mobile ad-hoc wireless networks, intelligent highway systems, emergency, military and security vehicles. The statistical model for mobile to mobile communica- tion was first developed by Akki and Haber [9] with the statistical properties described in [10]. Based on the work of [10], many M2M simulators have been designed and implemented. Ref. [11] pre- sented a discrete line spectrum based approach to simulate the channel. The work in [12] is based on sum of sinusoids (SOS) ∗ Corresponding author. Tel.: +966 38605846 E-mail address: miakram@kfupm.edu.sa (M.I. Akram). approach for simulator design. In [13] the simulation of MIMO M2M is presented. The simulator proposed in [14] is based on Kullback–Leibler divergence which is compared with IFFT based approach of simulator design. Ref. [15] uses Gaussian quadrature rules for simulator design. Ref. [16] proposes an efficient sum of sinusoids (SOS) based approach for M2M simulator design. All the simulator design approaches mentioned above are restricted to M2M Rayleigh fading channel only. Few works have been done for non-Rayleigh fading channels as well. The second order statistics of Nakagami Hoyt channel has been derived in [17]. Ref. [18] derives the statistical properties of double Nakagami Hoyt channel. In many real world scenarios, however, non-isotropic scattering is often experienced by the mobile transmitter and the mobile receiver. It has been shown in [19–21] that in dense urban and indoor environments, non-isotropic scattering around the mobile station exists. Ref. [22] derives the second order statistics of M2M Ricean fading channel under non-isotropic conditions and compares the theoretical results with the measured data. Ref. [23] presented M2M model for Rayleigh fading under non-isotropic condition. To the best of authors’ knowledge no work has been done on M2M Nakagami-Hoyt channel and its simulation. This paper gives the second order statistics of mobile to mobile Nakagami- Hoyt channel under non-isotropic condition. It covers the isotropic scattering as its special case. Many non-uniform distributions have been discussed for Angle of Arrival (AoA) and Angle of Departure (AoD). These include Gaussian, Laplacian, quadratic and Von Misses distributions. Von Misses distribution (assumed in this paper), a generic case described in [19], covers the other distributions (Gaussian, Laplacian, cosine and uniform distributions) as its 1434-8411/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.aeue.2012.12.003