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This paper presents the statistical properties of the vehicle-to-vehicle Nakagami-Hoyt (Nakagami-q) channel model under non-isotropic condition. The spatial time correlation function (STCF), the power spectral density (PSD), squared time autocorrelation function (SQCF), 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 nonstationary having nonomnidirectional antennas. A simulator that uses the inverse-fast-fourier-transform- (IFFT-) based computation method is designed for this model. The simulator and analytical results are compared.

With passage of time, applications of wireless communication, their usefulness, and reliability are increasing. The recent applications where wireless communications is extensively used include wireless local area network (WLAN), multimedia messaging cellular telephone systems, satellite systems, femtocells, Bluetooth, and Zigbee devices. The wireless devices are also extensively used in in-car security systems equipment, home television systems private mobile systems, and so forth. In the conventional wireless communication systems, all the mobile stations communicate with each other via fixed base stations which are normally placed at elevated locations. Since mobile station is likely to be surrounded by objects having different shapes and orientations, the direct propagation path may not always present, and communication results from scattering that occurs near the mobile station. The channel between the transmitter and receiver is usually multipath fading channel; the signal fading occurs due to terminal mobility.

An in-depth knowledge leads to an accurate model of mobile propagation channel which is essential for a simulator design that provides 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 [

Over the past decade, the research has been focused on vehicle-to-vehicle (V2V) or mobile-to-mobile (M2M) communication systems where no base station is present and both the transmitter

During the past decade, a large number of research projects have been done on V2V communications [

A small number of works have used non-Rayleigh fading channel models. The second order statistics of Nakagami-Hoyt channel have been derived in [

In many real world scenarios, nonisotropic scattering is often experienced by both the mobile transmitter and receiver. It has been shown in [

In this paper, a novel V2V Nakagami-Hoyt channel model under non-isotropic scattering condition is proposed. The existing channel models [

The remainder of this paper is organized as follows. Section

The Nakagami-Hoyt (also known as

In this section, we briefly describe the proposed channel model along with its usefulness and derive the first and second order statistics of Hoyt fading channel under the assumptions that the channel is narrow band, and the receiver and transmitter are moving with velocities

A Hoyt process,

The parameters

Reference [

Assuming that

Von Mises PDF showing nonisotropic scattering.

The measurements made in the rural environment demonstrated that the channel is more accurately modeled only when the variance of the in-phase and the quadrature components are not identical [

The channel models described previously do not consider the following two scenarios simultaneously. First, when the antennas are not omnidirectional, and scatterers around the receiver and transmitter are not uniformly distributed. This is normally the case in V2V communications when transmit and receive antennas are present inside the vehicles. Second, when the fading is severe and the channel gains are no longer Rayleigh ie

The probability density function of the envelope

Since the pdfs are independent of time so they will remain independent for V2V Nakagami-Hoyt channels. The mean

In this section, The STCF, PSD, SQCF, LCR and ADF of the Nakagami-Hoyt V2V fading process are derived. These quantities are useful in estimation of burst error, mobile velocity and Markov modeling of fading channels [

For derivation of spatial time correlation function of

The spatial time correlation function of the envelope is given by [

The time correlation function is obtained by setting

The power spectral density

For isotropic scattering, the power spectral density is obtained by taking the Fourier transform of (

Now, for the case

The squared time autocorrelation function is used in computation of carrier to noise ratio (CNR). For the proposed channel, it is defined as

The level crossing rate of the process

The average duration of fade of a signal is defined as average duration of time for which the signal

The simulator described in this paper uses Smith spectrum method used in [

Input number of frequency samples

Specify maximum doppler frequency of the receiver

Specify the value of parameter

Specify the value of

Generate two

Generate

The frequency spacing between the adjacent spectral lines is given by

The time resolution is given by

Multiply the in-phase and quadrature components by

Quadrature component will yield

The root of the sum of squared envelop of both will generate random variable Nakagami Hoyt distribution for the given value of

The phase distribution is obtained by using the phase random variable

Block diagram of IFFT based simulator.

The simulation was run with the following parameters, carrier frequency

Output of the hoyt simulator.

Hoyt amplitude PDF plot

Hoyt phase PDF plot

The power spectral density plots for

PSD plot for

The autocorrelation plots for

Time autocorrelation function of real part of envelope.

Time Autocorrelation function of Real part of Envelope for

The normalized squared autocorrelation plots of real part for

Squared Autocorrelation function of Real part for

The LCR and ADF of envelop for

Level crossing rates for

Level crossing rates for

Level crossing rates for

Average duration of fade for

Average duration of fade for

Average duration of fade for

The mean square error (MSE) of the time autocorrelation function is given by

Mean square error of autocorrelation function

The second order statistical properties for vehicle to vehicle Nakagami-Hoyt channels, under the non-isotropic scattering conditions at both the transmitter and receiver, have been developed. These include expressions for space time correlation function, power spectral density, squared time autocorrelation, level crossing rates, and average duration of fade. The Nakagami-Hoyt V2V simulator has also been developed to verify the above mentioned theoretical expressions. It has been found that the theoretical results match closely with the simulated data verifying the validity of the model.

The spatial time correlation function is given by

Also, assuming

The values of

Similarly, we get

For the case of isotropic scattering (

The squared time autocorrelation function is given by (

The authors would like to acknowledge the support provided by King Abdulaziz City for Science and Technology (KACST) through the Science and Technology Unit at King Fahd University of Petroleum and Minerals (KFUPM) for funding this work through Project no. NSTP08-ELEC42-4 as part of the National Science, Technology and Innovation Plan (NSTIP).