Progress In Electromagnetics Research Symposium Proceedings, Stockholm, Sweden, Aug. 12-15, 2013 355

Some Insights on the Amount of Fading in Radio Channels Hassan El-Sallabi1 , Khalid Qaraqe1 , and Erchin Serpedin2 1

Wireless Communications Laboratory, Electrical Engineering Department Texas A&M University at Qatar, Qatar 2 Electrical and Computer Engineering Department, Texas A&M University College Station, TX, USA

Abstract— In this work we present an experimental investigation on the amount of fading as a measure of fading severity in radio channels. The presented results are for indoor environments and assume a multi-dimensional ray based model. The amount of fading of Rayleigh channel, which is equal to one, is used as a reference to know if the channel is less or more severely affected than Rayleigh radio channel. For the tested environment, it has been found that placing the antenna of indoor cell at a height close to the pedestrian height leads to less fading than placing it on the ceiling and at this preferred height. The amount of fading for line of sight propagation conditions exhibits higher correlation with coherence time than that corresponding to non-line of sight propagation. 1. INTRODUCTION

Wireless radio channels are known of their fading phenomena, where received signal fluctuates randomly due to the multipath arrival of radio signal at the receiver point. Fading phenomena can be fast fading and slow fading. Slow fading describes the signal variation slowly over tenths of wavelength distance. It is usually modeled as lognormal distribution. The fast fading results due to the phase difference of multipath components and user equipment (UE) speed defined by locations of scatterers and their electrical parameters as well as the position and antenna height of the transmitter and receiver and their antenna patterns. The geometry of the propagation scenarios defines the angular and delay domain properties of the channel. These properties are directly related to fast fading. The fast fading has been modeled in literature with many models based on the existence or non-existence of the line of sight (LOS) component. The widely known models are the Rayleigh model for non-line of sight (NLOS) component and Rician model when the LOS component exists. There are already many models that describe the fading channel subject to different fading patterns. A survey of various propagation models for mobile communications is presented in [1]. A real channel could be a combination of scenarios and propagation conditions described by different models. Instead of describing the channel with a particular model, we simulate the channel with a physics based channel model that represents how the signal might propagate in a multipath environment. The severity of fading is described in this work by a measure called the amount of fading. This measure is used to characterize different models that describe the fading conditions in radio channels. In this work we present some detailed insights on characterizing the amount of fading as a measure of fading severity in radio channels. 2. AMOUNT OF FADING

Due to the fading nature of radio channels, which results in signal fluctuations, diversity methods were introduced to improve performance of communications system. The focus of these methods is to reduce the variability of the received signal power to overcome the unreliability of the communication system due to poor fading conditions. Average signal-to-noise power ratio (SNR) at diversity combiner output ignores the variation of the received SNR, and presents the diversity benefit without increasing the transmit power. In order to study the impact of SNR variance, a measure that accounts its variability is needed This measure has to account for higher moments of SNR at the diversity combiner output. The selected measure of severity of fading in this work is the amount of fading (AF), which can be computed using the first and second central moments of SNRs at diversity output. The AF is defined in [2] as © ª var α2 AF = E {α2 }2 where α is the instantaneous fading amplitude of a complex fading channel, E{·} and var{·} are the statistical mean and variance, respectively. To quantify the probability distribution of fading, it

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is mentioned in [2] that for Nakagami-m fading distribution of α, AF = 1/m, whose range is [0, 2]. When m = ∞, AF = 0, which corresponds to the situation of “no fading”. When m = 1, AF = 1, which corresponds to Rayleigh fading, and when m = 0.5, AF = 2, which corresponds to the onesided Gaussian distribution and the severest fading assumed by the Nakagami-m fading channel. The AF has been generalized in [3] to describe the performance of the diversity combing system over correlated lognormal channels. The inverse of AF might be considered as diversity factor. As noted in [4], the amount of fading relates directly with diversity order of the symbol error probability for Nakagami-m fading distribution and is not linked directly to the average symbol error probability of Nakagami-q (Hoyt), Nakagami-n (Rice) fading distributions. The AF is used to quantify the level of fading experienced at the output of a multiple-input multiple-output (MIMO) system in [5]. In [6], different formulations for AF for different fading distributions are given for Nakagami-q (Hoyt), Nakagami-n (Rice), Nakagami-m, Weibull, and log-normal shadowing fading distributions. 3. CHANNEL MODEL

The investigation of this work is simulation based using multi-ray an RF multi-dimensional propagation model. The RF model is for indoor cubical shaped environments that can be used to represent a corridor, office, lecture hall, convention center, etc., as a function of the indoor environment geometry. The model formulation in its essence is very similar to that presented in [7]. The input parameters of the model include operating frequency, system bandwidth, signal polarization, number of wall, floor and ceiling reflections, and electrical properties of reflecting surfaces. The ray parameters are derived from the environment geometry using electromagnetic image theory and vector mathematical operations to extract the needed path length and angles for every ray in terms of angle of arrivals and departures as well as surface reflection angles. Each ray is defined by its parameters such as its path length, azimuthal and co-elevation angle of arrival, azimuthal and co-elevation angle of departure. Its amplitude is computed with electromagnetic formulations for free space loss and loss due to interaction with scatterers in the environment. The interaction with scatterers takes place in different propagation mechanisms: reflection, transmission, diffraction and scattering. In this work only the reflection propagation mechanism is included. Different coefficients can be used for interaction losses that depend on waveform, plane wave, cylindrical wave or spherical wave. The most commonly used reflection coefficient is the Fresnel plane wave reflection coefficient, which is valid for flat surfaces and is a function of the incidence angle and the electrical properties of the reflecting surface. The received signal is obtained as a sum of multi-ray components as vector superposition of N individual rays, and it can be represented as follows: XN h (t) = An δ (t − τn ) e−jk(rn −V·Ψn t) , n=1

where k is the wave number expressed as k = 2π λ , λ is the wavelength of operating frequency, V denotes the velocity vector of the UE, which is assumed at the receiver in this notation, and defined by V = vx ~x + vy ~y + vz ~z and Ψn stands forthearrival direction vector defined for ray n as Ψn = cos (φn ) sin (θn ) ~x + sin (φn ) sin (θn ) ~y + cos(θn )~z where φn represents the horizontal arrival angle relative to the x-axis of ray n, θn denotes the elevation arrival angle relative to the z-axis of ray n, and rn is the path length of ray n defined as: rn =

Pn X

dn,p

p=1

Notation dn,p denotes the distance traversed by the specular wave between the (p − 1) and p-th boundary intersections and the complex amplitude An is defined as An =

Yn λ p Γp e−jkdn,p . Gtx (ϕn , ϑn ) Grx (φn , θn ) p=1 4πrn

Parameter Γp denotes the surface reflection coefficient for the p-th wave-interface intersection, while λ the term 4πr represents the free space path loss that accounts for the wave spreading loss, and n finally, Gtx (ϕn , ϑn ), Grx (φn , θn ) are the transmitter and receiver antenna gain, respectively.

Progress In Electromagnetics Research Symposium Proceedings, Stockholm, Sweden, Aug. 12-15, 2013 357 4. NUMERICAL RESULTS

The simulated results represent a lecture hall of a convention center indoor environment. The simulation results show the impact of antenna height and operating frequency of indoor cell The receiver antenna height was 1.7 m. The lecture hall room dimensions are as follows: width is equal to 10 m, length is 15 m and height is 10 m. The receiver speed was 3 km/hr which is defined as the pedestrian speed in 3GPP standard. The fast walking speed of 10 km/hr is tested for AF comparison. Reflecting surfaces have permittivity of 5 and conductivity of 0.02. Rays with surface reflection order of up to 6 are included in addition to the line of sight component. This reflection order is per surface. This means that when the signal bounces between two walls, then rays of up to 12 reflection order could result and so on for rays bouncing between three surfaces would result in rays of up to 18 reflection order. In order to study the impact of operating frequency on the amount of fading, two different frequency ranges have been tested 0.9 GHz and 1.8 GHz. These bands represent cellular and personal communications (PCs) bands The simulated temporal range is for 2 seconds for every spatial location. The temporal sampling rate is 26000 samples/sec The simulated spatial range is 5 m with a spatial resolution of 2.5 cm. Antenna polarization is vertical. The three dimensional antenna pattern is the well-known omnidirectional pattern, where signals propagating in the xy-plane experience no antenna loss irrespective of azimuthal angles but the attenuation takes place in the non-horizontal plane propagation, where the amount of antenna loss depends on the elevation angles. The antenna loss increases as the elevation angle of the arrived signal gets away from the 90-degrees plane (i.e., xy-plane). The minimum value of AF is zero, which means no signal variation. For different channels of similar mean value, the AF is a good indicator for comparing the severity of fading between them. In order to get the feeling of the AF numbers, Figure 1 shows the cumulative distribution function of the fading patterns for Rayleigh, double Rayleigh and triple Rayleigh with their corresponding AF values as 1, 1.73, and 2.56, respectively. The double Rayleigh fading exhibits double severity of fading than the single Rayleigh, which means the channel varies twice faster. The Rayleigh fading channel is just one type of fading channels. Our model is a multi-ray model, whose ray parameters change with the movement of mobile receiver environment dimensions and communication link setup such as antenna heights, polarizations, etc Rate of changes of ray parameters depend on mobility velocity. This work investigated the impact of indoor cell antenna height. Two antenna heights have been tested: 2 m representing a similar height to receiver and 9.9 m (presented as a 10 m height in the figures below), which represents an antenna mounted on the ceiling. Figure 2 depicts the empirical cumulative distribution function of AF computed from channel traces for 900 MHz and 1800 MHz frequency ranges generated with the channel model described earlier. The AF ranges from slightly greater than zero till AF is slightly greater than 2. This indicates that the channel does not follow one fading model and the severity of channel fading varies too. Figure 2 shows that for this particular tested line of sight propagation scenario, placing antenna on ceiling causes more severe fading than placing the antenna at a height close to the receiver antenna height. It can be read from the figure that when the transmitter antenna height is 2 m for both frequencies, 95% of channel traces are less severe than Rayleigh fading, while when the transmitter antenna height is

Figure 1: Different Rayleigh fading with their corresponding AF values.

Figure 2: CDF of AF for moving MS with different transmitter antenna heights, f = 900 MHz.

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10 m, about 90% and 85% of channel traces are subject to less fading severity than Rayleigh fading for 900 MHz and 1800 MHz frequency ranges, respectively. Furthermore, channel traces of both antenna heights have very low percentage of fading severity greater than double-Rayleigh fading. Samples of received signal strength due to different channel traces with different AF values for the tested frequency ranges are depicted in Figure 3. The presented AF values are well correlated with the fading patterns of the received signal fading profile. Figure 4 shows a comparison between the AF of LOS and NLOS propagation scenarios. The channel environment and communications link are the same. The only difference is the blocking LOS rays, which are not considered in the computation of channel traces in the NLOS propagation conditions. It is pretty clear that the AF for NLOS is higher than that of LOS as expected. The medians of AF for LOS at 900 MHz and 1800 MHz are 0.28 and 0.39 compared to the corresponding values of NLOS, which are 0.36 and 0.55, respectively. The AF of fading channel traces is well correlated with the coherence time of the channel. The computed correlation value of coherence time is 0.5. Figure 5 shows a scatter plot of coherence time of simulated channel traces with their AF for the LOS case with indoor cell antenna height of 10 m and frequency range of 1800 MHz. Table 1 shows the corresponding correlation values for LOS and NLOS propagation conditions for the two tested antenna heights and frequency ranges. Figure 6 shows the impact of mobile speed on AF for two different speeds 3 km/hr and 10 km/hr for indoor cells at a frequency range of 900 MHz and two different indoor cell antenna heights. The severe fading pattern is observed at higher speeds when the antenna of the indoor cell is placed very close to the ceiling. The relative increase in the median of AF for a low antenna height with the increase of mobile speed is higher than that of a higher antenna height.

Figure 3: Impact of frequency range on AF.

Figure 4: CDF of AF for moving MS with indoor cell antenna height of 2 m for LOS and NLOS.

Figure 5: Coherence time versus amount of fading.

Figure 6: Samples of received signals for different channel traces with two different values of AF.

Progress In Electromagnetics Research Symposium Proceedings, Stockholm, Sweden, Aug. 12-15, 2013 359 Table 1: Correlation values between AF and coherence time. Frequency (MHz) Antenna Height (m) LOS NLOS

900 2 −0.81 −0.82

10 −0.62 −0.65

1800 2 −0.82 −0.75

10 −0.65 −0.54

5. CONCLUSION

Amount of fading is a parameter that describes the severity of channel fading conditions. Physics based modeling shows that the channel presents variable AF, which means that there is not a single statistical model such as Rayleigh but the latter represents only one possible case of channel realizations. According to the simulated environment, placing the antenna of the indoor cell on the ceiling causes more fading than if it is on a height close to the pedestrian height. As expected the higher operating frequency range and higher mobile speed lead to higher AF. The AF corresponding to LOS propagation conditions presents higher correlation with the coherence time than that of NLOS. ACKNOWLEDGMENT

This publication was made possible by NPRP grant #: NPRP 09-341-2-128 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors. REFERENCES

1. Sarkar, T. K., et al., “A survey of various propagation models for mobile communication,” IEEE Antennas and Propagation Magazine, Vol. 45, No. 3, 51–82, Jun. 2003. 2. Charash, U., “Reception through Nakagami multipath channels with random delays,” IEEE Trans. on Commun., Vol. 27, No. 4, 657–670, Apr. 1979. 3. Alouini, M. and M. Simon, “Dual diversity over log-normal fading channels,” Proc. IEEE Int. Conf. Commun., ICC’01, Helsinki, Finland, Jun. 2001. 4. Wang, Z. and G. B. Giannakis, “A simple and general parameterization quantifying performance in fading channels,” IEEE Trans. on Commun., Vol. 51, No. 8, 1389–1398, Aug. 2003. 5. Holter, B. and G. E. Øien, “On the amount of fading in MIMO diversity systems,” IEEE Trans. on Wireless Commun., Vol. 4, No. 5, 2498–2507, Sep. 2005. 6. Simon, M. K. and M. S. Alouini, Digital Communication over Fading Channels, 2nd Edition, Wiley, New York, 2005. 7. Malik, W. Q., C. J. Stevens, and D. J. Edwards, “Spatiotemporal ultrawideband indoor propagation modelling by reduced complexity geometric optics,” IET Commun., Vol. 1, No. 4, 751–759, 2007.