Statistical Modeling, Simulation, and Experimental Verification of Wideband Indoor Mobile Radio Channels

This paper focuses on the modeling, simulation, and experimental verification of wideband single-input single-output (SISO) mobile fading channels for indoor propagation environments. The indoor reference channel model is derived from a geometrical rectangle scattering model, which consists of an infinite number of scatterers. It is assumed that the scatterers are exponentially distributed over the two-dimensional (2D) horizontal plane of a rectangular room. Analytical expressions are derived for the probability density function (PDF) of the angle of arrival (AOA), the PDF of the propagation path length, the power delay profile (PDP), and the frequency correlation function (FCF). An efficient sum-of-cisoids (SOC) channel simulator is derived from the nonrealizable reference model by employing the SOC principle. It is shown that the SOC channel simulator approximates closely the reference model with respect to the FCF. The SOC channel simulator enables the performance evaluation of wideband indoor wireless communication systems with reduced realization expenditure. Moreover, the rationality and usefulness of the derived indoor channel model is confirmed by various measurements at 2.4, 5, and 60GHz.


Introduction
Indoor wireless communications has attracted considerable attention in recent years due to a broad set of emerging indoor services offered by personal communication systems [1,2], wireless local area networks [3,4], and wireless private branch exchange networks [5].The interest in indoor wireless communications is growing especially when optical wireless communication techniques [6,7] are applied to indoor deployment scenarios.Numerous researches on modulation techniques [8], multiple access techniques [9], and propagation modeling [10] have been carried out for indoor optical wireless communications.In order to design an efficient indoor wireless communication system and to predict accurately its system performance, a prerequisite is to develop an appropriate indoor channel model that describes realistically the underlying propagation conditions.
To improve the indoor channel characterization and modeling, numerous measurement campaigns have been conducted in a variety of indoor environments, such as offices, corridors, buildings, and factory halls.Measurement results have been reported in the literature for various frequency bands, including the frequency bands at 900 MHz [11][12][13], 1.5 GHz [14,15], 2.4 GHz [16], 4-5.5 GHz [17][18][19], 17-18 GHz [18,20], and 60 GHz [21][22][23][24].Based on measurement results, several empirical statistical channel models [13,[24][25][26][27] have been developed for the simulation and performance analysis of various indoor communication systems.The advantage of measurement-based channel models is that they are characterizing the fading behavior utterly realistic.By changing the model parameters, the developed statistical channel models can be employed to simulate indoor propagation channels for a broad range of different scenarios.However, to determine appropriate parameters for different propagation scenarios, a large number of measurement data are required, which is time-and materialconsuming and leads thus to high development costs.Alternatively, approaches based on ray-tracing techniques [28][29][30][31] have been developed to enable the simulation of indoor 2 Wireless Communications and Mobile Computing propagation channels.Ray-tracing channel models [29,[32][33][34] can efficiently capture the fading behavior of specified indoor environments.Many developed ray-tracing channel models have shown good agreement with measured channels [35][36][37].However, ray-tracing models greatly depend on the physical layouts and materials through which electromagnetic waves propagate, for example, walls, floors, and ceilings.In addition, the main drawback of ray-tracing models comes from their computational costs, which are widely determined by the size and complexity of the geographic database as well as the strategy used for the ray search.Therefore, a tradeoff has to be found between the prediction accuracy and the simulation efficiency when modeling indoor propagation channels using ray-tracing techniques.
The two main types of indoor channel models, namely, the empirical statistical channel models and the ray-tracing channel models, have their own strengths and limitations.To cope with the drawbacks mentioned above, a geometrical channel model has been proposed in [38] for indoor environments, where it is assumed that the scatterers are randomly distributed inside of a circle with a base station (BS) in its centre.More specifically, this model is based on the assumption that the distance between the BS and the scatterers follows an exponential distribution.Such an assumption imposes severe restrictions on the applicability of the model.In addition, from the physical point of view, it is questionable whether it is reasonable to represent the geometry of indoor scattering areas, such as offices and corridors, by a circle.On the contrary, a rectangle is a more appropriate geometric figure to model typical indoor propagation environments.A geometrical rectangle scattering model has been proposed in [39] to characterize narrowband indoor radio propagation channels.However, to the best of the authors' knowledge, the modeling of wideband indoor radio channels by employing an appropriate geometrical scattering model that takes into consideration the unique indoor propagation conditions is still an open problem.
Motivated by the scarcity of proper wideband geometrybased indoor channel models, such a model was developed in [40] by extending the geometrical rectangle scattering model in [39] with respect to frequency selectivity.In this paper, we improve the statistical models in [39][40][41] for the characterization of the scatterer distribution.We concentrate on the statistical characterization of a wideband reference channel model, which is based on the assumption that an infinite number of scatterers are randomly distributed over the two-dimensional (2D) horizontal plane of a rectangular room.To be more specific, we assume that the probability for the occurrence of a scatterer decays exponentially with the distance from the walls.This assumption includes the uniform distribution of the scatterers as a specific case.In contrast to [42][43][44], we apply a different procedure for studying the statistical properties of the resulting reference channel model, which requires no knowledge of the complex channel gain.We derive the analytical expressions for the probability density function (PDF) of the angle of arrival (AOA), the PDF of the propagation path length, the power delay profile (PDP), and the frequency correlation function (FCF).Moreover, we derive a wideband sum-of-cisoids (SOC) channel simulator from the reference model.It is shown that the designed wideband SOC channel simulator matches the underlying reference model accurately with respect to the FCF.The obtained SOC channel simulator enables the simulation of indoor mobile fading channels with reduced realization expenditure.At the end, we demonstrate the closeness to reality of the proposed reference channel model by comparing its mean excess delay and the root mean square (RMS) delay spread with the corresponding empirical quantities obtained from measured channels in laboratories at 2.4 GHz [16] and a conference room at 5 GHz [19] as well as corridors and offices at 60 GHz [23].
The remainder of this paper is structured as follows.In Section 2, we introduce the 2D geometrical indoor scattering model, which serves as a starting point for the derivation of the reference channel model.Section 3 analyzes the statistical characteristics of the wideband reference channel model with emphasis on the PDF of the AOA, the PDF of the propagation path length, the PDP, and the FCF.Section 4 introduces a design procedure for wideband indoor SOC channel simulators.Numerical and experimental results are presented in Section 5 to confirm the correctness of the obtained theoretical results.Section 6 validates the usefulness of the proposed indoor channel model by matching its statistical properties to those of measured (real-world) channels.Finally, Section 7 draws the conclusion.

The Geometrical Indoor Scattering Model
This section briefly describes the geometrical scattering model, which was first proposed in [40] to characterize indoor propagation scenarios.Although a room has three dimensions, we only consider the 2D horizontal plane in which all local scatterers as well as the BS and the mobile station (MS) are located.As shown in Figure 1, the rectangle represents the 2D horizontal plane of a room.Its length and width are denoted by  and , respectively.The BS is considered as the transmitter, leaving the MS to play the role as the receiver.For convenience, it is also assumed that the MS moves along the -axis.Moreover, we consider single bounce scattering, which means that the plane waves emitted from the BS are only bounced once by scatterers before reaching the MS.The black star in Figure 1 represents a single local scatterer.In real-world environments, the number of scatterers is limited and their locations differ from one propagation scenario to another.To avoid studying the fading characteristics for a specific indoor propagation scenario characterized by a specific realization of a finite number of scatterers, we focus on a general statistical model that results from averaging over all possible propagation scenarios.Therefore, we assume that an infinite number of scatterers are randomly distributed inside the room.Such a model acts here as a nonrealizable stochastic reference model.From the reference channel model, an efficient channel simulator with low realization expenditure can be derived by making use of the SOC principle [45].
A straightforward assumption would be that the scatterers are uniformly distributed inside the room.For the modeling of indoor channels, however, it is more realistic to assume that the probability of the occurrence of a scatterer decays exponentially with the distance from the walls.This implies that it is more likely that the received scattered components are coming from the walls rather than from objects located in the room's centre.Instead of the uniform distribution, we use therefore a mixture of exponential functions to model the distribution of the scatterers inside the 2D horizontal plane of the room.The exponential functions are more general and include the uniform distribution as a special case, as explained in the next section.

Statistical Characterization of the Reference Channel Model
This section studies the statistical properties of the proposed indoor wideband reference channel model.In this regard, the PDF of the AOA, the PDP, and the FCF are of special interest.It is shown in Figure 1 that the BS is located at the position (, 0) ( < 0), while the MS is located at the origin of the coordinate system.The position of the local scatterer  is described by (x, y), where x and y are independent random variables.As mentioned in Section 2, it is assumed that the scatterers are exponentially distributed within the 2D horizontal plane of the room.This implies that the random variables x and y must be exponentially distributed over the intervals  x = [−/2 − , /2 − ] and  y = [−/2 − , /2 − ], respectively.Thus, the PDF  x () of x and the PDF  y () of y are given by where   ≥ 0 (,  = 1, 2) are real-valued parameters and It should be mentioned that the distributions in (1a) and (1b) include the uniform distribution as a special case if   → 0 for ,  = 1, 2. With the rule of de l'Hospital, it can be shown that in this case  1 and  2 tend to  1 = 1/(2) and  2 = 1/(2), respectively.Owing to the assumption that the random variables x and y are statistically independent, we can express the joint PDF  xy (, ) of x and y as the product of the marginal PDFs  x () and  y (); that is, Next, we describe the position of the scatterers by using polar coordinates (z, ), where z denotes the path length from the position of the scatterer  to the MS, and  is the AOA (see Figure 1).Notice that z and  are random variables.The joint PDF  z (, ) of the position of the scatterers in polar coordinates (z, ) can be written by using (3) as Let D be the propagation path length, which is the plane wave's overall traveling distance from the BS via the scatterer  to the MS; then D is given by Our next focus is on finding the joint PDF of the path length D and the AOA  using (4).For this purpose, we introduce the auxiliary random variable  = .Solving the system of equations determined by D = z + √z 2 − 2z cos() +  2 and  =  gives us the following two solutions: By applying the fundamental theorem of transformation of random variables [46, p. 201], the joint PDF  D (, ) of the path length D and the auxiliary random variable  is given by where denotes the Jacobian determinant of the inverse transformation.Substituting ( 8) into (7) and using ( 4), (6a), and (6b), we find the expression for the joint PDF  D (, ).Owing to  = , the joint PDF  D (, ) can be expressed directly using the joint PDF  D (, ) by replacing  in (7) by .Thus, we obtain where  x (⋅) and  y (⋅) are the densities given by (1a) and (1b), respectively.
3.1.The PDF of the AOA.In this subsection, we are concerned with the derivation of the PDF   () of the AOA .This PDF can be obtained from the joint PDF  D (, ) in ( 9) by integrating over the range of ; that is, where I D represents the interval ( min ,  max ()] in which  min and  max () are the minimum and the maximum propagation path length, respectively.The minimum propagation path length  min follows from (5) for  = 0; that is,  min = ||.
Notice that the maximum propagation path length  max () depends on .It is shown in Appendix A that  max () is given as in (11), where With  min = || and  max (), as given in (11), the PDF   () can readily be obtained by solving the integral in (10) numerically.

The PDF of the
It is shown in Appendix B [see (B.9)] that the integral in ( 13) can be expressed by (14), which is presented as follows: where the path lengths  1 ,  2 , . . .,  8 are given in Appendix B, and (  ,   ) denotes the integral in which 3.3.The PDF and PDP of the Propagation Delays.The objective of this subsection is to find the PDF    (  ) of the propagation delays   .Here, the propagation delay   is defined as where  0 denotes the speed of light.Taking this relation into account and applying the concept of transformation of random variables [46, p. 130], we can express the PDF    (  ) of the propagation delays   as Here,  D ( 0   + ||) can be obtained directly from the PDF in ( 14) by replacing the variable  by the term  0   + ||.For brevity, the expression for  D ( 0   + ||) is not presented here.Let the total power of the received multipath components be represented by 2 2 0 , and let us denote the PDP by    (  ).Then, it follows that ∫ ∞ 0    (  )  = 2 2 0 holds.By taking the relationship    (  ) ∼    (  ) and the property ∫ ∞ 0    (  )  = 1 into account, we can conclude that the following equation must hold for the PDP: Hence, the PDP    (  ) can be obtained directly from the PDF  D () in (14).

The FCF.
According to the Wiener-Khinchin theorem, the PDP and the FCF form a Fourier transform pair.The FCF    (V  ) is defined as the Fourier transform of the PDP    (  ); that is, Substituting (19) in (20) results in the following expression for the FCF: Since no closed-form solution exists, the integral above has to be solved numerically.

Design of an SOC Wideband Indoor Channel Simulator
This section deals with the design of a stochastic SOC channel simulator for the proposed wideband indoor channel model.The time-variant impulse response of a wideband SOC channel simulator consisting of L discrete propagation paths can be expressed as follows [47, Eq. (7.55)]: Here, the path gains  ℓ are determined by the square root of the PDP assigned to the ℓth discrete propagation delay.By applying the procedure described in [47, p. 374], we have where  ℓ are the intervals defined in [47, p. 374].The stochastic complex process μℓ () in ( 22) models the sum of all received scattered components having the same propagation delay   ℓ .According to the SOC principle, such a stochastic process can be represented by a sum of  ℓ cisoids of the form [45] Here, the quantities  ,ℓ ,  ,ℓ , and  ,ℓ represent the gain, the Doppler frequency, and the Doppler phase of the th component of the ℓth discrete path, respectively.The gains  ,ℓ and the Doppler frequencies  ,ℓ are constant.They can be determined by a proper parameter computation method, for example, the modified method of equal areas (MMEA) [48], according to which the gains  ,ℓ are given by The Doppler frequencies  ,ℓ are determined by the AOAs  ,ℓ according to the well-known relation where  max stands for the maximum Doppler frequency.The AOAs  ,ℓ are constant parameters, which can be computed by means of the MMEA.This method requires solving the following equation: for all  = 1, 2, . . .,  ℓ .The phases  ,ℓ of the stochastic SOC channel simulator are independent and identically distributed (i.i.d.) random variables, each following a uniform distribution over [0, 2).Thus, the stochastic SOC channel simulator can be interpreted as a family of sample functions determined by the realizations of the phases  ,ℓ .A sample function can be obtained from the stochastic channel simulator by fixing all phases.Such a sample function, which can be interpreted as a waveform generated by a deterministic channel simulator, can be used to simulate the proposed wideband indoor channel.

Numerical and Simulation Results
This section illustrates the theoretical results given by ( 10) and (21).The correctness of the theoretical results will be verified by simulations.We will also show that the SOC channel simulator matches the reference channel model with respect to the FCF.The validity of the proposed indoor channel model is also confirmed by indoor channel measurements by studying the mean delay and the RMS delay spread.In all simulations, we consider a room with length  = 10 m and width  = 5 m as our indoor environment.The parameters  and  have been chosen to be equal to 2 and 1, respectively.The SOC channel simulator is designed by applying the MMEA [48] using  ℓ = 8 (ℓ = 1, 2, . . ., L) cisoids for each discrete propagation path.The theoretical result of the PDF   () of the AOA  [see (10)] of the wideband reference channel model is presented in Figure 2 for different BS locations ( = −2 and  = −4).It can be observed from this figure that the shape of the PDF of the AOA is independent of the position of the BS.The theoretical results illustrated in Figure 2  be mentioned that the results in Figure 2 correspond to the PDF of the AOA of the narrowband channel model (see [39, Eq. (9)]).In Section 6, we will graphically present the PDF of the AOA in case that the locations of the scatterers are exponentially distributed.The impact of the parameters  and  on the shape of the PDF   () of the AOA  is illustrated in Figures 3 and 4, respectively.It can be observed from Figure 3  Figure 4 reveals that an increase in  leads to an inverse effect on the shape of the PDF   () compared to an increase in .Figures 3 and 4 show that both the parameters  and , which control the symmetry of the room, have impacts on the shape of the PDF of AOA.The main reason is that when  or  changes, it means the location of the mobile station relative to the room area moves (see the geometrical indoor scattering model in Figure 1).While a scatterer is fixed, the position of the mobile station determines the value of the AOA.If the mobile station moves closer to a wall, the AOA bounced by the scatterers in the triangle formed by the mobile station and two corners of the wall takes a larger range.Therefore, the PDF of one angle from that range decreases.
Figure 5 shows the absolute value of the FCF    (V  ) that has been calculated by using (21) for different values of the room length .For comparison purposes, we also plot the theoretical curve for the absolute value of the FCF of the designed SOC simulation model by using Eq.(31) in [42].We consider L = 20 discrete propagation paths for the SOC channel simulator, where the corresponding delays   ℓ are equally spaced between 0 and the maximum propagation delay   max .The value of   max can be obtained from (18) as the maximum value of   such that    (  ) ̸ = 0.The path powers assigned to different propagation paths have been calculated according to the method described in [47, pp. 374-375].The AOAs of the SOC channel simulator are computed by employing the MMEA [48].We observe from Figure 5 that the FCF of the SOC channel simulator can be brought into extremely good agreement with that of the reference model.The FCF decays faster with increasing the frequency separation V  if the room length  increases (here from 10 m to 30 m).This means that the coherence bandwidth   becomes smaller as  increases (the coherence bandwidth   of a wideband mobile radio channel is the smallest positive value of the frequency separation variable   =   for which the condition The influence of the room width  on the FCF is presented in Figure 6 from which similar conclusions can be drawn as from Figure 5.When the dimensions of the room increase, the frequency correlation of time-variant transfer functions reduces at the same frequency separation.In other words, the time-variant transfer functions of the developed SOC channel simulator become independent at a smaller frequency separation, which leads to a smaller coherence bandwidth.

Experimental Verification
To demonstrate the usefulness of the proposed geometricalbased indoor reference channel model, we will show how the statistics of the reference channel model can be fitted to the statistics of measured real-world channels by optimizing the key parameters of the reference model.Here, two of the most important characteristic quantities of wideband mobile radio channels are considered, namely, the mean excess delay and the RMS delay spread.
The mean excess delay    is defined as the first moment of the PDP [26,49]; that is, The RMS delay spread    is defined as the square root of the second central moment of the PDP [26,49]; that is, The mean excess delay   and the RMS delay spread    of the reference model can easily be calculated by substituting the PDP    (  ) [see (19)] into (28) and (29), respectively.
The measurement results of the mean excess delay  ⋆   and the RMS delay spread  ⋆   considered in this section are taken from [16,19,23].The measurement campaigns were carried out in laboratories, a conference room, and corridors.The measurements in [16] have been obtained at 2.4 GHz in a laboratory with dimensions 7.8 m × 9.95 m.Furthermore, the measurements reported in [19] have been obtained at 5 GHz in a conference room with dimensions 6.6 m × 5.9 m.Finally, the measurements in [23] have been obtained 60 GHz in We combine all the relevant model parameters (except the parameters  and ) which control the mean excess delay    and the RMS delay spread    of the reference channel model into a parameter vector denoted and defined by Ω fl (, , ,  11 ,  12 ,  21 ,  22 ).We also introduce the following error function: for measuring the deviations between the mean excess delays  ⋆   and    as well as between the RMS delay spreads  ⋆   and    .In (30),  1 and  2 represent proper weighting factors.
The optimization of the parameter vector Ω has been carried out by minimizing numerically the above error function (Ω) by means of the quasi-Newton optimization procedure [50].The optimization results are presented in Tables 1, 2, and 3, for the laboratory, the conference room, and corridor scenarios.For comparison purpose, the measured mean assess delay  ⋆   and the measured RMS delay spread  ⋆   , presented in [16,19,23], are also shown in Tables 1, 2, and 3. Note that the dimensions of the different rooms, which are controlled by the parameters  and , have been chosen such that they are equal to the lengths and widths of the rooms in which the corresponding measurement campaigns have been conducted.Hence,  and  are fixed, and thus they have not been included in the optimization procedure.In  measured mean assess delay  ⋆   is in the range from 16.40 ns to 24.0 ns, while the RMS delay spread  ⋆   varies from 15.5 ns to 20.7 ns.In Table 3, finally, the measured mean assess delay  ⋆   covers the range from 3.84 ns to 8.18 ns and holds for hallways, while the range from 3.52 ns to 14.69 ns refers to offices.In addition, the measured RMS delay spread  ⋆   varies from 12.34 ns to 15.04 ns for corridors and from 12.56 ns to 21.09 ns for laboratories.In our optimization procedure, the weighting factors  1 and  2 were chosen to be 0.35 and 0.65, respectively.For reasons of brevity, we have only presented the values of the optimized parameters in all tables with two decimals of precision.As shown in Tables 1, 2, and 3, the mean excess delay    and the RMS delay spread    of the proposed wideband indoor channel model are very close to the corresponding measured quantities for all considered indoor propagation scenarios, which demonstrates that the reference channel model is useful for characterizing realworld wideband indoor mobile radio channels.
For completeness, we present in Figure 7 the nonuniform PDF   () of the AOA  for three of the indoor propagation scenarios, namely, the Average Corridor, the Average Lab (NLOS), and the overall channel scenario.In this figure, we see that the PDF of the AOA has 4 peaks corresponding to the characteristics of the exponential distribution within the 2D horizontal plan of the room.The results in this figure have been obtained by evaluating (10) with the optimized channel parameters listed in Table 1.

Conclusion
In this paper, we have developed a wideband mobile radio channel model for indoor propagation environments.The starting point for the derivation of the reference channel model was a geometrical scattering model, where we have assumed that an infinite number of scatterers are exponentially distributed within the 2D horizontal plane of a rectangular room.Analytical expressions have been derived for the PDF of the AOA, the PDF of the propagation delays, the PDP, and the FCF.We have shown that the shape of the PDF of the AOA is independent of the position of the transmitter (BS).Both the room length and width have a strong influence on the PDF of the AOA and the FCF.If the room length or width increases, the FCF decays faster if the frequency separation increases.The coherence bandwidth decreases with increasing the room size.The usefulness of the proposed reference channel model has been demonstrated by a close match between the channel statistics of the reference model and measured channels.
An efficient channel simulator has been derived from the reference channel model by applying the SOC principle.It has been shown that the SOC channel simulator matches closely the wideband reference model with respect to the FCF.The designed SOC channel simulator can be used for the performance evaluation of wideband indoor wireless communication systems under realistic propagation conditions.which depends only on the AOA .The maximum propagation path length  max () for the other subregions  2 ,  3 , and  4 can be computed analogously.For brevity, we only present the final expression for  max () in (11).

B. Determination of the Values for
and   in (14) In this appendix, we first determine the maximum value and the minimum value of  max for the four scattering subregions illustrated in Figure 8.
Subregion  1 .− arctan( + / − ) <  ≤ arctan( − / − ).It can easily be seen from (A.4) that  max () is a monotonic increasing function with respect to  within the range [0, arctan( − / − )].We find that  max () takes the minimum value  1 if  = 0, whereas  max () equals the maximum value  2 if  = arctan( − / − ); that is, If  ∈ (−arctan( + / − ), 0), then  max () decreases if  increases.Thus, the maximum  max () over this range is given by  An example for the maximum path length  max () is illustrated in Figure 9.It should be mentioned that the path length  is always less than or equal to  max ().Since  4 is the minimum value of  max () [see Figure 9], for a given value of the path length  ≤  4 , we can conclude that all AOAs  ∈ (−, ] satisfy the inequality  ≤  max () ≤  4 .However, if the path length  For the other given values of , it is necessary to meet the condition  ≤  max ().According to Figure 9, we obtained the relations in (B.9), which are presented as follows: (B.9) The AOAs   ( = 3, 4, . . ., 8) can be determined similarly by solving (B.8).The expression for  max () on the left-hand side of (B.8) is chosen in accordance with the range of   .For example, as  3 ∈ (− + arctan( + / + ), − arctan( + / − )], the fourth part of  max () [see (11)] corresponding to the Subregion  4 is selected.

Disclosure
This paper is an extended version of "Modeling and Statistical Characterization of Wideband Indoor Radio Propagation Channels," which was published in the proceedings of the International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), 2010.The starting point in this submitted paper is new.A mixture of exponential functions is used to model the distribution of scatterers.The new mixture exponential functions are more general and include the uniform distribution considered in the ICUMT paper as a special case.This influences all key results of the paper.In addition, the authors in this paper validate the developed channel model with experimental data.The paper shows, by optimizing some of the key parameters with proper methods, that it is possible to use

Figure 1 :
Figure 1: Geometrical indoor scattering model with local scatterers , which are randomly distributed over the 2D horizontal plane of a room with length  and width  ( ≥ 0 and  ≥ 0).
Propagation Path Length.The PDF of the propagation path length D, denoted by  D (), can be calculated by means of the relation  D () = ∫   D (, ) .

4 Simulation, c = − 4 Figure 2 :
Figure 2: The PDF   () of the AOA  for different locations of the BS.

4 Figure 3 : 2 Figure 4 :
Figure 3: The PDF   () of the AOA  for different locations of the MS.

Figure 5 :
Figure 5: Absolute values of the FCFs |   (V  )| (reference model) and |r   (V  )| (simulation model) for different values of the room length .

Figure 6 :
Figure 6: Absolute values of the FCFs |   (V  )| (reference model) and |r   (V  )| (simulation model) for different values of the room width .

Figure 7 :
Figure 7: The PDF   () of the AOA  for three different indoor propagation scenarios.

Table 1 :
[16]mized parameters of the reference models for laboratory scenarios at 2.4 GHz based on the measurements in[16].

Table 2 :
[19]mized parameters of the reference models for the conference room at 5 GHz based on the measurements in[19].

Table 3 :
[23]mized parameters of the reference models for the corridor and laboratory (Lab) scenarios at 60 GHz based on the measurements in[23].