A Fading Channel Simulator Implementation Based on GPU Computing Techniques

Abstract

Channel simulators are powerful tools that permit performance tests of the individual parts of a wireless communication system. This is relevant when new communication algorithms are tested, because it allows us to determine if they fulfill the communications standard requirements. One of these tests consists of evaluating the system performance when a communication channel is considered. In this sense, it is possible to model the channel as an FIR filter with time-varying random coefficients. If the number of coefficients is increased, then a better approach to real scenarios can be achieved; however, in that case, the computational complexity is increased. In order to address this issue, a design methodology for computing the time-varying coefficients of the fading channel simulators using consumer-designed graphic processing units (GPUs) is proposed. With the use of GPUs and the proposed methodology, it is possible for nonspecialized users in parallel computing to accelerate their simulation developments when compared to conventional software. Implementation results show that the proposed approach allows the easy generation of communication channels while reducing the processing time. Finally, GPU-based implementation takes precedence when compared with the CPU-based implementation, due to the scattered nature of the channel.

R. Carrasco-Alvarez 1 and J. Vazquez Castillo 2 and A. Castillo Atoche 3 and J. Ortegon Aguilar 2

Academic Editor:Chunlin Chen

1, Universidad de Guadalajara, Boulevard Marcelino Garcia Barragan 1421, 44430 Guadalajara, JAL, Mexico
2, Universidad de Quintana Roo, Boulevard Bahia s/n, Esquina Ignacio Comonfort, 77091 Chetumal, QRoo, Mexico
3, Universidad Autonoma de Yucatan, Avenida Industrias No Contaminantes, S/N, 97310 Merida, YUC, Mexico

Received 13 September 2014; Revised 11 March 2015; Accepted 11 March 2015; 5 April 2015

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Currently, the high demand for integrated services (voice, data, and video) means that new data transmission schemes have to be developed for dealing with high transmission data rates and at the same time for offering high levels of quality of service. The fourth generation (4G) of mobile communication systems is still under development; its main goal is to provide a digital communication network (land, mobile, and satellite) with peak data rates of 100 Mbps for high mobility devices and high data rates of 1 Gbps for users or devices in low mobility environments or stationary conditions. The main technologies used in 4G include techniques based on multiple-input and multiple-output (MIMO) antennas, turbo decoding, adaptive modulation, coding schemes and error correction, and orthogonal FDMA (orthogonal FDMA, OFDM) [1, 2]. Current versions of standards that incorporate 4G are LTE-A (long term evolution-advanced) and IEEE 802.16 m WiMAX (Worldwide Interoperability for Microwave Access) mobile. Therefore, the new issues imposed by the standards require new processing algorithms to be tested on high mobility environments affected by Doppler shifts (time-selective channels) and multipath propagation (frequency-selective channels). The temporal channel variability occurs when the characteristics of the transmission medium change over time or when there is a relative motion between the receiver and transmitter, as in communication systems such as LTE and WiMAX. The frequency selectivity appears when multiple copies of the transmitted signal arrive at the receiver due to physical mechanisms such as multipath propagation.

Moreover, knowing the behavior or performance of a mobile communication system under real conditions (in situ test) can be very expensive, owing to the transfer of the communications system and test equipment to the place under study, among other issues. Additionally, the system behavior can not be tested under the same propagation conditions due to the nature of the communication channel. Faced with this problem, an economical alternative is to use mathematical models, which represent the radio channels under consideration. In this sense, we can define a channel simulator as a software tool that permits reproduction of the behavior or the propagation conditions of a mobile communications channel under controlled or laboratory conditions.

On the other hand, GPU-accelerated computing is the use of a graphics processing unit (GPU) together with a CPU in order to accelerate scientific, engineering, and business applications [3]. Recently, several works related to the wireless communication area, which uses GPU devices, have been published [4-7]. Those works follow an implementation strategy in order to handle the channel complexity using multiple cores. For example, in [4] a wireless channel simulator is implemented. In that work, the potential of GPU-based processing is studied in order to improve the runtime performance of computationally intensive accurate wireless network simulation. In [5], the use of general purpose GPUs is investigated in order to provide the computational capabilities required for performing the radio frequency path loss computation. A discussion of the acceleration of wireless channel simulation using GPUs is provided in [6]. In addition, in [7], an implementation of parallel lattice reduction-aided 2 × 2 MIMO detector using GPUs for the WiMAX standard is presented.

Although several works related to the use of GPUs in communication systems exist, there are currently no works that describe in detail the implementation of a fading channel simulator based on GPUs. In this paper, the methodology for implementing a fading channel simulator (time and frequency selective) via GPU computing is presented.

The proposed methodology considers the use of common GPU software libraries that permit nonspecialized users in GPU programming to easily implement the proposed simulator. On the other hand, the generation of the Rayleigh fading variates is achieved using the filtering method [8-10]. In this case, the filtering method is carried out in time domain by using a finite impulse response (FIR) filter for coloring Gaussian noise samples. Furthermore, it is well known that if the filter order is increased, then the accuracy of the channel statistics can be improved, though at the cost of increasing the computational complexity. Therefore, in this work, we take advantage of GPUs for handling such computational complexity (multiplication and addition operations) in order to implement an accurate communication channel for SISO systems. Moreover, this methodology paves the way for implementing MIMO channel simulators in the future.

The rest of this paper is organized as follows: In the second section, the background of the wireless communication system is stated, specifically as regards the channel communication model. In Section 3, how to simulate the communication channel is explained. Next, in Section 4, the GPU implementation of the fading channel simulator is detailed. Section 5 is devoted to presenting the implementation results when a WiMAX scenario is considered. Finally, the conclusions are presented in Section 6.

2. Communication System

Consider a single-input and single-output (SISO) communication system where the transmission of in-phase [figure omitted; refer to PDF] and quadrature [figure omitted; refer to PDF] signals modulated by orthogonal carriers [figure omitted; refer to PDF] and [figure omitted; refer to PDF] , respectively, are assumed, which are mixed for obtaining [figure omitted; refer to PDF] . This signal [figure omitted; refer to PDF] is propagated through the communication channel [figure omitted; refer to PDF] , which is considered to be a causal time-varying linear system. The signal filtered by the channel reaches the receiver where a noisy version [figure omitted; refer to PDF] is detected. It can be expressed mathematically as follows: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] is a time variable. The impulse response [figure omitted; refer to PDF] states the response of the channel in the instant [figure omitted; refer to PDF] when a stimulus is applied in [figure omitted; refer to PDF] , which reflects the time variability of the channel impulse response. Likewise, [figure omitted; refer to PDF] is the aggregated stochastic noise. This received signal [figure omitted; refer to PDF] is demodulated in order to obtain the in-phase and quadrature signals [figure omitted; refer to PDF] and [figure omitted; refer to PDF] .

For sake of simplicity, if [figure omitted; refer to PDF] and [figure omitted; refer to PDF] , where [figure omitted; refer to PDF] is any carrier frequency and [figure omitted; refer to PDF] is any phase, the system becomes the well known single carrier communication system. It is important to emphasize that an OFDM system implemented with IFFT/FFT produces a base-band signal that is modulated as in a single carrier system.

If we consider that both signals [figure omitted; refer to PDF] and [figure omitted; refer to PDF] are band limited to a maximum frequency of [figure omitted; refer to PDF] and [figure omitted; refer to PDF] (this condition is always accomplished in real communication systems) it is easy to demonstrate [11, 12] with the aid of the Hilbert transform the existence of base-band equivalent signals [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] for [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] , respectively. In general, these equivalent base-band signals are complex, where the real part corresponds to the in-phase component and the imaginary to the quadrature component; thus, [figure omitted; refer to PDF] and [figure omitted; refer to PDF] for [figure omitted; refer to PDF] . The relations between the original pass-band signals and their baseband equivalents are as follows [12]: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the real part of the complex number in parentheses. Considering (2), the base-band equivalent of (1) is [figure omitted; refer to PDF] which can be interpreted as a collection of multiple paths (scatters), where the transmitted signal [figure omitted; refer to PDF] is propagated. The fact that these paths have different lengths and pass through different conditions of propagation causes the received signal from a specific path to be a delayed, attenuated, and phase-shifted version of the [figure omitted; refer to PDF] . In this sense, for a specific time [figure omitted; refer to PDF] and a specific delay [figure omitted; refer to PDF] , the channel coefficient [figure omitted; refer to PDF] will be a complex variable, where the magnitude represents the attenuation factor and the phase shift factor. On the other hand, due to the constant changes in the environment and the possible relative movement between transmitter and receptor, these factors are time dependent. According to [12], [figure omitted; refer to PDF] can be modeled as a complex stochastic process composed of the sum of a deterministic part (the ensemble average of [figure omitted; refer to PDF] ) and a random part (zero mean random process). From this point, we will only consider the random part (an assumption generally accepted when a channel simulator is developed). The autocorrelation function of this random process is equal to [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the expectation operator and [figure omitted; refer to PDF] represents the complex conjugate. This channel model is difficult to implement; nevertheless, some assumptions can be asserted which simplify the model. The first is the absence of correlation between the different scatters, and the second is that each scatter is a wide-sense stationary process, which together comprise the well known wide-sense stationary uncorrelated scattering (WSSUS) model. Therefore, (4) transforms into [figure omitted; refer to PDF] where [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] is the autocorrelation function with respect to the time difference variable [figure omitted; refer to PDF] for the scatter located in the delay variable [figure omitted; refer to PDF] . From (5), it is possible to calculate the scattering function, which is defined as the Fourier transform of the correlation function with respect to the time difference variable [figure omitted; refer to PDF] , as follows: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the Fourier transform operator. This scattering function [figure omitted; refer to PDF] indicates how the Doppler spectrum is for a given delay value in the variable [figure omitted; refer to PDF] .

In many communication standards, a discrete number of scatters are considered instead of a continuous number, as suggested in previous equations. If this assumption is considered, then [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is an index variable that enumerates the [figure omitted; refer to PDF] discrete scatters and [figure omitted; refer to PDF] is a complex variable that encloses the gain and phase shift factor of such scatter. If a WSSUS channel is considered, the correlation function of (7) is [figure omitted; refer to PDF] with scattering function [figure omitted; refer to PDF]

3. Channel Simulation

In order to perform a computational simulation of the communication channel, it is necessary to deal with the discrete version of the baseband equivalent channel presented in (7). This discrete channel results in band-limiting and sampling (7) in time and time-delay domains at a rate of [figure omitted; refer to PDF] . Thus, it is defined as [figure omitted; refer to PDF] where [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , the symbol [figure omitted; refer to PDF] represents the convolution operator, and [figure omitted; refer to PDF] is a function for band-limiting the channel to [figure omitted; refer to PDF] , which, for practical purposes, could be a time windowed cardinal sine function. Substituting (7) into (10) results in [figure omitted; refer to PDF] where [figure omitted; refer to PDF] corresponds to the coefficients of the FIR filter for simulating the communication channel, [figure omitted; refer to PDF] enumerates the samples in the time domain, and [figure omitted; refer to PDF] enumerates the taps of the filter. Likewise, [figure omitted; refer to PDF] can be calculated as [figure omitted; refer to PDF] , where [figure omitted; refer to PDF] is the maximum delay of the paths in the channel [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] is the length of the filter [figure omitted; refer to PDF] . This filter could be anticausal; nevertheless, it is possible to introduce a delay in order to convert this filter into a causal filter and therefore physically feasible.

In order to implement (11), it is necessary to generate [figure omitted; refer to PDF] uncorrelated discrete Gaussian stochastic complex processes at rate [figure omitted; refer to PDF] . In the state of the art many algorithms for obtaining these stochastic processes are stated, as mentioned in [13-16] and references therein. Such processes must be filtered (colored) in order to accomplish the desired scattering function. It is important to note that these filters only affect the frequency components below a maximum Doppler frequency [figure omitted; refer to PDF] ; therefore, it is possible to generate the samples at a rate of at least [figure omitted; refer to PDF] , where typically [figure omitted; refer to PDF] , and then to use any upsampling technique for accomplishing the [figure omitted; refer to PDF] rate.

The impulse response of the filter for coloring the [figure omitted; refer to PDF] th process is the discrete version (at rate [figure omitted; refer to PDF] ) of the following expression: [figure omitted; refer to PDF]

Finally, an interpolation technique such as splines, polynomial, or basis expansion is used for obtaining the samples at [figure omitted; refer to PDF] rate. The entire process is presented in Figure 1 and summarized in Algorithm 1.

Algorithm 1: Channel generation procedure.

Require : Scattering function

Require : Define the gain [figure omitted; refer to PDF] that correspond to the variance of the process [figure omitted; refer to PDF] for all the [figure omitted; refer to PDF] paths

(1) for all [figure omitted; refer to PDF] such that [figure omitted; refer to PDF] do

(2) Generate the zero mean unitary variance complex Gaussian stochastic process at rate [figure omitted; refer to PDF] samples per second

(3) Multiply the stochastic process by [figure omitted; refer to PDF] for ensuring the gains of the paths

(4) Filter the process with discrete [figure omitted; refer to PDF]

(5) Interpolate the process for obtaining samples at rate [figure omitted; refer to PDF]

(6) end for

(7) for all [figure omitted; refer to PDF] do

(8) Obtain [figure omitted; refer to PDF] filter's coefficients

[figure omitted; refer to PDF]

(9) end for

Figure 1: Structure of the fading channel simulator.

[figure omitted; refer to PDF]

4. GPU Implementation

The emergence of GPUs has allowed complex algorithms to be executed almost in real time. GPU is conceptualized as a set of streaming multiproccesors (SM), where each SM is characterized by a single instruction multiple data (SIMD) architecture. Therefore, in each clock cycle, each processor of the multiprocessor executes the same instruction, operating on multiple data streams; that is, each of these processors has the possibility of accessing a shared memory (common to all processors belonging to the same SM) and a local cache memory. In addition, all the processors have access to the global GPU (device) memory. Figure 2 illustrates the GPU hardware architecture.

Figure 2: GPU data distribution for [figure omitted; refer to PDF] multiprocessors with [figure omitted; refer to PDF] processors each.

[figure omitted; refer to PDF]

Our strategy for implementing the fading channel simulator is aimed at improving the overall performance by chaining software functions (called kernels) representing each communication step. In order to implement the parallel fading simulator as illustrated in Figure 3, we distinguish five stages in the GPU design methodology as follows.

Figure 3: Proposed GPU design flow.

[figure omitted; refer to PDF]

4.1. Gaussian Random Number Generator

In this stage, the CUDA Random Number Generation (cuRand) library [17] is employed in order to obtain Gaussian random numbers (GRN) by means of efficient generation of high-quality pseudorandom numbers. Particularly, curand_init function is launched for creating a random number generator in a massively parallel scheme. There are seven types of random number generators in cuRand; in this study, we have selected the XORWOW algorithm, which is a member of the Xor_shift family of pseudorandom number generators, with customized parameters for operating on GPUs.

The curand_normal2 function generates two normally distributed pseudorandom numbers in each call. Because the underlying algorithm is based on the Box-Muller transform, it is suitable for generating random complex numbers; that is, each call generates real and imaginary parts at the same time.

There is a CUDA kernel for computing a set of [figure omitted; refer to PDF] independent GRN vectors. Each vector corresponds to a path, which is computed in chunks by the GPU multiprocessors and then stored on device global memory. The implementation of the GNR generator is presented in the Algorithm 2, where the function setup_kernel initializes the threads of the same block with a different sequence number but the same seed and offset (zero offset). Furthermore, generate_normal_kernel computes several pseudorandom values with Gaussian distribution through the calling of curand_normal2.

Algorithm 2: Pseudorandom noise generation code.

_ global_ void setup_kernel(curandState [figure omitted; refer to PDF] state)

{ int id = threadIdx.x + blockIdx.x [figure omitted; refer to PDF] 6;

curand_init(1234 [figure omitted; refer to PDF] blockIdx.x, id, 0, &state[id]);

[figure omitted; refer to PDF]

_global_ void generate_normal_kernel(curandState [figure omitted; refer to PDF] state, int n, float [figure omitted; refer to PDF] result)

{ int id = threadIdx.x + blockIdx.x [figure omitted; refer to PDF] 6;

float2 x;

curandState localState = state[id];

for(int i=0; i<n; i++)

{ / [figure omitted; refer to PDF] Generate pseudorandom normals [figure omitted; refer to PDF] /

x=curand_normal2(&localState);

result[id]= x.x;

}

/ [figure omitted; refer to PDF] Copy state back to global memory [figure omitted; refer to PDF] /

state[id] = localState;

[figure omitted; refer to PDF]

4.2. Parallel Doppler FIR-Filter

The Doppler filter uses the resulting coefficients obtained by sampling (12) and the random numbers generated in the previous subsection. Since the filter coefficients are fixed for all channel realizations and paths, they are stored in the constant memory of GPU. This memory is devoted to storing and broadcasting read-only data to all threads on the GPU. In addition, the results of GRN are stored in shared memory, since many threads must access them simultaneously. The filtering is conceptualized as a convolution, so a kernel that performs the convolution in parallel is used.

There is a set of [figure omitted; refer to PDF] independent 1D signal convolutions to be computed, one for each path. However, the filtering is performed using the NVIDIA Performance Primitives library (npp) [18]; specifically, one of the nppiFilterRow functions is used, which performs a 1D filtering on 2D data, each row being a channel path.

4.3. Path Gain Implementation

The path gain is implemented with a multiplication function. The resulting colored noise from the previous stage is multiplied by a scalar. This could be carried out with a specific kernel or by using a standard library, such as CUDA Basic Linear Algebra Subroutines (cuBLAS) [19] or npp. The proposed implementation uses the nppiMulC function of the npp library.

4.4. Upsampler

The upsampler stage is responsible for generating noise samples at the rate [figure omitted; refer to PDF] , implemented as an interpolation. The usual interpolation available for GPUs is the linear interpolation offered by texture memory; npp offers other methods for more accurate results. In this case, the nppiResize function with a cubic interpolation is used. It returns the interpolated value for a given coordinate within two known noise values.

4.5. Tap Generator

Multiple paths have been treated separately. In this stage, they are correlated using predefined (computed offline) coefficients according to (11). This correlation operation can be seen as the multiplication of [figure omitted; refer to PDF] upsampled scaled colored noise (path) by the coefficient matrix [figure omitted; refer to PDF] . This could be carried out with a programmer's own implementation or by using a standard library, such as cuBLAS as well. This proposal uses the cublasSgemm kernel that performs a matrix-matrix multiplication with optional scalar product.

5. Implementation Results

In order to corroborate the functionality of the proposed fading channel simulator in modern communication systems such as WiMAX, it was configured with the following parameters [20, page 404]: a maximum frequency Doppler [figure omitted; refer to PDF] Hz and a sample rate [figure omitted; refer to PDF] Msps, [figure omitted; refer to PDF] . In addition, the vehicular class B ITU multipath channel model was considered, which consists of six discrete paths with relative power [figure omitted; refer to PDF] dB at delay time [figure omitted; refer to PDF] nsec, respectively. For implementing the filter [figure omitted; refer to PDF] , a raised cosine function with a roll-off factor of [figure omitted; refer to PDF] and a duration of [figure omitted; refer to PDF] sec was considered. This delay results in the generation of [figure omitted; refer to PDF] taps. In Figure 4, a resulting GPU-based realization of the fading channel according to the specified parameters for [figure omitted; refer to PDF] time samples is presented. It is important to note that the offline computed data (see Figure 3) are transferred to GPU simulator by text files.

Figure 4: Impulse response realization of the fading channel simulator considering the vehicular class B ITU multipath channel model ( [figure omitted; refer to PDF] Hz, [figure omitted; refer to PDF] Msps).

[figure omitted; refer to PDF]

The simulation was carried out using an iMAC computer with the following specifications: OS 10.9.4 (Maverics), Intel Core processor i5 (3.4 GHz), 16 GB of RAM, graphic card GeForce GTX 780 M with 4 GB of RAM, and 1536 CUDA cores.

For evaluating the time performance, the parameters used in the previous test have been maintained; however, the parameter [figure omitted; refer to PDF] was fixed to [figure omitted; refer to PDF] samples. In this sense, Table 1 presents the average, maximum, and minimum time consumption for a CPU-based implementation (Matlab) versus the proposed GPU-based methodology (CUDA). It is clear that the GPU methodology has gains of [figure omitted; refer to PDF] -fold (mean value) when compared with CPU-based implementations, which is attractive if parallel versions of the channel simulator are required, as could be the case in MIMO applications.

Table 1: Channel emulator implementation comparison. Time consumption for [figure omitted; refer to PDF] mega samples generation and [figure omitted; refer to PDF] channel realizations (in milliseconds).

	Matlab1	CUDA Libs2
Min	1640.895	37.376
Max	1821.171	75.186
Mean	1760.821	46.935

[figure omitted; refer to PDF] CPU: Intel Core i5 3.4 GHz 16 GB.

² GPU: GeForce GTX 780M 4 GB.

Table 2 reports the time percentage for accomplishing each task of the channel simulator in the GPU. It should be noted that in this table the reading and device memory allocation-the most time-consuming tasks-are not considered. These tasks are performed only once at the initialization stage of the simulation.

Table 2: Time consumption by module computing 10 channel realizations.

Time (%)	Module
78.18%	Matrix-matrix multiplication
13.62%	Initializing random number generator1
3.83%	FIR filter
2.37%	Upsampling
1.62%	Gaussian number generation
0.01%	Path gain

[figure omitted; refer to PDF] The seed initialization is carried out only once before the first channel realization.

On the other hand, Table 3 and Figure 5 present the overall time consumption in milliseconds for CPU- and GPU-based implementations when the number of samples is fixed to [figure omitted; refer to PDF] = 5120, 10240, 20480, 81920, 327680, 655360, 1000000, and [figure omitted; refer to PDF] samples. This shows that while the time consumption in the CPU-based implementation increments exponentially, it remains almost linear in the GPU-based implementation.

Table 3: Time consumption comparative (in milliseconds): CPU-based implementation (Matlab) versus GPU-based implementation (CUDA).

[figure omitted; refer to PDF]	Matlab1	CUDA2 Libs	x-fold
(samples)	(gain)
5,120	31.5466	0.614496	51
10,240	38.5282	1.350240	28
20,480	54.7829	2.331968	23
81,920	179.8391	5.785952	31
327,680	633.4515	17.09622	37
655,360	1204.584	25.36316	47
1,000,000	1769.243	37.81030	47
1,310,720	3024.966	47.43065	64

[figure omitted; refer to PDF] CPU: Intel Core i5 3.4 GHz 16 GB.

² GPU: GeForce GTX 780M 4 GB.

Figure 5: Time consumption comparative: CPU-based implementation versus GPU-based implementation.

[figure omitted; refer to PDF]

Similarly, the good performance achieved with the GPU implementation with respect to the CPU implementation can be observed in the x-fold gain reported in Table 3. This gain is calculated as the time consumption quotient of both implementations. The behavior of this gain has been reported for each of [figure omitted; refer to PDF] samples stated in the previous paragraph.

Finally, it is important to emphasize that the presented approach can deal with several path realizations. This suggests that the developed fading channel simulator can be considered for generating large MIMO channels, which represents a new simulation paradigm.

6. Conclusions

The principal result of this study is the introduction of a methodology for designing fading channel simulators via GPU devices. Such a methodology permits nonspecialized users to easily implement channel simulators in parallel. As was shown, the use of GPUs in the development of fading channel simulators greatly saves simulation time when channel realizations are generated for testing communication systems. Moreover, a case of study for WiMAX systems demonstrated the functionality of the implemented channel simulator. We believe that the proposed parallel channel simulator can aid in testing mobile communication systems based on LTE and WiMAX. Additionally, the presented approach based on GPU will allow the design of more sophisticated simulators of complex channel models such as triply selective MIMO fading channels (i.e., time, frequency, and space selective).

Acknowledgments

This work was supported by the Programa para el Desarrollo Profesional Docente (PRODEP) 2014 and CONACYT, Ciencia Basica, 2014 (CB2014-241272), Mexico.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

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