- Research
- Open Access
Design considerations of conventional angle diversity receivers for indoor optical wireless communications
- Silvestre Rodríguez Pérez^{1}Email author,
- Beatriz Rodríguez Mendoza^{1},
- Rafael Pérez Jiménez^{2},
- Oswaldo González Hernández^{1} and
- Alberto García-Viera Fernández^{1}
https://doi.org/10.1186/1687-1499-2013-221
© Rodríguez et al.; licensee Springer. 2013
Received: 28 January 2013
Accepted: 20 August 2013
Published: 4 September 2013
Abstract
A conventional angle diversity receiver uses multiple receiving elements that are oriented in different directions, where each element employs its own filter and nonimaging concentrator, such as a compound parabolic concentrator (CPC) or hemispheric lens. In this paper, a study of the design of a conventional receiver structure using angle diversity that offers improved performance with respect to the infrared channel characteristics is presented. To this end, a recently proposed model for the effective signal collection area of a conventional angle diversity receiver that more closely approximates real behaviour than the ideal model is used. The inclusion of this model in a Monte Carlo ray-tracing algorithm allows us to investigate the effects of conventional receiver parameters on the main infrared channel parameters, such as path loss and rms delay spread. Furthermore, in order to determine the number of receiver elements, the outage probability and the average error probability are also considered. Based on the results, a conventional angle diversity receiver composed of seven elements is proposed, with one of them oriented towards the ceiling, and six angled at a 56° elevation with a 60° separation in azimuth. For each element, a CPC with a 50° field of view must be used.
Keywords
- Angle diversity
- Receiver design
- Infrared channel
- Effective area model
- Outage probability
1. Introduction
Nondirected infrared (IR) radiation has been considered as a very attractive alternative to radio frequency waves for indoor wireless local area networks. However, there are two major limitations for establishing a wideband infrared communications link: the power requirements and the intersymbol interference caused by multipath dispersion. In general, the use of multibeam transmitter in conjunction with angle diversity receivers makes it possible to reduce the impact of ambient light noise, path loss and multipath distortion, in part by exploiting the fact that they are often received from different directions than the desired signal [1–9]. Basically, the angle diversity detection can be obtained using conventional, imaging or sectored receivers. A conventional receiver uses multiple photodetectors that are oriented in various directions [4, 5]; an imaging diversity receiver is composed of an optical concentrator that focuses on a segmented photodetector array [2, 6, 7] and a sectored receiver which is a hemisphere, where a set of parallels and meridians defines the photodetector boundaries [8, 9].
The propagation characteristics of the indoor infrared channel are fully described by the channel’s impulse response, which depends on multiple factors such as the room geometry, the reflection pattern of surfaces, the emitter and receiver characteristics, and their relative locations. In this paper, we study by simulation those indoor IR links that are characterised by the use of conventional angle diversity receivers. As discussed above, a conventional angle diversity receiver consists of multiple photodetectors that are oriented in various directions, where each receiving element usually employs a band-pass filter and nonimaging concentrator, such as a compound parabolic concentrator (CPC) or hemispheric lens. In order to estimate the impulse response in IR wireless indoor channels, several simulation methods have been put forth [10, 11], but all of them share the same problem, namely, the intensive computational effort. However, we make use of a Monte Carlo ray-tracing algorithm [12, 13], which presents a lower computational cost than previous methods, especially when a high temporal resolution and a large number of reflections are required. Indoor optical channel simulation can significantly enhance the design of angle diversity receivers but requires models that correctly fit the receiver characteristics and the remaining elements of the IR channel. That is why, in this work, we use models for the reflection pattern of surfaces, background light-induced shot noise and an effective signal collection area for a conventional angle diversity receiver that more closely approximate real behaviour than those previously reported. The inclusion of these models in the Monte Carlo ray-tracing algorithm allows us to study more precisely those optical links that are characterised by the use of conventional angle diversity receivers.
This paper is organised as follows. In Section 2, the channel model of the IR link for the conventional receivers using angle diversity and the expression for the calculation of signal-to-noise ratio are defined. Section 3 presents the study for the design of the conventional receiver structure using angle diversity that yields improved performance with respect to the main indoor IR channel parameters. Furthermore, the outage probability and the average error probability are used as a metric for determining the number of receiver elements. Finally, Section 4 outlines the conclusions of this paper.
2. Channel model and signal-to-noise ratio
where I(t) represents the received instantaneous current at the output of the photodetector, t is the time, x(t) is the transmitted instantaneous optical power, ⊗ denotes convolution, R is the photodetector responsivity and n(t) is the background noise, which is modelled as white and Gaussian, and independent of the received signal.
2.1. Channel impulse response
2.2. Effective signal collection area model
A conventional angle diversity receiver uses multiple receiving elements or branches that are oriented in different directions, where each element employs its own filter and nonimaging concentrator, such as a CPC or hemispheric lens. A principal advantage of angle diversity reception is that it allows the receiver to achieve high optical gain and a wide field of view (FOV) simultaneously. Moreover, an angle diversity receiver can reduce the impact of ambient light noise, cochannel interference and multipath distortion.
2.3. Error estimation for angle diversity receivers
The use of an algorithm based on the Monte Carlo method allows for the error in computing the impulse response to be estimated with just one simulation run, as long as the number of rays is large enough. Different error estimations are obtained for several simulations. Nevertheless, we can be confident that the standard deviation of the estimates decreases as the number of rays is increased. Moreover, the method allows for the accuracy of the results to be assessed. The partial results of one simulation can also be used to achieve a more accurate solution by selecting a suitable number of rays.
Simulation parameters
Element | Parameter | A | B |
---|---|---|---|
Room | Width (x), m | 6 | 6 |
Length (y), m | 7.8 | 13.14 | |
Height (z), m | 2.75 | 2.75 | |
Emitter | Mode (n) | 1 | 1 |
Power (P_{E}), W | 0.4 | 0.4 | |
Position (x, y, z), m | (3, 3.9, 1) | (3, 6.57, 1) | |
IR detector | Active area (A_{R}), mm^{2} | 2 | 2 |
Height (z), m | 1 | 1 | |
Responsivity (R), A/W | 0.6 | 0.6 | |
Minimum power detected, W | 10^{-12} | 10^{-12} | |
Concentrator | Refractive index | 1.8 | 1.8 |
Exit aperture, mm | 0.8 | 0.8 | |
Band-pass filter | Number of layers | 20 | 20 |
Peak transmission (T_{0}) | 0.92 | 0.92 | |
Effective index (n_{s}) | 2.293 | 2.293 | |
Filter order (m) | 3 | 3 | |
Angular bandwidth (Δψ) | ψ _{c} | ψ _{c} | |
λ_{0}, nm | 810 | 810 | |
Tungsten lamps | The corner lamp is located at (x, y) | - | (1.5, 3.57) |
Lamp spectral density, W/nm | - | 0.037 | |
Windows | Diffused solar radiation, W/m^{2} | 10 | 10 |
Window area, m^{2} | 3.6 | 5.3 | |
Simulation | Resolution (Δt), ns | 0.2 | 0.2 |
Bounces (k) | 20 | 20 | |
Number of rays (N) | 500,000 | 500,000 | |
Materials | Wood (ρ, r_{d}, m) | (0.63, 0.6, 3) | (0.63, 0.6, 3) |
Varnished wood (ρ, r_{d}, m) | (0.75, 0.3, 97) | (0.75, 0.3, 97) | |
Cement (ρ, r_{d}, m) | (0.40, 1.0, -) | (0.40, 1.0, -) | |
Ceramic floor (ρ, r_{d}, m) | (0.16, 0.7, 20) | (0.16, 0.7, 20) | |
Glass (ρ, r_{d}, m) | (0.03, 0.0, 280) | (0.03, 0.0, 280) |
2.4. Signal-to-noise ratio
where k is Boltzmann’s constant, T is absolute temperature, R_{f} is the feedback resistor, g_{m} is the transconductance, C_{T} is the total input capacitance of receiver, R_{ D } is the polarisation resistance, Γ is the FET channel noise factor, K and a are the FET 1/f noise coefficients, I_{D} is the FET drain current, and I_{2}, I_{3} and I_{f} are noise-bandwidth factors. In this paper, we consider that the thermal noise at the receiver amplifier is negligible compared to the shot noise. In order to perform the comparison, we evaluated the shot noise and thermal noise variances for an IR diffuse link placed in room B (see Figure 3). The remaining parameters used in the simulation match those shown in Table 1. In room B, the ambient light is provided by four windows and six tungsten lamps in the ceiling. The average shot noise variance obtained is 2.10 × 10^{-15} A^{2}, which was evaluated at over 400 different locations of a receiver based on a single detector element, oriented vertically toward the ceiling, and with a physical area of 2 mm^{2}. Assuming the parameters that might be typical of a receiver operating in a 100 Mbps diffuse link, i.e. k = 1.38 × 10^{-23} J/K, T = 295 K, R_{f} = 10 kΩ, g_{m} = 40 mS, C_{T} = 4.5 pF (for 2 mm^{2} physical area), R_{D} = 146 Ω, Γ = 1.5, K = 294 fA, a = 1, I_{D} = 20 mA, I_{2} = 0.562, I_{3} = 0.0868 and I_{f} = 0.184, the thermal noise variance obtained is 9.15 × 10^{-17} A^{2}. As we can observe, the thermal noise is two orders of magnitude lower than the shot noise.
3. Study of the design of a conventional angle diversity receiver
The algorithm described in the previous section, including the conventional receiver model, was implemented. In what follows, several simulation results obtained for different optical links that are characterised by the use of conventional angle diversity receivers are studied. Using these results, it is possible to establish those parameters of the receiver structure that offer the best performance with respect to the IR channel features.
3.1. Effects of receiver parameters on the IR channel
In order to investigate the effects of the design of the parameters of a conventional receiver on the IR channel characteristics, the impulse response h(t), the path loss (PL) and rms delay spread (D) for different configurations of optical links were computed. Once h(t) has been computed, PL and D are easily calculated [1]. To this end, the IR signal propagation in the room B was studied. Figure 3 shows the graphical representation of the room and Table 1, the parameters used in the simulations. In order to ensure that any contribution above the minimum power detected by the photodetector is computed, the maximum number of reflections has been fixed to 20. The emitter is located at the centre of the room, 1 m above the floor and aimed towards the ceiling, and the IR detector is located at 3 m from the emitter, in the southwest direction on the diagonal: x = 5.2 and y = 4.4.
Number of elements obtained as a function of FOV for a 30° elevation angle
FOV (deg) | Azimuth variation (deg) | Number of elements |
---|---|---|
20 | 81.5 | 4 |
30 | 121.1 | 3 |
40 | 66.2 | 5 |
50 | 90.4 | 4 |
70 | 101.9 | 3 |
90 | 114.4 | 3 |
Number of elements obtained as a function of FOV for a 180° azimuth angle
FOV (deg) | Elevation variation (deg) | Number of elements |
---|---|---|
20 | 15.5 | 6 |
30 | 37.9 | 2 |
40 | 42.2 | 2 |
50 | 42.0 | 2 |
70 | 40.4 | 2 |
90 | 44.0 | 2 |
3.2. Effects of receiver parameters on the IR channel regardless of the receiver location
The study of the dependence of the IR channel characteristics on the parameters that define the structure of a conventional angle diversity receiver provided a procedure for selecting the location of the detectors of the receiver so as to yield channels with different characteristics (independent channels). The results of the study detailed in the previous section, however, are only valid for the receiver location considered, namely, the southwest corner of room B. Moreover, the angular arrangement of the elements was obtained following an azimuth study carried out for a specific elevation angle of 30° and an elevation study for a specific azimuth angle of 180°. If a structure completely independent of receiver location and valid for all elevation and azimuth angles is desired, the analysis must be extended to consider all possible receiver positions and elevation and azimuth angles. So as to gather the necessary data to conduct such a study, multiple simulations were carried out using the two rooms shown in Figure 3. The emitter was located at the centre of each room, 1 m above the floor and aimed vertically towards the ceiling. The receiver was also located on a plane 1 m above the floor and was moved in concentric circles with respect to the emitter position. On each circle, spaced 0.5 m apart, eight uniformly spaced positions were considered. In each location, the impulse response was determined for receivers with FOVs from 10° to 90° in steps of 10° for 100 different orientations. The remaining parameters used in the simulations matched those shown in Table 1. As in the previous section and based on the measurement plan presented, we conducted a study of the dependence of the channel characteristics on the FOV and orientation of a detecting element.
A similar procedure for the study in elevation was executed in azimuth, i.e. the average and standard deviation of the angular separation in azimuth that result in independent channels as a function of elevation angle for several FOVs were studied. The procedure used to compile both parameters is similar to that used for the study in elevation. Starting from the normalised autocorrelation for the rms delay spread in azimuth, we determined the angular separation in the azimuth required for the rms delay spread to fall below 0.4, along with the average and standard deviation of the values obtained for each of the elevation angles analysed. According to the obtained results and independently of FOV, the receivers with elevation angles close to zero present angular separations in azimuth greater than those with near horizontal orientations or high elevation angles. This fact implies a minor number of receivers distributed in azimuth for small elevation angles. For a 50° FOV, the resulting angular separation is approximately 235° in azimuth, i.e. it is not possible to have two or more receivers to verify this condition (360°/235° = 1.5). Therefore, the number of elements in azimuth must be localised in order that the receiver has axial symmetry and to cover all possible directions of reception. As in the elevation study, the average rms delay spread and path loss as a function of azimuth angle for several FOVs were computed. Both parameters were obtained after analysing all the orientations in elevation for each possible receiver position within the two rooms. For selected FOV, both parameters present less variation with respect to the azimuth angle and offer the best performance in both parameters, i.e. the lowest values of rms delay spread and path loss, simultaneously.
3.3. Selecting the number of receiver branches: outage probability and average error probability
In summary, the results of the elevation and azimuth analysis only revealed that the conventional receiver must consist of detector elements with concentrators with a 50° FOV, where one is oriented vertically towards the ceiling, and the rest are in a uniform azimuthal arrangement, forming a 56° angle with respect to the vertically oriented detector. So as to determine the number of elements or branches to be arranged in azimuth, this section presents a study similar to that conducted in [20], where the outage probability and the average error probability are used as measures of link quality to analyse angle diversity at the receiver, the objective being to determine the number of branches required. In this paper, the outage probability is defined by the percentage of receiver locations corresponding to an error probability greater than 10^{-9}, as reported in [20].
where h(t) represents the combined impulse response when a conventional angle diversity receiver is employed. In this article, in order to obtain the output of the conventional angle diversity receiver (the combined channel response), two combining methods were considered: equal-gain combining (EGC) and selection combining (SC). While in EGC, h(t) is obtained by summing the impulse response of each receiver branch; in SC, h(t) is the impulse response of the receiver branch with the lowest delay spread.
In order to obtain the average error probability for random input data, we average the P_{ b } given in (30) over all possible chip sequences b_{ k } having a duration equal to the length of the impulse response h_{ k }. In the study, the effect of the symbols or bits farther than ±6T can be neglected [20], as was corroborated by the simulated impulse responses.
Arrangements of conventional angle diversity receivers
Receiver number | Number of branches | Structure description |
---|---|---|
1 | 1 | One branch oriented vertically towards the ceiling |
3 | 3 | One branch oriented vertically with two uniformly spaced in azimuth |
4 | 4 | One branch oriented vertically with three uniformly spaced in azimuth |
5 | 5 | One branch oriented vertically with four uniformly spaced in azimuth |
6 | 6 | One branch oriented vertically with five uniformly spaced in azimuth |
7 | 7 | One branch oriented vertically with six uniformly spaced in azimuth |
8 | 8 | One branch oriented vertically with seven uniformly spaced in azimuth |
9 | 9 | One branch oriented vertically with eight uniformly spaced in azimuth |
In short, according to the obtained results and assuming that a conventional receiver should have a detector oriented towards the ceiling, which is the main reflector of power, and that it must have axial symmetry, a receiver using angle diversity that relies on the use of concentrators with a 50° FOV must consist of seven branches or detectors, one oriented vertically towards the ceiling, with the other six uniformly spaced in azimuth, forming a 56° angle with respect to the vertical element (see Figure 1).
4. Conclusions
The propagation characteristics of an indoor infrared channel are fully described by the channel’s impulse response, which depends on multiple factors such as the room geometry, the reflection pattern of surfaces, the emitter and receiver characteristics, and their relative locations. In this article, we studied those indoor IR links that are characterised by the use of conventional angle diversity receivers. A conventional receiver uses multiple photodetectors that are oriented in various directions, where each receiving element usually employs a filter and nonimaging concentrator, such as a CPC or hemispheric lens. Simulating an indoor IR channel can significantly benefit the design of high performance systems but requires computationally efficient algorithms and models that accurately match the characteristics of the channel elements. In this work, a Monte Carlo ray-tracing algorithm was used, which exhibits a high computational efficiency with respect to the previous algorithms, especially when a high temporal resolution and a large number of reflections are considered. This discussion can be extended to the evaluation of the shot noise variance from ambient light, since the incident optical power that results from the windows and lamps is also computed using the Monte Carlo ray-tracing algorithm, that is, in contrast to previous works, in this study, we considered not only the noise due to the incident optical power that directly reaches the receiver but also the optical power from multiple reflections. In short, the channel’s impulse response and noise variance were determined with a higher degree of accuracy than in the previous research, which affects the calculation of the performance, in terms of SNR and bit error probability, of those IR communication systems that are characterised by the utilisation of conventional angle diversity receivers. In fact, obtaining an impulse response with a high temporal resolution is necessary in order to study systems operating at a high bit rate.
As discussed previously, in addition to the simulation algorithm, the models that accurately fit the characteristics of the channel elements are required. To this end, the models for the reflection pattern of surfaces and the effective signal collection area of a conventional angle diversity receiver were proposed, which more closely approximate real behaviour than those previously reported. The inclusion of these models was possible because of the high computational efficiency of the Monte Carlo ray-tracing algorithm. In conclusion, based on the results of the study of the influence of the conventional receiver parameters on the main IR channel parameters and on the effect that the increasing diversity order of the receiver (number of branches) has on the average error probability and the outage probability, as defined by the percentage of locations that correspond to an error probability greater than 10^{-9} employing 2-PPM systems with EGC and SC, a receiver structure composed of seven branches or detector elements was proposed, with one of the branches oriented towards the ceiling, and six at a 56° elevation with a 60° separation in azimuth. For each detector, a CPC with a 50° FOV must be used.
Declarations
Acknowledgements
This work was funded in part by the Spanish Ministerio de Ciencia e Innovación (project TEC2009-14059-C03-02/01/03), Plan E (Spanish Economy and Employment Stimulation Plan) and the Government of the Canary Islands (ProID20100117).
Authors’ Affiliations
References
- Kahn JM, Barry JR: Wireless infrared communications. Proc. IEEE 1997, 85(2):367-379. 10.1109/5.554222View ArticleGoogle Scholar
- Alsaadi FE, Elmirghani JMH: Adaptive mobile line strip multibeam MC-CDMA optical wireless system employing imaging detection in a real indoor environment. IEEE J. Sel. Areas Commun. 2009, 27(9):1663-1675. 10.1109/JSAC.2009.091216View ArticleGoogle Scholar
- Alsaadi FE, Elmirghani JMH: Adaptive mobile multicarrier code division multiple access optical wireless systems employing a beam clustering method and diversity detection. IET Optoelectron. 2010, 4(3):95-112. 10.1049/IET-OPT.2009.0006 10.1049/iet-opt.2009.0006View ArticleGoogle Scholar
- Al-Ghamdi AG, Elmirghani JMH: Analysis of diffuse optical wireless channels employing spot-diffusing techniques, diversity receivers, and combining schemes. IEEE Trans. Commun. 2004, 52(10):1622-1631. 10.1109/TCOMM.2004.836509 10.1109/TCOMM.2004.836509View ArticleGoogle Scholar
- Carruthers JB, Kahn JM: Angle diversity for nondirected wireless infrared communication. IEEE Trans. Commun. 2000, 48(6):906-969. 10.1109/26.848557Google Scholar
- Jivkova S, Hristov BA, Kaverhrad M: Power-efficient multispot-diffuse multiple-input-multiple-output approach to broad-band optical wireless communications. IEEE Trans. Veh. Technol. 2004, 53(3):882-888. 10.1109/TVT.2004.825779 10.1109/TVT.2004.825779View ArticleGoogle Scholar
- Djahani P, Kahn JM: Analysis of infrared wireless links employing multibeam transmitters and imaging diversity receivers. IEEE Trans. Commun. 2000, 48(12):2077-2088. 10.1109/26.891218 10.1109/26.891218View ArticleGoogle Scholar
- Lomba CRAT, Valadas RT, De Oliveira Duarte AM: Sectored receivers to combat the multipath dispersion of the indoor optical channel. In Proceeding of Sixth IEEE International Symposium on Personal, Indoor and Mobile Communications (PIMRC '95). Edited by: IEEE. New York: IEEE; 1995:pp. 321-325.View ArticleGoogle Scholar
- Mendoza BR, Rodríguez S, Pérez-Jiménez R, González O, Poves E: Considerations on the design of sectored receivers for wireless optical channels using a Monte-Carlo-based ray-tracing algorithm. IET Optoelectron 2007, 1(5):226-232. 10.1049/IET-OPT:20060062 10.1049/iet-opt:20060062View ArticleGoogle Scholar
- Barry JR, Kahn JM, Lee EA, Messerschmitt DG: Simulation of multipath impulse response for indoor wireless optical channels. IEEE J. Sel. Areas Commun. 1993, 11(3):367-379. 10.1109/49.219552 10.1109/49.219552View ArticleGoogle Scholar
- López-Hernández FJ, Betancor MJ: DUSTIN: a novel algorithm for the calculation of the impulse response on IR wireless indoor channels. Electron. Lett. 1997, 33(21):1804-1805. 10.1049/EL:19971224 10.1049/el:19971224View ArticleGoogle Scholar
- López-Hernandez FJ, Pérez-Jiménez R, Santamaría A: Ray-tracing algorithms for fast calculation of the channel impulse response on diffuse IR-wireless indoor channels. Opt Eng 2000, 39(10):2775-2780. 10.1117/1.1287397 10.1117/1.1287397View ArticleGoogle Scholar
- Rodríguez S, Pérez-Jiménez R, López-Hernádez FJ, González O, Ayala A: Reflection model for calculation of the impulse response on IR-wireless indoor channels using ray-tracing algorithm. Microw. Opt. Techn. Lett. 2002, 32(4):296-300. 10.1002/MOP.10159 10.1002/mop.10159View ArticleGoogle Scholar
- Rodríguez S, Pérez Jiménez R, González O, Rabadán J, Mendoza BR: Concentrator and lens models for calculating the impulse response on IR-wireless indoor channels using a ray-tracing algorithmi. Microw. Opt. Techn. Lett 2003, 36(4):262-267. 10.1002/MOP.10738 10.1002/mop.10738View ArticleGoogle Scholar
- Barry JR, Kahn JM: Link design for nondirected wireless infrared communications. Appl. Opt. 1995, 34(19):3764-3776. 10.1364/AO.34.003764 10.1364/AO.34.003764View ArticleGoogle Scholar
- González O, Rodríguez S, Pérez-Jiménez R, Mendoza BR, Ayala A: Error analysis of the simulated impulse response on indoor wireless optical channels using a Monte Carlo-based ray-tracing algorithm. IEEE Trans. Commun. 2005, 53: 124-130. 10.1109/TCOMM.2004.840625 10.1109/TCOMM.2004.840625View ArticleGoogle Scholar
- González O, Militello C, Rodríguez S, Pérez-Jiménez R, Ayala A: Error estimation of the impulse response on diffuse wireless infrared indoor channels using a Monte Carlo ray-tracing algorithm. IEEE Proc. Optoelectron. 2002, 149(5/6):222-227. 10.1049/IP-OPT:20020545View ArticleGoogle Scholar
- Jivkova ST, Kavehrad M: Multispot diffusing configuration for wireless infrared access. IEEE Trans. Commun. 2000, 48(6):970-978. 10.1109/26.848558 10.1109/26.848558View ArticleGoogle Scholar
- Pakravan MR, Kaverhad M: Design considerations for broadband indoor infrared wireless communication systems. Int. J. Wirel. Inform. Netw. 1995, 2(4):223-237. 10.1007/BF01538147 10.1007/BF01538147View ArticleGoogle Scholar
- Alqudah YA, Kavehrad M: Optimum order of angle diversity with equal-gain combining receivers for broad-band indoor optical wireless communications. IEEE Trans. Veh. Technol. 2004, 53(1):94-105. 10.1109/TVT.2003.822023 10.1109/TVT.2003.822023View ArticleGoogle Scholar
- Audeh MD, Kahn JM, Barry JR: Performance of pulse-position modulation on measured non-directed indoor infrared channels. IEEE Trans. Commun. 1996, 44(6):654-659. 10.1109/26.506380 10.1109/26.506380View ArticleGoogle Scholar
Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.