INVESTIGATION OF WIRELESS CHANNELS ACCORDING TO THE STANDARD 802.11 IN THE FREQUENCY RANGE OF 5 GHZ FOR TWO SUBSCRIBERS

In the given work the research of wireless channels of the family of standards of 802.11x in the frequency range of 5 GHz was taken into account taking into account the influence of architectural obstacles in the premises. As the main parameters for the research the effective transmission rate, the signal strength at the receiver input and the channel throughput are chosen. It has been established that the rate of transmission of information has a direct dependence on the signal transmission characteristic, therefore, to assess the level of signal fluctuations, it is necessary to use a confidence interval of power. On the basis of experimental research, a mathematical expression was obtained for evaluating the efficiency of wireless channels of the 802.11x family of standards for a frequency range of 5 GHz, taking into account the architectural obstacles in the room. It is established that in the presence of two subscribers in the network there are quite significant restrictions for high-performance modes.


INTRODUCTION
Widespread distribution of the 'Internet of Things' conception causes the wider introduction of the wireless technologies [1].This conception envisages availability of substantial quantity of the devices, which require permanent connection with the relevant network.Depending on the type of a relevant device, it is possible to use both channels with low transmission capacity, and highly-productive channels.In order to ensure this possibility, it is worth to utilise the technology of family of standards 802.11х, as one of the sufficiently efficient technologies [2].It can ensure both integration of the devices in accordance with the 'Internet of Things' and provision of access to the communication and informationcommunication services.
In the course of designing of networks according to the standard 802.11, the main task is to achieve better of stability of channels and increase the efficient rate of information transmission.At the same time, efficient rate of information transmission is in direct proportion to the level of the signal power at the input of receiving device and this efficient rate determines quality parameters of signals [3].Quite widespread distribution of the wireless networks causes occurrence of a number of negative factors, which ensure appearance of delays and of mistakes in the course of sessions of traffic transmission.Therefore, search of new methods and means is essential with the purpose of minimisation of influence of these factors, as well as with the purpose of improvement of the main criterion of the channel efficiency -the efficient rate of information transmission.Again, at the same time, it is impossible to create a new method without information on the nature and character of influence of the destabilising factors of the wireless channels.One of the very essential factors is connected with the architectural obstacles and barriers that occur due to the structure of those premises, within which wireless networks are created.Therefore, goal of this article is to perform investigation of the wireless channels in accordance with the 802.11х standards taking into account various architectural barriers; however, we will restrict this investigation by a single situation, where only two subscribers exist in a network.

LITERATURE REVIEW
As it is known, there exists a quite great quantity of the destabilising of factors in the wireless transmission environment, which have influence upon the main figures of efficiency of the wireless channels of the 802.11х standards.It is possible to list the following main factors: change of parameters of a wireless channel in the course of transmission in time; obstructions, which are independent sources of emission; architectural obstacles and barriers.In order to decrease influence of these factors, it is necessary to determine dependences of connection between them and the main efficiency criteria.
In this regard, it is possible to list a number of the research articles, which can be separated in two groups: investigations of the energetic of parameter and investigations of the efficient information transmission rate.As concerns the first group of investigations, it is possible to name articles and [4].They have proposed mathematical models and a new method on the basis of these models in order to estimate spatial distribution of a signal for any premises with angular and central position of the point of access.This method allows taking into account all existing destabilising factors, which can exist within the wireless environment.
Results of the investigations that were performed in the articles and demonstrate availability of the threshold value of the power level [5,6].In the course of these investigations, the following characteristic properties were determined: as concerns the subscriber device, the established level of emission was equal to 10-6 W/m at the distance from one metre and more metres.In the course of transmission of information through the wireless channel, power improves by an order of magnitude.In addition, a number of factors, which influence upon the estimate of the RSSI (received signal strength indicator), were established, such as: position of receiver in space, distance between receiver and transmitter, time of measurement, obstructions from other devices, and availability of architectural obstructions.It was established that there exist essential fluctuations, as well as that they depend from of the specific of the manufacturer equipment due to different frequencies of sampling and discretisation.In addition, it was established that different position of device changes level of signal by 2 dB•m, while deviation in space by 1 metre adds 6 dB•m to the level of these fluctuations.This fact can cause certain restrictions in respect of withstandability of channels to the external factors.
It is possible to include investigations of the factors, which influence upon the transmission capacity of channel, to the second group.For example, it is possible to remember articles and, where the following problem is stated of correct operation of the CSMA/CD technology in the wireless networks, which function according to the standard 802.11[7,8].Because of this technology is the probabilistic protocol of the MAC level (Media Access Control according to the IEEE 802), then in this case a number of problems occurs in the course of distribution of the transmission capacity of a channel between the existing subscribers in a network.As the result of this, it was established that increase of quantity of subscribers causes decrease of the signal/noise ratio, as well as decrease of efficiency of the synchronisation algorithm of the МАС level.
Beginning from the standard 802.11n, it is envisaged to use of highlyproductive channels, which will operate in accordance with the spectrum broadening technology.In this case, it is necessary to analyse the problem of the estimation of operation taking into account of the channel width.Investigation of influence of the 40 MHz channels upon the productivity of networks was performed in article [9].In this case, it was established that increase of the channel bandwidth causes increase of the transmission capacity, as well as decrease of the coverage area and increase of sensitivity to obstructions.
As concerns comparison of the estimation of the main energetic parameter for the ranges of 2.4GHz and 5GHz, and simultaneous analysis of architectural barriers, it is possible to remember article [10].This article describes sufficiently essential quantity of results of the RSSI parameter for six multi-storey structures in two countries of the European Union.This analysis has demonstrated that waves of the 5GHz range are characterized by essentially greater attenuations in the wireless channel.Predominantly, such phenomena are observed in the vertical direction, where materials with the higher density are utilised.Therefore, waves of the 5GHz range have the lower transmission capacity through the architectural obstacles and barriers.In addition, it is also possible to underline that the higher sensitivity of device causes the higher flatness of characteristics, as well as that, as a rule, it causes decrease of the efficient information transmission rate.
Summarizing all above-mentioned information, it is possible to say that sufficiently essential quantity of the destabilising factors has influence upon the parameters of the wireless channels of the 802.11х standards.In this case, if we want analyse the criterion of the channel efficiency, classic models will be improper and inappropriate ones due to the availability of random components.Therefore, goal of this article will be as follows: search for a universal model of estimation of the channel efficiency criterion on the basis of the experimental investigations for any premises with architectural barriers.In addition, it will be necessary to analyse the active CSMA/CD technology and utilisation of the 5GHz frequency range.

MATERIALS AND METHODS
In order to achieve the target goal, it is necessary to have relevant condition of activation of the CSMA/CD technology.Such condition is as follows: availability of two radio circuits -two movable subscribers in a network.This methodology of investigations is based on the network, which functions according to the standard 802.11 and includes the transmitting-and-receiving equipment of the point of access (the PoA), as well as the subscriber's devices (SD1 and SD2).
Scheme of the wireless network is presented in Figure 1.The network supports all existing standards 802.11 for the 5GHz range.The PoA supports the МІМО technology (multiple-input/multiple-output) with three transmitting-and-receiving antennas (as the most common situation, which is presented in the market.In order to perform these investigations, a typical room was chosen, and length of the wireless channel "l" within this section could be equal up to 15 metres.The channel for information transmission consists of the receiving-and-transmitting equipment, the PoA, as well as of two subscriber's devices (SD1, SD2), which form two wireless channels (WC1 and WC2).In order to ensure estimation of influence of the architectural barriers, availability of two insertion barriers was envisaged: B1 barrier at the distance of l1=3 metres and B2 barrier at the distance of l1 + l2 = 6 metres.
Taking into account the fact that (from the point of view of the top-level applications of the OSI model) the main criterion is to ensure transmission of information through the channel without any changes, and then it is possible to state that this criterion is the parameter of efficient information transmission rate V (Mb/s).From the point of view of a channel, the main parameter is transmission of frames without mistakes per unit time, and such operation is determined as the parameter of the transmission capacity of a channel Vpl (Mb/s).Because of transmission capacity of a channel includes the parameter of the efficient information transmission rate, as well as service information of the data link layer and of physical layer, therefore (from the point of view of the above-listed applications) it is possible to determine the criterion of the channel efficiency as follows: Then, it is possible to choose the efficient information transmission rate V (which is determined at the level of applications) as the main parameter for investigations.In addition, it is also possible to choose the signal power at the input of receiver P as the main energetic parameter, which has a direct influence upon V.Because of the parameter of the information transmission rate is in direct dependence on the characteristic of the signal transmission, then (in order to estimate level of fluctuations of a signal) it is possible to utilise the limiting values of the admissible changes of the attenuation coefficient (of a signal), which has received the name as follows: confidence interval of power.To this end, we will write down the following condition: where ∆c, ∆g, ∆a, ∆b are coefficients, which determine limiting values of the admissible changes of the coefficients of attenuation of a signal; Pc is the average value of the signal power; δ -coefficient of fluctuations of a signal.
The parameter of the efficient information transmission rate has fluctuations as well, and it is possible to describe these fluctuations with the help of the relevant confidence interval, which will correspond to the interval of fluctuations of power: where ∆V is the confidence interval of the efficient information transmission rate, and Vc is the averaged value of the efficient information transmission rate or mathematical expectation.Therefore, the main parameters for these investigations, which determine efficiency of a channel, are as follows: the efficient information transmission rate, transmission capacity, power of signal at the input of receiver, as well as their confidence intervals.

Analysis of experimental investigations
The experimental investigations of the main determined parameters of the wireless channels according to the 802.11х standards in the 5GHz range were performed on the basis of the proposed methodology in order to estimate dependence of their characteristics from the typical architectural barriers.To this end, the following wireless channels were investigated: 802.11a, 802.11n-20MHz, 802.11n-40MHz, 802.11ac 20 MHz, 802.11ac-40MHz, 802.11ac-80MHz.
Length of the wireless channel WC1 under investigation is determined by the parameter l, while length of the channel WC2 is constant and it is equal to 2 metres.In order to simulate architectural barriers, we have used various structures, which were made of wooden components and bricks and which have been installed between the PoA and SUBS-R1 (subscriber 1).These investigations have been performed for the following typical situations (in the similar manner, as they were performed in article [4]): line-of-sight; availability of a single door; availability of two doors; availability of one wall or two walls.

Line-of-sight
It is one of the most the most widespread situations for creation of a wireless channel: it is envisaged that the PoA and subscribers are within the same room.In this case, the architectural obstacles and barriers have only influence upon the signal due to creation of the reflecting surfaces thus increasing the effect of the multipath wave propagation.Results of these investigations are presented in Figure 2. As is evident from the graphs, characteristics of the efficient information transmission rate have a character of attenuation and they have a similar character for various standards.The same situation was observed in the case with the single wireless channel: the channel according to the standard 802.11а had the more stable characteristics.The most unstable characteristic was found for the channel according to the standard 802.11асdue to the decreased quantity of protection intervals in the course of formation of the OFDM (orthogonal frequency division multiplexing) of a signal.In addition, increase of instability is connected with utilisation of the greater channel width, because of the fact that two subscribers use one and the same frequency resource.
With the help of inequalities ( 2) and ( 3), let us determine the confidence interval of change of the main parameters of efficiency.Therefore, we will have the following: Results of the transmission capacity of the channels demonstrate that in the case of availability of two subscribers in the network, sufficiently essential restrictions exist for the highly-productive modes according to the standard 802.11ас.These restrictions are connected with the sufficiently high value of the signal/noise ratio.Under actual usage conditions, that is in the case of availability of any destabilising factors within the transmission environment (these factors include interference obstructions) it is only possible to ensure the highly-productive mode within the immediate vicinity of subscriber to the PoA.As an exception, it is possible to create the situation, in accordance with which the subscriber device will be situated within the zone of maximum of the spatial distribution of a signal, and this fact can increase level of the signal/noise ratio, as well as increase transmission capacity of a channel (maximum at the distance of 11 metres from the PoA; see Fig. 2c).

A single barrier -wooden components
Such transmission environment envisages availability of doors or a wooden partition between the PoA and the subscriber device.In its turn, this fact adds an additional coefficient of attenuation of a signal.Results of these investigations are presented in Figure 3.The characteristics, which were obtained, have similar characters, but level of fluctuations is higher.The highest fluctuations are observed for the wideband channel 802.11ас 80 MHz.
In this case, it is possible to write down that the confidence interval will be as follows: ≈ ±6; ∆  ≈ ±2Mb/s  20 ≈ ±7; ∆ 20 ≈ ±4Mb/s  40 ≈ ±6; ∆ 40 ≈ ±5Mb/s  20 ≈ ±8; ∆ 20 ≈ ±3Mb/s  40 ≈ ±6; ∆ 40 ≈ ±5Mb/s  80 ≈ ±10; ∆ 80 ≈ ±10Mb/s The above-listed parameters of fluctuations are correct for the results at the following distances: 3 metres before and 3 metres behind the installed barrier.In other case, fluctuations are lesser by 1.5…2 times depending on the standard and they correspond to the direct visibility (line-of-sight situation).From the point of view of the physical layer, availability of one barrier causes occurrence of essential mistakes in the frames in the course of transmission.In this case, small protection intervals of the standard 802.11ас are considered as a negative factor, which increases its instability.In this case, channel 802.11n with 40 MHz bandwidth is the most efficient and stable one.The above-listed fluctuations are correct at the distance of 3 metres before the first barrier and 3 metres behind the second barrier (this situation is the same as in the previous case).The sufficiently high instability of the main characteristics is observed within this short distance.As the result of this, it is possible to assume that the effect of the multipath wave propagation is increased in the case of availability of the closely adjacent reflecting surfaces due to repeated reflection from the neighbouring surface of the barrier.Then level of fluctuations is the same as in the case of the single barrier.From the point of view of the physical layer, transmission capacity of channels behind the barrier is restricted at the level of the standard 802.11n and it depends on the channel bandwidth.
Quite essential attenuations make it impossible to utilise the highlyproductive modes of the standard 802.11ас.

Barriers -walls
As a rule, availability of walls as barriers in the wireless channel causes sufficiently high attenuations of signals.Results of these investigations are presented in Figure 5.As is evident from the graphs, if the CSMA technology will be activated, it is possible to observe the sufficiently essential decrease of the efficient information transmission rate.In contrast with the single channel, in this situation we observe jumping and negative-going sections on the characteristics.In this case, the decreasing coefficient is in direct dependence on the density of the architectural barrier.
The confidence interval has the following values: δ_a≈±14dBm; 〖∆V〗_a≈±3Mb/s δ_n20≈±16dBm; 〖∆V〗_n20≈±5Mb/s δ_n40≈±16dBm; 〖∆V〗_n40≈±10Mb/s δ_ac20≈±13dBm; 〖∆V〗_ac20≈±4Mb/s δ_ac40≈±18dBm; 〖∆V〗_ac40≈±12Mb/s δ_ac80≈±20dBm; 〖∆V〗_ac80≈±14Mb/s In the case of availability of the architectural barriers with high density, fluctuations of a signal transform into quite high fluctuations, which can achieve levels of ±13...20 dB•m.This fact allows to make an assumption that density of material has direct influence upon the coefficient of the multipath wave propagation as well.Availability of two architectural barriers ensures essential decrease of the signal level but working capacity of the channel can be kept with low transmission capacity due to switching of the channel to the mode with the lower transmission rate.

Estimation of the coefficient of efficiency for two wireless channels
The experimental data, which were obtained, include information on the main parameters of the wireless channel.Estimation of these parameters includes the random component, which is determined by the confidence interval.Then, method of the mathematical regression is the most expedient method in order to estimate the coefficient of efficiency of the wireless channel.Therefore, the quadratic model and logarithmical model will be the most optimum ones for the parameter of the efficient information transmission rate.Each of these models has relevant restrictions in respect of the channel length: ; 15 ; where f, u, s are coefficients of the regression reduction, which have dimension of Mb/m; x and v are initial coefficients of the efficient information transmission rate.Coefficients of the regression reduction are presented in Table 1.On the basis of the results that are presented in Table 1, it is possible to assume that there exists a possibility to determine general model of estimation of the efficient transmission rate with the help of methods of averaging.In this case, it is necessary to take into account the average values of reduction coefficients and intervals of their deviations, values of which will demonstrate availability and type of the architectural barriers in a channel.In principle, it is possible to write down the following: , , where Δf, Δu, Δs are coefficients, which determine intervals of deviation from the averaged values of the reduction coefficients.Then, on the basis of the results presented in In order to decrease influence of the restrictions, which are connected with the parameter "l" in the formulae (4) and ( 5), it is possible to apply methods of averaging in respect of these restrictions.On the basis of the mathematical simulation and the determined reduction coefficients, it was established that the most optimum method of averaging is the harmonic mean averaging.In addition, it was established that v ≈ x+3 (Mb/s).Then, it is possible to write down the formula for estimation of the efficient information transmission rate in the following manner: This parameter of the efficient information transmission rate must be determined on the basis of the minimum value of fluctuations in the confidence interval.Therefore, coefficient of efficiency of the wireless channel in the case of existence of two subscribers in a network (taking into account the architectural barriers within the room for the 5GHz range) will be formulated in the following manner: ( ) ( ) Coefficient of efficiency of the wireless channel in the case of availability of two subscribers in a network depends on the reduction coefficients and on their intervals of deviations.With the help of these intervals, it is possible to perform estimation of parameters of the wireless channels of the 802.11х standards in the 5GHz range, as well as their fluctuations and type of the architectural barriers.
In order to confirm the obtained model ( 10), we will analyse it with the help of the mathematical simulation.For example, Figure 6  Influence of architectural barriers determines intervals Δf, Δu, and Δs.On the basis of these intervals, it is possible to determine the manner of changes of efficiency of a channel depending on the availability of the direct visibility (line-of-sight), availability and quantity of architectural barriers and density of these barriers.These intervals are changed in accordance with the confidence intervals of the efficiency parameters taking into account the fluctuations of the signal power and the efficient information transmission rate.This mathematical model of the efficiency coefficient is true and correct for any premises, minimum length of which does not exceed 40 metres.
In addition, it is worth to note that the above-presented model of estimation of the efficiency coefficient has a failure.This failure is connected with the correct selection of the deviation coefficient.Such correct selection can be achieved with the help of the obtained information concerning the essential quantity of experimental and statistical investigations of wireless channels.

CONCLUSIONS
On the basis of the performed investigations of wireless channels of the 802.11х standards in the 5GHz range in the case of existence of two subscribers in a network, the following characteristic properties were established: • in the case of existence of architectural barriers, as well as in the case of the activated CSMA technology, level of fluctuations is higher than in the case of a single wireless channel -approximately up to 25% for the highly-productive modes.This makes it clear that in the case of increase of the subscriber's quantity in a network, instability of the channel parameters increases as well; • architectural obstacles and barriers cause the same coefficient of attenuation of parameters V and Vpl for all standards under investigation (except for 802.11а standard); • level of fluctuations of the efficiency parameters is the same in the case of utilisation of the same bandwidth of a frequency channel (for any range of channels).This fact gives the substantiation to stet that increase of the channel bandwidth is in direct dependence on the level of fluctuations.
It was developed a new mathematical model of estimation of the efficiency coefficient for the wireless channels according to the 802.11х standards, and this model takes into account the fluctuations of the main parameters.This model is true and correct for the 5GHz frequency range, as well as for any premises, length of which does not exceed 40 metres, as well as for the premises where architectural barriers and obstacles exist.

Figure 1 :
Figure 1: Structure of the network for investigation of the channel parameters

Figure 2 :
Figure 2: Experimental characteristics of the channel parameters for the direct visibility (line-of-sight situation): a -dependence of the efficient transmission rate on the distance between receiver and transmitter; b -dependence of the efficient transmission rate on the signal power at the input of receiver; c -dependence of the transmission rate of the physical layer on the distance between receiver and transmitter; d -dependence of the transmission rate of the physical layer on the signal power at the input of receiver.

Figure 3 :Figure 4 :
Figure 3: Experimental characteristics of the channel parameters in the case of availability of one barrier: a -dependence of the efficient transmission rate on the distance between receiver and transmitter; b -dependence of the efficient transmission rate on the signal power at the input of receiver; cdependence of the transmission rate of the physical layer on the distance between receiver and transmitter; d -dependence of the transmission rate of the physical layer on the signal power at the input of receiver

Figure 5 :
Figure 5: Experimental characteristics of the channel parameters in the case of availability of two walls: a -dependence of the efficient transmission rate on the distance between receiver and transmitter; b -dependence of the efficient transmission rate on the signal power at the input of receiver; cdependence of the transmission rate of the physical layer on the distance between receiver and transmitter; d -dependence of the transmission rate of the physical layer on the signal power at the input of receiver

Figure 6 :
Figure 6: Dependence of the coefficient of efficiency of the wireless channel on: a -Δf; b -Δu; c -Δs; d -ΔxAs it may be seen from the obtained graphs, the Δx interval demonstrates dependence of the coefficient of the channel efficiency on the utilised mode of operation of the standard.Determination of the variable value x in the real-time operation will make it possible to estimate the efficiency of a channel taking into account the maximum possible quantity of the destabilising factors within the transmission environment.

Table 1 :
Coefficients of the regression reduction for the efficient information transmission rate

Table 1 ,
we will determine general values of the reduction coefficients of characteristics of the efficient information transmission rate, Mb/m: