Industrial wireless channel measurements in a 2.4 GHz ISM radio band using a low-cost SDR-based channel sounder

Wireless communication is one of the greatest engineering achievements of the last several years. It has had an enormous impact on science, markets, and society, allowing us to communicate anytime, anyplace. Industry 4.0, the fourth industrial revolution, could not have come about without this technology. Its application can be found in various diagnostic and surveillance systems, sensor networks, and many others. One of the leading concepts for the modern industry is the Industrial Wireless Sensor Network (IWSN) technology, a network of sensors that can communicate with each other, increasing production efficiency throughout the industry. Another technology currently in high demand is the Internet of Things (IoT), which requires constant improvements to wireless communication systems.

Despite the abundance of improvements that wireless communication offers industry, several disadvantages must be considered. Different physical phenomena degrade the performance of a communication channel (i.e., multipath propagation, path loss, shadowing, channel interference, noise, and others), making the connection less reliable and more vulnerable. Consequently, it is important to investigate radio propagation, especially in industrial environments.

Channel sounding can be used to improve wireless communication systems. It is crucial to sound and analyze the transmission medium for network design upgrades. The knowledge ob- tained will increase link reliability and decrease maintenance expenses, in turn reducing production time and cost - a great benefit for industrial companies that decide to implement such innovations in their facilities.

There are various types of environments in industry, such as mines, fabrics, laboratories, etc., and each has different propagation characteristics. For example, there can be an environment which intensifies the multipath propagation effect due to many metallic objects in the area. More- over, working electric motors in fabrics can produce shot-type noise.

To study the different propagation environments, several site-specific measurement campaigns are needed. To date, few investigations have attempted to characterize wireless channels in differ- ent industrial environments. In (Coll, 2014), channel parameters were measured in a metal work- shop, a paper warehouse, a mine tunnel, and other sites. (Syed & Green, 2019) and (Düngen et al., 2019) present measurements for indoor industrial facilities with an application for IoT and indus- trial automation. In (Al-Samman et al., 2017), research was carried out on Ultrawideband wireless indoor channels in stationary and mobile scenarios. Similar measurements were carried out in (MacLeod et al., 2005), (Miaoudakis et al., 2005), (Luo et al., 2011). Likewise, a complete channel measurement campaign was conducted in (Cheffena, 2016) for the IWSN application. (Cheffena, 2014) presented a physical-statistical approach to channel characterization, while (Wassie et al., 2018) was focused on ultra-reliable communication techniques.

In general, the previous works were conducted using specialized and expensive channel sound- ing devices, such as Vector Network Analyzer (VNA), which complicates the study of new indus- trial propagation environments. An alternative to those systems is Software Defined Radio (SDR) based channel sounders, which are affordable and have an easily reconfigurable structure. How- ever, there are still some serious drawbacks to this type of sounder, such as synchronization problems, sampling resolution, or hardware throughput limitations. Some projects have already implemented such SDR sounding systems (Wassie et al., 2019), (Boeglen et al., 2017), (Samayoa et al., 2018), (Hosseini & Matolak, 2018), (Maas et al., 2012) with different sounding techniques, such as OFDM modulation or the cross-correlation method. (Jamison & Frolik, 2018) has proved to be, in comparison with VNA, a highly-efficient channel sounder based on one of the cheapest SDR devices available on the market. (Boeglen et al., 2017) presented an SDR-based embed- ded, portable channel sounding system. (Fliedner et al., 2018) showed a design for an industrial environment channel sounder with the use of SDR equipment.

The purpose of this article is to enrich knowledge about wireless channel performance in in- dustrial environments. A measurement campaign will be conducted in a mechanical engineering workshop, focusing on an analysis of the multipath propagation effect in the 2.4 GHz Industrial, Scientific, Medical (ISM) radio band. The collected data, together with the results from similar studies, will be helpful for network design improvements.

A further objective is to design a channel sounding system which would be accessible for a larger group of researchers, enabling the engineering society to gain a deeper comprehension of wireless propagation efficiency. The plan is to achieve this with low-cost SDR equipment. The proposed system concept and the mathematical model will be suitable for any application, envi- ronment, or frequency configuration, facilitating a possible reproduction of the presented measure- ment campaign in any other transmission band. Particular attention is paid for offering a solution to the synchronization problem. Additionally, system mobility will be enhanced with the use of Rasp- berry Pi 4 and GPS disciplined oscillators (GPSDO). Performance of the designed system will be tested by taking the aforementioned measurements in an industrial environment and validated using theoretical propagation models.

This article is organized as follows: Chapter 2 introduces the basics of radio wave propaga- tion, while Chapter 3 presents the mathematical model of the channel sounding process. Chapter 4 explains physical implementation of the system. Chapter 5 describes the measurement cam- paign. Chapter 6 offers a discussion of the sounding system, and Chapter 7 presents the project conclusions.

In wireless communication, information is propagated by means of an electromagnetic wave. There are many phenomena that interfere with wave propagation, the most important being re- flection, diffraction, and scattering. Reflection occurs when the propagated electromagnetic wave strikes an object significantly larger than the wavelength, i.e., buildings, walls, or the ground. Diffraction takes place on the sharp edges of the objects, causing the wave to bend. Scatter- ing happens when the wave is propagated through a medium containing many small objects per unit volume (e.g. tree leaves, street signs, or lamp posts) (Rappaport, 2002).

In the following sections, the basic concepts of the radio channel and the physical phenomena that affect its performance will be explained.

2.1 Channel model

The word ”channel” can have many meanings, but in its general sense, it means everything be- tween the signal source and its sink. Basically, a channel model can be considered a mathematical or algorithmic representation of the propagation medium’s transfer characteristics (Jeruchim et al., 2002).

In the figure 1, the channel model is mathematically represented as a linear, time-invariant filter with impulse response h(t), whose input is the transmitted signal x(t). If the signal is transmitted in the presence of white Gaussian noise n(t), filtered signal and noise components are summed and the output signal y(t) has the form of Equation (1) (Grzybkowski et al., 2006).

To characterize a radio channel, it is necessary to analyze the physical phenomena which assist with the propagation of electromagnetic waves and their interaction with the environment. Channel performance greatly depends on the operating frequency, the transmission environment, transceiver movement, and other factors. Typically, the channel parameter analysis is divided into two propagation modes. One of these is the Line-of-Sight (LoS) scenario, in which there are

no obstacles in the path between the transceivers (the devices ”see” each other). In the other, non-Line-of-Sight (NLoS), the path is obstructed.

Unlike the stationary and predictable wired techniques, the wireless channel is random and difficult to analyze. It is often defined as a stochastic process and requires a statistical approach for its description. In practice, many channel models are based on fitting external (empirical) observations (Stuber, 2017).

2.2 Fading channel classification

The fading channel is a communication channel which experiences variation of the attenuation of a signal as a function of time, geographic position, and radiofrequency. Fading is often described as a random process. Classification of fading types is depicted in Figure 2 (Stuber, 2017).

The two main groups of fading type are large-scale fading and small-scale fading. Large scale fading is due to distance-depended path loss of signal and shadowing provoked by large objects such as buildings and hills. Small-scale fading is characterized as rapid fluctuations of the signal over a small distance or a short period. One small-scale effect is multipath propagation, which can be further divided into flat and frequency selective fading. Small-scale fading also refers to the Doppler effect, which can be interpreted as fast or slow (Tse & Viswanath, 2004). Each of the abovementioned effects will be explained in the following chapters.

2.3 Large-scale fading

Large-scale fading models signal strength over a large distance between the transmitter and the receiver. The signal received by a mobile radio from a transmitter can be represented as

where Sr is the power of the received signal in dBm, St is the power of transmitted signal in dBm, Gtx and Grx are antenna gain (dB) of a transmitter and receiver, respectively, and Lp is the propagation loss in dB. The equation 2 is often called a ”link budget”. The antenna gain depends

on the antenna’s physical design, position, and orientation. The Lp component is the most difficult to define and relies on two effects: path loss and shadowing (Jeruchim et al., 2002).

2.3.1 Pathloss

Most propagation loss models are based on the fact that the average received signal power de- creases logarithmically with distance. Path loss is an exponential function and can be represented by Equation 3

where α and β are parameters determined by the propagation medium, and R is the transmitter- receiver separation distance. The parameter values for each model can be defined by measure- ment campaigns in specific environments and scenarios (Jeruchim et al., 2002).

2.3.2 Shadowing

The equation 3 does not consider the shadowing effect. In the analysis, it is necessary to include the case in which the propagated wave is ”shadowed” by buildings or other obstacles, leading to the immense difference between the measured signal and its predicted average strength. It can be mathematically represented by adding to the Equation 3 a random variable Xσ, as follows

Xσ is a zero-mean Gaussian distributed random value in dB with standard variation σ. It symbol- izes a random shadowing effect that occurs over a large number of measurements for the same transmitter-receiver separation but with different obstacles in the propagation path (Rappaport, 2002).

2.4 Small-scale fading

Small-scale fading describes rapid fluctuations to signal strength over a short-range or period, so the large-scale effect can be neglected for this analysis. This fading type is the consequence of the constructive and destructive interference of the multiple signal paths between the transmitter and the receiver. This means that the radio receives many copies of the emitted signal a phenomenon known as multipath propagation. Furthermore, the movement of transceivers or enclosing objects results in the Doppler frequency shift on multipath components (Rappaport, 2002).

2.4.1 Multipath propagation

The example of multipath propagation is presented in Figure 3. Emitted waves can be reflected in the environment by reflectors, for example surrounding buildings and objects, creating ”echoes” of the signal. Echoes of the signal are called multipath components. These multipath components are weighted and delayed versions of the original propagated signal, which combine at the receiver antenna. Thus, the impulse response h(t) of a multipath channel is defined mathematically as follows:

where am and τm are the amplitude and arrival time of a m-th signal path, respectively, δ(t) is the Dirac delta function, and M is the maximum number of paths.

Each component has a random amplitude and phase, inducing small-scale signal strength fluctuations and provoking signal time dispersion and delays, leading to intersymbol interference (Rappaport, 2002). This has a significant impact on communication performance, making it crucial to analyze the following channel parameters related to this phenomenon:

• Power Delay Profile (PDP), Ph(t), describes the distribution of the received signal power in time from a transmitted impulse and is defined as a spatial average of squared channel impulse response h(t), as follows:

where E[·] is the expected value and Rhh is the autocorrelation function.

• Mean delay spread, τmean, s the averaged multipath delay and is defined as the first moment of the PDP (Eq.7), with the units in seconds.

RMS delay spread, τrms, is a measurement of the channel time dispersiveness and deter- mines the maximum symbol rate achievable by a communication system before intersymbol interference occurs. Therefore, it is often cited as the most important multipath parameter, determining the overall wireless channel performance. It is defined as the second central moment of the PDP (Eq.8) (Grzybkowski et al., 2006).

Max delay spread, τmax, is the maximum time spread of the multipath components when a predefined threshold is exceeded and is defined as

where τfirst and τlast are the arrival time of the first and the last multipath components, respectively.

• Coherence bandwidth, Bx%, is a statistical parameter that helps to define whether the channel is frequency selective over a given frequency band or frequency non-selective (flat). It is a measure of a frequency range over which the attenuation is constant and linear in phase. The coherence bandwidth has been related by inverse proportionality to τrms, as defined in the following equation:

where values of α span between 5 and 50, which corresponds to the respective correlation values of 50% and 90% (Coll, 2014).

Figure 4: RMS delay spread, mean delay spread and max delay spread shown in an example of an indoor power delay profile (Rappaport, 2002).

In Figure 4, the aforementioned parameters are highlighted in the power delay profile of an indoor channel. In this example, the received power is normalized. The threshold for the maximum excess delay is set to -10 dB and the noise level to -20 dB. It can be seen that the delay values for the indoor environment are in the range of 1-200 ns.

2.4.2 Doppler Effect

The relative movement of the transmitter and the receiver cause multipath components to experi- ence a shift in frequency. This effect is called the Doppler effect and is proportional to the velocity and motion direction of a transceiver with respect to the direction of arrival of the received multipath wave. Doppler shift fd is given by the following equation:

where fc is the carrier frequency( in Hz), v is the velocity of the source or sink of the signal and c is the speed of light (both in m ). Doppler shift is negative when the transceivers move away from each other (Rappaport, 2002).

2.5

s Importar tabla

Industrial environment characteristics

All the aforementioned concepts occur in the real communication system, and their intensity de- pends greatly on the site and surroundings. In the industrial environment, more Non-Line-of-Sight type of propagation is expected due to the communication medium being filled with obstacles, lead- ing to signal attenuation and shadowing. Moreover, metallic machinery can provoke an intensified multipath effect caused by many reflections, diffractions, and scattering, and any random move- ment by people or robots in the area may cause time-variant effects in the propagation. Channel performance can be highly degraded if these phenomena are not taken into consideration when designing an industrial wireless communication system (Coll, 2014).

In this chapter, the mathematical foundations of the channel sounding process will be presented, showing how the channel impulse response (which is a stochastic process) can be estimated by means of cross-correlation function and white Gaussian noise. Furthermore, the estimation of PDP, using the autocorrelation matrix method, will be presented.

3.1 White Gaussian noise

The first step in designing the mathematical model is to understand what white Gaussian noise is and what its properties are. White Gaussian noise is a sequence of uncorrelated random variables with a Gaussian distribution. Without a loss of generality, an assumption of zero mean and variance E[n2(t)] = σ2 is made for the Gaussian noise. An important property of white noise is its constant power spectral density, meaning uniform power of each frequency. The average noise power at a period (t1, t2) can be calculated as follows:

In the channel sounding process, it helps to analyze all frequencies of the bandwidth at the same time. An example of white Gaussian noise (samples in time domain and power spectral density) is shown in Figure 5.

Figure 5: Example of white Gaussian noise. Time domain samples and power spectral density.

Another significant characteristic of white noise is its autocorrelation function, which is defined

as:

where∗denotes the convolution operation. This implies R(τ) = 0 for any lag τ = 0. The autocor-

relation function of white noise will play a crucial role in the design of a channel sounding process (Hayes, 1996).

3.2 Channel impulse response estimation

Cross-correlation is a measure of similarity of two signals as a function of the displacement of one relative to the other. This function will be used to estimate the channel impulse response. By definition, the cross-correlation function between signal y(t) and x(t) can represented as (Proakis & Manolakis, 2006)

The channel can be thought of as a Linear, Time-Invariant system (LTI). The output signal y(t) of the system can be represented as a convolution of the impulse response function h(t) and the input signal x(t) (Sharif & Sha’ameri, 2007)

In this case, the input of the system x(t) will be white Gaussian noise and h(t) is the channel impulse response that will be estimated.

If the signal y(t) in the Eq.14 is substituted by the signal definition shown in Eq.15, the cross- correlation can be represented as follows:

It can be easily seen that x(τ ) ∗ x(−τ ) is the autocorrelation of white noise (eq. 13).

Using convolution properties for scalars and delta functions, the equation is developed in the following manner:

where σ2 is the average power of the input signal.

As proved by means of equations 14 - 18, the cross correlation function of an output signal of a system with white noise input is equal to the system’s impulse response

As noted above, the channel impulse response function is a stochastic process. To improve estimation, it is necessary to analyze several realizations of the process. Cross-correlation should be repeated several times, and the results should be averaged to obtain a better channel impulse response estimation.

3.3 Estimation of power delay profile

The next part of the channel analysis is to estimate the power delay profile. For this, the autocor- relation function will be calculated using the previously estimated channel impulse response h(t), as shown in the Eq.6.

The autocorrelation function is a second-order statistical characterization of a random process. Before this function can be computed, a conversion of the continuous impulse response h(t) into discrete domain h[n]c is needed, which is carried out as follows:

where Ts is the sampling period, and g(t) is the function that delimits the signal bandwidth to a certain value.

As a result, the discrete impulse response h[n] can be represented, based on the Equation 5, as follows:

and can be stated in a vector form as:

where p is given by the maximum delay of am and the duration of g(t) function.

The autocorrelation function Rhh of impulse response h[n] is established as follows:

Further, am is a random variable, and for PDP estimation, is assumed to be uncorrelated scat- tered (US). The US assumption is satisfied if the phase of any multipath component is uncorrelated to another component with a different delay (Molisch, 2011). Thus, the final form of the autocor- relation function is

where σ2 is the power of the m-th component.

The autocorrelation function Rhh[n1, n2] can be expressed in a matrix form, as follows:

The elements of the main diagonal of the matrix Rhh are the values of the autocorrelation function that define the estimation of Power Delay Profile

In practice, the channel sounding process requires a device capable of sampling a radio signal at the desired frequency, with a suitable antenna gain and radiation pattern. The most important factor to consider is the synchronization between transceivers. The physical implementation of the channel sounding system will be presented in this chapter. Additionally, a sounding signal structure and a solution for the synchronization problem will be offered.

4.1 Equipment

The key equipment used for channel sounding is the bladeRF x40. This product from the Nuand company is an SDR, which means that the radio components (such as mixers, filters, modulators, etc.) can be implemented by software. The frequency range of 300 MHz to 3.8 GHz is suitable for measurements in the 2.4 GHz ISM band. The maximum bandwidth of the instrument is 28 MHz. It is capable of acquiring 12-bit IQ samples with a sample rate of up to 40 MS/s, which results in the maximum time resolution of 25 ns. To achieve such a high data rate between the bladeRF board and the controller unit, the producer implemented a USB 3.0 interface. BladeRF has an independent transmission and reception signal paths, so it can operate in a Full-Duplex mode. It also has an external clock port, crucial for solving the synchronization problem. Two bladeRF boards are used in the system: one for signal transmission and another for reception (Nuand, 2014).

The outcoming signal is amplified by an external power amplifier to reach 15 dBm of trans- mission power. A Crystek CRBAMP-100-6000 amplifier, with 18 dB gain and 1 dB compression point at 17 dBm, is used in this implementation. The received signal is amplified using bladeRF’s onboard low noise amplifier. Both bladeRFs are connected, via an SMA connector, to omnidirec- tional antennas suitable for the 2.4 GHz frequency band. The gain of the antennas is 2 dBi and the length is 10.8 cm.

A pair of Leo Bodnar’s Mini Precision GPSDOs provide a reference clock for the SDR devices. The instrument output is a 3.3 V CMOS signal. The output frequency can be programmed to any value between 400 Hz and 810 MHz. For the purposes of this project, the frequency is set to 38.4 MHz to meet the bladeRF specifications. The GPSDOs are connected to bladeRF’s external clock port with an SMB cable. The device uses an active GPS antenna with a 3 m cable and is powered by 5V DC from a USB port (LeoBodnar, 2015).

In the proposed bladeRF system configuration, a controlling unit with a USB 3.0 interface and a minimum 2 GB RAM is required to both input the transmission signal to the SDR device and to receive data. The newest version of a single-board computer, Raspberry Pi 4 with 2 GB RAM, has been chosen to be the transmission side of the sounder due to its USB 3.0 ports, essential for correct sounder operation. For the reception part and system controlling unit, an ASUS N550J laptop with Ubuntu Linux 18.04 operating system, Intel Core i7 CPU, and 16 GB RAM was used.

4.2 Channel sounding system

Figure 6: Sounding system diagram.

Figure 6 shows the channel sounding system, which is divided into 2 sections: hardware im- plementation and signal processing. The PC unit is the sounder controller unit. One of its tasks is to establish a connection (over a local WiFi network) with the remote transmission part of the system, which is controlled by Raspberry Pi, and send it a command to start the channel sounding process. The PC’s other task is to handle the signal processing part of the system. Both tasks are performed by a Python program developed by the author, with the help of open-source Python libraries.

The first step of the sounding process is to generate a white noise sequence, which is pro- duced by the PC unit and sent to Raspberry Pi. The same signal is stored for further processing in the signal processing part. The sounding signal is passed to bladeRF, amplified, and propa- gated through the omnidirectional antenna to the industrial environment. On the receiver side,

there is another bladeRF device connected to the antenna and controlled by the PC unit. Both bladeRF boards are controlled via USB 3.0 interface and bladeRF-cli (bladeRF Command Line Interface, a software tool provided by the board’s producer) basic commands. The main problem with the sounding system is the synchronization between the transceivers, clarified in chapter 4.4. Received samples are stored and passed to the signal processing part.

The cross-correlation function of transmitted and received white noise is calculated in the signal processing section, obtaining the estimation of the channel impulse response used to compute the auto-correlation matrix in order to estimate the PDP.

The proposed system software is available in a public repository (link to the repository), which contains Python scripts and a Graphical User Interface to perform channel impulse response es- timation with a user-friendly program.

4.3 Sounding signal structure

The following transmission signal structure is proposed for the sounding system: The duration of the signal is 1 second, and the signal is divided into 100 000 windows of a duration of 10 µs. Each window is filled with white Gaussian noise in a time ratio of 1% (0.1 µs), leaving the remaining part with a null value, as shown in Figure 7. This is to assure that each window will be an uncorrelated realization of the sounding process. Filling the window with only white Gaussian noise would influence the subsequent estimation, which does not coincide with the assumptions made in the mathematical model proposed in chapter 3. The estimation of the impulse response is concluded with an average of 100,000 realizations.

Figure 7: Sounding signal structure diagram.

4.4 Synchronization

Synchronization is an important part of the channel sounding process. Leaving this problem un- solved leads to several errors in signal modulation and processing. In SDR-based sounders, there are two issues to deal with.

The first problem to solve is radio oscillator synchronization. In the modulation process, it is crucial that the transceivers rely on the same reference clock in order to avoid synchronization errors, i.e., frequency shift. In this article, the proposed solution is to use GPSDO. This reference oscillator locks its output to pulses sent by GPS satellites. Hence, every SDR used will share the same reference clock for the modulation process.

Another synchronization process must be done in the data processing part. In order for the received white noise to correspond to the transmission sequence samples, it must first be aligned to its first sample. In practice, the sounding signal will not necessarily be at the beginning of received samples due to hardware (bladeRF and the controller unit) delays. The solution is to add

a synchronization sequence at the beginning of the transmission. In this case, a single tone of a known 20 kHz frequency is transmitted for 0.5 seconds, followed by a 0.1-second break, and then the sounding signal transmission is begun (the values were chosen empirically). A diagram of the synchronization sequence is shown in Figure 8. This enables determining precisely where the sounding process starts. It is a pure post-processing problem, meaning that this alignment is set after the transmission, not in the real-time operation.

Figure 8: Transmission synchronization sequence diagram.

This section describes a measurement campaign. First, the details of the measured environment will be presented. Furthermore, several data will be analyzed. The main focus of the experiment was on the multipath propagation effect. A spatially-averaged PDP was estimated and the results were compared with the Saleh-Valenzuela indoor channel model.

5.1 Environment description

The measurement campaign was performed in a workshop of the mechanic faculty at the Univer- sity of Guadalajara, Mexico. The building has an open space hall with dimensions of 42 m× 18 m. It consists of concrete floor and walls, a 12-m high metallic ceiling, metallic stairs, balcony, and railings. The outside wall is made of glass. A view of the workshop is shown in Figure 9.

Due to the absence of machinery or other obstacles, each measurement was performed in a Line-of-Sight scenario. There was no movement during the experiment by the antennas, the people, or the objects.

Figure 10 presents the building dimensions along with measurements points. The transmitting antenna was situated at a fixed position Tx, and the receiver antenna at four different measurement points (Rx1-Rx4). It is worth noting that the Rx1 point was placed under the balcony. The height of the transmitter and receiver antenna was 0.45 m and 0.75 m, respectively.

5.2 Multipath propagation analysis

During the measurement campaign, the multipath propagation effect was analyzed with equipment calibrated for the carrier frequency of 2.3 GHz, 28 MHz bandwidth, and 25 ns of sample time resolution. At each Rx position, the channel was sounded 5 times and an average PDP was estimated. Figures 11 a)-d) show the estimation of normalized PDP at each measuring points.

A dominant multipath component, corresponding to the Line-of-Sight signal path, is observed in each of the estimated PDPs. Moreover, several paths are noticeably delayed and attenuated with respect to the dominant component and can be related to signal reflections off the building’s walls, floor, or ceiling.

The parameters τmean , τrms and τmax were computed for each of the estimated PDPs. Fur- thermore, coherence bandwidth B50% was estimated for the correlation value of 50%. The results are presented in Table 1, along with the separation distance.

As can be seen, values of delay parameters increase with distance, while the coherence band- width decreases simultaneously, deteriorating wireless channel performance. Special attention must be given to trms, as it is often a crucial parameter when defining overall network link effi- ciency. A similar increase of distance leading to an increase of trms has been seen in the literature (Düngen et al., 2019), (Karedal et al., 2007). For the purposes of this article, an estimation model of RMS delay spread propagation, proposed in (Greenstein et al., 1997), will be used, defined as:

where d is the distance between antennas, T1 is the value of trms at 1m of distance, and p is the exponent of the propagation.

A curve fitting method was used to estimate the parameters of Equation 26. The estimated values are T1 = 20.12 ns and p = 0.43. The value of the exponent p is bigger than the reported p = 0.1 in (Karedal et al., 2007), where an industrial hall in an NLoS scenario was analyzed on a short Tx-Rx separation (2 m to 16 m). This greater p value might be due to a different type of analyzed environment, but it also shows that in a relatively large, open space, the propagation medium tends to experience a rapid distance-related increase of trms despite its Line-of-Sight nature. Figure 12 illustrates the RMS delay spread as a function of distance between transceivers and the model approximation in logarithmic scale.

The next step in the analysis is to compute a spatially-averaged PDP (sPDP) using the locally estimated PDPs. sPDP is illustrated in Figure 13. Similar to the local profile outlines, a Line- of- Sight path is remarked as the dominant component, and some paths with significant delay differences are perceived as well.

The propagation parameters are estimated once again for sPDP and presented in Table 2. The measured RMS delay spread trms = 77.2 ns is not as high as the results for high-delay envi- ronments (trms > 150 ns), but greater than low-delay environment values (<30 ns), both reported in (Coll, 2014). Additionally, the estimated RMS delay is higher than a compared trms = 34 ns, measured for a similar environment in LoS scenario in (Syed & Green, 2019). The factors that may provoke an elevated RMS delay spread value are metallic ceiling and rails. Also, the building lacks materials that could absorb the signal energy, such as wood, paper, or others, provoking a possible RMS delay reduction. Nevertheless, the glass wall could be the element which decreases the final value of the parameter. In addition, the working area, free of metallic machinery or other obstacles in the Line-of-Sight, does not provoke an intensified signal reflection occurrence.

In the following step, the measured sPDP is compared with the Saleh-Valenzuela indoor chan- nel model (Saleh & Valenzuela, 1987) chosen because it is referenced in a wide range of studies. This simulation model separates multipath rays into groups called clusters. The power of arriving clusters decays exponentially, as do rays inside the cluster (Fig. 14).

The Saleh-Valenuzela model defines the impulse response h(t) as follows:

where L and K are maximum number of clusters and multipath components inside clusters, re- spectively, βkl is the amplitude of k-th ray in l-th cluster, and θkl is the phase of the kl-th ray. Tl refers to time arrival of the l-th cluster and τkl is the arrival delay of k-th ray with respect to first ray of the l-th cluster. The amplitudekβl kl is computed with the following equation:

where β2(0, 0) is the average power of the first ray received, Γ and γ are exponential decay con- stants for cluster and rays, respectively. The ray decay constant is reported to increase as a function of time delay γ(τ ), thus is modeled as follows:

where γ0 is the ray power decay constant of the first cluster and a is the function slope. The arrival times of clusters Tl and rays τkl are Poisson-distributed, with different interval time constants. Λ parameter indicates an average cluster arrival ratio (average number of clusters per nanosecond), and λ represents the same ratio for rays inside the cluster (Karedal et al., 2007).

To compute the model parameters, the sPDP samples are divided into clusters by the visual decision of the author. Decay factors are estimated with the help of the curve-fitting method. The parameters of the S-V model used for the simulation are listed in Table 3.

Finally, the RMS delay spread of the simulated PDP is calculated and compared to the mea- sured value, which is presented in Table 4. Figure 15 shows the comparison between the mea- sured sPDP of the building and the simulation. As can be noted, the measured and the simulated trms value is within the same range, and the outline of model approximation PDP matches the estimated value.

Table 5 shows a comparison of the designed system with other similar projects. The parameters compared are the software used in each project, the sampling resolution, the mobility, and the approximate system cost for a 2-node (Tx and Rx) sounder. The system cost approximation does not consider the cost of a PC unit.

As can be seen, the achieved sampling resolution of the proposed system - 25 ns - can be considered a satisfactory value, as it is better than the values reported in (Maas et al., 2012), (Jamison & Frolik, 2018), (Samayoa et al., 2018) and equal to the sampling resolution of a more expensive high-end system presented in (Wassie et al., 2019). However, (Fliedner et al., 2018) and (Hosseini & Matolak, 2018) show that there is still room for improvement; the sampling resolution is not as high as in VNAs (<2 ns), but it is sufficient for a good multipath effect analysis.

Several factors could contribute to such a good sampling resolution. First, the use of a USB 3.0 interface between the SDR device and the controller unit eliminates ”bottlenecks” of other inter- faces, i.e., the previous USB generation (USB 2.0), widely implemented in low-cost SDR devices. Second, the cross-correlation sounding method used does not require modulation techniques as other sounding routines do, which allows taking advantage of the full sampling rate provided by the SDR equipment without limiting controller unit performance. Hence, the system implementation uses only basic bladeRF-cli commands and Python libraries, which also speeds up the signal pro- cessing part. The GNU Radio, used in almost every similar project mentioned above, is a useful tool, but it consumes many controller unit processing resources and slows down the achievable system sampling rate.

Most of the aforementioned projects tend to have high sounder mobility. This is due to the nature of the small and integrated SDR boards. Additionally, mobility may be enhanced by an embedded system implementation, as presented in (Boeglen et al., 2017). The proposed sounder also follows this trend with reasonably high-mobility due to the use of Raspberry Pi 4 for the trans- mission part of the system. This single-board computer is a small, cheap, and powerful solution for the controlling unit.

Finally, a comparison of the approximate system costs is carried out. It can be seen that the use of SDR equipment does not necessarily mean a low-cost sounder. The budget for this project was approximately $1,250 USD, which includes two bladeRF x40 boards, two GPS DOs, a signal amplifier, and a Raspberry Pi 4 - significantly cheaper than those presented in (Wassie et al., 2019), (Boeglen et al., 2017), (Fliedner et al., 2018). The proposed sounder is within the budget range defined by those projects.

The analysis of the proposed channel sounding system performance and the comparison with similar projects will define future work. First, a change of the frequency operation range is required to perform a propagation analysis in 5.8 GHz transmission band. This will be accomplished by implementing the newer version of the bladeRF board (BladeRF 2.0) or by changing the RF front end. Second, a possible new approach to the subject would be an increased system sampling rate, as this would permit a 5G wireless channel performance analysis. It is hoped to solve this using an array of multiple synchronized SDR devices performing a shifted sampling. Another solution would be the use of an additional FPGA to act as the controller unit, replacing the limited USB interface. The authors look forward to enlarging the number of possible sounder applications by implementing MIMO propagation techniques. Lastly, a future system reconfiguration is considered to perform a real-time sounding, which could be used in cognitive radio technology to continuously sound and analyze channel performance. However, this would require a powerful processing unit, such as an FPGA or a DSP.

In this article, two achievements were demonstrated. First, the design process and the complete implementation of a channel sounding system were presented. Second, the system was used to perform a measurement campaign, whose objective was to characterize an industrial environment wireless channel.

This article offers a detailed mathematical model, a hardware implementation and a solution to the synchronization problem. The developed sounder software is available in an open repository to facilitate access to a channel sounding tool to a larger group of researchers.

The proposed wireless channel sounder system was validated with a popular Saleh-Valenzuela indoor channel simulation model and both the estimated PDP and the RMS delay spread were within the same value range, demonstrating that an SDR equipment allows a reasonable multipath effect analysis and can successfully substitute VNA devices for the sounding purpose.

The analyzed industrial environment can be identified as an intermediate delay propagation medium. The measured RMS delay spread (77.2 ns) is higher than in a high-delay environment (approx. >150 ns) and lower than in low-delay environments (approx. <30 ns). However, the estimated value is surprisingly higher than that expected for a LoS scenario. Such an increased value is due to the intensified signal reflections caused by the open hall’s dimensions and building materials.

The multipath propagation effect was measured at various positions and antenna separation lengths. The collected data analysis confirms that there is an increase in the RMS delay spread as a function of distance. The delay value follows Equation 26 with parameters T1 = 20.12 ns and p = 0.43. A comparison of the p exponent with other studies shows that this parameter is closely related to the type of environment being analyzed. Its value is influenced by building dimensions, site equipment, and machinery, and LoS/NLoS type of propagation. The analyzed workshop experienced a fast RMS delay increase.

System performance was compared to other SDR-based projects, demonstrating that the pro- posed system has achieved a good sampling rate (reachable for such systems) and that the pro- posed sounder follows the high mobility trend. In addition, the goal for a low-cost system has also been accomplished, with an approximate cost of $1,250 USD. The proposed mathematical model and solutions to SDR limitations facilitate system reconfiguration. The flexibility of this sounder encourages seeking more applications and performing more wireless channel measurements.