Test method for narrowband F/TDMA-based wireless sensor/actuator networks including radio channel emulation in severe multipath environments

2.1 Radio channel models

Rayleigh, Rice, Nakagami and Weibull channel models are oftenly employed to describe the magnitude or envelope of the signals in terms of small-scale fading for non-line-of-sight (NLOS) or partially obstructed line-of-sight (OLOS) radio channels, respectively (Rappaport, 2001; Shankar, 2012). In addition, the log-normal distribution is commonly used to model large-scale fading and shadowing (Rappaport, 2001; Shankar, 2012), but is also occasionally employed to model small-scale fading, too (Rappaport, 1989; Rappaport and McGillem, 1989; Shankar, 2012).

2.2 Rice distribution

The fundamental scenario which is described by a Rician fading channel is a dominant path with signal power A² at the receiver (e.g., a line-of-sight component: LOS case) and superimposed multipath components with a mean signal power 2σ² resulting in a probability density function (PDF) of the signal's amplitude r (Rappaport, 2001):

where I₀ is the modified Bessel function of the first kind and zero order. The ratio

is commonly denoted as the Rician K factor (Rappaport, 2001). A sketch to visualize the physical interpretation of a Rician faded receiving signal is shown in Fig. 2, whereby the length of the arrows corresponds to the magnitude of the specific multipath component and the direction represents the phase of that multipath component.

2.3 Rayleigh distribution

As the dominant component in Rician fading vanishes, which is equivalent to a Rician K factor approaching zero (or −∞ dB, respectively) or the limit A→0, the Rician distribution becomes a Rayleigh distribution with (Rappaport, 2001)

There 2σ² represents the mean signal power level. In this sense Rayleigh fading is the worst-case scenario of Rician fading, because fading dips of the received amplitude occur statistically more frequently for Rayleigh fading than for Rician fading. The fundamental scenario to obtain a Rayleigh fading channel is a non-line-of-sight (NLOS) path between transmitter and receiver. Therewith the signal arrives at the receiver over different paths. The signal components from the reflections exhibit approximately the same amplitude and their phases are uniformly distributed (Rappaport, 2001).

Figure 3 shows a visualization of the physical interpretation. Many (scattered) multipath components arrive at the receiver with approximately the same magnitude (length of the arrows) and approximately uniformly distributed phases (directions of the arrows).

2.4 Nakagami distribution

The Nakagami distribution is also used to model small-scale fading (Shankar, 2012) and fits so-called delay clusters, meaning scenarios where the delay time spreads occur in clusters with roughly the same delay times within a single cluster but significant differences between the clusters (Eluma and Arshad, 2013). In Agrawal et al. (2014) it was pointed out that the Nakagami distribution characterizes deep fading as well. A physical interpretation of the Nakagami distribution is given in Abbas and Sheikh (1996). The PDF of the Nakagami distribution

has two parameters, typically denoted as m and Ω, whereby Γ(…) is the Gamma function and the Nakagami parameter m is limited to $m\ge \frac{\mathrm{1}}{\mathrm{2}}$ (Abbas and Sheikh, 1996). m is also referred to as the shape factor (Eluma and Arshad, 2013) or a fading figure (Abbas and Sheikh, 1996), and represents the severity of fading (Agrawal et al., 2014). The scaling or spreading parameter Ω represents the mean signal power (Abbas and Sheikh, 1996; Eluma and Arshad, 2013).

Figure 3Illustration for the physical interpretation of Rayleigh fading: no dominant path exists and many scattered components (arrows) with roughly the same power level (similar length to the arrows) are superimposed.

Download

Figure 4Illustration for the physical interpretation of Nakagami fading.

Download

The Nakagami distribution is an approximate solution of the distribution of the sum of random vectors, even if the magnitudes of the components have random magnitudes (as in contrast to the Rayleigh distribution) (Abbas and Sheikh, 1996; Agrawal et al., 2014; Hashemi, 1993; Riback et al., 2005). The Nakagami distribution is also a good approximation for a Rice distribution (Abbas and Sheikh, 1996; Hashemi, 1993; Riback et al., 2005), and the Nakagami parameter m is directly related to the Rician K factor by (Abbas and Sheikh, 1996)

A coarse visualization of the physical interpretation is shown in Fig. 4. Scattered components with a variety of magnitudes are superimposed by a few dominating clusters.

Figure 5PDFs for Rayleigh, Rician, Nakagami and log-normal fading with different parameters. Where applicable, the parameter σ was chosen equal to unity.

Download

The Nakagami distribution can be considered a generalized Rayleigh distribution (Shankar, 2012) and for m=1 both distributions correspond to each other (Abbas and Sheikh, 1996; Shankar, 2012). More accurately, the Nakagami PDF with m=1 has to represent the same mean power to equal a Rayleigh PDF, meaning to fulfill

e.g., with σ=1, $⟹\mathrm{\Omega }=\mathrm{2}$, as shown in Figs. 5 and 6. As a further consequence, the scaling factor ω_N has no influence on the CDF, if the CDF is normalized to its median.

2.5 Weibull distribution

The Weibull distribution is also used to model small-scale fading, although no physical explanation for the Weibull distribution exists (Hashemi, 1993; Riback et al., 2005). Commonly, the Weibull distribution is expressed with two parameters, a shape parameter α and a scale parameter β (Eluma and Arshad, 2013; Riback et al., 2005; Shankar, 2012), as

Also, a simplified form using just one parameter exists (Shankar, 2012). The Weibull distribution can also be considered a generalized Rayleigh distribution and corresponds to it in the special case α=2. More accurately, the Weibull PDF with α=2 and $\mathit{\beta }=\sqrt{\mathrm{2}}$ equals the Rayleigh PDF with σ=1, as shown in Figs. 5 and 6. For the Weibull parameter α>2 less deep fading occurs compared with a Rayleigh model.

Figure 6PDFs for Rayleigh, Rician, Nakagami and log-normal fading with different parameters for small amplitudes r. Where applicable, the parameter σ was chosen equal to unity.

Download

2.6 Log-normal distribution

The log-normal distribution is commonly used to describe large-scale fading and shadowing (ITU, 2017; Rappaport, 2001; Shankar, 2012). But it is also used to model small-scale fading in factory environments in some cases (Hashemi, 1993; Rappaport, 1989; Rappaport and McGillem, 1989). According to Rappaport and McGillem (1989) and Hashemi (1993), the log-normal distribution fits the measured data well for signal levels below the median. The log-normal distribution

also has two parameters, a shape parameter σ>0 and a scale parameter μ_LN (Riback et al., 2005).

2.7 Comparison

The PDFs of the distributions considered in this chapter with different parameters are shown in Fig. 5. For the Rayleigh and Rician distribution, the parameter σ was chosen equal to unity.

According to Cox et al. (1984), Stein (1987), Rappaport and McGillem (1989), and Agrawal et al. (2014), the performance of a wireless system during deep fading is predominantly determined by the lower tail region of the distributions. Therefore in Fig. 6 a magnified view of the lower tail region is shown.

The cumulative distribution functions (CDFs) of the previously shown distributions with different parameters are shown in Fig. 7, whereby the graphs are normalized to their median value. For the Rayleigh and Rician distribution the parameter σ was again chosen equal to unity. According to Stein (1987), Rappaport and McGillem (1989), and Agrawal et al. (2014), the probability of deep fading which might cause outage can be derived from this plot. As previously mentioned, the Rayleigh distribution with σ=1 equals the Nakagami distribution with m=1 and Ω=2 and the Weibull distribution with α=2 and $\mathit{\beta }=\sqrt{\mathrm{2}}$.

Figure 7CDFs for Rayleigh, Rician, Nakagami and log-normal fading with different parameters. Where applicable, the parameter σ was chosen equal to unity.

Download

The Rice CDFs with any parameter K>0 lie always below the CDF of the Rayleigh distribution for relative levels below the median. This means that deep fading occurs less frequently in a Rice channel than in a Rayleigh channel. This result is equivalent to the statement that if a dominant path (e.g., a direct LOS component) exists between the transmitter and the receiver, deep fading occurs with less probability than in a NLOS or Rayleigh scenario. Measurements have shown that Nakagami's parameter m is significantly larger than unity in many scenarios (e.g., m≈2.5 in Agrawal et al., 2014 or m≈35.7 in Eluma and Arshad, 2013). For m>1 fading dips are also less frequent than for Rayleigh distributed signal amplitudes. As Nakagami and Rice distributions are good approximations of each other, they are most often best fits for the measurements presented in Riback et al. (2005). The measurements in Eluma and Arshad (2013) yield for the Weibull parameter α≈38.1, so the condition α>2 is significantly fulfilled in that case, which results in less deep fading than in a Rayleigh model. According to Riback et al. (2005) the Weibull distribution can imitate other distributions like the Nakagami or Rician distributions very well and furthermore also usually shows better fits than the Rayleigh distribution in the measurements presented there. For relative levels from about −25 to 0 dB below the median, the CDF of the log-normal distribution lies above the Rayleigh's CDF, meaning that fading in these levels occurs more frequently in a log-normal model than in a Rayleigh model. For relative levels lower than about −25 dB below the median, which corresponds to deep fading and usually a high outage, probability fading occurs much less frequently in a log-normal model than in a Rayleigh model. This qualitative outcome is also shown in, e.g., Rappaport and McGillem (1989) and Agrawal et al. (2014). As an interpretation, the log-normal channel model can also be considered to be less severe regarding deep fading than the Rayleigh channel model. As a conclusion the Rayleigh channel model is considered as a worst-case scenario, generally.

Figure 8Generic sketch of a (half-duplex) F/TDMA communication system. The frequencies change between the frames in this example.

Download

4.1 Node testing

In order to provide a communication partner for the EUT, for node testing (sensor/actuator testing) the TE has to include a BS as well. To test the EUT as a part of the wireless communication system, all other network nodes up to the system capacity limit have to be emulated by the TC, as shown in Fig. 9. In this example the EUT is assigned to frequency track i and time slot j. So all other signals except that particular frequency track i and time slot j are generated by the TE.

Figure 9Sketch of the DL and UL signals for node testing. The parts of the hardware setup that generate the corresponding signals are denoted in italics.

Download

An exemplary hardware setup for the TE is presented in Fig. 10. For better clarity, control lines are omitted in this block diagram with the exception of the synchronization (Sync) and setting (Set) connections. The TE consists of the subsystems BS, TC and CE. The CE provides the associated attenuation for each UL and DL signal that is applied to the EUT. As the BS represents the master of the communication system, the overall system timing for the TDMA is provided by the BS. Therefore it is convenient to derive the synchronization for the TC and the CE from the DL signal of the BS. Optionally, further interferers (e.g., WLAN) can be added. The whole TE is designed to accurately meet the specification of the standard and can therefore considered golden equipment, according to a golden master in IO-Link Community (2014).

Figure 10General test setup for node testing.

Download

4.2 Base station testing

Especially for BS, testing under full communication load is important. At least parts of the data handling in a BS are realized by serial processing, e.g., data processing or the communication over a wired network or fieldbus, and thus possible bottlenecks should be identified. Here the TC is the communication partner for the EUT (BS) emulating the UL signals of all nodes, as shown in Fig. 11.

Figure 11Sketch of the DL and UL signals for node testing. The parts of the hardware setup that generate the corresponding signals are denoted in italics.

Download

The hardware test setup for a BS is presented in Fig. 12 where EUT (BS) acts as communication master. For better clarity, control lines are omitted in this block diagram with the exception of the synchronization (Sync) and setting (Set) connections. The TC generates the emulated UL signals from the nodes and the CE provides the specific $\left|H\right(f_i,t_j\left)\right|$. Also, the timing accuracy has to be tested by the TC and external measurement instruments. As the TC emulates node signals and provides measurement routines in this symmetric test setup, the TC acts as an inverted BS (BS⁻¹) in this context. Here also the overall TE is designed to accurately meet the specification of the wireless standard and can therefore considered a golden device in accordance with the IO-Link Community (2014).

Figure 12Test setup for BS testing.

Download

4.3 EUT with integrated antenna

To couple signals wirelessly into EUT with integrated antennas, several shielded test enclosures (e.g., semi/full anechoic chamber, gigahertz transverse electromagnetic cell, GTEM cell, reverberation chamber, RC) were suggested (Schwab and Kürner, 2011). A RC consists of a shielded volume, which is equipped with mode stirrers. Usually these are rotating or moving plates to stir the electromagnetic fields within the chamber stepwise or continuously (Holloway et al., 2006; Schwab and Kürner, 2011). Besides these mechanical mode stirrers, other types of mode stirrers can also be utilized (Kildal et al., 2015; Moglie et al., 2015; Rosengren et al., 2001).

In contrast to most other test enclosures, RCs provide stochastically isotropic fields (Schwab and Kürner, 2011) and intrinsic radio channels with Rayleigh (or Rician) fading behavior (Chen et al., 2015; Corona et al., 2000; Holloway et al., 2006; Kildal et al., 2012, 2014; Kostas and Boverie, 1991). This means that for a full mode-stirring cycle the corresponding set of measurements results in an isotropic and homogeneous environment for the EUT. Figure 13 shows a test setup including a RC.

Figure 13Test setup for EUT with integrated antenna.

Download

The coherence bandwidth of the RC-Rayleigh channel can be adjusted to the same values as measured in industrial environments (Chen et al., 2011; Coder et al., 2010); i.e., the intrinsic channel can be tuned to emulate a particular environment by loading the RC, e.g., with absorbers (Cammin et al., 2017b; Chen et al., 2011; Coder et al., 2010; Cui et al., 2012; Rajamani et al., 2013; Schwab and Kürner, 2011). This allows us to omit an additional CE, if a Rayleigh channel is desired (Lötbäck et al., 2015).

For quality testing during the production process, a simplified approach is suggested, which is similar to the relative measurements in (ETSI EN 300 328, 2016). First, a prototype of the series product is tested in a RC according to the approach presented above. In a second step the same prototype is mounted in a small absorber chamber, or more specifically, in a test fixture (TF) instead of a RC, and the test is repeated. The measured FEP/BEP obtained in the TF can then be used as reference values. In contrast to a test in a RC, a TF does not provide a (statistically) isotropic and homogeneous field distribution. But the measured reference values can be used if the EUT is always mounted in the same position and orientation within the TF.

4.4 Test equipment design considerations

In the previous Figs. 10, 12, and, 13, block diagrams for test setups are shown. The radio frequency (RF) components, meaning the ATTs, power splitter/combiners and RF connections, are standard components with a good availability on the market. The BS in Figs. 10 and 13 can be a standard BS, augmented by capabilities for FEP/BEP measurements. In addition, further measurement capabilities, e.g., for power/RSSI (received signal strength indicator) or communication retries (in the case of transmission errors), would be beneficial. As indicated before, the realization of the TC as inverted BS (BS⁻¹) employing the same narrowband transceivers used in the communication system can significantly reduce the effort and cost for both the development and hardware of the TC, as the design of the TC is very similar to the ordinary BS. For comparable testing, the CE should contain a standardized (Rayleigh) channel model or a set of channel models. For the BS, TC and CE components, the same software and hardware tools which are employed for the BS and the nodes for standard operation can be used. The complete measurement setup will be controlled by a standard computer with appropriate software tools (e.g., MATLAB, LabVIEW).