In modern industrial wireless applications, communication between sensor nodes is indispensable. In the last years, ultra-wideband or UWB systems evolved for both data transfer and localization. Due to multipath propagation, a received RF signal is often a superposition of multiple echoes of the transmit signal, reflected on walls and other obstacles. The limited bandwidth of the transmit signal leads to constructive or destructive interference between the single signal echoes. An analysis of multipath propagation is challenging since interference is hard to detect, even for UWB signals. Therefore, we develop an interference model for adaptive UWB transmission bands and simulate the efects of interference. For reliable detection of multipath interference, we suggest adapting the transmission bands to vary the result of the interference. By applying the Search Subtract and Readjust-Algorithm of Falsi et al. in 2006, we achieve a reliable identification of signal echoes with improved resolution accuracy depending on the transmission bandwidth. For real systems with limited bandwidth, we assemble received signals of multiple distinct adjacent transmission bands, e.g., the UWB channels, to increase the bandwidth and thereby the resolution accuracy. We evaluate our approach by measurements and found that the resolution for correct identification of interfering signal echoes is improved from 2.32 ns to 0.78 ns by assembling signals from three transmission bands.
The Internet of Things (IoT) is one of the most important application areas for localization. In
the IoT, stationary and mobile devices exchange information wirelessly. The current position of
devices adds the necessary context for interpreting the information provided by the devices,
e.g. data of sensors in industrial production. State-of-the-art solutions employ a localization
infrastructure with ultra-wideband (UWB) technology and multiple anchors to estimate the
position of a tag by measurement of the signal propagation time (e.g. Time Distance of Arrival
[
In wireless communication, a transmitted signal overlaps with echoes that occur in reflection paths and superpose at the receiver. In UWB technology embedded for localization, the received signal is processed with a time resolution in the range of nanoseconds to measure the arrival time of the pulses.
The multipath propagation and the resulting superposition of the signal echoes, e.g. at walls, deteriorate the performance of a localization system. If two interfering signal echoes are too close to each other, the superposition of these echoes prevents the identification of the origin signal echoes. The result of the interference changes for distinct transmission bands. To the best of our knowledge we are the first to investigate and exploit the usage of distinct transmission bands in real systems. By adapting the transmission band e.g. changing the UWB channel in the same radio environment and setup, the superposition of the signal echoes is detectable. By assembling the signals from distinct transmission bands we increase the reliability and resolution of identification of multipath interference.
The contributions of this paper are as follows:
• We design an UWB transceiver model including multipath signal propagation.
• We investigate the impact of transmission bands on interfering signal echoes and introduce
a concept for detection of interference with an adaption of distinct transmission bands.
• We extend the Search Subtract and Readjust-Algorithm of [
• We evaluate the approach by real measurements.
The rest of the paper is organized as follows. Section 2 outlines related work in the field of UWB transceiver models, including multipath propagation and detection and identification of interference, as well as localization systems. In Section 3, we depict our proposed transceiver model and describe the impact of the transmission band on signal echo interference. Section 4 introduces our concept of interference detection and identification. Section 5 provides an evaluation of the approach with real measurements. Section 6 concludes the article and gives a short outlook on future work.
In this section, we briefly summarize the current state-of-the-art of interference detection and identification.
Our concept of detection and identification is applied to modeled multipath propagation. In
[
Multiple algorithms for estimation of the signal echo propagation delays are explored. In [7], Vanderveen et al. presented an ESPRIT-based approach for delay estimation of multipath transmitted signal echoes. Zhao et al. as well as Paredes et al., both developed an UWB channel estimator based on compressed sensing [8, 9]. Yang et al. introduced in [10] the CLEANalgorithm for multipath channel estimation, which is based on the deconvolution technique. In contrast, we focus on the matched-filter theory for identification of the echoes. Yousef et al. formulate an algorithm for detection and identification of constructive signal echo interference following a RAKE-receiver approach [11]. However, in our work, we additionally covered destructive interference based on opposed signal echo phase states.
While some current localization systems mitigate the multipath interference, like Xie et
al. [12] or Dogru et al. [13], our work focuses on identification of interference to exploit the
corresponding information for further processing. Meanwhile, many localization systems rely
on multipath propagation of UWB signals for position estimation. Systems like the device-free
system MAMPI by Cimdins et al. [14] and the single anchor system SALMA by Großwindhager
et al. [
The proposed algorithm decreases the minimum needed resolution accuracy between two interfering signals, which is also important for other applications than UWB localization. The search for correct transmit signals to decline the influence of interference is also possible by the algorithm. Multiple image restoration systems sufer from interfering signals. Sharped images are recovered from blurred ones by application of deconvolution and matched filter approaches, similar to the proposed algorithm [17]. Also in medical ultra-sonic systems, pulse detection techniques are applied to reduce range sidelobe artifacts of pulse compression methods for more than 20 years [18].
In this section, we introduce our UWB transceiver model, including multipath interference. Afterwards, we show how varying the transmission band afects the interference of signal echoes.
In this section, we analyze the impact of multipath propagation on received UWB signals (). To generate the UWB transmit signal (), we select a center frequency and a bandwidth to construct a rectangular transmission spectrum ( ) of width around . In the following, this spectral range is called transmission band B = [ − /2, + /2].
In time domain, the rectangular spectrum corresponds to a sinc-function, while the frequency shift by transforms to a cosine-wave. So, () results to be a cosine-wave of frequency , which is weighted with a sinc-function with zeros in the range of = 1/ around = 0: () = √︀ · sin( · / ) · / · cos(2 · · ), (1) where √ is the amplitude resulting from the given transmit power . We have chosen this basic transmit signal representation to focus on the generality of the following theoretical derivation.
The signal () transmitted on the Line-Of-Sight-Path (LOS) between Tx and Rx is always the first signal sensed by Rx. Additionally, () is reflected at obstacles like furniture or walls and reaches Rx as well. The signal echoes traveling the Non-Line-Of-Sight-Paths (NLOS) result in a longer distance, e.g. for the -th path. The signals () reaching Rx are called signal , = , , with , = ︂( 4 · · )︂ 0 = (4 · · ) ,
Each reflection at a surface of a material with a higher refractive index than the transmission medium causes an additional phase shift of (inverting the signal). By definition, in NLOS paths, the signal echoes () are reflected at least once, with ⩾ 1.
All single signal echoes superpose at the receiver Rx. They difer in propagation delay, power level and phase shift. The Channel Impulse Response (CIR) ℎ() describes the overall multipath propagation with paths: echoes. We assume an ideal transmission and disregard noise and interference by other devices in this work.
Each signal echo is received after a specific propagation delay = /0 (speed of light 0 ≈
3 · 108 m/s) with a characteristic receive power , for the -th path, = 0, ..., − 1. The power , results from the given transmit power , decreased by the distance-depending Friis Free Space Path-Losses , with path-loss coeficient : − 1
=0 − 1
=0 ℎ() = ∑︁(− 1) − 1 =0 √︃
1 , ·
( − ) = − 2 ∑︁(− 1) (4 · )
− 2 · ( − ), (2) (3) (4) (5) () = () * ℎ()
= − 2 ∑︁(− 1) (4 · )− 2 · ( − ). where ( − ) is the Dirac-Function shifted by . Eq. (4) shows that the CIR of distinct transmission bands difers only in scaling factor depending on center frequency . The CIR of the setup shown on the left of Figure 2 is sketched on the right. With increasing delay , the receive power , decreases.
The received signal () is the convolution of the CIR ℎ() with the signal (): Here, the signal on the LOS path with delay 0 = 1.66 ns is received without any interference. The echoes with delay 1 = 6.8 ns and 2 = 8.13 ns interfere, because the delay diference Δ = | 2 − 1| = 1.33 ns is smaller than the main pulse width = 4 ns > 1.33 ns. While the single signal echoes are marked in green and blue, the period of interference is marked in red color. The result of the interference of two signal echoes is modeled in the next step.
This subsection investigates the impact of transmission bands on the interference of two signal echoes. As shown in Figure 1, we assume a main pulse width = 2/ for the given realistic signal (). Therefore, two signal echoes with delay and do interfere, if the delay diference Δ = | − | < = 2/. According to Eq. (1), the oscillation of signal () corresponds to the center frequency of B . Therefore, () of duration includes · oscillations of periodic time 0 = 1/.
The oscillation phase at time 0 is named phase state Θ(0) and depends on as the period of the oscillation is 1/. The phase diference between two signal echos and is constant: ΔΘ, = |Θ − Θ| = 2 · | − | · = 2 · Δ · (6)
This phase diference ΔΘ, is important for a constructive or destructive superposition. Figure 4 depicts two results for ΔΘ, = {60∘ , 150∘ }. On the left, the superposition of the samples results in an overall stronger magnitude (constructive interference). When ΔΘ, is increased by 90∘ , as depicted in the right plot, the sum results in mitigation of the superposed magnitude (destructive interference). It is important to note that the phase shift in these two cases may result from only a change of the center frequency. To illustrate the efect of the change of the center frequency of the transmission band B on the interference, the superposition of two interfering signal echos and is shown, with = 6.87 ns, = 8.2 ns and Θ(0) = 0∘ . This delay diference of Δ = 1.33 ns results in completely diferent phase shifts ΔΘ, for the three selected UWB channels 1, 2 and 3 as shown in Table 1 and Figure 5.
The transmission bands of the UWB channels 1 and 2 superpose to the same magnitude as the phase diference ΔΘ, is ± 120∘ . Choosing the transmission band B,3 of UWB channel 3 leads to the phase diference ΔΘ, = 0∘ , which corresponds to the maximum constructive superposition. Since ΔΘ, is constant (independent of time) for the signal echoes and , the superposition is also constant (either destructive or constructive) for the total period of interference.
Note, that the phase diference ΔΘ, is always equal for two transmission bands, if ,1 = · ,2 holds, with ∈ N. The impact of the transmission band on the superposition of signal echoes is applied in the next section to detect and identify interference.
In this section, we first introduce our approach for detection and identification of interfering signal echoes and calculate the resolution and limitations. Second, we show how to improve the resolution accuracy by combining multiple transmission bands.
In the last section, we depicted, how the transmission band B afects the superposition of two interfering signal echoes. Since the overall magnitude of the superposition varies, depending on the chosen center frequency , the adaption of evinces interference in the received signal (). Neglecting the scalar factor − / 2 (comp. to Eq. (5)), the complex envelope’s magnitude |()| of the received signal () of multiple distinct transmission bands only difers in the period of interfering signal echoes. To calculate (), we shift the received signal from the transmission band at center frequency back to baseband at 0 = 0 Hz and apply a lowpass-filter.
Figure 6 shows the magnitude of the complex envelopes ,1(), ,2() and ,3(), for a certain multipath setup with 0 = 1.66 ns, 1 = 6.87 ns, 2 = 8.2 ns and 3 = 12.05 ns. The chosen transmission bands are the UWB channels 1, 2 and 3 of Table 1. Due to the bandwidth of = 500 MHz, the echoes at delay 1 and 2 interfere with delay diference of Δ = 1.33 ns, which corresponds to the setup in Figure 5.
As expected, the non-interfering signal echoes at 0 and 3 do not difer for the distinct transmission bands. However, the magnitude of the highlighted period of interference changes with the frequency. While the complex envelope’s magnitudes of the transmission bands B,1 and B,2 are nearly equal, the envelope’s magnitude of transmission band B,3 is maximal at this area.
For identification of an unknown number of signal echoes in the received signal, we modified
the Search Subtract and Readjust-algorithm (SSR) of Falsi et al. [
First, a received signal (), the amplitude threshold , and counter are initialized. Next, the iterative algorithm starts and proceeds as long as none of the estimated amplitudes is smaller than the threshold, with |a^[′]| ⩾ (Line 1-9).
Neglecting noise and following Eq. (5), the overall received signal () is equivalent to the
CIR ℎ() which was convolved (filtered) with the transmit signal (). We apply the matched
iflter approach to find the corresponding propagation delays and amplitudes of the signal echoes
w = [︀ 1[] , ..., [] ]︀ , ∈ N;
⎡ a^[
a^[] = + 1; () = () − ∑︀=1 a^[] · ( − ^[]); in (). In Line 2 we convolve our processed received signal () with (− ), the conjugate time-reversed version of (), and determine the argument ^[], which maximizes the resulting () (Line 3).
Next, we calculate the estimated amplitudes a^ of all delays [^(1), ..., ^()]. For this, we define () as signal () shifted by ^[] (Line 4) and discretize it with sample time to align it with the predefined shifted signals in matrix w in Line 5, ∈ N. In Line 6 we multiply the original received signal () with ([︀ w · w︀] − 1 × w), the pseudo-inverse of w, to (re-)estimate all amplitudes a^.
Afterward, we increase the counter by one and determine the new () as the diference between () and the estimated signal echoes with respective propagation delay and amplitude.
We predict that the resolution accuracy for identification of interfering signal echoes is limited to a minimum delay diference Δ . Signal echoes with smaller Δ are not distinguished and may not be identified anymore.
The predefined resolution accuracy depends on the pulse width = 2/ and, therefore, on bandwidth of transmission band B . A way to decrease and increase the resolution accuracy is to increase the bandwidth . As for real systems, the bandwidth is limited. So, we suggest adjusting the transmission band and performing several measurements combined in further signal processing.
We combine the measured received signals () of transmission bands B,1, B,2 and B,3 (see Table 1). Adding up the spectrum of these signals assembles a transmission band B, = [3.25, 4.75] GHz with bandwidth = 1.5 GHz. This is possible, if the corresponding combined transmit signal () is similar to the transmit signal ℎ() of the homogeneous transmission band B,ℎ = [3.25, 4.75] GHz.
Figure 7 depicts the transmission bands B, and B,ℎ, as well as the corresponding transmit signals () and ℎ(). Note, that for ℎ(), we consider the realistic pulse shape with ,ℎ = 3· 2/ = 1.33 ns. The cross-correlation of both variants of signal results in xcorr((), ℎ()) = 96.7%. For the main pulse width ,ℎ, the similarity is 99.8%. Thus applied:
Note, that the pulse width of () is still , = = 4 ns. Following Eq. (5), also the corresponding received signal () of the signal () is the sum of all received signals with:
In summary, the assembled transmit signals are very similar to the homogeneous signal. We will investigate how much the assemblage increases the resolution accuracy of signal echo identification compared to single transmission bands.
The modified SSR-algorithm, introduced in Section 4.2, identifies an unknown number of interfering signal echoes. We assume that the reconstruction is possible up to a certain resolution in the form of a delay diference Δ of the echoes. In this section, we analyze simulated received signals 1(), 2() and 3() of transmission bands B,1, B,2 and B,3 for this resolution. Additionally, we generate the assembled () with Eq. (8). We suppose, that reducing the main pulse width ,ℎ < and increasing the bandwidth will improve the resolution.
As input, a multipath propagation with two signal echoes is set up accordingly. The first
signal echo has a delay 1 = 14 ns and for the second one, we choose a flexible delay of 2 =
[10, 14] ns with a spacing of 0.01 ns between the single values, resulting in a delay diference of
Δ = [
Since the algorithm stops when at least one estimated amplitude is smaller than the predefined threshold , first the number of estimated signal echoes is of interest. Based on the known receive power ,, we choose = 0.08.
Figure 8 shows the for the received signals 1(), 2(), 3() and () for a decreasing
delay diference of Δ = [
Table 2 lists the delay diference for the first erroneous and the last correct number of estimated signal echoes , as well as the overall percentage of wrong estimations for all four transmission bands. The first erroneous estimation for is also marked in the single plots.
The single transmission bands B,1, B,2 and B,3 result in similar delay diferences for the ifrst occurring erroneous as well as for and the last correct estimated number of signal echoes. The relative number of erroneous estimates moves in the same range.
As expected due to increase of the bandwidth, these results are decreased by the assemblage to the combined received signal (). While the first occurring error is at least 1.54 ns = 0.38 · smaller, the last correct estimation for is decreased by at least 1.26 ns = 0.31 · . Also, the relative number of errors is decreased by a minimum 35.5%.
The diference between the estimation for the delays of the signal echoes ^[
Again, the three single transmission bands result in similar values for the first occurring
erroneous delay estimation. Also, the relative number of errors with respect to the successful
estimation of the numbers of signal echoes with = 2 does not vary much either. This
proves the existence of the resolution accuracy. It limits the minimum needed delay diference
Δ for correct identification of , as well as for the correct estimation of delays ^[
Applying the SSR on the assembled () of the three transmission bands lowers the delay diference Δ of the first occurring erroneous delay estimation by at least 1.38 ns = 0.35 · . The relative number of erroneous delay estimations is also decreased. Note that the resulting overall number of 10 erroneous delay estimations is also the lowest overall number for all four considered transmission bands. So, the assembling of the single distinct transmission bands decreases the minimum needed Δ and increases the resolution accuracy of the SSR.
In the next section, we evaluate the approach and algorithms by real measurements.
In this section, we depict our measurement setup and evaluate our approach for detection and identification of interference additionally by real measurements. Also, we investigate if the combination of transmission bands works the same as the homogeneous spectrum.
The measurement setup is designed in relation to Figure 2. It is installed in an indoor environment with transmitter Tx and receiver Rx at the height of 0.84 m with a distance of 0 = 0.3 m and omnidirectional PCB antennas. The predicted delay is 0 ≈ 1 ns. Another signal echo passes a ground reflection with a path length of 1 = 1.7 m and a delay of 1 = 5.7 ns.
Additionally, a static but flexible reflector is placed at a distance of 1.04 m to the LOS, resulting in a path length of 2 = 2.1 m and delay of 2 = 7 ns. The diference between the reflector path length and the ground path results in a delay diference of Δ = 1.33 ns.
A last signal component is a reflection at the ceiling with a path length of 3 = 3.8 m and delay 3 = 12.7 ns. This signal echo neither interferes with the ground signal echo nor with the reflector signal echo.
For measurement, we transmit three signals () ( = 1, 2, 3) in three diferent transmission bands B,1, B,2 and B,3 (see Table 1) with a Tektronix AWG 70002A arbitrary waveform generator with transmit power = 180 mW. The received signals 1(), 2() and 3() are measured by a Tektronix DPO 72304DX oscilloscope. We calculate the mean of 5.000 measurements for each received signal to decrease the environmental noise.
For the determination of the transmission delays of these signal echoes an usual 8th generation Intel Core i7 processor needs around 0.25 s. Since this unit works separately to the UWB signal exchange, both setups are parallelizable. So, also the usage of common UWB hardware is possible, if the transmit pulse and the signal alternation due to the hardware are known.
Figure 10 depicts the complex envelopes of the measured received signals of the UWB Channels 1, 2 and 3 (at B,1, B,2 and B,3). We see a large variation of the amplitude of the received signals ,1(), ,2() and ,3() in the expected period of interference. Between [3.75, 9] ns interfering signal echoes from ground and reflector path vary similar to the simulation results in Figure 6. There are additional signal echoes around 13 ns resulting from longer signal paths in our indoor environment. The measurements confirm our findings from Section 4.1 when we adopt the transmission band and compare the resulting complex envelopes of the magnitude.
Next, we will analyze if assembling distinct received signals increases the bandwidth of the transmission band to evaluate if the resolution of the multipath detection increases the same way as a comparable homogeneous spectrum. Therefore, we create the signal ℎ() = () from Figure 7 and measure the received signal ℎ() with a total bandwidth of 1.5GHz. As expected from Section 4.3, the shape of both received signals ℎ() and () are very similar with a cross correlation coeficient of xcorr((), ℎ()) = 98.79%. It proves that assembling received signals of distinct transmission bands provides the same benefits as a homogeneous signal with the same bandwidth.
Finally, we will investigate the performance of the modified SSR-algorithm introduced in Section 4.2 with the measured received signals. For this, we choose an amplitude threshold of = 0.1 · | ,( 0)|. This is a good approximation for the expected amplitude relation √︀,0/,2 ≈ 0.14 (see Eq. (2)) for the highest covered center frequency ,3 = 4.5 GHz, with path-loss coeficient = 2.
In this paper, we introduced a concept for detection and identification of multipath interference based on an adaption of the transmission bands for UWB signals. We showed by a systematic analysis that switching the transmission band, namely the center frequency, changes the phase diference between interfering signal echoes and, therefore, the interference, namely the amplitude of the resulting signal. By this, varying amplitude interference of signal echoes is detectable in a multipath setup in theory and measured in practical experiments. With the assemblage of the signals from multiple distinct transmission bands, we can even identify several signal echoes with an accuracy of (Δ ) = 0.08 ns, which corresponds to a distance error of approximately 2.5 cm. As the concepts are implemented and confirmed by real measurements, our solution for detection and identification of interference is ready for application in real localization systems.
In the future, we will implement an application with out-of-box hardware like the DecaWave DW1000-RF-Chip and extend the algorithms to adjust for a dynamic multipath environment. Subsequently, we will embed the detection and identification approach in a real localization system. In this context we will focus on the increase of localization accuracy by application of the proposed algorithm compared to other approaches. Also we will evaluate the trade-of between accuracy and the computional complexity and the influence of external interfering devices in the future.
This publication results from the research of the Center of Excellence CoSA and funded by the Federal Ministry for Economic Afairs and Energy of the Federal Republic of Germany (BMWi FKZ ZF4186108BZ8, MOIN). Horst Hellbrück is adjunct professor at the Institute of Telematics of University of Lübeck.