=Paper=
{{Paper
|id=Vol-3097/paper4
|storemode=property
|title=Detection and Identification of Multipath Interference With Adaption of Transmission Band for
UWB Transceiver Systems
|pdfUrl=https://ceur-ws.org/Vol-3097/paper4.pdf
|volume=Vol-3097
|authors=Sven Ole Schmidt,Horst Hellbrück
|dblpUrl=https://dblp.org/rec/conf/ipin/SchmidtH21
}}
==Detection and Identification of Multipath Interference With Adaption of Transmission Band for
UWB Transceiver Systems==
https://ceur-ws.org/Vol-3097/paper4.pdf
Detection and Identification of Multipath
Interference with Adaption of Transmission Band for
UWB Transceiver Systems
Sven Ole Schmidt, Horst Hellbrück
Technische Hochschule Lübeck - University of Applied Sciences, Germany
Department of Electrical Engineering and Computer Science
Abstract
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 trans-
mit 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 effects of inter-
ference. 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 re-
ceived 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.
Keywords
Multipath Interference, Detection, Identification, Transmission Band, Ultra-Wideband, UWB Transceiver
System, Signal Echo, Signal Assemblage
1. Introduction
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
[1], Time of Flight [2]). Such systems with many anchors are costly in hardware and deployment
as well as maintenance. To decrease the costs, a reduction of anchor hardware is beneficial. In
recent publications, virtual anchors provide an approach for reducing the number of anchors
IPIN 2021 WiP Proceedings, November 29 – December 2, 2021, Lloret de Mar, Spain
" sven.ole.schmidt@th-luebeck.de (S. O. Schmidt); horst.hellbrueck@th-luebeck.de (H. Hellbrück)
© 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
[3]. These systems process and interpret multipath signals for an improved localization in a
known environment. The work here is in this context of virtual anchor localization.
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 [4] for identification of an
arbitrary number of interfering signal echoes of UWB signals.
• We determine the minimum distance between two signal echoes for correct identification
and show that the assemblage of multiple distinct received signals of several UWB
channels increases the resolution.
• 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.
2. Related 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
[5], Liberti et al. derived a general geometry-based model for multipath propagation, including
a Line-of-Sight connection. Cimdins et al. addressed an UWB transceiver model with multipath
in [6], but neglected interference by focusing on an interference-free setup. In this work, we
derive the UWB-channel model, including Friis-Path losses and the behavior of interfering
signal echoes.
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 CLEAN-
algorithm 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. [3] exploit this information. Also, Mohammadmoradi et al. developed an UWB single-
anchor indoor localization system based on parameter distribution of the multipath propagation
[15]. For this purpose, in our previous work [16], we developed a concept for positioning of the
anchors of multipath-assisted localization systems, but we neglect the interference.
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 suffer 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].
3. Multipath Interference in UWB Transmissions
In this section, we introduce our UWB transceiver model, including multipath interference.
Afterwards, we show how varying the transmission band affects the interference of signal
echoes.
3.1. UWB Multipath Propagation and Interference of Signal Echoes
In this section, we analyze the impact of multipath propagation on received UWB signals 𝑦(𝑡).
To generate the UWB transmit signal 𝑥(𝑡), we select a center frequency 𝑓𝑐 and a bandwidth 𝐵
to construct a rectangular transmission spectrum 𝑋(𝑓 ) of width 𝐵 around 𝑓𝑐 . In the following,
this spectral range is called transmission band B𝑇 = [𝑓𝑐 − 𝐵/2, 𝑓𝑐 + 𝐵/2].
In time domain, the rectangular spectrum corresponds to a sinc-function, while the frequency
shift by 𝑓𝑐 transforms to a cosine-wave. So, 𝑥(𝑡) results to be a cosine-wave of frequency 𝑓𝑐 ,
which is weighted with a sinc-function with zeros in the range of 𝑇 = 1/𝐵 around 𝑡 = 0:
√︀ sin(𝜋 · 𝑡/𝑇 )
𝑥(𝑡) = 𝑃𝑇 𝑥 · · cos(2𝜋 · 𝑓𝑐 · 𝑡), (1)
𝜋 · 𝑡/𝑇
√
where 𝑃𝑇 𝑥 is the amplitude resulting from the given transmit power 𝑃𝑇 𝑥 . We have chosen
this basic transmit signal representation to focus on the generality of the following theoretical
derivation.
Figure 1: Transmit Signal 𝑥(𝑡) of UWB channel 2 at B𝑇,2
Figure 1 shows the theoretical and the realistic UWB transmit signal 𝑥(𝑡) of UWB channel 2
on transmission band B𝑇,2 = [3.75, 4.25] GHz as well as the corresponding spectrums 𝑋(𝑓 ).
The main pulse width 𝑡𝑃 results from the sinc-function in 𝑥(𝑡) and therefore from the chosen
bandwidth with 𝑡𝑃 = 2/𝐵 = 4 ns. Since the infinite sinc-function is not practicable in real
transceiver systems, the transmission signal is cut to the main pulse of width 𝑡𝑃 , like done e.g.,
for the Decawave DW1000-RF Chip [19]. This changes the transmission spectrum to a little
broader spectrum. In the following, we will focus on the realistic transmit signal 𝑥(𝑡).
This signal 𝑥(𝑡) propagates from transmitter Tx to receiver Rx as illustrated in Figure 2. We
assume that Tx omits 𝑥(𝑡) omni-directional into the free space with an ideal antenna. We also
assume that the receiver Rx is not able to detect the angle of arrival of the incoming signal
echoes.
Figure 2: Multipath propagation including LOS and NLOS paths
The signal 𝑥(𝑡) transmitted on the Line-Of-Sight-Path (LOS) between Tx and Rx is always
the first signal sensed by Rx. Additionally, 𝑥(𝑡) 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. 𝑑𝑖 for the 𝑖-th path. The 𝐼 signals 𝑥(𝑡) reaching Rx are called signal
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 𝜏𝑖 = 𝑑𝑖 /𝑐0 (speed of light
𝑐0 ≈ 3 · 108 m/s) with a characteristic receive power 𝑃𝑅𝑥,𝑖 for the 𝑖-th path, 𝑖 = 0, ..., 𝐼 − 1. The
power 𝑃𝑅𝑥,𝑖 results from the given transmit power 𝑃𝑇 𝑥 , decreased by the distance-depending
Friis Free Space Path-Losses 𝑃𝑃 𝐿,𝑖 with path-loss coefficient 𝛾:
𝑃𝑇 𝑥
𝑃𝑅𝑥,𝑖 = , with (2)
𝑃𝑃 𝐿,𝑖
(︂ )︂𝛾
4𝜋 · 𝑑𝑖 · 𝑓𝑐
𝑃𝑃 𝐿,𝑖 = = (4𝜋 · 𝜏𝑖 · 𝑓𝑐 )𝛾 , (3)
𝑐0
Each reflection at a surface of a material with a higher refractive index than the transmission
medium causes an additional phase shift of 𝜋 (inverting the signal). By definition, in NLOS
paths, the signal echoes 𝑥(𝑡) are reflected at least once, with 𝑛𝑖 ⩾ 1.
All single signal echoes superpose at the receiver Rx. They differ in propagation delay, power
level and phase shift. The Channel Impulse Response (CIR) ℎ(𝑡) describes the overall multipath
propagation with 𝐼 paths:
𝐼−1
√︃
∑︁ 1
ℎ(𝑡) = (−1)𝑛𝑖 · 𝛿(𝑡 − 𝜏𝑖 )
𝑃𝑃 𝐿,𝑖
𝑖=0
𝐼−1
− 𝛾 ∑︁ 𝛾
= 𝑓𝑐 2 (−1)𝑛𝑖 (4𝜋 · 𝜏𝑖 )− 2 · 𝛿(𝑡 − 𝜏𝑖 ), (4)
𝑖=0
where 𝛿(𝑡 − 𝜏𝑖 ) is the Dirac-Function shifted by 𝜏𝑖 . Eq. (4) shows that the CIR of distinct
transmission bands differs only in scaling factor depending on center frequency 𝑓𝑐 . The CIR of
the setup shown on the left of Figure 2 is sketched on the right. With increasing delay 𝜏𝑖 , the
receive power 𝑅𝑅𝑥,𝑖 decreases.
The received signal 𝑦(𝑡) is the convolution of the CIR ℎ(𝑡) with the signal 𝑥(𝑡):
𝑦(𝑡) = 𝑥(𝑡) * ℎ(𝑡)
𝐼−1
− 𝛾 ∑︁ 𝛾
= 𝑓𝑐 2 (−1)𝑛𝑖 (4𝜋 · 𝜏𝑖 )− 2 · 𝑥(𝑡 − 𝜏𝑖 ). (5)
𝑖=0
Figure 3 shows a received signal 𝑦(𝑡) on transmission band B𝑇,2 including three signal echoes.
Here, the signal on the LOS path with delay 𝜏0 = 1.66 ns is received without any interference.
The echoes with delay 𝜏1 = 6.8 ns and 𝜏2 = 8.13 ns interfere, because the delay difference
Δ𝜏 = |𝜏2 − 𝜏1 | = 1.33 ns is smaller than the main pulse width 𝑡𝑃 = 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.
Figure 3: Exemplary received signal 𝑦(𝑡) with three signal echoes
3.2. Impact of the Transmission Band on Signal Echo Interference
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 𝑡𝑝 = 2/𝐵 for the given realistic
signal 𝑥(𝑡). Therefore, two signal echoes with delay 𝜏𝑖 and 𝜏𝑗 do interfere, if the delay difference
Δ𝜏 = |𝜏𝑖 − 𝜏𝑗 | < 𝑡𝑝 = 2/𝐵. According to Eq. (1), the oscillation of signal 𝑥(𝑡) corresponds to
the center frequency 𝑓𝑐 of B𝑇 . Therefore, 𝑥(𝑡) of duration 𝑡𝑃 includes 𝑡𝑃 · 𝑓𝑐 oscillations of
periodic time 𝑇0 = 1/𝑓𝑐 .
The oscillation phase at time 𝑡0 is named phase state Θ(𝑡0 ) and depends on 𝑓𝑐 as the period
of the oscillation is 1/𝑓𝑐 . The phase difference between two signal echos 𝑖 and 𝑗 is constant:
ΔΘ𝑖,𝑗 = |Θ𝑗 − Θ𝑖 | = 2𝜋 · |𝜏𝑗 − 𝜏𝑖 | · 𝑓𝑐 = 2𝜋 · Δ𝜏 · 𝑓𝑐 (6)
Figure 4: Superposition of two signal echoes depending on ΔΘ𝑖,𝑗
This phase difference ΔΘ𝑖,𝑗 is important for a constructive or destructive superposition.
Figure 4 depicts two results for ΔΘ𝑖,𝑗 = {60∘ , 150∘ }. On the left, the superposition of the
samples results in an overall stronger magnitude (constructive interference). When ΔΘ𝑖,𝑗 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 effect of the change
of the center frequency 𝑓𝑐 of the transmission band B𝑇 on the interference, the superposition
of two interfering signal echos 𝑖 and 𝑗 is shown, with 𝜏𝑖 = 6.87 ns, 𝜏𝑗 = 8.2 ns and Θ𝑖 (𝑡0 ) = 0∘ .
This delay difference of Δ𝜏 = 1.33 ns results in completely different phase shifts ΔΘ𝑖,𝑗 for the
three selected UWB channels 1, 2 and 3 as shown in Table 1 and Figure 5.
Table 1
Band B𝑇,𝑘 of UWB channels 1, 2, 3 as well as resulting phase difference ΔΘ1,2 (Δ𝜏 = 1.33 ns).
UWB channel 𝑘 B𝑇,𝑘 [GHz] 𝑓𝑐,𝑘 [GHz] ΔΘ𝑖,𝑗 (1.33 ns)
1 [3.25, 3.75] 3.5 240∘
2 [3.75, 4.25] 4.0 120∘
3 [4.25, 4.75] 4.5 0∘
Figure 5: Impact of UWB channel B𝑇,𝑘 on the signal echo superposition
The transmission bands of the UWB channels 1 and 2 superpose to the same magnitude as
the phase difference ΔΘ𝑖,𝑗 is ±120∘ . Choosing the transmission band B𝑇,3 of UWB channel
3 leads to the phase difference ΔΘ𝑖,𝑗 = 0∘ , which corresponds to the maximum constructive
superposition. Since ΔΘ𝑖,𝑗 is constant (independent of time) for the signal echoes 𝑖 and 𝑗,
the superposition is also constant (either destructive or constructive) for the total period of
interference.
Note, that the phase difference ΔΘ𝑖,𝑗 is always equal for two transmission bands, if 𝑓𝑐,1 =
𝑙 · 𝑓𝑐,2 holds, with 𝑙 ∈ N. The impact of the transmission band on the superposition of signal
echoes is applied in the next section to detect and identify interference.
4. Detection and Identification of Interference with
transmission band analysis
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.
4.1. Detection of Interference by Adaption of Transmission Bands
In the last section, we depicted, how the transmission band B𝑇 affects the superposition of two
interfering signal echoes. Since the overall magnitude of the superposition varies, depending on
the chosen center frequency 𝑓𝑐 , the adaption of 𝑓𝑐 evinces interference in the received signal 𝑦(𝑡).
−𝛾/2
Neglecting the scalar factor 𝑓𝑐 (comp. to Eq. (5)), the complex envelope’s magnitude |𝑦𝑐 (𝑡)|
of the received signal 𝑦(𝑡) of multiple distinct transmission bands only differs in the period of
interfering signal echoes. To calculate 𝑦𝑐 (𝑡), we shift the received signal from the transmission
band at center frequency 𝑓𝑐 back to baseband at 𝑓𝑐0 = 0 Hz and apply a lowpass-filter.
Figure 6: Detection of Interference by Comparison
Figure 6 shows the magnitude of the complex envelopes 𝑦𝑐,1 (𝑡), 𝑦𝑐,2 (𝑡) and 𝑦𝑐,3 (𝑡), for a
certain multipath setup with 𝜏0 = 1.66 ns, 𝜏1 = 6.87 ns, 𝜏2 = 8.2 ns and 𝜏3 = 12.05 ns. The
chosen transmission bands are the UWB channels 1, 2 and 3 of Table 1. Due to the bandwidth
of 𝐵 = 500 MHz, the echoes at delay 𝜏1 and 𝜏2 interfere with delay difference of Δ𝜏 = 1.33 ns,
which corresponds to the setup in Figure 5.
As expected, the non-interfering signal echoes at 𝜏0 and 𝜏3 do not differ 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 B𝑇,1
and B𝑇,2 are nearly equal, the envelope’s magnitude of transmission band B𝑇,3 is maximal at
this area.
4.2. Identification of Signal Echoes with the Search Subtract and
Readjust-Algorithm
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. [4]. The SSR was originally
designed to identify a known number of delays of overlapping LOS connections of multiple
transmitters Tx in multipath-suffering UWB received signals. In our setup, we do not know
the number of signal echoes in advance. Algorithm 1 depicts, how the individual propagation
delays 𝜏^ and amplitudes a ^ are estimated by the modified SSR-algorithm until a threshold is
reached.
First, a received signal 𝑦𝐼𝑡 (𝑡), the amplitude threshold 𝑎𝑡 , and counter 𝑐 are initialized. Next,
the iterative algorithm starts and proceeds as long as none of the estimated amplitudes is smaller
than the threshold, with |a ^[𝑐′ ]| ⩾ 𝑎𝑡 (Line 1-9).
Neglecting noise and following Eq. (5), the overall received signal 𝑦(𝑡) is equivalent to the
CIR ℎ(𝑡) which was convolved (filtered) with the transmit signal 𝑥(𝑡). We apply the matched
filter approach to find the corresponding propagation delays and amplitudes of the signal echoes
Algorithm 1: Modified Pseudo code for Search Subtract and Readjust Algorithm from
[4]
Data:
received signal 𝑦𝐼𝑡 (𝑡) = 𝑦(𝑡);
threshold: 𝑎𝑡 ∈ R+ ;
counter: 𝑐 ← 1;
1 while ∄ 𝑐′ : |a
^[𝑐′ ]| < 𝑎𝑡 do
2 𝑦𝑐𝑜𝑛𝑣 (𝑡) = 𝑦𝐼𝑡 (𝑡) * 𝑥(−𝑡);
3 𝜏^[𝑐] ← arg max(𝑦𝑐𝑜𝑛𝑣 (𝑡));
𝑡∈R+
4 𝑤𝑐 (𝑡) = 𝑥(𝑡 − 𝜏^[𝑐]);
]︀𝑇
w𝑐𝑚𝑏 = 𝑤1 [𝑘𝑇𝑆 ]𝑇 , ..., 𝑤𝑐 [𝑘𝑇𝑆 ]𝑇 , 𝑘 ∈ N;
[︀
5
⎡ ⎤
^[1]
a
⎢ .. ⎥ [︀ 𝑇
]︀−1
6 ⎣ . ⎦ = w𝑐𝑚𝑏 · w𝑐𝑚𝑏 × [w𝑐𝑚𝑏 · 𝑦[𝑘𝑇𝑆 ]𝑇 ];
^[𝑐]
a
7 𝑐 = 𝑐 + 1;
𝑦𝐼𝑡 (𝑡) = 𝑦(𝑡) − 𝑐𝑖=1 a
∑︀
8 ^[𝑖] · 𝑥(𝑡 − 𝜏^[𝑖]);
9 end
in 𝑦(𝑡). In Line 2 we convolve our processed received signal 𝑦𝐼𝑡 (𝑡) with 𝑥(−𝑡), the conjugate
time-reversed version of 𝑥(𝑡), and determine the argument 𝜏^[𝑐], which maximizes the resulting
𝑦𝑐𝑜𝑛𝑣 (𝑡) (Line 3).
Next, we calculate the estimated amplitudes a ^ of all delays [𝜏^(1), ..., 𝜏^(𝑐)]. For this, we define
𝑤𝑐 (𝑡) as signal 𝑥(𝑡) shifted by 𝜏^[𝑐] (Line 4) and discretize it with sample time 𝑇𝑆 to align it
with the predefined shifted signals in matrix w𝑐𝑚𝑏 in Line 5, 𝑘 ∈ N. In Line 6 we multiply the
]︀−1
original received signal 𝑦(𝑡) with ( w𝑐𝑚𝑏 · w𝑐𝑚𝑏 𝑇 × w𝑐𝑚𝑏 ), the pseudo-inverse of w𝑐𝑚𝑏 , to
[︀
(re-)estimate all amplitudes a^.
Afterward, we increase the counter 𝑐 by one and determine the new 𝑦𝐼𝑡 (𝑡) as the difference
between 𝑦(𝑡) 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 difference Δ𝜏 . Signal echoes with smaller Δ𝜏 are not distinguished
and may not be identified anymore.
4.3. Assemblage of Signals of distinct Transmission Bands
The predefined resolution accuracy depends on the pulse width 𝑡𝑃 = 2/𝐵 and, therefore, on
bandwidth 𝐵 of transmission band B𝑇 . A way to decrease 𝑡𝑃 and increase the resolution
accuracy is to increase the bandwidth 𝐵. 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 𝑦𝑘 (𝑡) of transmission bands B𝑇,1 , B𝑇,2 and
B𝑇,3 (see Table 1). Adding up the spectrum of these signals assembles a transmission band
B𝑇,𝑎 = [3.25, 4.75] GHz with bandwidth 𝐵 = 1.5 GHz. This is possible, if the corresponding
combined transmit signal 𝑥𝑎 (𝑡) is similar to the transmit signal 𝑥ℎ (𝑡) of the homogeneous
transmission band B𝑇,ℎ = [3.25, 4.75] GHz.
Figure 7: Assembled transmit signal 𝑥𝑎 (𝑡) compared to homogeneous signal 𝑥ℎ (𝑡)
Figure 7 depicts the transmission bands B𝑇,𝑎 and B𝑇,ℎ , as well as the corresponding transmit
signals 𝑥𝑎 (𝑡) and 𝑥ℎ (𝑡). Note, that for 𝑥ℎ (𝑡), we consider the realistic pulse shape with 𝑡𝑃,ℎ = 3·
2/𝐵 = 1.33 ns. The cross-correlation of both variants of signal results in xcorr(𝑥𝑎 (𝑡), 𝑥ℎ (𝑡)) =
96.7%. For the main pulse width 𝑡𝑃,ℎ , the similarity is 99.8%. Thus applied:
3
∑︁
𝑥ℎ (𝑡) ≈ 𝑥𝑎 (𝑡) = 𝑥𝑘 (𝑡) (7)
𝑘=1
Note, that the pulse width of 𝑥𝑎 (𝑡) is still 𝑡𝑃,𝑎 = 𝑡𝑃 = 4 ns. Following Eq. (5), also the
corresponding received signal 𝑦𝑎 (𝑡) of the signal 𝑥𝑎 (𝑡) is the sum of all received signals with:
𝑦𝑎 (𝑡) = 𝑥𝑎 (𝑡) * ℎ(𝑡)
3
∑︁ 3
∑︁
= 𝑥𝑘 (𝑡) * ℎ(𝑡) = 𝑦𝑘 (𝑡). (8)
𝑘=1 𝑘=1
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.
4.4. Increasing Accuracy for Identification of Signal Echoes
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 difference Δ𝜏 of the echoes. In this section, we analyze simulated received
signals 𝑦1 (𝑡), 𝑦2 (𝑡) and 𝑦3 (𝑡) of transmission bands B𝑇,1 , B𝑇,2 and B𝑇,3 for this resolution.
Additionally, we generate the assembled 𝑦𝑎 (𝑡) with Eq. (8). We suppose, that reducing the main
pulse width 𝑡𝑃,ℎ < 𝑡𝑃 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 𝜏1 = 14 ns and for the second one, we choose a flexible delay of 𝜏2 =
[10, 14] ns with a spacing of 0.01 ns between the single values, resulting in a delay difference of
Δ𝜏 = [4, 0] ns. Both echo paths include 𝑛1 = 𝑛2 = 1 reflection and the path loss coefficient is
𝛾 = 2. For modeling these received signals, we follow Eq. (1) and Eq. (5).
Since the algorithm stops when at least one estimated amplitude is smaller than the pre-
defined threshold 𝑎𝑡 , first the number of estimated signal echoes 𝑁𝑆𝐸 is of interest. Based on
the known receive power 𝑃𝑅𝑥,𝑖 , we choose 𝑎𝑡 = 0.08.
Figure 8: Number of SSR-estimated signal echoes 𝑁𝑆𝐸
Figure 8 shows the 𝑁𝑆𝐸 for the received signals 𝑦1 (𝑡), 𝑦2 (𝑡), 𝑦3 (𝑡) and 𝑦𝑎 (𝑡) for a decreasing
delay difference of Δ𝜏 = [4, 0] ns between two signal echoes.
Table 2 lists the delay difference for the first erroneous and the last correct number of
estimated signal echoes 𝑁𝑆𝐸 , as well as the overall percentage of wrong estimations for all four
transmission bands. The first erroneous estimation for 𝑁𝑆𝐸 is also marked in the single plots.
Table 2
Delay difference of the first erroneous and last correct calculation of 𝑁𝑆𝐸 , as well as the relative number
of erroneous estimations.
Errors
Bands first error (Δ𝜏 ) last correct (Δ𝜏 ) All Setups
B𝑇,1 2.32 ns = 0.58 · 𝑡𝑃 2.08 ns = 0.52 · 𝑡𝑃 59.5%
B𝑇,2 2.52 ns = 0.63 · 𝑡𝑃 1.92 ns = 0.48 · 𝑡𝑃 54.5%
B𝑇,3 2.46 ns = 0.62 · 𝑡𝑃 1.84 ns = 0.46 · 𝑡𝑃 53.0%
B𝑇,𝑎 0.78 ns = 0.20 · 𝑡𝑃 0.58 ns = 0.15 · 𝑡𝑃 17.5%
The single transmission bands B𝑇,1 , B𝑇,2 and B𝑇,3 result in similar delay differences for the
first 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 𝑦𝑎 (𝑡). While the first occurring error is at least 1.54 ns = 0.38 · 𝑡𝑃
smaller, the last correct estimation for 𝑁𝑆𝐸 is decreased by at least 1.26 ns = 0.31 · 𝑡𝑃 . Also,
the relative number of errors is decreased by a minimum 35.5%.
The difference between the estimation for the delays of the signal echoes 𝜏^[1] and 𝜏^[2] and
the origin delays 𝜏1 and 𝜏2 is calculated by the ℓ1 -norm:
2
∑︁
𝑑𝑒 (Δ𝜏 ) = |𝜏𝑖 − 𝜏^[𝑖]| (9)
𝑖=1
Figure 9: ℓ1 -norm 𝑑𝑒 (Δ𝜏 ) for all SSR results with 𝑁𝑆𝐸 = 2
Figure 9 depicts the estimation errors 𝑑𝑒 (Δ𝜏 ) > 0 of all SSR-results with 𝑁𝑆𝐸 = 2 for the
transmission bands B𝑇,1 , B𝑇,2 , B𝑇,3 and B𝑇,𝑎 .
Table 3 lists the delay difference for the first error and the overall percentage of wrong
estimations in all estimations for all four transmission bands. The first occurring erroneous
estimation 𝑑𝑒 (Δ𝜏 ) > 0 is also marked in the single plots.
Table 3
Delay Difference of the first erroneous delay estimation with 𝑑𝑒 (Δ𝜏 ) > 0 as well as the relative number
of erroneous estimations.
Erroneous Delay
Bands first error with 𝑑𝑒 (Δ𝜏 ) > 0 All correct𝑁𝑆𝐸
B𝑇,1 Δ𝜏 = 2.88 ns = 0.72 · 𝑡𝑃 28%
B𝑇,2 Δ𝜏 = 2.76 ns = 0.69 · 𝑡𝑃 24%
B𝑇,3 Δ𝜏 = 2.90 ns = 0.73 · 𝑡𝑃 32%
B𝑇,𝑎 Δ𝜏 = 1.38 ns = 0.35 · 𝑡𝑃 6%
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 𝑁𝑆𝐸 = 2 does not vary much either. This
proves the existence of the resolution accuracy. It limits the minimum needed delay difference
Δ𝜏 for correct identification of 𝑁𝑆𝐸 , as well as for the correct estimation of delays 𝜏^[1] and
𝜏^[2].
Applying the SSR on the assembled 𝑦𝑎 (𝑡) of the three transmission bands lowers the delay
difference Δ𝜏 of the first occurring erroneous delay estimation by at least 1.38 ns = 0.35 · 𝑡𝑃 .
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 Δ𝜏 and increases the resolution accuracy of the SSR.
In the next section, we evaluate the approach and algorithms by real measurements.
5. Evaluation
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.
5.1. Measurement Setup
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 𝑑0 = 0.3 m and
omnidirectional PCB antennas. The predicted delay is 𝜏0 ≈ 1 ns. Another signal echo passes a
ground reflection with a path length of 𝑑1 = 1.7 m and a delay of 𝜏1 = 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 𝑑2 = 2.1 m and delay of 𝜏2 = 7 ns. The difference between the reflector path
length and the ground path results in a delay difference of Δ𝜏 = 1.33 ns.
A last signal component is a reflection at the ceiling with a path length of 𝑑3 = 3.8 m and
delay 𝜏3 = 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 𝑥𝑘 (𝑡) (𝑘 = 1, 2, 3) in three different transmission
bands B𝑇,1 , B𝑇,2 and B𝑇,3 (see Table 1) with a Tektronix AWG 70002A arbitrary waveform
generator with transmit power 𝑃𝑇 𝑥 = 180 mW. The received signals 𝑦1 (𝑡), 𝑦2 (𝑡) and 𝑦3 (𝑡)
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.
5.2. Detection of measured Interference by Adaption of Transmission Bands
Figure 10: Detection of measured Interference
Figure 10 depicts the complex envelopes of the measured received signals of the UWB Chan-
nels 1, 2 and 3 (at B𝑇,1 , B𝑇,2 and B𝑇,3 ). We see a large variation of the amplitude of the received
signals 𝑦𝑐,1 (𝑡), 𝑦𝑐,2 (𝑡) and 𝑦𝑐,3 (𝑡) 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.
5.3. Assemblage of measured Received Signals of distinct Transmission
Bands
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 𝑥ℎ (𝑡) = 𝑥𝑎 (𝑡)
from Figure 7 and measure the received signal 𝑦ℎ (𝑡) with a total bandwidth of 1.5GHz. As
expected from Section 4.3, the shape of both received signals 𝑦ℎ (𝑡) and 𝑦𝑎 (𝑡) are very similar
with a cross correlation coefficient of xcorr(𝑦𝑎 (𝑡), 𝑦ℎ (𝑡)) = 98.79%. It proves that assembling
received signals of distinct transmission bands provides the same benefits as a homogeneous
signal with the same bandwidth.
5.4. Identification of Interference of Measured Received Signals
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
√︀ 𝑎𝑡 = 0.1 · |𝑦𝑐,𝑘 (𝜏0 )|. This is a good approximation for the expected amplitude relation
𝑃𝑅𝑥,0 /𝑃𝑅𝑥,2 ≈ 0.14 (see Eq. (2)) for the highest covered center frequency 𝑓𝑐,3 = 4.5 GHz,
with path-loss coefficient 𝛾 = 2.
Table 4
SSR-based delay estimation of measured interfering echoes at 𝜏1 = 5.7 ns and 𝜏2 = 7 ns for band B𝑇,𝑘
Band 𝑁𝑆𝐸 𝜏^[1] 𝜏^[2] 𝑑𝑒 (Δ𝜏 )
B𝑇,1 2 5.6 ns 7.64 ns 0.74 ns
B𝑇,2 2 6 ns 7.66 ns 0.96 ns
B𝑇,3 1 6.62 ns — —
B𝑇,𝑎 2 5.74 ns 7.04 ns 0.08 ns
Table 4 illustrates the results for all signals. For the signals 𝑦1 (𝑡) and 𝑦2 (𝑡) the algorithm
detects the correct number of signal echoes 𝑁𝑆𝐸 for the measured setup, and achieves an
accuracy of 0.74 ns and 0.96 ns respectively. The SSR-algorithm does not provide the correct
number of signal echoes for signal 𝑦3 (𝑡). Based on the interference, the algorithm has estimated
the wrong delay 𝜏^[1] with too high a ^[1]. This caused the amplitude of the estimated delay 𝜏^[2]
to fall below the threshold a ^[2] < 𝑎𝑡 . When assembling these received signals to 𝑦𝑎 (𝑡), the
reliability and the accuracy is increased to 𝑑𝑒 (Δ𝜏 ) = 0.08 ns, which corresponds to an averaged
delay identification error of approximately 0.04 ns = 1.25 cm for each of the two signal echoes.
As derived in Section 4.2, the limited bandwidth of 500 MHz results in unreliable and imprecise
identification of the signal echoes with distance Δ𝜏 = 1.3 ns. By assembling three signals
into 𝑦𝑎 (𝑡) and increasing the bandwidth to 1.5 GHz, the identification performs precisely and
reliably.
6. Conclusion and Future Work
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 difference 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 𝑑𝑒 (Δ𝜏 ) = 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-off
between accuracy and the computional complexity and the influence of external interfering
devices in the future.
Acknowledgements
This publication results from the research of the Center of Excellence CoSA and funded by the
Federal Ministry for Economic Affairs 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.
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