# Time-Varying Ultra-Wideband Channel Modeling and Prediction

^{*}

## Abstract

**:**

## 1. Introduction

## 2. UWB Channel Impulse Response

#### 2.1. Channel Model

#### 2.2. UWB Channel Measurement

^{®}410 transceivers. Each transceiver had a vertically polarized omnidirectional wide-band dipole antenna mounted on it with operating frequencies of $3.1$ to $10.6$ GHz. The heights of the transmitter (Tx) and receiver (Rx) antennas were set to 2 m and $1.7$ m, respectively. In our measurement setup, a pulse bandwidth of $2.2$ GHz over the frequency range of 3.1–5.3 GHz was used. The Rx was locked at 61 ps to capture the signal transmitted by the Tx. The measurements occurred in front of the Wireless Communication Center, Universiti Teknologi Malaysia, as depicted in Figure 1. This outdoor environment consisted of a concrete floor, wooden column roofing, and a parking space with several cars. The choice of this environment was done to illustrate an infostation scenario [37,38], where users can download data as they move along the corridor. Throughout this measurement, the Rx was located at a fixed position in front of the metallic sheet. This metallic sheet was placed between the person operating the setup and the setup itself to ensure a stationary environment. The Tx was then positioned along a straight line away from the Rx, which is marked by the white tape in Figure 1. The channel realization was captured starting at a Tx–Rx separation distance of $d=3$ m and at each $\u25b5d=1$ cm transmitter movement away from the Rx. The final channel realization was captured at a separation distance of $d=4.26$ m. As a result, the measurement campaign contained $P=127$ sets of measurement data corresponding to all the Tx–Rx separation distances.

#### 2.3. UWB Channel Impulse Response Extraction

^{®}410 platform was used to log and capture the received UWB radio frequency (RF) waveforms in CAT logfile format (.csv file), which is compatible for processing using MATLAB. To obtain a high-resolution CIR, the received waveform can be further processed using the CLEAN algorithm [39]. The CLEAN algorithm is capable of resolving dense multipath components (MPCs) that are usually irresolvable by the conventional inverse filter, by deploying an iterative, high-resolution, and subtractive deconvolution procedure. To obtain $h(p,\tau )$ from $r(p,\tau )$, the CLEAN algorithm correlates the received waveform $r(p,\tau )$ with a template waveform $q\left(p\right)$, finds the highest correlation, assigns a weight, and then subtracts the template waveform from the received waveform [16,40]. This process is repeated until the maximum iterations expire or when an MPC with gain of a certain threshold value below the strongest MPC is detected. A 20 dB threshold value is recommended by the International Telecommunication Union-Radiocommunication (ITU-R) [41].

## 3. Window-Based UWB Channel Impulse Response Proposed Model

#### 3.1. Window Selection

#### 3.2. Channel Tap Selection

## 4. Channel Impulse Response Tap Prediction Algorithms

## 5. Evaluation Criterion

## 6. Complexity Analysis

## 7. Results and Discussion

#### 7.1. Modeling Results

#### 7.2. Prediction Results

#### 7.3. CDF of RMS Delay Spread

## 8. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Benedetto, M.G.D.; Kaiser, T.; Molisch, A.F.; Oppermann, I.; Politano, C.; Porcino, D. UWB Communications Systems: A Comprehensive Overview (EURASIP Book Series on Signal Processing and Communications); Hindawi Publishing Corporation: New York, NY, USA, 2006. [Google Scholar]
- Yang, L.; Giannakis, G. Ultra-wideband communications: An idea whose time has come. IEEE Signal Process. Mag.
**2004**, 21, 26–54. [Google Scholar] [CrossRef] - Roy, S.; Foerster, J.; Somayazulu, V.; Leeper, D. Ultrawideband radio design: The promise of high-speed, short-range wireless connectivity. Proc. IEEE
**2004**, 92, 295–311. [Google Scholar] [CrossRef] - Molisch, A. Ultrawideband propagation channels-theory, measurement, and modeling. IEEE Trans. Veh. Technol.
**2005**, 54, 1528–1545. [Google Scholar] [CrossRef] [Green Version] - FCC Notice of Proposed Rule Making, Revision of Part 15 of the Commission’s Rules Regarding Ultra-Wideband Transmission Systems. ET-Docket; 2005; pp. 98–153. Available online: https://www.fcc.gov/document/revision-part-15-commissions-rules-regarding-ultra-wideband-transmission-systems-2 (accessed on 1 October 2018).
- Tsiropoulou, E.E.; Kapoukakis, A.; Papavassiliou, S. Uplink resource allocation in SC-FDMA wireless networks: A survey and taxonomy. Comput. Netw.
**2016**, 96, 1–28. [Google Scholar] [CrossRef] - Myung, H.G.; Lim, J.; Goodman, D.J. Single carrier FDMA for uplink wireless transmission. IEEE Veh. Technol. Mag.
**2006**, 1, 30–38. [Google Scholar] [CrossRef] - Tsiropoulou, E.E.; Kapoukakis, A.; Papavassiliou, S. Energy-efficient subcarrier allocation in SC-FDMA wireless networks based on multilateral model of bargaining. In Proceedings of the 2013 IFIP Networking Conference, Brooklyn, NY, USA, 22–24 May 2013; pp. 1–9. [Google Scholar]
- Myung, H.G. Introduction to single carrier FDMA. In Proceedings of the 15th European Signal Processing Conference, Poznan, Poland, 3–7 September 2007; pp. 2144–2148. [Google Scholar]
- Gustafson, C.; Haneda, K.; Wyne, S.; Tufvesson, F. On mm-Wave Multipath Clustering and Channel Modeling. IEEE Trans. Antennas Propag.
**2014**, 62, 1445–1455. [Google Scholar] [CrossRef] [Green Version] - Sulyman, A.I.; Alwarafy, A.; Maccartney, G.; Rappaport, T.; Al-Sanie, A. Directional Radio Propagation Path Loss Models for Millimeter-Wave Wireless Networks in the 28, 60, and 73 GHz Bands. IEEE Trans. Wirel. Commun.
**2016**, 15, 6939–6947. [Google Scholar] [CrossRef] - Andrews, J.; Buzzi, S.; Choi, W.; Hanly, S.; Lozano, A.; Soong, A.; Zhang, J. What Will 5G Be? IEEE J. Sel. Areas Commun.
**2014**, 32, 1065–1082. [Google Scholar] [CrossRef] - Li, Y.; Jin, Z.; Wang, Y. Adaptive Channel Estimation Based on an Improved Norm-Constrained Set-Membership Normalized Least Mean Square Algorithm. Wirel. Commun. Mob. Comput.
**2017**, 2017, 8056126. [Google Scholar] [CrossRef] - Molish, A.; Tufvesson, F. Propagation channel models for next-generation wireless communications systems. IEICE Trans. Commun.
**2014**, 97, 2022–2034. [Google Scholar] [CrossRef] - METIS ICT-317669-METIS/D1.1, S. Scenarios, Requirements and KPIs for 5G Mobile and Wireless System. Available online: www.metis2020.com (accessed on 1 October 2018).
- Anderson, C.R.; Volos, H.I.; Buehrer, R.M. Characterization of Low-Antenna Ultrawideband Propagation in a Forest Environment. IEEE Trans. Veh. Technol.
**2013**, 62, 2878–2895. [Google Scholar] [CrossRef] - Cramer, R.M.; Scholtz, R.; Win, M. Evaluation of an ultra-wide-band propagation channel. IEEE Trans. Antennas Propag.
**2002**, 50, 561–570. [Google Scholar] [CrossRef] [Green Version] - Molisch, A.F. Ultra-Wide-Band Propagation Channels. Proc. IEEE
**2009**, 97, 353–371. [Google Scholar] [CrossRef] - Athanasiadou, G.; Nix, A. A novel 3-D indoor ray-tracing propagation model: The path generator and evaluation of narrow-band and wide-band predictions. IEEE Trans. Veh. Technol.
**2000**, 49, 1152–1168. [Google Scholar] [CrossRef] - Al-Samman, A.M.; Rahman, T.A.; Hadri, M.; Khan, I.; Chua, T.H. Experimental UWB Indoor Channel Characterization in Stationary and Mobility Scheme. Measurement
**2017**, 111, 333–339. [Google Scholar] [CrossRef] - Al-Samman, A.M.; Rahman, T.A.; Azmi, M.H.; Hindia, M.N.; Khan, I.; Hanafi, E. Statistical Modelling and Characterization of Experimental mm-Wave Indoor Channels for Future 5G Wireless Communication Networks. PLoS ONE
**2016**, 11, e0163034. [Google Scholar] [CrossRef] [PubMed] - Maccartney, G.R.; Rappaport, T.S.; Sun, S.; Deng, S. Indoor Office Wideband Millimeter-Wave Propagation Measurements and Channel Models at 28 and 73 GHz for Ultra-Dense 5G Wireless Networks. IEEE Access
**2015**, 3, 2388–2424. [Google Scholar] [CrossRef] - Rappaport, T.S.; MacCartney, G.R.; Samimi, M.K.; Sun, S. Wideband Millimeter-Wave Propagation Measurements and Channel Models for Future Wireless Communication System Design. IEEE Trans. Commun.
**2015**, 63, 3029–3056. [Google Scholar] [CrossRef] - Al-Samman, A.M.; Rahman, T.A.; Azmi, M.H.; Hindia, M. Large-scale path loss models and time dispersion in an outdoor line-of-sight environment for 5G wireless communications. AEU—Int. J. Electron. Commun.
**2016**, 70, 1515–1521. [Google Scholar] [CrossRef] - Gupta, A.; Jha, R.K. A Survey of 5G Network: Architecture and Emerging Technologies. IEEE Access
**2015**, 3, 1206–1232. [Google Scholar] [CrossRef] [Green Version] - Huo, Y.; Member, S.; Dong, X.; Member, S. 5G Cellular User Equipment: From Theory to Practical Hardware Design. IEEE Access
**2017**, 5, 13992–14010. [Google Scholar] [CrossRef] - Duel-Hallen, A. Fading channel prediction for mobile radio adaptive transmission systems. Proc. IEEE
**2007**, 95, 2299–2313. [Google Scholar] [CrossRef] - Al-Samman, A.M.; Nunoo, S.; Rahman, T.A.; Chude-Okonkwo, U.A.K.; Ngah, R. Hybrid Channel Estimation Technique with Reduced Complexity for LTE Downlink. Wirel. Pers. Commun.
**2015**, 82, 1147–1159. [Google Scholar] [CrossRef] - Heo, J.; Wang, Y.P.; Chang, K.H. A novel two-step channel-prediction technique for supporting adaptive transmission in OFDM/FDD system. IEEE Trans. Veh. Technol.
**2008**, 57, 188–193. [Google Scholar] [CrossRef] - Akhtman, J.; Hanzo, L. Channel Impulse Response Tap Prediction for Time-Varying Wireless Channels. IEEE Trans. Veh. Technol.
**2007**, 56, 2767–2769. [Google Scholar] [CrossRef] [Green Version] - Malmirchegini, M.; Mostofi, Y. On the Spatial Predictability of Communication Channels. IEEE Trans. Wirel. Commun.
**2012**, 11, 964–978. [Google Scholar] [CrossRef] [Green Version] - Jarinová, D. On autoregressive model order for long-range prediction of fast fading wireless channel. Telecommun. Syst.
**2011**, 52, 1533–1539. [Google Scholar] [CrossRef] - Wang, Y.; Li, Y. Sparse Multipath Channel Estimation Using Norm Combination Constrained Set-Membership NLMS Algorithms. Wirel. Commun. Mob. Comput.
**2017**, 2017, 8140702. [Google Scholar] [CrossRef] - Tsao, J.; Porrat, D.; Tse, D. Prediction and Modeling for the Time-Evolving Ultra-Wideband Channel. IEEE J. Sel. Top. Signal Process.
**2007**, 1, 340–356. [Google Scholar] [CrossRef] [Green Version] - Tse, D. Fundamentals of Wireless Communication; Cambridge University Press: Cambridge, UK, 2005. [Google Scholar]
- Saleh, A.; Valenzuela, R. A Statistical Model for Indoor Multipath Propagation. IEEE J. Sel. Areas Commun.
**1987**, 5, 128–137. [Google Scholar] [CrossRef] [Green Version] - Santos, T.; Karedal, J.; Almers, P.; Tufvesson, F.; Molisch, A.F. Modeling the ultra-wideband outdoor channel: Measurements and parameter extraction method. IEEE Trans. Wirel. Commun.
**2010**, 9, 282–290. [Google Scholar] [CrossRef] [Green Version] - Nunoo, S.; Chude-Okonkwo, U.A.K.; Ngah, R.; Al-Samman, A.; Onubogu, J. UWB channel measurement and data transfer analysis for multiuser Infostation applications. In Proceedings of the 2014 IEEE 10th International Colloquium on Signal Processing and its Applications, Kuala Lumpur, Malaysia, 7–9 March 2014. [Google Scholar] [CrossRef]
- Liu, T.K.; Kim, D.I.; Vaughan, R.G. A high-resolution, multi-template deconvolution algorithm for time-domain UWB channel characterization. Can. J. Electr. Comput. Eng.
**2007**, 32, 207–213. [Google Scholar] [CrossRef] - Chandra, A.; Blumenstein, J.; Mikulasek, T.; Vychodil, J.; Pospisil, M.; Marsalek, R.; Prokes, A.; Zemen, T.; Mecklenbrauker, C. CLEAN Algorithms for Intra-vehicular Time-domain UWB Channel Sounding. In Proceedings of the 2015 International Conference on Pervasive and Embedded Computing and Communication Systems (PECCS), Angers, France, 11–13 February 2015. [Google Scholar]
- Propagation, M. Multipath Propagation and Parameterization of Its Characteristics; International Telecommunication Union: Geneva, Switzerland, 2017. [Google Scholar]
- Varela, M.; Sanchez, M. RMS delay and coherence bandwidth measurements in indoor radio channels in the UHF band. IEEE Trans. Veh. Technol.
**2001**, 50, 515–525. [Google Scholar] [CrossRef] - Sayed, A.H. Adaptive Filters; John Wiley & Sons: New York, NY, USA, 2011. [Google Scholar]

**Figure 3.**Comparison of channel impulse response (CIR) samples at the Tx–Rx separation distance of 4.07 m (

**a**) CA-ITUR20dB, (

**b**) CA-WDT-15dB, (

**c**) CA-WDT-10dB, and (

**d**) the proposed WB-BD model.

**Figure 4.**The modeling mean square error (MSE) for windowing-based on bin delay (WB-BD), windowing-based on window delay (WB-WD), CA-WDT and CA-ITUR20dB CIRs.

**Figure 7.**The prediction mean square error (MSE) for different window sizes and prediction orders of the WB-BD approach.

**Figure 8.**The prediction mean square error (MSE) for different window sizes and prediction orders of WB-WD approach.

**Figure 11.**CDF of the RMS delay spread for the predicted CIRs using the recursive least square (RLS) algorithm with M = 10.

**Table 1.**Computational cost of the recursive least square (RLS) algorithm per iteration [43].

Operation | × | + | / |
---|---|---|---|

${e}_{A,w}^{*}\left(p\right)$ | M | M | |

${A}_{w,i}^{H}\left(p\right){\underline{R}}_{A,w}(p-1)$ | $M(M+1)$ | $M(M-1)$ | |

$A\left(p\right){\underline{R}}_{A,w}(p-1){\underline{A}}_{w,i}\left(p\right)$ | M | $M-1$ | |

$\lambda +{\underline{A}}_{w,i}^{H}\left(p\right){\underline{R}}_{A,w}(p-1){\underline{A}}_{w,i}\left(p\right)$ | 1 | ||

${\underline{R}}_{A,w}\left(p\right)$ | M | ||

${\underline{R}}_{A,w}(p-1){\underline{A}}_{w,i}\left(p\right)$ | M | ||

${\underline{G}}_{A,w}(p-1)$ | 1 | 1 | |

${\underline{G}}_{A,w}(p-1)$.${e}_{A,w}^{*}\left(p\right)$ | M | ||

${\underline{C}}_{A,w}\left(p\right)$ | M | ||

Total cost per iteration | ${M}^{2}+5M+1$ | ${M}^{2}+3M$ | 1 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

M. Al-Sammna, A.; Hadri Azmi, M.; Abd Rahman, T.
Time-Varying Ultra-Wideband Channel Modeling and Prediction. *Symmetry* **2018**, *10*, 631.
https://doi.org/10.3390/sym10110631

**AMA Style**

M. Al-Sammna A, Hadri Azmi M, Abd Rahman T.
Time-Varying Ultra-Wideband Channel Modeling and Prediction. *Symmetry*. 2018; 10(11):631.
https://doi.org/10.3390/sym10110631

**Chicago/Turabian Style**

M. Al-Sammna, Ahmed, Marwan Hadri Azmi, and Tharek Abd Rahman.
2018. "Time-Varying Ultra-Wideband Channel Modeling and Prediction" *Symmetry* 10, no. 11: 631.
https://doi.org/10.3390/sym10110631