3  Ultra-wide band

The following chapter will introduce the ultra-wide band according to IEEE 802.15.4 [1]. Another definition exists by Federal Communications Commission (FCC), but it will not be discussed in this thesis.

To fully understand what ultra-wide band means it is necessary to define what bandwidth means by equation 3.1 and what center frequency means by equation 3.2.

\[ \mathrm{bandwidth_{-3 dB}} = f_{max} - f_{min} \tag{3.1}\]

\[ f_{center} = \frac{f_{max} - f_{min}}{2} = f_{0 db} \tag{3.2}\]

The ultra-wide band radio uses a bandwidth of 500 Mhz and more. This fact provides UWB with its unique ranging capabilities. The IEEE 802.15.4 Low-Rate Wireless Personal Area Networks [1] specifies the physical and data link layers of the ISO-OSI network model 1.

Today, UWB is mainly used in consumer electronics ¹ or in manufacturing plants to track assets, ground vehicles and people ²³.

3.1 MAC layer

IEEE 802.15.4 describes the MAC layer for low-rate wireless personal networks, including UWB. The MAC layer is responsible for coordinating access to the shared wireless channel, managing network associations and disassociations, and providing security and reliability features. The MAC layer inserts an MAC header and an MAC footer before and after a network-layer frame, respectively. The MAC header contains information such as frame type, source and destination addresses, sequence number, and security parameters. The MAC footer contains a CRC check. The IEEE 802.15.4 MAC layer supports two modes of operation: beacon-enabled and non-beacon-enabled. In beacon-enabled mode, a coordinator device periodically broadcasts beacons to synchronize devices on its network and allocate contention-free periods for data transmission. In non-beacon-enabled mode, devices use a slotted or unslotted carrier sense multiple access with collision avoidance (CSMA-CA) mechanism to access the channel. The exact layout of the MAC frame format is described in figure 3.1.

Figure 3.1: MAC frame format. [3]

3.2 Physical Layer

The physical layer (PHY) of the UWB was described in IEEE 802.15.4-2011 [1] as the UWB PHY. Later in IEEE 802.15.4-2015 [3] the PHY was named High repetition pulse (HRP) UWB PHY. This decision was made due to the introduction of Low repetition pulse (LRP) UWB PHY. Only the HRP UWB PHY will be discussed. The standard defines three operation bands:

• sub-gigahertz band consisting of a single channel spectrum from 249.6 MHz to 749.6 MHz.
• Low band with spectrum from 3.1 GHz to 4.8 GHz.
• High band with spectrum from 6 GHz to 10.6 GHz.

Figure 3.2: Data flow according to. [1]

The PHY uses an impulse radio signaling scheme with band-limited pulses and supports high data rates and precise ranging applications. It also uses a combination of burst position modulation (BPM) and binary phase-shift keying (BPSK) to modulate symbols. The overview of the physical layer is shown in figure 3.2.

PPDU format

Each physical layer protocol data unit (PPDU) consists of a preamble, PHY header, and the data itself. The process of encoding the whole PPDU can be seen in figure 3.3.

Reed-Solomon encoding is used to encode the physical service data unit (PSDU) of the HRP UWB PHY. It adds redundant symbols to the original message symbols to form a codeword that can be decoded using polynomial interpolation or factorization techniques. Reed-Solomon encoding improves the error-correction performance of the HRP UWB PHY and enables it to handle burst errors or random errors that may occur in the wireless channel ⁴.

Convolutional encoding is used to encode the PSDU of the HRP UWB PHY after Reed-Solomon encoding. It uses a finite state machine with memory cells to generate output bits based on the current and previous input bits. It adds parity bits to the original information bits to form a codeword that can be decoded using the Viterbi algorithm or other sequential decoding techniques. Convolutional encoding improves the error correction performance of the HRP UWB PHY and enables it to handle noisy or fading channels.

Figure 3.3: PPDU encoding process. [1]

A preamble in HRP UWB PHY is a sequence of known bits sent at the beginning of each frame. It is used for frame synchronization, channel estimation, and ranging measurements. It consists of two parts: a synchronization header (SHR) 3.4 and a physical layer header (PHR) 3.5.

The SHR contains a preamble symbol (SYNC) and a start-of-frame delimiter (SFD). The SFD is a fixed sequence of pulses that indicates the start of a frame. The PS is a burst of UWB pulses that can be modulated by burst position modulation (BPM) or binary phase-shift keying (BPSK). The preamble symbol repetitions (PSR) define the number of repeated sequences, ranging from 16 to 4,096 repetitions.

Figure 3.4: SHR field structure. [3]

The PHR contains information about the data to be received, including the length of the data and the data rate used to transmit the data. It also contains additional information elements to facilitate ranging information exchange.

Figure 3.5: PHR field structure. [3]

Symbol structure

Figure 3.6: Symbol stucture. [3]

A symbol is the basic unit of information in the HWP UWB PHY. It consists of a short burst of UWB pulses that lasts for \(2 \; \mathrm{ns}\) and occupies a bandwidth of 0.5-1.3 GHz. The burst can be placed in one of the two possible burst intervals, and its phase can be inverted or not, as can be seen in Figure 3.6. These two choices allow each symbol to carry two bits of information using burst position modulation (BPM) and binary phase-shift keying (BPSK); an example of the modulation can be found in figure 3.7.

Figure 3.7: Example of BPM-BPSK modulation,

The burst hopping position is a parameter that determines the time position of the UWB pulses within a burst interval. Scrambling code is a pseudo-random sequence that is applied to the data bits before modulation. It is used to randomize the data bits and reduce the peak-to-average power ratio (PAPR) of the UWB pulses.

IEEE defines the reference pulse as a root-raised cosine pulse with roll-off factor \(\beta = 0.5\) 3.3.

\[ r(t) = \frac{4 \beta}{\pi \sqrt{T_p}} \frac{\cos{[(1+ \beta) \pi t / T_p]} + \frac{\sin{[(1 - \beta) \pi t / T_p}]}{4 \beta(t / T_p)}}{1-(4 \beta t / T_p)^2} \tag{3.3}\]

The parameter \(T_p\) stands for the duration of the pulse. The duration is defined for each channel by table 3.1.

Table 3.1: The duration of the reference pulse for each channel. [1]

Channel number	Pulse duration \(T_p\) (ns)	Main lobe width \(T_w\) (ns)
{0:3, 5:6, 8:10, 12:14}	2.00	0.5
7	0.92	0.2
{4, 11}	0.75	0.2
15	0.74	0.2

Figure 3.8 further illustrates a waveform of the pulse. However, an actual hardware system cannot fully realize the shape of the reference pulse. Therefore IEEE 802.15.4 constrains the transmitted pulse \(p(t)\) by a cross-correlation function 3.4 where \(E_r\) is the energy of r(t) and \(E_p\) is the energy of p(t).

\[ \mathrm{\phi}(\tau) = \frac{1}{\sqrt{E_r E_p}} Re \int^{\infty}_{-\infty} \mathrm{r}(t) \mathrm{p}(t - \tau) \mathrm{dt} \tag{3.4}\]

For PHY to be IEEE compliant, the main lobe of the transmitted pulse must have a magnitude of cross correlation \(|\phi(\tau)|\) at least 0.8, and the magnitude of the sidelobes must not be greater than 0.3.

Figure 3.8: Reference pulse of UWB radio.

3.3 Ranging techniques

Time Difference of Arrival

Time difference of arrival (TDOA) position estimation is a technique that uses the difference in the arrival times of UWB signals at multiple receivers to estimate the position of a transmitter.

TDOA position estimation requires at least four receivers and one transmitter for 3D localization. The receivers measure the time of arrival (TOA) of the UWB signals. The TOA measurements are then used to calculate the TDOA values between different pairs of receivers [6].

\[ \sqrt{\mathbf{x_r}^T \mathbf{\hat{x}}} - \sqrt{\mathbf{x_i}^T \mathbf{\hat{x}}} = c(t_r - t_i) \tag{3.5}\] Where: \[ \begin{aligned} \mathbf{\hat{x}} &= \text{estimated position of the transmitter.} \\ \mathbf{x_r} &= \text{Position of the reference receiver.} \\ \mathbf{x_i} &= \text{Position of receiver \textit{i}.} \\ t_r &= \text{Time of arrival for the reference receiver.} \\ t_r &= \text{Time of arrival for the receiver \textit{i}.} \\ c &= \text{Speed of light.} \\ \end{aligned} \]

To estimate the position of the transmitter system of equations 3.5 is solved [4]. The main challenge in implementing TDoA is synchronizing the clock in all receivers [5].

The TDoA system can be used in a variety of applications, such as indoor positioning, vehicle or people tracking, and asset tracking. The accuracy of the TDoA system depends on the number and placement of the UWB sensors and the timing resolution of the system.

Two-way ranging

Two-way ranging (TWR) is a technique used by UWB systems to estimate the distance between two devices. TWR requires two-way communication between two devices, where one device sends a signal to another device and waits for a response, as shown in figure 3.9. The time difference between the transmission and reception of the signal is used to calculate the distance between the two devices.

Figure 3.9: Two way ranging with two round trips.

Single-sided two-way ranging (SS-TWR) is a technique where only one device sends a signal and waits for a response from another device. The time difference between the transmission and reception of the signal is used to calculate the distance between the two devices.

\[ \mathrm{TOF} = \frac{R_a - D_b}{2} \] Where: \[ \begin{aligned} \mathrm{TOF} &= \text{Time of flight.} \\ R_a &= \text{Time of round trip} \\ D_b &= \text{Response delay.} \\ \end{aligned} \]

Double-sided two-way ranging (DS-TWR) is a technique where both devices send signals and wait for responses from each other. The time difference between the transmission and reception of signals from both devices is used to calculate the distance between them.

\[ \mathrm{TOF} = \frac{R_a R_b - D_a D_b}{R_a + D_a + R_b + D_b} \]

The main advantage of DS-TWR is its ability to compensate for the effect of clock drift [2]. Clock drift refers to several related phenomena where a clock does not run at exactly the same rate as a reference clock. That is, after some time, the clock drifts apart or gradually desynchronizes from the other clock. All clocks are subject to drift, causing eventual divergence unless the are resynchronized. The drift of the clock can be caused by many factors, such as changes in temperature, aging of components, and changes in power supply voltage [2].

1.

2011. IEEE standard for local and metropolitan area networks–part 15.4: Low-rate wireless personal area networks (LR-WPANs). IEEE Std 802.15.4-2011 (Revision of IEEE Std 802.15.4-2006): 1–314. https://doi.org/10.1109/IEEESTD.2011.6012487

2.

2014. A sources of error in DW1000 based two-way ranging scheme APS011. Decawave; https://www.qorvo.com/products/d/da008446.

3.

2016. IEEE standard for low-rate wireless networks. IEEE Std 802.15.4-2015 (Revision of IEEE Std 802.15.4-2011): 1–709. https://doi.org/10.1109/IEEESTD.2016.7460875

4.

2021. Object tracking using time difference of arrival. MathWorks; https://www.mathworks.com/help/fusion/ug/object-tracking-using-time-difference-of-arrival.html.

5.

Yan Xie, Gerard J. M. Janssen, and Alle-Jan van der Veen. 2016. A practical clock synchronization algorithm for UWB positioning systems. In 2016 IEEE international conference on acoustics, speech and signal processing (ICASSP), 3891–3895. https://doi.org/10.1109/ICASSP.2016.7472406

6.

Wenda Zhao, Abhishek Goudar, and Angela P. Schoellig. 2022. Finding the right place: Sensor placement for UWB time difference of arrival localization in cluttered indoor environments. IEEE Robotics and Automation Letters 7, 3: 6075–6082. https://doi.org/10.1109/LRA.2022.3165181

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1. Apple AirTag https://www.apple.com/airtag/

2. Siemens RTLS https://www.siemens.com/global/en/products/automation/industrial-identification/simatic-rtls.html/

3. Sewio real-time location system https://www.sewio.net/

4. Mathworks HRP UWB IEEE 802.15.4a/z Waveform Generation https://www.mathworks.com/help/comm/ug/hrp-uwb-ieee-802.15.4az-waveform-generation.html