# UWB Localization Using IEEE 802.15.4z

This example shows how to estimate the location of a single device as per the IEEE® 802.15.4z™ standard [ 2 ], using the Communications Toolbox™ Library for ZigBee® and UWB add-on.

### Overview

The IEEE 802.15.4z amendment [ 2 ] of the IEEE® 802.15.4 standard [ 1 ] is a MAC and PHY specification designed for ranging and localization using ultra wideband (UWB) communication. The very short pulse durations of UWB allow a finer granularity in the time domain and therefore more accurate estimates in the spatial domain.

The key ranging and localization functionality of the 802.15.4z amendment includes 3 MAC-level techniques:

• Single-sided two-way ranging (SS-TWR) - One device estimates the distance between two devices by using frame transmission in both directions of a wireless 802.15.4z link. This technique is demonstrated in the UWB Ranging Using IEEE 802.15.4z example.

• Double-sided two-way ranging (DS-TWR) - Both devices estimate the distance between the two devices by using frame transmission in both directions of a wireless 802.15.4z link.

• One-way ranging / time-difference of arrival (OWR/TDOA) - Network-assisted localization whereby one device communicates with a set of synchronized nodes to estimate the position of the device.

This example demonstrates the OWR/TDOA technique for uplink transmissions, by using MAC and PHY frames are compatible with the IEEE 802.15.4 standard [ 1 ] and the IEEE 802.15.4z amendment [ 2 ]. For more information on generating PHY-level IEEE 802.15.4z waveforms, see the HRP UWB IEEE 802.15.4a/z Waveform Generation example. For more information on generating IEEE 802.15.4 MAC frames, see the IEEE 802.15.4 - MAC Frame Generation and Decoding example.

### One-Way Ranging / Time-Difference of Arrival (OWR/TDOA)

The time-difference of arrival (TDOA) between the periodic messages places the device in one hyperbolic surface for each pair of synchronized nodes [ 3 ]. The intersection of all hyperbolic surfaces (for every pair of synchronized nodes) gives the location estimate for the device.

This example demonstrates the uplink OWR case.

### Setup

Confirm installation of the Communications Toolbox™ Library for ZigBee® and UWB add-on.

`commSupportPackageCheck('ZIGBEE');`

#### Configure Network

Set up a network with 3 synchronized nodes and 1 device, in a 100x100 plane:

```numNodes = 3; deviceLoc = [50 50]; % place device at the center nodeLoc = [40 41; 62 83; 87 24]; TDOA = nan(numNodes); helperShowLocations(deviceLoc,nodeLoc);```

Calculate the actual distance and time of flight (TOF) between nodes and the device.

```actualDistances = sqrt(sum((nodeLoc - deviceLoc).^2, 2)); c = physconst('LightSpeed'); % speed of light (m/s) actualTOF = actualDistances/c; SNR = 30; % in dB```

Use a short (IEEE 802.15.4 MAC) data frame as a blink.

```numBlinks = 1; % MAC layer: payload = '00'; cfg = lrwpan.MACFrameConfig( ... FrameType='Data', ... SourceAddressing='Short address', ... SourcePANIdentifier='AB12', ... SourceAddress='CD77'); blinkMAC = lrwpan.MACFrameGenerator(cfg,payload); % PHY layer: % Ensure the Ranging field is enabled. % Also set the proper PSDU length. blinkPHYConfig = lrwpanHRPConfig( ... Mode='HPRF', ... STSPacketConfiguration=1, ... PSDULength=length(blinkMAC), ... Ranging=true); blinkPHY = lrwpanWaveformGenerator( ... blinkMAC, ... blinkPHYConfig); % Cache preamble, to use in preamble detection. % Get the 1st instance out of the Nsync=PreambleDuration repetitions. indices = lrwpanHRPFieldIndices(blinkPHYConfig); % length (start/end) of each field blinkPreamble = blinkPHY( ... 1:indices.SYNC(end)/blinkPHYConfig.PreambleDuration); % 1 of the Nsync repetitions```

### Run Simulation

In the simulation loop, a blink propagates to each node with a propagation delay that is determined by their distinct distance. Next, each pair of nodes calculates the difference of their blink arrival times. As a result, the position of the device is estimated within a hyperbolic surface for each pair of nodes. The intersection of all surfaces gives the position estimate for the device. Here, a plot of 2D curves shows the intersection point to indicate the position estimate for the device.

```vfd = dsp.VariableFractionalDelay; arrivalTime = zeros(1,numNodes); plotStr = {'r--','b--','g--'}; [x, y] = deal(cell(1, 3)); for idx = 1:numBlinks for node = 1:numNodes % Transmission and reception of blink % Each node receives a specifically delayed version of the blink tof = actualTOF(node); samplesToDelay = tof * blinkPHYConfig.SampleRate; reset(vfd); release(vfd); vfd.MaximumDelay = ceil(1.1*samplesToDelay); delayedBlink = vfd( ... [blinkPHY; zeros(ceil(samplesToDelay), 1)], ... samplesToDelay); % Add white Gaussian noise receivedBlink = awgn(delayedBlink,SNR); % Node receiver detection of preamble preamPos = helperFindFirstHRPPreamble( ... receivedBlink,blinkPreamble,blinkPHYConfig); % Transmit each blink at t=0 of each period. The blink arrives % at different instances at each node, due to their dissimilar % distance to the device. arrivalTime(node) = ( ... preamPos - indices.SYNC(end) / ... blinkPHYConfig.PreambleDuration)/blinkPHYConfig.SampleRate; end % Localization: Estimate position at the synchronized backbone for % each pair of nodes. pairCnt = 1; for node1 = 1:numNodes for node2 = (node1+1):numNodes % Calculate Time Difference of Arrival (TDOA) TDOA(node1, node2) = arrivalTime(node1)-arrivalTime(node2); % Get hyperbolic surface for the TDOA between node1 and node2 [x{pairCnt}, y{pairCnt}] = helperGetHyperbolicSurface( ... nodeLoc(node1,:), ... nodeLoc(node2,:), ... TDOA(node1,node2)); plot(x{pairCnt},y{pairCnt},plotStr{pairCnt}); pairCnt = pairCnt + 1; end end % Find intersection points between hyperbolic surfaces [xC,yC] = helperFindHyperbolicIntersection(x,y); % Estimate location as the center of intersection triangle xO = mean(xC, 2); yO = mean(yC, 2); plot(xO, yO, 'ro') plot(xC',yC','rx') end leg = legend( ... 'Device', ... 'Synchronized nodes', ... 'A-B', ... 'A-C', ... 'B-C', ... 'Estimation', ... 'Intersections', ... 'location','northwest');```

Zoom in to estimation area:

`zoomInToEstimationArea(deviceLoc,xC,yC,xO,yO,leg);`

The IEEE 802.15.4z localization algorithm allows for multiple intersection points between 2 hyperbolic surfaces, thus either one or two possible localization answers exist. Calculate the localization error for each answer:

```for idx = 1:numel(xO) locError = sqrt(sum([xO(idx) yO(idx)]-deviceLoc).^2); fprintf('Localization error #%d = %0.3f m.\n',idx,locError); end```
```Localization error #1 = 0.012 m. ```

For localization methods that rely on estimating the time of arrival, errors in the distance estimate are primarily caused when the arrival time is not an integer multiple of the sample time. The largest distance error for such localization methods occurs when the arrival time lasts half a sample time more than an integer multiple of sample time. The smallest distance error occurs when the arrival time is an integer multiple of sample time. For the higher pulse repetition frequency (HRPF) mode of the high rate pulse repetition frequency (HRP) PHY used in this example, the symbol rate is 499.2 MHz and the number of samples per symbol is 10. The maximum distance estimation error is $0.5×c/\left(499.2×10\right)$, which is approximately 3 cm.

In general, the larger channel bandwidth in UWB corresponds to shorter symbol duration and smaller ranging error as compared to narrowband communication. For the narrowband communication as specified in IEEE 802.11az, the channel bandwidth ranges from 20 MHz to 160 MHz. Considering the maximum distance error for narrowband communication, estimates for the localization error lie between 0 and 10 cm for 160 MHz and between 0 and 75 cm for 20 MHz. For more information regarding positioning with IEEE 802.11az, see the 802.11az Positioning Using Super-Resolution Time of Arrival Estimation (WLAN Toolbox) example.

### Further Exploration

This example uses these objects and functions from the Communications Toolbox™ Library for ZigBee® and UWB add-on.

• lrwpan.MACFrameConfig: Create configuration for 802.15.4 MAC frames

• lrwpan.MACFrameGenerator: Generate 802.15.4 MAC frames

• lrwpanHRPConfig: HRP waveform configuration

• lrwpanWaveformGenerator: Create an IEEE 802.15.4a/z HRP UWB waveform

These utilities are undocumented and their API or functionality may change in the future. To view the source code for any of these utilities, use the `edit` function. For example, enter:

` edit lrwpan.MACFrameConfig`

at the MATLAB® command line to open `lrwpan.MACFrameConfig`.

```function zoomInToEstimationArea(deviceLoc,xC,yC,xO,yO,leg) % Zoom 2D plane into region around device location allX = [deviceLoc(1); xO(:); xC(:)]; allY = [deviceLoc(2); yO(:); yC(:)]; minX = min(allX); maxX = max(allX); minY = min(allY); maxY = max(allY); axis([ ... minX-0.1*(maxX-minX), ... maxX+0.1*(maxX-minX), ... minY-0.1*(maxY-minY), ... maxY+0.1*(maxY-minY)]) leg.Location = 'NorthEast'; end```

### Selected Bibliography

1 - "IEEE Standard for Low-Rate Wireless Networks," in IEEE Std 802.15.4-2020 (Revision of IEEE Std 802.15.4-2015), pp.1-800, 23 July 2020, doi: 10.1109/IEEESTD.2020.9144691.

2 - "IEEE Standard for Low-Rate Wireless Networks – Amendment 1: Enhanced Ultra Wideband (UWB) Physical Layers (PHYs) and Associated Ranging Techniques," in IEEE Std 802.15.4z-2020 (Amendment to IEEE Std 802.15.4-2020), pp.1-174, 25 Aug. 2020, doi: 10.1109/IEEESTD.2020.9179124.

3 - Wong, S.; Zargani, R. Jassemi; Brookes, D. & Kim, B. "Passive target localization using a geometric approach to the time-difference-of-arrival method", Defence Research and Development Canada Scientific Report, DRDC-RDDC-2017-R079, June 2017, pp. 1-77.