Determining the error distribution of BLE beacons at antenna near and far fields

Abstract

This paper investigates the error distribution and packet loss characteristics of Bluetooth Low Energy (BLE) beacons across near-field and far-field antenna zones. A custom experimental setup was developed using ESP32-based transmitters and an Ubertooth One receiver, supported by automated data collection scripts and time-synchronized measurements. The study quantifies how environmental conditions, distance, and transmission power afect BLE signal stability, particularly focusing on packet reception rates and RSSI behavior over distances from 0 to 2 meters. Cubic regression was employed to model the error distribution, highlighting a critical peak within the near-field boundary. The results emphasize the importance of adaptive beacon power management and advanced filtering for precise indoor positioning, especially in industrial and interference-prone environments.

Keywords

• eol>Bluetooth Low Energy
• near-field
• far-field
• RSSI
• packet loss
• error distribution
• Ubertooth One

1. Introduction

BLE beacon errors in indoor positioning systems are primarily caused by environmental factors such as multipath efects, signal fading, and interference from metallic objects, which distort the Received Signal Strength Indicator (RSSI) and lead to inaccurate distance estimations. Advanced methods like beacon weighting, Bayesian filtering, and location fingerprinting have been shown to reduce these errors. For instance, beacon weighting based on RSSI distributions can lower mean distance errors by over 66% compared to traditional three-point positioning, achieving errors as low as 0.45 meters [ 1 ]. Bayesian ifltering techniques, including Kalman and particle filters, can improve proximity estimation accuracy by up to 30% when the beacon and receiver are within 3 meters, efectively mitigating environmental noise [ 2 ]. Location fingerprinting, especially with dense beacon deployment, can achieve sub-2.6-meter errors 95% of the time, outperforming WiFi-based systems [ 3 ]. In challenging environments like factories, selecting beacons based on RSSI variance helps exclude non-line-of-sight signals, reducing average positioning errors [ 4 ]. Adjusting beacon transmission power and using multiple power levels can also keep estimation errors below one meter [ 5, 6 ]. Overall, minimizing BLE beacon errors requires a combination of optimized beacon placement, advanced signal processing algorithms, and adaptive ifltering to ensure reliable and precise indoor positioning across diverse environments [ 4 ].

While previous papers have addressed interference issues in Wi-Fi [ 7, 8, 9 ], Bluetooth [ 10 ], and ZigBee [ 11 ] wireless networks, the goal of this paper is to determine the impact of near-field and far-field antenna zones on packet loss.

2. Sources review

Using multiple transmission power levels in BLE beacons can significantly influence error rates in industrial environments, where obstacles, metallic surfaces, and interference often challenge signal propagation. Studies show that higher transmission power (e.g., +4 dBm) generally improves positioning accuracy, as stronger signals are less susceptible to attenuation and multipath efects. Still, the improvement over the lowest power settings (e.g., –20 dBm) may be modest—sometimes only around 12%—depending on the environment and beacon density [ 12, 13 ]. Customizing transmission power for each beacon, rather than a uniform setting, can enhance localization accuracy by adapting to specific site conditions and reducing overlap or interference between beacons [ 14 ]. Employing multiple power levels at each beacon point can also help keep estimation errors below one meter, allowing the system to balance coverage and precision dynamically [ 5 ]. However, in complex industrial settings, even with optimal power settings, RSSI-based distance estimation remains vulnerable to environmental noise, and additional filtering techniques (such as Gaussian or Kalman filters) are often needed to recover or maintain accuracy [ 13, 15 ]. Moreover, while higher power increases coverage, it can also introduce more interference and reduce battery life, so a trade-of must be managed [ 3, 12 ]. Overall, using multiple and adaptive transmission power levels, advanced filtering, and careful beacon placement can minimize BLE beacon error rates and improve reliability in industrial environments [ 13 ].

Distance significantly impacts BLE packet loss, with the probability of successful packet reception generally decreasing as the distance between devices increases. Empirical models show that packet reception probability can be described as a quadratic function of distance, beacon power, and advertising frequency, with greater distances leading to higher packet loss rates and lower received signal strength (RSSI) values; for example, mean RSSI drops from about –65.5 dBm at 1 meter to –90.8 dBm at 16 meters, indicating weaker signals and more frequent packet loss at longer ranges [ 16, 17, 18 ]. In addition, environmental factors such as interference, human presence, and device orientation can further exacerbate packet loss, with interference alone reducing packet delivery rates by 13% to 40% in some scenarios [ 18, 19, 20 ]. Overcrowded environments can also cause substantial signal strength and coverage fluctuations, with distance estimation accuracy dropping by up to 41% in highly crowded settings [ 21, 22 ]. These findings highlight the importance of considering distance and environmental conditions when designing BLE-based systems, especially for applications like indoor localization, where packet loss directly afects accuracy [ 16 ].

3. Design of the experimental setup

To conduct the experiment, a BLE packet transmitter (with the required frequency, signal level, and content), a receiver and a controller were used, as shown in Figure 1.

For ease of synchronization, the transmitter and receiver (Figure 2) were connected to the controller directly, minimizing measurement errors.

However, additional software modifications were required to experiment.

4. Transmitter hardware selection

When selecting available boards for the transmitter, Software Defined Radios, Bluetooth dongles, and single-board computers were considered. However, for miniaturization and the availability of SDK and code examples, the choice fell on the family of single-board computers in the ESP32 series. Table 1 shows the characteristics of the board modifications.

According to the table above, the choice of the ESP32-S3 N16R8 Type-C board is advantageous: the dual-core LX7 processor allows you to handle several tasks in parallel (for example, receiving commands and generating packets), and a large amount of SRAM and Flash memory makes it possible to cache a suficient amount of data, and the program code can be more functional, so make this board universal for surveillance tasks. With all the available boards on sale, the ESP32-S3 N16R8 Type-C board is the most universal for a dual-core processor. In addition, some boards are equipped with Micro-SMA connectors, which allow the use of external antennas.

5. Transmitter software preparation

To secure work from BLE, use external libraries:

1. NimBLE-Arduino is a BLE stack based on Apache Mynewt, which provides an API for transmitting advertising packages and securing connections [ 25 ].

2. U8g2 for OLED screen (optional) [ 26 ].

Example of packet generation: #include <Arduino.h> #include <NimBLEDevice.h> #include <NimBLEExtAdvertising.h> String mac; void setup() { Serial.begin(115200); while(!Serial) delay(10); NimBLEDevice::init("ESP32_Beacon"); NimBLEDevice::setPower(ESP_PWR_LVL_N24); } void loop() { static NimBLEExtAdvertising* pExtAdv = NimBLEDevice::getAdvertising(); if (Serial.available()) { String ts = Serial.readStringUntil(’n’); ts.trim(); NimBLEExtAdvertisement extAdv; extAdv.setLegacyAdvertising(true); extAdv.setManufacturerData(ts.c_str()); if (pExtAdv->isAdvertising()) { pExtAdv->stop(); delay(10); } pExtAdv->removeInstance(0); if (!pExtAdv->setInstanceData(0, extAdv)) { Serial.println("Bad data func setInstanceData()"); return; } if (pExtAdv->start(0, /*duration=*/0, /*maxEvents=*/1)) { unsigned long start = millis(); while (pExtAdv->isAdvertising() && (millis() - start < 500)) { delay(10); } if (!pExtAdv->isAdvertising()) { Serial.println("Advertised done (confirmed via polling)"); } else { Serial.println("Timed out waiting for adv complete"); pExtAdv->stop(); } } } }

The strength of the signal is set to the additional NimBLEDevice::setPower(ESP_PWR_LVL_N24), which will send packets that receive the following values:

ESP_PWR_LVL_N24 = 0 (corresponding to –24 dBm) ESP_PWR_LVL_N21 = 1 (–21 dBm) ...

ESP_PWR_LVL_N0 = 8 (0 dBm) ...

ESP_PWR_LVL_P18 = 14 (+18 dBm) ESP_PWR_LVL_P21 = 15 (+21 dBm) To assemble the code, PlatformIO was used with the commands: 1. pio run (build the project in “release” mode). 2. pio run -e esp_env -t debug (build the project in “debug” mode).

Basic setup of platformio.ini: [env:esp32-s3-devkitm-1] platform = espressif32 board = esp32-s3-devkitm-1 framework = arduino lib_deps = h2zero/NimBLE-Arduino@2ˆ.3.2 build_type = release build_flags = -O3 -function-sections -fdata-sections -Wl,–gc-sections -DNDEBUG -DCONFIG_BT_NIMBLE_ROLE_BROADCASTER=1 -DCONFIG_BT_NIMBLE_EXT_ADV=1

Also in Visual Studio Code is an extension called Platformio, which allows you to automate and visualize all configurations and commands.

6. Receiver hardware selection and software preparation

To collect packets, you can use standard BLE modules (for example, the utility BlueZ Bluemoon [ 27 ]), but they limit the controllability of the process of saving packets. Similar limitations are inherent in hardware packet snifers (for example, nRF52833/40 [ 28 ] or TI CC2540 [ 29 ]). Therefore, the flexible open-source Ubertooth One platform was chosen [ 30 ].

Ubertooth-btle is a utility used by Ubertooth One to store and analyze BLE trafic. The utility is compiled in C and, if changes are necessary, it must be recompiled. The standard view of the software looks like this: printf("systime=%u freq=%d addr=%08x delta_t=%.03f ms rssi=%dn", systime, rx->channel + 2402, lell_get_access_address(pkt), ts_dif / 10000.0, rx->rssi_min - 54);

The systime is in seconds, which does not match our world’s accuracy level. There is a need to increase the accuracy by adding the nanosystime parameter, which will represent the hour in nanoseconds.

Such changes are made to improve the accuracy. Programming through the Python library could also be done. Still, daily filtering by the device’s MAC address on the hardware level, only on the software level, would enhance the processing package and increase the loss of time.

7. Automation of the data collection process

To control the process of sending packages to software packages, a Python script that sends packages through the Serial port (via USB) to the ESP32 transmission: import serial import time SERIAL_PORT = ’/dev/ttyACM0’ BAUDRATE = 115200 ITERATIONS = 1000 idle_timeout = 10 def measure_one(ser, num_iter): sent_ts = time.time_ns() ser.write(f"{sent_ts}n".encode()) last_try = time.time() num_try = 0 while True: num_try += 1 print(f"Try #{num_try} for {sent_ts} ## {num_iter} item") timeout = idle_timeout - int((time.time() - last_try)) if timeout <= 0: break line = ser.readline() if line and str(line).startswith("b’Advertised done"): break return 1 def main(): ser = serial.Serial(SERIAL_PORT, BAUDRATE, timeout=1) try: for i in range(ITERATIONS): measure_one(ser, i) ifnally: ser.close() if __name__ == ’__main__’: main()

The function measure_one(ser, num_iter) is a whole block of code that sends just one packet and synchronously reads the ESP32 output about the capture and processing of the packet.

Here’s a Bash script to make it easier to carry out the experiment: #!/bin/bash START_NUM=${1:-0} INCREMENT=5 CURR_NUM=$START_NUM echo "Starting from number: $CURR_NUM" while true; do echo "Starting Ubertooth and Python storage..." ubertooth-btle -t 10:20:ba:4b:b1:41 -n > recieved_packets.txt & PID_UBER=$! python3 send_packets.py > sented_packets.txt echo "Python has finished. Waiting for 3 seconds..." sleep 3 echo "Completing Ubertooth (PID=$PID_UBER)..." kill $PID_UBER wait $PID_UBER 2>/dev/null FOLDER_NAME="$CURR_NUM cm" mkdir -p "$FOLDER_NAME" mv recieved_packets.txt "$FOLDER_NAME/" mv sented_packets.txt "$FOLDER_NAME/" 2>/dev/null || echo "sended_packets.txt not found" echo "Files moved to $FOLDER_NAME" read -p "Press Enter to start the cycle..." CURR_NUM=$((CURR_NUM + INCREMENT)) done

Shard measurements were carried out at 5 cm intervals of 2 m, the script allows you to simplify the time required to save data, and itself:

1. START_NUM=${1:-0} is specified tracking number, which will be in cm. 2. Ubertooth-btle -t 10:20:ba:4b:b1:41 -n > recieved_packets.tx – launch the modified command ubertooth-btle, which is used to catch packets sent from the ESP32.

3. Python3 send_packets.py > sented_packets.txt This runs the package sending script and redirects its output to a text file.

4. “mv recieved_packets.txt "$FOLDER_NAME/"" and "mv sented_packets.txt "$FOLDER_NAME/" 2>/dev/null || echo "sended_packets.txt not found" are automated movement of created result files of robot programs to a directory under the name that coincides with the location in cm.

5. CURR_NUM=$((CURR_NUM + INCREMENT)) increase the cycle number according to the duration in cm.

8. Features and implementation problems

During the implementation, some problems arose. For example, the issue of bufering the subprocess output and parallelism with threads when transferring data is that Python has limited true parallelism, which entails alternating code execution by diferent threads, which reduces the accuracy of measurements.

It should be noted that the launch order matters; if you start sending packets first and then ubertoothbtle, packet loss may occur when scanning through the utility, since the initialization of the ubertoothbtle software tool takes some time.

When using a standard BLE stack based on BLEDevice and BLEAdvertising, there is a problem of controlling the number of sent packets (events): instead of controlling the number of events, only advertising time control is available — as a result, if the advertising time is too short, no packets are sent, and if it is too long, several are sent.

9. Verification of the experimental results

An experiment was conducted using the established experimental setup. One thousand time-stamped Beacon packets were sent at diferent distances, and the number of lost packets was measured (see Table 2). The time delay between the received packets was also calculated.

The delay value was ignored since the first packet incorrectly returns its time. The results can be approximated using the cubic regression equation () = 3 + 2 + + , (1) where is the distance between receiver and transmitter, , , , and are the coeficients. To calculate the coeficients, we will make a system of equations ⎧ ⎪⎪⎪ ∑︁ 3 + ∑︁ 2 + ∑︁ + = ∑︁ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪ ∑︁ 4=+1 ∑︁ 3=+1 ∑︁ 2=+1 ∑︁ = ∑=︁1 ⎪⎨ =1 =1 =1 =1 =1

⎪⎪⎪⎪ ∑︁ 5 + ∑︁ 4 + ∑︁ 3 + ∑︁ 2 = ∑︁ 2 ⎪⎪⎪⎪⎪⎪⎪ =1 =1 =1 =1 =1 ⎪⎪⎪⎪ ∑︁ 6 + ∑︁ 5 + ∑︁ 4 + ∑︁ 3 = ∑︁ 3 ⎩ =1 =1 =1 =1 =1 Then, fill out Table 3 with the summarization results.

And obtain Equation (2) with sums from Table 2, a system of linear equations ⎧ 84.050 + 55.350 + 41 + 41 = 11135 ⎪ ⎪⎨⎪ 136.133 + 84.050 + 55.350 + 41 = 9265.200 ⎪ 229.667 + 136.133 + 84.050 + 55.350 = 12717.905 ⎪ ⎪⎩398.514 + 229.667 + 136.133 + 84.050 = 19616.834 The total sought cubic regression equation is as follows:

() ≈ 71 3 − 196 2 + 151 + 189.

From the experimental plot and graph, the regression equations are presented in Figure 3. The experiments were conducted on the 37 BLE channel corresponding to the frequency 2.402 GHz. Let’s calculate the antenna far-field limits for this frequency, because the linear size of the antenna is less than its linear dimensions, so we use the formula for approximate calculation ∼ 6...10, = 0.75...1.25 m. The regression plot shows a local maximum of errors within the near-field boundary.

To assess the significance of regression and correlation parameters, we determine the average number of errors

Let’s determine the correlation index = 1 ∑︁ = 220.5.

=1 ⎯ ⎸ ⎸ = ⎷⎸1 − ∑︀=1 ︁( − ̂︀︁) 2 ∑︀=1 ︀( − )︀ 2 ≈ 0.834 from where we obtain the determination index 2 > 0.5, which means that the approximation of the function can be used to represent the law of distribution of errors depending on the range of the receiver. The average error of approximation left (2) (3) (4) (5) (6) 1 ∑=︁1 ⃒⃒⃒⃒⃒ − ̂︀ ⃒⃒⃒⃒⃒ · 100% ≈ 4.1%. where the indices are calculated from the sampling parameters 1 = 3 and 2 = − 1 − 1 = 37 . The value of Fisher’s criterion indicates that for the sample, we can only observe the type of process, but it does not correspond to the approximated function.

Also when calculating the actual Durbin-Watson criterion we get: = ∑︀=1∑(︀ − −1 )2 ≈ 0.27 < 2, (9)

=1 2 where is the deviation from the mean error rate. The criterion value indicates a positive autocorrelation, which indirectly confirms the conclusion about the qualitative assessment of the investigated process. 10. Conclusions The work involved selecting the tools, preparing software for the experiment, and conducting the experiment itself in a distance range of up to 2 meters. Since the near zone for a frequency of 2.402 GHz is about 1 meter, the selected distance covers the transition from the near to the far zone of the antenna. When approximating the measurement results, it was shown that in the center of the near zone, the number of errors increases slightly, and decreases when moving to the far zone, which indicates the formation of an electromagnetic wave front at the junction of zones. The calculated coeficients confirm the reliability of the approximation results.

Further studies are planned to be carried out to check the rate of signal loss at significant distances and compare the results obtained by diferent packet snifers.

Declaration on Generative AI

The authors have not employed any Generative AI tools.

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