This paper presents a ranging receiver architecture able to timestamp IEEE 802.11b Wireless LAN signals with sub-100 picosecond precision enabling time-based range measurements. Starting from the signal model, the performance of the proposed architecture is assessed in terms of statistical bounds when perturbed by zero-mean additive white Gaussian noise (AWGN) as well as in case of multipath propagation. Results of the proposed architecture, implemented in a Field Programmable Gate Array-(FPGA-) based prototype, are presented for different environments. For AWGN channels, the prototype system is able to attain an accuracy of 1.2 cm while the ranging accuracy degrades in dynamic multipath scenarios to about 0.6 m for 80% of the measurements due to the limited bandwidth of the signal.
Despite the fact that Global Navigation Satellite Systems (GNSSes) cover nearly 100% of the planet, satellite-based localization is not available within buildings as the roofing and walls deteriorate the signal to a degree where an errorless decoding is no longer possible. Mounting pseudolites, devices transmitting the navigation signals, under the roofs are certainly not a valid solution, not only due to legal restrictions. The differences between indoor and outdoor localization are more substantial than just the received power. Radio propagation within complex environments, typical for indoor scenarios, are challenging for high-speed wireless communication, but even tougher for any form of localization service.
Many localization concepts (e.g., based on ultrasonic, electromagnetic waves, inertial sensors) have been proposed to bridge the gap between GNSSes and the lack of indoor locating systems. Nevertheless, for indoor environments, there is still no general satisfactory solution available as different key factors, such as low power consumption and high refreshment rate are incompatible. One major reason why indoor radio localization systems are way behind satellite navigation solutions is that the majority of all current wireless communication standards have not been designed with position determination in mind. These signals are often referred to as Signals of Opportunity (SoO). In theory, adding a localization service upon an existing standard is always possible. However, the key parameters like accuracy, reliability, or cost depend on the restrictions of the wireless standard. As a result, retrofitting a localization service to an existing technology might turn out to be highly complex as, for example, the integration of the Enhanced 911 service into GSM networks. The degree of complexity depends primarily on the measurement principles ranging from Received Signal Strength (RSS) to time or angle measurements, or a combination of these. Some principles require proprietary hardware, while others only require software modifications, but impose other restrictions, such as limited range or accuracy. As a result, there is no generally best solution to retrofit localization to a communication standard.
In particular, Wireless LAN (WLAN) seems to be an interesting candidate for localization as it is a widely accepted industrial standard deployed in billions of mobile devices in home and office environments. RSS-based WLAN localization is a thoroughly investigated subject, and still the positional accuracy can be considered rather poor. Time-based localization methods like Time of Arrival (ToA) or Time Difference of Arrival (TDoA) are attractive not only for satellite-based positioning, but also for indoor applications. The fact that the measured time is a linear function of the range makes it an ideal candidate even for larger distances in contrast to RSS.
The outline of the paper is as follows. Section
Locating a target in a radio localization system is based on the exchange of signals between the target and a number of base stations with known positions. In a network-based localization system, the location of the target can be calculated directly from the received signals collected by a locating unit or by the mobile device in case of handset-based localization. This approach is called direct position determination (DPD) [
Two-step position determination.
The simulations performed by [
RSS localization in WLANs is the most investigated solution as the measurement of the RSS is a mandatory feature in standard compliant WLAN devices. All that is required is to read the RSS information from the devices and collect it at the locating unit performing the localization based on fingerprinting or geometric approaches. One of the oldest RSS system is the RADAR system from Microsoft research [
Time-based WLAN ranging has been analyzed by the authors of [
Even higher accuracy can be achieved directly in the physical layer. A WLAN mechanism exploiting the Request to Send/Clear to Send (RTS/CTS) handshake mechanism for two-way range measurements is presented in [
As alternative to cross-correlation, some authors have proposed to use subsample interpolation methods belonging to the group of super resolution methods, such as the Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), Root-MUltiple Signal Classification (RootMUSIC), or Matrix Pencil (MP) [
The Global Positioning System (GPS) also belongs to the group of time-based systems and can be considered similar to ToA WLAN localization. However, the properties of GPS are specifically designed for ranging applications, whereas WLAN was designed as more or less a cable replacement. The largest difference is that the GPS C/A code is permanently transmitted with a chip rate of 1.023 MChips/s and a data rate of just 50 bit/s [
The work presented in this paper is based on previous investigations extended in terms of accuracy, multipath mitigation, and a detailed analysis of impairments. In [
The data of a WLAN frame, according to the IEEE 802.11b standard [
The baseband signal is modulated to the RF carrier and demodulated again in the receiver. If the carrier frequencies in the receiver and the target are sourced from different oscillators, the carrier frequencies are not exactly the same as each oscillator is subject to different tolerances and jitter. The frequency of an oscillator can be modeled as the sum of the nominal frequency
Depending on the length of the transmitted frame and the joint stability of
Not only the carrier can be subject to minor frequency skews. The chip rate of receiver and transmitter may slightly vary due to oscillator tolerances. As the chip rate is considerably lower than the carrier frequency by a factor of more than 200, the impact of imprecise clocks on the receiver performance is far lower. As 20 ppm chip frequency skew is equivalent to a time stretch of
The estimate
This approach works without the knowledge of the transmitted data or modulation, given the transmitted signal's autocorrelation has a significant peak. Hence, continuous wave signals cannot be used as their autocorrelation is periodic.
The performance of the estimator can be improved by passing the signals through a filter with matched frequency response
Apart from cross-correlation approaches neglecting the DSSS modulation characteristics, Cyclic Cross-Correlation (CCC) approaches can be applied to the baseband signal as well. CCC algorithms exploit the fact that the autocorrelation function of a cyclostationary signal is periodic and can therefore be expressed by a sum of functions
Although cross-correlation is a feasible instrument for estimating the TDoA in the baseband (e.g., for audio applications like [
Even in presence of carrier frequency skews, CCC methods can still be used. However, the introduction of carrier frequency skews increases the complexity by adding one search dimension. As the chip rate of common WLAN devices is uncorrelated to the carrier frequency, the estimation problem is extended by another dimension.
A particular issue with distributed signal capturing and centralized correlation methods is the transport of the sampling data to the correlation unit. If the system is intended to capture the data continuously, then a high-speed connection is required. For WLAN, a sample rate of at least 44 MHz is required, and given that each sample contains 8 bits, it requires a connection with at least 352 Mbps per receiver. Hence, for a simple scenario with 4 receivers, even a 1 Gbps connection to the locating unit is not sufficient. Due to these substantial drawbacks of correlation-based localization in WLANs, this paper proposes to perform ToA estimation in each base station and to calculate the position based on the TDoAs (from the ToAs) in the locating unit. Hence, the TDoA estimation is factored into ToA timestamping in each base station instead of a joint estimation of the TDoAs using correlation methods.
In the previous section, we have identified that the localization of a target by means of timestamping is an attractive approach. Timestamping requires that all base stations use a commonly agreed algorithm to capture the instant when a frame is received at a base station, which can range from stopping a counter, when a certain part of the frame is received (like in [
Generic receiver architecture.
In many DSSS receivers (e.g., GPS chipsets), the code NCO is purely binary, and therefore the NCO only outputs a sign function simplifying the multiplication to an adjustable inverter. The drawback of this approach is that the alignment of the code replica is quantized by the clock period of the NCO. In this case, the clock period of the NCO should be significantly shorter than the chip period of the received signal. For instance, the GPS receiver presented in [
For the proposed ranging WLAN Fractional Delay Ranging Receiver (FDRR), we assume that the received signal is sampled using a fixed local clock with period
Despite the dependency of the baseband pulse shape
This leads to the modified receiver architecture shown in Figure
Proposed fractional delay ranging receiver architecture.
The timing recovery calculates the fractional delay estimate
The residual frequency and phase offset are wiped off in the timing-aided (D
Range estimates.
Parameter | Variable | Ambiguity | Resolution |
---|---|---|---|
Fractional delay |
|
91 ns | Arbitrary |
Correlator lock-in |
|
1 |
|
Epoch | None | None |
|
Carrier freq. skew |
|
None | Arbitrary |
Carrier phase |
|
408 ps | Arbitrary |
CIR |
|
None | Arbitrary |
The baseband code synchronization is factored into the timing recovery and correlator. The correlator lock-in position
The term resolution in Table
However, there is a common misconception by several authors (e.g., [
Until now, we have considered taking a single timestamp at one specific instant in a frame, the epoch, and submit it to the locating unit calculating the position based on the timestamp set from different base stations. It is known from estimation theory that averaging as many realizations of a stochastic function as possible decreases the estimation variance by the improvement of the test statistic. For ranging, the estimation should be averaged, if possible, over the entire frame requiring very narrow bandwidths in the timing recovery. As a solution, we propose a two-step approach. The loop bandwidth in the timing recovery is optimized for chip synchronization, while the noisy outputs are filtered in a separate timestamping unit after the receiver control unit using a linear regression model. The timestamp optimization using linear regression, as described in the Appendix
The performance of various ranging estimators can be assessed by statistical bounds, which are used for comparison in Section
Then, the CRLB defines a lower bound for any unbiased estimator as
Increasing the effective bandwidth
Multipath propagation is present when the transmitted signal arrives at the receiver via multiple echoes. In contrast to interference with AWGN, the multipath components (MPCs) have similar statistical properties and are correlated to the direct signal. If the number of MPCs is
When multipath is present, the tracking loop of the timing recovery locks on the composite signal consisting of the line-of-sight signal (LOS) and the MPCs as the receiver is unable to differentiate between this perturbed signal and the desired signal. An MLE receiver tries to find the ToA by maximizing the cross-correlation function of the received signal
Hence, the cross-correlation function becomes a nonsymmetric function with a correlation peak that may be shifted with respect to the correlation peak of the direct signal. The estimation error due to the distortion is known as multipath error. It is dependent on the current channel coefficients (amplitude, phase, delay), which are defined by the propagation conditions. As the phase of the channel coefficients changes for movements as small as the carrier wavelength, the error is not predictable by a receiver in the vicinity. This small-scale multipath effect is well known for GPS and addressed by a number of mitigation strategies such as modified synchronizer discriminator functions (e.g., narrow correlators for delay-locked loops [
In spite of the limited realism, it is a common model to describe multipath propagation by the two-path channel model, where the CIR consists only of two terms, the LOS signal and a single multipath component. We consider the CIR as time-invariant, which represents the case of zero Doppler spread or infinite coherence time, respectively. This setup is, for instance, present if all transmitters, receivers, and IOs are static. Without loss of generality, we assume in the two-path scenarios that the LOS signal has unity amplitude (
Even for the two-path channel model, three parameters influence the multipath error: the amplitude
Let us recall that a spectral-line generating squaring synchronizer, as used by our proposed FDRR, squares the absolute of the signal and calculates the Fourier coefficient
If we insert the composite signal
It can be seen that the multipath error depends not only on
The Fourier coefficients
For certain multipath amplitudes, the error can be depicted in form of a ranging error envelope by varying the multipath delay and selecting the phase that generates the largest multipath error. The ranging error envelopes for 10, 30 and 50% multipath field strength are depicted in Figure
Multipath error envelope.
The multipath error depends on the cyclic function
Envelope for MPCs with long delays.
The drawback that the multipath error can be influenced by far specular reflections is alleviated, if we consider that the extra time delay causes an additional path loss. In addition, depending on the environment, large smooth surfaces acting as specular reflectors are unlikely. In terms of resolvability, delays, which are longer than the chip period, can be resolved (e.g., by spectral estimation of the equalizer or pseudospectrum estimates of superresolution methods). As a consequence, we can conclude that the multipath ranging error is mainly induced by MPCs with short delays, which are unfortunately not resolvable due to the limited bandwidth and the lack of the pulse shape definition.
Multipath can cause significant ranging errors in the order of several meters as the receiver tracks the composite signal. Despite particular antenna designs which attenuate the MPCs, multipath can also be tackled by signal and data processing using nonparametric, parametric, and averaging techniques. Nonparametric techniques use a modified receiver template, which rather tracks the derivative of the pulse shape than the pulse shape itself, such as a narrow correlator setup commonly used in GPS receivers. The modified template is designed to achieve a sharper correlation result that is less influenced by multipath propagation. Parametric techniques rely on a certain CIR model and estimate the nuisance parameters such as phases, amplitudes, and delays of the MPCs. A common approach within this group is superresolution techniques in the time and frequency domain [
A necessary assumption for all estimation methods is that the signal (or at least its autocorrelation and covariance) is either known in advance or the receiver is able to reconstruct this information. Whereas the digital information and signal constellation of each chip in the baseband can be reconstructed, the WLAN pulse shape is not defined and may vary from device to device. Hence, an estimation of the CIR is not possible because the transmitted signal cannot be reconstructed. On the other hand, nonparametric multipath mitigation techniques, such as narrow correlators with an early-late spacing of
Multipath is in particular the limiting factor for point positioning applications. When the channel is static and therefore the channel coherence time is infinite, the range estimate may include a constant ranging bias. In principle, multipath mitigation through averaging can be done by any kind of frequency or space diversity, which is able to change the CIR or minimize the coherence time. If the target changes the position by about 10 times the carrier wavelength, the small-scale fading effects and connected to these the multipath errors average. For WLAN, this equates to a displacement of more than 1 m. Spatial averaging is impractical as it prohibits point positioning and requires a constant movement to generate varying CIRs.
Frequency diversity is another option to mitigate multipath errors as different carrier frequencies change the CIR. The main disadvantage of this approach is that changing the WLAN channel causes a loss of connection, if not enforced simultaneously by the AP and all associated targets. Yet, we still propose this method as it is one of the few methods, which requires only software modifications of the target, namely, preplanned channel hopping. As shown in the next section, frequency diversity can significantly improve the multipath performance.
This section presents the results of the FDRR architecture introduced in Section
The proposed FDRR architecture has been implemented using the SMart integrated Localization Extension 3 (SMiLE 3) base station hardware, which is a revised version of our previous hardware described in [
Various measurements have been conducted by deploying either two or four base stations for one- and two-dimensional setups. The RF mixer of SMiLE 3 platform has a dependency of the delay on the premixer and postmixer amplification by a few nanoseconds. In all measurements, these systematic errors are compensated by a table lookup.
First, we assess the synthetic performance of the hardware, when the RF signal between the base stations is connected via cables and attenuators as depicted in Figure
Cabled setup for assessing the synthetic performance.
The measurement results for both synchronization approaches (Ethernet and Board-Link) for variable frame lengths are depicted in Figure
Ranging performance: frame length dependency.
The resolution
The GCC CRLB for
When attenuators are inserted into the cabling between the target and the base stations, an increased distance and degradation of the SNR can be tested. For the experiment a frame length of
Ranging performance: SNR dependency.
The GCC CRLB applies to the cross-correlation of the entire baseband signal with a noise-free template in each receiver given that there are
This bound is depicted as CCC CRLB in Figure
In all the following measurements, a Linksys WRT54GL wireless access point has been used sending beacons with
A two-dimensional medium-scale measurement has been performed on a flat meadow with four base stations positioned in the corners of a 36 m square. The square has been divided into sections of 6 m forming a grid. To assess the point localization performance, the target is located on each grid point and the position estimates are recorded. The base stations and the target are mounted on tripods with a height of 1.6 m to enable LOS propagation without the Fresnel zone touching the ground.
Figure
2D position measurement in LOS conditions.
2D position error.
An evaluation of the measured data shows that the TDoA RMS error of the unfiltered timestamps is 2.45 ns. As the TDoA standard deviation is only 390 ps, the largest contribution to the RMS error is the offset. Compared to the synthetic range measurements, the standard deviation is larger and a significant average offset exists. Offsets may arise due to positioning errors of the target and the base stations. These errors are inevitable as the markings of the positions on the meadow are accurate to approximately
For the assessment of the multipath performance, we consider a one-dimensional setup as there is only a single range to be extracted, and the ranging and position error are independent of the geometric setup in contrast to multidimensional locating. This allows for a more intuitive interpretation of the results as only a single time error is present. Clearly, the setup can be extended to more dimensions as well.
In the experiment, the target
Multipath measurement setup.
The results of the unfiltered ranges for this experiment are shown in Figure
Multipath ranging error.
Figure
Frequency hopping multipath ranging error.
As FHSS over 15 channels takes 150 ms with 10 ms frame period, the question arises, if a similar performance can be achieved with fewer channels. If only 4 channels are evaluated (1, 5, 9, and 13), the TDoA ranging error is slightly higher with maximum range offsets of −2.8 up to 2.4 m. The empirical CDF for the unfiltered ranging error is shown in Figure
Frequency hopping ranging error for 1, 4, and 15 channels.
Interestingly, multiple measurements in different environments showed that ranging errors using FHSS are significantly larger when the target is moving, while for stationary targets the FHSS-averaged ranging bias is always below 1 m. A possible interpretation is that fast-fading channels generate temporary ranging errors as the channel conditions change during the reception of the frame, while the equalizer is set into tracking mode and cannot compensate for the distortions. This open point is to be investigated in the future.
In this paper, we proposed a novel fractional delay ranging receiver architecture for ranging purposes in IEEE 802.11b WLANs. The particular feature of this architecture is that the timing recovery estimates the chip timing by a CCC approach and outputs its fractional delay estimate to all subsequent blocks. It has been shown that the proposed architecture can achieve a timestamping precision in the sub-100 picosecond range, which imposes a significant improvement to previously presented architectures. This high precision makes noise filtering techniques more or less obsolete.
The multipath-induced ranging bias, however, imposes the largest restriction to WLAN ranging. As WLAN has a narrow signal bandwidth and the baseband pulse is not defined, common multipath mitigation techniques, such as narrow correlators, showed no improvements. Yet this is not a limitation caused by a poor receiver implementation but justified by the fact that the wideband CIR is not resolvable with the limited signal bandwidth. The problem can be mitigated by performing frequency hopping or by averaging the TDoA estimates over all selected channels. With frequency hopping, the multipath error improved from 1.73 m with a probability of 80% for a single channel to 0.59 m when using all channels. As the WLAN channels overlap, using only 4 channels resulted in almost the same multipath resilience.
The future development of the system will focus on minimizing the impact of multipath propagation as further improvements in terms of ranging variance have virtually no impact on the practical accuracy. The receiver architecture already implements an equalizer compensating for the CIR of the channel. It is planned to develop an algorithm which reconstructs the specific pulse shape of each transmitter based on the equalizer coefficients captured from all base stations. With the knowledge of the pulse shape, parametric multipath mitigation techniques, such as superresolution methods, can be applied and multipath compensation values can be calculated. Particularly for point positioning with a static CIR, this technique has the potential to significantly reduce the multipath error without the necessity to transport the sampled signals of each base station to the central locating PC.
The linear regression model enables to generate an optimized timestamp exploiting the high accuracy of the fractional timing delay
Either these parameters are directly transmitted to the location unit or a filtered version of a timestamp for any arbitrary position in the frame can be calculated. For a TDoA architecture, this can be simplified as the locating unit uses range differences from two base stations. The distance estimation
This paper was partly financed by the province of Lower Austria, the European Regional Development Fund, the FIT-IT project