Timestamping of IEEE 802.15.4 CSS by CORDIC-based Chirp ...

Timestamping of IEEE 802.15.4 CSS by CORDIC-based Chirp Interpolation Reinhard Exel, Thomas Bigler, Thilo Sauter

Paolo Ferrari, Mattia Rizzi, Alessandra Flammini

Center for Integrated Sensor Systems, Danube University Krems Dept. of Information Engineering, University of Brescia Brescia, Italy Wiener Neustadt, Austria [email protected] [email protected]

Abstract—Accurate timestamps of wireless frames are the basis for clock synchronization of distributed measurement devices as well as for time-based wireless localization. Wireless sensor networks (WSNs) benefit from both synchronization and localization as it enables the sensor node to fuse measurement data with temporal and spatial information. The lower communication layers of WSNs are often based on the IEEE 802.15.4 standard, whereas only for Ultra-wideband (UWB) timestamping and ranging abilities are specified. The Chirp Spread Spectrum (CSS) physical layer, recently introduced into IEEE 802.15.42011, is another promising modulation scheme for highly accurate timestamping. This paper presents a timestamping receiver architecture for 802.15.4 CSS based on a Delay-Locked Loop and subsample interpolation (chirp generation) using the CORDIC algorithm. This architecture generates arbitrary subsample- and frequency-shifted chirp templates on the fly and therefore does not require large correlation filters. Simulations of the timestamp performance show that the proposed architecture offers equal performance as post-correlation delay estimators, yet with a significantly reduced amount of multipliers. This facilitates the implementation of precision clock synchronization and localization into low-power wireless sensor nodes.

I. I NTRODUCTION In the field of instrumentation and measurement, it is often not sufficient to determine the magnitude of a certain physical or chemical quantity only, but also the temporal relationship to other observed variables and possibly the location of a measurement. As a result, some form of clock synchronization is required in distributed measurement systems to correlate measurements taken by spatially distributed devices. Stimulated by recent advances in packet-based synchronization technologies, legacy synchronization networks are more and more replaced by packet-based networks providing means for data communication and synchronization. Nowadays, accurate synchronization using IEEE 1588 in wired Ethernet has become a standard technology widely deployed in the telecom, manufacturing, and even the financial industry. Despite the reduced cabling cost, increased flexibility and mobility of wireless communication, wireless is commonly not used for timing sensitive measurement applications as most wireless standards do not offer hardware support for timestamping. Therefore, wireless synchronization approaches have to use inaccurate software timestamping instead which is deteriorated by the indeterministic processing delays of the networks

stacks. With the increased mobility of wireless devices, location determination is often equally important as synchronization. Historically, synchronization and locating have been tackled separately, primarily due to the lack of sufficiently accurate timestamping to support time-based localization of mobile devices, e. g., using Time of Arrival (ToA) or Time Difference of Arrival (TDoA). Today, more and more communication technologies are designed for highly accurate timestamping. Thus, the hardware timestamping capabilities of recent wireless standards can be used to jointly provide synchronization and location determination. For 802.11 WLAN, for instance, timestamping and synchronization schemes have been specified within the IEEE 802.11v amendment [1] in 2011, and these are now part of IEEE 802.11-2012. The IEEE 802.15.4-2011 standard [2] is commonly used as physical and media access layer for wireless sensor networks (WSNs), such as ZigBee or 6LowPAN. It specifies a number of different physical layer implementations, whereas only for Ultra-Wideband (UWB) timestamping and ranging functions are defined. Yet, UWB has its limitations in terms of communication range and energy demand. The Chirp Spread Spectrum (CSS) modulation of 802.15.4 appears to be an appealing physical layer implementation for support of timestamping for synchronization and ranging applications. It offers a good trade-off between the very narrowband 802.15.4 DSSS modulation and the wideband, but energy-demanding UWB implementations. In particular, the simplified modulation schemes of 802.15.4 CSS offer significant energy advantages and increased robustness against interference compared to WLAN [3] which makes 802.15.4 the favorite choice for WSNs. This paper presents a receiver architecture for 802.15.4 CSS signals able to precisely timestamp received CSS frames. It takes into account carrier frequency offsets, incoherent sampling of the baseband signal with respect to the transmitting device, noise and multipath propagation. The outline of the paper is as follows: in subsection II we introduce the CSS signals and review timestamping approaches for 802.15.4 CSS. In section III an efficient timestamping receiver with reduced hardware demands is introduced. In the following section, the proposed design is compared by means of simulation and a

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Fig. 1. CSS Symbol type IV composed of four subchirps

conclusion is given. II. BACKGROUND AND R ELATED W ORK A. IEEE 802.15.4 CSS signaling Each symbol of the IEEE 802.15.4 CSS physical layer is composed of four so-called subchirps s which have the form of a linear frequency chirp multiplied by a raised-cosine time window PRC (t) by s(t, φ, ω, µ) = PRC (t) exp[j(φ + ωt + t2 µ/2)].

(1)

The time window PRC (t) attenuates the signal power at the start and end of each chirp, φ is the starting phase, ω is the angular starting frequency (rad/s), and µ is the chirp rate (rad/s2 ). A signal x(t) composed of N symbols can be written by N X 4 X x(t) = s(t − nT − Tn,k , φn,k , ωk , µk ). (2) n=1 k=1

The symbol period T , i. e., the duration of all four subchirps including gaps is 6 µs. Each symbol is composed of k = 4 subchirps (1), two up and two down-chirps, with a particular time gap between the chirps realized by Tn,k . The phase φn,k of the complex subchirps is modulated using differential quadrature phase-shift keying (DQPSK). The start frequency and chirp rate are selected to follow one of the four subchirp sequences termed I, II, III, and IV in the standard. Fig. 1 depicts a waveform of a type IV symbol with φn,k = 0. B. CSS timestamping receivers in the literature The accuracy of timestamps and range estimates can be improved on different levels, either by post-processing measures limiting the noise impact or by improving the timestamp estimate for each CSS subchirp or symbol. The mobile robot localization approach of [4] falls into the former category; it post-processes the range measurements by an extended Kalman filter. By using the symmetric double-sided two-way ranging (SDS-TWR) the approach is also tolerant to frequency offsets. Yet, the improvement of the timestamp estimate has recently gained increasing attention as it can be combined with

filtering approaches to deliver an even better accuracy. There are two particular issues with 802.15.4 CSS: The incoherent nature of baseband sampling, and carrier frequency offsets. The received signal is incoherent to the baseband sampling and therefore it may arrive anytime between two sampling instants. Peak detectors usually have a finite resolution and therefore a timestamping error is created. Carrier frequency offsets (CFOs) shift the correlation peak of a subchirp forward or backward in time depending on the sign of the frequency offset and the chirp rate. In [5] a timestamping/ranging approach using two phaseshifted (up- or down) chirps is proposed. The subsample phase shift of the baseband signal is resolved using singular value decomposition (SVD) and subspace-based algorithms. In [6] the SDS-TWR approach is used to determine the range between two CSS transceivers. The timestamps are calculated by a fixed matched filter template and by post-processing with a subspace-based inverse Fast Fourier transform (IFFT) algorithm. As the phase after the matched filter is dependent on the distance and CFO, the authors remove the CFO-induced error by averaging over up and down chirps. Simulations showed timestamping standard deviations in the sub-ns range for additive white Gaussian noise (AWGN) channels. A hardware implementation using a Field Programmable Gate Array (FPGA) platform of the system is shown in [7] proving that ranging errors below 1 m are attainable. Yet, this accuracy requires dedicated hardware support for the eigenvector analysis. In [8] timestamping with subsample accuracy is achieved by interpolation. The authors determine the correlation peak of each subchirp with a resolution of 31.25 ns and improve this estimate by a parabolic interpolator (estimator) which uses the absolute value of two samples, one before and one after the correlation peak. As above, timestamp errors due to CFOs are resolved by averaging over all subchirps of a symbol. The implementation of this approach using a software-defined radio (SDR) with 25 MHz sampling rate showed timestamp standard deviations of about 2 ns. A hardware implementation with the full 802.15.4 CSS sampling rate of 32 MHz is presented in [9]. It has been shown that timestamp standard deviations below 0.5 ns are feasible with support of frequency synchronization of the selected hardware. III. T IMESTAMPING FOR 802.15.4 CSS The approaches presented in subsection II-B deliver decent timestamp accuracy for ranging and precision clock synchronization and can also tolerate frequency offsets. All time quantities (symbol duration, time gaps, subchirp delays) in 802.15.4 CSS are an integer multiple of 31.25 ns, equivalent to a 32 MHz clock period. This allows for a simplified decoding with no interpolation when using 32 MHz sampling frequency. Thus, in theory 802.15.4 CSS signals can be decoded by correlation (by means of a matched filter) with the corresponding up or down-subchirp. However, real-world receivers have to take a number of impairments into account: limited signal-to-noise ratio (SNR), carrier phase and frequency offsets, baseband

phase and frequency offsets, imperfections and non-linearities in the transceiver logic, and multipath propagation [8], [10]. Yet, the hardware demand and complexity associated with the presented solutions are rather high. For instance, the eigenvector analysis in [5]–[7] requires matrix pseudo inverses. The solution of [8] using matched filtering together with parabolic interpolation appears to be simpler at a first glance. Yet, just the matched filtering with 32 MHz requires four complex Finite Impulse Response (FIR) Filters (one for each subchirp) each having 38 taps, thus requiring 152 complex (or 608 real-valued multiplication respectively) per clock tick. This leads to a large hardware demand and high energy consumption – both attributes may impair the use in WSNs. In this section, we present a simple and efficient timestamping approach for 802.15.4 CSS using the CORDIC (COordinate Rotation DIgital Computer) algorithm to implement the CSS modulation scheme.

The received signal is inherently incoherent to the transmitted signal (i. e., the correlation peak may be located at any position between two samples). Let  be the fractional time delay such that −Ts /2 ≤  < Ts /2 with Ts the sampling period. Inserting t +  for t into (1) leads to

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Fig. 3. Delayed-locked loop CSS receiver: Detailed architecture based on the concept of Fig. 2b

s(t + , φ, ω, µ) = PRC (t + ) exp[j(φ + ω + µ2 /2) (3)

The raised-cosine time windowing function PRC (t + ) can be approximated by PRC (t) for small  or can even be omitted (equivalent to a rectangular window) as in [8]. The substitution of t with t+ reveals other important properties: The time shift changes the phase and frequency, but the chirp rate remains unaltered. Thus the time-shifted subchirp s(t + , φ, ω, µ) can be approximated by the original subchirp with additive phase and frequency by s(t + , φ, ω, µ) ≈ s(t, φ + ω + µ2 /2, ω + µ, µ).

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+ jt(ω + µ) + jt2 µ/2].

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The peak-detector receiver in Fig. 2a (used in all CSS receivers cited in subsection II-B) operates with discrete-time signals and correlates the received shifted subchirp r[n] = s(nTs + , φ, ω, µ) with the fixed correlation pattern p[n] = s(nTs , φ, ω, µ). The delay estimate (timestamp) is estimated by a peak detector, together with a fractional estimator (e. g., subspace-based approaches, parabolic interpolator). B. Proposed Receiver Architecture Instead of estimating the fractional delay from the (asymmetric) shape of the sampled cross-correlation function, the delay can also be estimated by shifting the correlation pattern in a way to maximize the correlation peak, as depicted in Fig. 2b. This approach is often termed delay-locked loop (DLL) as the delay  in the adaptive pattern p[n] is adjusted. The filter taps for this approach could be calculated using (3). However, the requirement to have adjustable filter taps even increases the hardware complexity.

We select to generate the adaptive pattern on the fly with the help of a phase generator and a CORDIC block as shown in Fig. 3. The argument of the exponential function in (3) is composed of a phase constant, a linear increasing phase (i. e., the frequency) and quadratic phase increase (i. e., the chirp). Thus, the argument can be efficiently calculated in a phase generator via a phase constant, the integration of a frequency constant, and the double integration of a chirp constant. The complex exponential, equivalent to sine and cosine calculation, can be done by the CORDIC algorithm with an arctan-table [11] using i iterations by xi+1 = xi − di yi 2−i yi+1 = yi + di xi 2−i zi+1 = zi − di arctan(2−i ).

(5)

If the argument of the exponential function is put into z1 and di = sgn(zi ), then zi is driven to zero. When x (or y) has been initialized with a given amplitude, the algorithm calculates the sine and cosine for the given argument. Using the CORDIC algorithm and the phase generator, arbitrary chirp sequences can be generated. Additionally, by exploiting (4) time-shifted chirp sequences can be generated as well. If r[n] is the received signal (see Fig. 2b), the adaptive chirp pattern p[n] is shifted accordingly to maximize the cross-correlation function Rpr and to find the delay estimate tˆ by 38 X tˆ = max |Rpr (t)| = max p[n + t]r∗ [n] . (6) t t n=1

(7)

the correlation peak is found with high accuracy given a symmetric shape of the cross-correlation function. These points are termed ’early’ and ’late’ arms and are marked with E and L in Fig. 3. We select to use one correlation point 62.5 ns before the peak, and 62.5 ns (two 32 MHz sampling clock periods) after the peak. The early and late values are correlated with the received signal and an integrate-and-dump block is used to calculate the points of the cross-correlation function. However, the DLL needs to be bootstrapped (i. e., aligned to the correlation peak) to synchronize the early and late arm to the peak. To identify the peak without searching, a downchirp correlator with the half sampling rate (i. e., 19 instead of 38 taps) is used, as depicted above the multiplier in Fig. 3. The output of the DLL feeds a carrier recovery algorithm which estimates the CFO by evaluating the phase output of the DLL. Finally the data is decoded and is output together with the delay estimate. IV. S IMULATION R ESULTS AND C OMPLEXITY E STIMATE

Delay Estimation Error (ns)

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A common approach (e. g., in ranging receivers) to achieve this maximization are delay-locked loops (DLLs). A DLL evaluates the cross-correlation function around the correlation peak by two distinct points (i. e., Rpr (t − δ/2) and Rpr (t + δ/2)) separated by the spacing δ. By using a zero-forcing feedback term e, for instance by

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A. Sensitivity to incoherent sampling First, the performance of the DLL is assessed for different fractional delays  ranging from −Ts /2 to Ts /2 without any noise. The performance of the parabolic estimator, a cosine estimator and the DLL with an early-late spacing of δ = 2 or 4 samples is shown in Fig. 4. The parabolic and cosine estimator offer a sub-nanosecond approximately sine-shaped error. The four sample-spaced DLL shows virtually no error while the two sample-spaced DLL shows a minor error. The errors for the DLLs arise as the DLL does not apply the raisedcosine pulse shaping window (see Fig. 3), equivalent to a rectangular window. For the simulation, the DLL algorithm is run until early and late arm are in equilibrium condition, i. e., until the early-late error term e = 0 (see (7)). In a practical implementation the DLL is only run once per subchirp, and the convergence is achieved by adjusting the delay term  for each subchirp until the error approaches zero, e. g., by an integrative controller as outlined below. B. Baseband clock skew The evaluation of the performance of the DLL in a scenario where the sampling frequency of the baseband signal is different between the the transmitting and receiving node (i. e., there is a baseband frequency skew) requires a time-domain analysis of the DLL. For this reason a suitable controller for minimizing the error e has to be be defined. A purely integrative law of control for the DLL has been used, as shown in (8), with α being the integration coefficient. A low value of

α results in an improved noise rejection, but with a reduced performance in case of high baseband frequency skew. On the contrary, a high value of α may have a better performance against frequency skew with a trade-off against sensitivity to AWGN (due to overshoot). n = n−1 + αe

(8)

A simulation has been done running the DLL once per subchirp with a frequency skew from 1 to 50 ppm (variable simulation time from 93 ms down to 1.8 ms in order to evaluate RMS error always on three full samples displacement). The results are shown in Fig. 5 as a function of the baseband clock skew when α = 0.2, 0.4, 0.8, 1.2. When analyzed versus time it has been confirmed that a higher value of α results in a reduced RMS error at higher frequency skews. However, the step response using α = 1.2 creates a significant overshoot, and an even larger α value makes the DLL unstable. Instead, α = 0.8 presents a damped step response (only a couple of runs to convergence) with an AWGN performance slightly better as in Fig. 6. C. Performance in Noise Fig. 6 depicts the root-mean square (RMS) timestamping error for one subchirp in additive white Gaussian noise (AWGN). The graph is calculated by a numerical simulation for different signal-to-noise ratios (SNRs) averaged over a

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Fig. 6. Timestamping Performance of cross-correlation peak selection, parabolic and cosine estimation, and the DLL

Fig. 7. Timestamping error due to Carrier Frequency Offset: Individual subchirps, and combination of all four subchirps

uniformly distributed delay . The SNR on the x-axis of Fig. 6 refers to the SNR after the correlation with the subchirp, i. e., the SNR before the correlator is about 6.45 dB lower. The cross-correlation peak selector has an RMS error slightly below 10 ns and approaches (due to the timestamping quantization) the standard deviation of the uniform distribution √ (Ts / 12=9.02 ns) for high SNR. Parabolic and cosine delay estimators perform approximately equally for SNRs between 10 and 40 dB, with the DLL offering slightly larger errors due to omitting the raised-cosine time window. This SNR region can be considered as a typical range which delivers sufficiently low bit errors on the receiver side. For higher SNR, the DLL achieves lower RMS errors due to the better interpolation (see Fig. 4).

receiving antenna, a composite signal is created. If only the direct signal exists and the correlation pattern p is identical to the transmitted signal (i. e., matched filtering), then the crosscorrelation function Rpr equals the autocorrelation function (ACF) Rtt of the transmitted signal. If additional echoes exist, Rpr is the sum of multiple ACFs weighted by βl and delayed by τl by L X Rpr (t) = βl Rtt (t − τl ). (9)

D. Sensitivity to CFO From (4) it can be seen that a delay estimator (e. g., cosine, parabolic, DLL) that evaluates the absolute of s is not affected by the phase shift (created by the delay), but is impaired by the induced frequency shift because it cannot distinguish between carrier frequency offset (CFO) and sampling delay (due to incoherent sampling). However, for a 802.15.4 CSS symbol composed of four subchirps with alternating signs of the chirp rate µ, the effects of CFO on the delay estimate cancel out. To illustrate the effect, simulations with a variable carrier CFOs have been done. The results are shown in Fig. 7. As expected, a CFO introduces a systematic timestamp error in each subchirp timestamp. This error is a linear function of the CFO and the chirp rate. As subchirp 1 and 3 use the same negative chirp rate, and subchirp 2 and 4 the positive chirp rate, there are two groups of CFO errors. An average of the four subchirp timestamps always cancels out the CFO contribution. Nevertheless, the phase errors induced by the incoherent sampling and CFO increase the bit error rate (BER) for the DQPSK decoding, and therefore should be corrected in the receiver. E. Multipath Ranging Error A common impairment for wireless communication and timestamping in indoor environments is multipath propagation where the received signal consists of the direct signal and many delayed echoes. As these echoes superimpose at the

l=1

Realistic indoor channel models often include multiple rays, often organized in multipath clusters. However, as each echo has three degrees of freedom (amplitude, phase, and delay), a realistic simulation requires a precise characterization of these parameters and their timely and spatial correlation. For a draft analysis of the multipath ranging error it is sufficient to use a two-ray model with one direct path and a single echo. For this case, the multipath amplitude can be fixed and the maximum multipath error (for an arbitrary phase) can be plotted in form of a multipath ranging error envelope. Fig. 8 depicts the timestamp error envelope for a 40 % signal amplitude of the echo with respect to the direct signal. All multipath timestamp errors for the given amplitude and delay (y-axis) fall within the envelope. When tracking the full CSS symbol, composed of four subchirps, the ranging error decays for delays larger than 100 ns. However, tracking a single subchirp or taking the average of four subchirps creates the red or blue line respectively. This approach is better for short multipath delays, but inferior in case larger multipath delays exist. The full symbol approach and the subchirp-based approaches differ in the way the timestamp is generated: The full symbol approach calculates the equilibrium of the absolute of early and late covering the full symbol ACF. However, subchirp tracking tracks the absolute of the ACF of each subchirp and averages over it. As the absolute of the sum is in general not the sum of the absolutes, the approaches differ. Fig. 9 depicts the empirical cumulative timestamp error distribution function for this setup. Full symbol correlation performs best, followed by subchirp correlation with averaging and single subchirp correlation. Note that the error created by multipath propagation is by far larger than the error due to other impairments. The error magnitude is consistent with

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reduced hardware demand improving energy efficiency and silicon size. This paves the way for an implementation of precision synchronization and time-based localization in lowpower measurement devices.

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[10], and is a result of the (rather narrow) bandwidth of the CSS signal. Similar multipath errors can be observed for WLAN as well [12]. F. Implementation Complexity The benefits of using a DLL with the CORDIC algorithm are the simplicity and versatility to generate arbitrary chirp waveforms without computational extensive interpolation. The algorithm requires just four complex multipliers for early and late correlator, plus 19 complex multipliers for the half-rate filter to bootstrap the receiver for each frame. Compared to the subchirp-based correlation approach in [9], only about 15 % of multiplier resources are required. V. C ONCLUSION This paper has presented a timestamping approach for 802.15.4 CSS using a Delay-Locked Loop and CORDIC-based chirp generation. This architecture offers similar performance for medium SNR as correlation-based receivers with postcorrelation parabolic or cosine interpolators. For high SNR the proposed approach even outperforms the interpolation approaches. The approach is tolerant to carrier frequency offsets as well to baseband frequency skews. The error created by multipath propagation can be in the range of 10 ns or even more, depending on the tracking strategy (subchirp or symbol tracking). Although the multipath errors may appear as rather large, these are bound by the limited bandwidth of the signal and apply to other timestamping approaches in the same way. The main benefit of the proposed design is the

[1] IEEE, IEEE Std. 802.11v – 2011, Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, Amendment 8: IEEE 802.11 Wireless Network Management, IEEE Std., Feb. 2011. [2] ——, IEEE Standard for Local and metropolitan area networks – Part 15.4: Low-Rate Wireless Personal Area Networks (LR-WPANs), IEEE Std., Sep. 2011. [3] A. Lewandowski, M. Putzke, V. K¨oster, and C. Wietfeld, “Coexistence of 802.11b and 802.15.4a-CSS: Measurements, Analytical Model and Simulation,” in Vehicular Technology Conference (VTC 2010-Spring), 2010 IEEE 71st, 2010, pp. 1–6. [4] H. Cho and S.-W. Kim, “Mobile Robot Localization Using Biased ChirpSpread-Spectrum Ranging,” Industrial Electronics, IEEE Transactions on, vol. 57, no. 8, pp. 2826–2835, 2010. [5] J. Lee and J. Chong, “A new range estimation algorithm with low complexity for IEEE 802.15.4a,” in Computers and Communications (ISCC), 2010 IEEE Symposium on, 2010, pp. 677–680. [6] Y.-C. Li and J.-W. Chong, “High-resolution range estimation technique using shift invariant TOA estimation algorithm for indoor localization of chirp spread spectrum system,” in Network Infrastructure and Digital Content (IC-NIDC), 2012 3rd IEEE International Conference on, 2012, pp. 567–572. [7] D. Oh, M. Kwak, and J.-W. Chong, “A Subspace-Based Two-Way Ranging System Using a Chirp Spread Spectrum Modem, Robust to Frequency Offset,” Wireless Communications, IEEE Transactions on, vol. 11, no. 4, pp. 1478–1487, 2012. [8] C. De Dominicis, P. Pivato, P. Ferrari, D. Macii, E. Sisinni, and A. Flammini, “Timestamping of IEEE 802.15.4a CSS Signals for Wireless Ranging and Time Synchronization,” Instrumentation and Measurement, IEEE Transactions on, vol. 62, no. 8, pp. 2286–2296, 2013. [9] P. Ferrari, A. Flammini, E. Sisinni, A. Depari, M. Rizzi, R. Exel, and T. Sauter, “New test bench for evaluation of IEEE 802.15.4 CSS timestamping capabilities,” in Instrumentation and Measurement Technology Conference (I2MTC), 2013 IEEE International, 2013, pp. 259–264. [10] E. S. Kim, J. I. Kim, I.-S. Kang, C.-G. Park, and J.-G. Lee, “Simulation results of ranging performance in two-ray multipath model,” in Control, Automation and Systems, 2008. ICCAS 2008. International Conference on, 2008, pp. 734–737. [11] J. E. Volder, “The CORDIC Trigonometric Computing Technique,” Electronic Computers, IRE Transactions on, vol. EC-8, no. 3, pp. 330– 334, Sep. 1959. [12] R. Exel, “Receiver Design for Time-Based Ranging with IEEE 802.11b Signals,” International Journal of Navigation and Observation, vol. 2012, no. 743625, p. 15, Jul. 2012.