Ranging Performance of the IEEE 802.15.4a UWB Standard under FCC/CEPT Regulations

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Introduction
Real-time locating systems (RTLSs) and sensor networks are challenging topics for research and development.Novel applications, such as the tracking of fire fighters in emergencies [1,2] and the tagging of cars in the manufacturing process, need very precise and reliable localization in multipath intensive environments.Common approaches as, for example, the global positioning system (GPS) or WLAN fail in such situations, because the signals are unable to penetrate the roof and the walls and/or they get disturbed by multipath propagation.Thus, researchers have focused on new radio frequency (RF) technologies in recent years, in particular ultra-wideband (UWB).UWB shows robustness against multipath interference and allows for highly accurate positioning [3][4][5][6][7][8][9].IEEE 802.15.4a [10] is a standard for wireless sensor networks with submeter ranging accuracy in indoor environments.The physical layer is designed for bidirectional communications using amplitude and position modulated, bandpass-type UWB signals.It thus supports highcomplexity coherent receivers and low-complexity energy detectors.A two-way time of arrival ranging scheme is proposed.The first part of each transmission is a pulse sequence with known codes, called the preamble, which is used for signal detection, synchronization, and the estimation of the channel impulse response (CIR) that is needed to obtain the time-of-arrival.The preamble sequences show perfect autocorrelation properties for both receiver types [11].Energy detectors promise low cost and low power consumption, but a performance loss occurs [12] and more vulnerability is unavoidable with respect to interfering signals [13].Sub-Nyquist-rate sampling can further reduce the complexity, but also the ranging performance [7,14].
The IEEE 802.15.4a standard has a large number of system parameters that influence the achievable ranging performance [15][16][17].Based on the results in [18], the maximal allowed transmit power is analyzed in this paper taking into account the regulations of the Federal Communication Commission (FCC) [19] and the Conférence Européenne des Postes et Télécommunications (CEPT) [20].The system performance is evaluated with respect to the achievable operating range and the maximum allowed pathloss for a coherent receiver and an energy detector.Our analysis shows the parameter settings and frequency channel selection for maximizing the performance.The paper is organized as follows.Section 2 presents the signal models according to the 802.15.4a standard, a signalto-noise ratio (SNR) analysis, and the performance metric definition.The FCC and CEPT regulations are discussed in Section 3, and the link budget is introduced in Section 4. This is followed by performance results and conclusions in Sections 5 and 6.

Problem Statement
An (indoor) ranging system needs to find the line-of-sight (LOS) component in the channel response, because the detection of a reflection or a noise component may lead to very large errors.Thus, the ranging performance can be characterized by the quality of the channel estimation at the receiver output.An appropriate performance metric is the receiver output SNR of the LOS component (LSNR), as it correlates strongly with the ranging performance [21].It is defined as where

the receiver output and var{ h[n]} is the noise variance of the estimated channel response h[n].
To study the operating range, it is necessary to relate the output SNR to the input SNR of the receiver.The input SNR is given by the transmit power regulations, the link budget, and the channel.The output SNR furthermore depends on the receiver structure, the hardware components, andin case of a noncoherent receiver-also on the preamble parameters, as analyzed below.The input SNR is defined by the energy of the despread LOS component over the noise spectral density E LOS /N 0 with E LOS = M 1 E (1)  LOS , where E (1)  LOS is the received energy for the LOS component of a single pulse and M 1 is the number of transmitted pulses.

Signal Models.
This section introduces the signal models for the IEEE 802.15.4a physical layer and the receivers.
2.1.1.IEEE 802.15.4a.The most important signal part for ranging is the preamble.It employs a code sequence c s of length N s = 31 or 127 [10] that consists of ternary elements {−1, 0, 1}.The preamble code vector c sp is created as where ⊗ denotes the Kronecker product, δ L is a unit vector with a one at the first position and length L to extend the spacing between the preamble chips, and 1 Npr denotes a vector of ones to repeat the preamble sequence N pr times.The vector c is the periodically repeated preamble code.The transmitted signal s(t) is defined as where E p is the energy per pulse, c m is the m-th element of c, w(t) is the energy-normalized pulse shape, M is the number of code elements in the preamble, ω c is the carrier frequency, T chip is the chip duration, and w(t) is the upconverted pulse assuming the carrier and the pulse are phase synchronous.Table 1 shows the timing characteristics of the preamble, where T pr is the total duration of the preamble, PRF is the peak pulse repetition frequency, MRF is the mean pulse repetition frequency, and N 1 ms is the number of preamble sequences within 1 ms.ERF is the effective pulse repetition frequency according to the regulations (see Section 3).
The transmitted signal (3) is sent over a multipath channel with channel impulse response h c (t), where also the effects of the antenna are contained for simplicity.Furthermore, h c (t) is assumed to be constant during T pr .Thus, the analog received signal is obtained from where ν(t) is modeled as additive white Gaussian noise and * is the convolution.Next, the receiver architectures are described.
2.1.2.Coherent Receiver.Figure 1 shows the system model of the coherent receiver.The signal is received by a UWB antenna and filtered by the transmit pulse shape w(t).Thus, a matched filtering to the pulse shape is applied.The signal is converted to complex baseband using the Hilbert transform h hilb (t) and carrier demodulation by the estimated frequency ω c .The complex baseband signal is given by where ϕ is the unknown carrier phase.Assuming synchronization and known carrier frequency, an estimated sampled channel response is obtained after despreading, because the preamble codes have perfect circular autocorrelation properties, thus interpulse interference (IPI) is canceled.(For this assumption it is necessary that the maximal excess delay τ max ≤ LN s T chip = T s , where T s is the period of the spread preamble sequence.The IEEE 802.15.4a standard has a T s ≥ 1 μs, which is usually sufficient for IPI free processing in indoor environments.)The despreading is first performed sequencewise ( m ) and then over the sequence repetitions ( q ).Since c 2 m = 1 for the nonzero code elements, it follows that q and m simply the number of nonzero code elements in the preamble M 1 = ((N s +1)/2)N pr , that is, the number of transmitted pulses.The number of samples within a chip is defined by A detailed derivation of the equations can be found in [15].
This receiver architecture needs high sampling rates according to the Nyquist theorem.Another disadvantage of this concept is the required synchronization of the carrier frequency and phase, which is critical for its performance.The energy detector is based on a different method for the downconversion that prevents these two problems.Thus, a low-complexity solution is obtained.

Energy Detector.
The energy detector works as shown in Figure 2. The signal is again received by a UWB antenna and filtered by a bandpass filter, which ideally is matched to the pulse shape.Next, the signal is squared and integrated for short-time windows T I .The length of T I also defines the sampling period.It causes a mean absolute error (MAE) of ranging greater or equal T I /4 [7], which limits T I to a few ns  for highly accurate ranging.The signal model after sampling is given by where ν f (t) is the passband filtered noise and the channel response where N chip = T chip /T I .The code despreading is performed sequencewise with q and i with the despreading code c i .
In contrast to the coherent receiver, the noncoherent receiver uses a different despreading code c than the spreading code to obtain perfect circular correlation properties for the squared sequences.This code is created by squaring c and setting all zeros to −1 [11].The output of the energy detector comprises a signal-by-signal term y ss [n], a linear signal-by-noise term y sν [n], and a quadratic noise-by-noise term y νν [n].The code correlation can completely cancel the IPI in the signal term y ss [n] but not for the cross-term y sν [n].A longer pulse spacing leads to less IPI such that it becomes negligible in indoor environments with a spacing of L ≥ 16 [15,16].The full derivation of the equations can also be found in these references.

Input-to-Output SNR Relation.
The input-to-output SNR relation for the coherent receiver is given by [15] LSNR For the energy detector, the relation is given by [15,16]   where W RRC is an equivalent bandwidth defined as W RRC = φ 2 w (μ)dμ.The first and second terms of the denominator correspond to the variance of the linear and the quadratic noise terms, respectively.The quadratic noise term depends on the receiver parameters that can be combined to the noise dimensionality ND = N s N pr T I W RRC [13].For practical values of ND, the output SNR is proportional to (E LOS /N 0 ) 2 , while it shows a linear relation to E LOS /N 0 for the coherent receiver.
Figure 3 shows the relation of the detector input SNR E LOS /N 0 and the output LSNR based on ( 9) and (10).The specific curves for the energy detector (ED) are obtained by increasing ND by factors of four.The depicted curves correspond to N pr = [16,64,256,1024,4096], N s = 31, T I = 2 ns, and W RRC = 1 GHz.Note that N pr = 256 is not included in the standard.The curves are separated if the quadratic noise term dominates and they merge if the linear noise term is dominant.Increasing E LOS /N 0 by 6 dB leads to LSNR +12 dB in the quadratic part and to +6 dB in the linear one.The horizontal line illustrates the LSNR at the working point LSNR WP = 12 dB for the energy detector (cf.[16]).At this working point, 80% of the range estimates are within 1 m.The coherent receiver shows a working point LSNR WP = 9 dB (cf.[21]).Both working points have been determined by extensive simulations (see [15]).It can be seen for the energy detector that 3 dB more E LOS /N 0 are required when N pr , the number of sequence repetitions, is increased by a factor of four.Note that the quadratic noise term dominates at this working point.As observable from (9), the LSNR for the coherent receiver is independent of the number of the pulses.It depends only on the transmitted energy.In other words, it does not matter if this energy is transmitted in one pulse or in a sequence of pulses.The coherent receiver shows an advantage ≥11 dB in the working point in comparison to the noncoherent receiver.

Maximal Operating Distance.
As N 0 is constant in the scenario, E LOS /N 0 for the maximal operating distance d max is obtained from the well-known pathloss model where η is the pathloss exponent and d 0 is a reference distance.The maximal operating distance for the coherent receiver is obtained from ( 9) and (11): where the reference distance d 0 is assumed to be 1 m.It follows for the energy detector 1/η (13) using (10) in (11).

Maximal Allowed Pathloss PL max .
A more general look at the achievable range is given by the maximal allowed pathloss, which is independent of the channel model, fading margins, or implementation losses.The pathloss model can be rewritten with (9) to obtain PL max for the coherent receiver where E LOS is the energy of the received LOS component at 1 m, which does not take fading margins or implementation losses into account (see Table 2).
For the energy detector follows, using (10) and (11), E LOS /N 0 (1 m) and E LOS /N 0 (1 m) are defined by the transmitted preamble energy E pr (see Section 3) and the link budget (see Section 4).

FCC Regulations
In this section, the maximal allowed transmit power is calculated with respect to the FCC regulations [19].In principle, the same regulations have been adopted by the CEPT in Europe for the band between 6 and 8.5 GHz [20].
In the band between 3.1 and 4.8 GHz, the CEPT requires detect and avoid (DAA) or low duty cycle (LDC) mitigation additionally, which does not influence this analysis.This analysis is done in accordance to [18].The FCC constraints essentially consist of an average and a peak power limit.In any band of bandwidth B av = 1 MHz, the average transmit power is limited to P FCC av = −41.3dBm for an averaging window of T av = 1 ms.The peak power within the bandwidth B pk = 50 MHz is restricted to P FCC pk = 0 dBm.Both peak and average transmit power are defined by the equivalent isotropically radiated power (EIRP).
The 802.15.4a preamble is a sequence of nonuniformly spaced pulses whose polarities are chosen pseudorandomly by the codes.According to [18], its average and peak power are determined by ERF and PRF, respectively.The pulse energy spectral density (ESD) E p,av |W ( f c )| 2 for the average power limit is given by where E p,av is the pulse energy limited by the average power limit and W( f c ) is the spectrum of the normalized pulse w(t) at the center frequency f c .ERF is defined as where M 1 = (N s + 1)/2 is the number of code elements not equal to zero.ERF is the compressed MRF due to stretching the preamble over the averaging time T av = 1 ms (FCC).If T pr is greater than T av , then it is MRF.The mean power is limited by the number of pulses within 1 ms (N 1 ms ) (see Table 1).The peak power limit is defined by the PRF, where the sequenced pulses within an observation window 1/B pk = 20 ns are added.The ESD E p,p |W ( f c )| 2 for the peak power limit is obtained by where E p,p is the pulse energy limited by the peak power limit.The maximal FCC compliant pulse ESD with respect to peak and average power is shown in Figure 4. To find the active ESD for a specific preamble, the smaller value between ESD pk at PRF and ESD av at ERF is considered.The peak power limit for the short preamble symbols with L = 16 and L = 64 is the same, while, for the long preamble sequences it is lower due to higher PRF.It can be observed that only the preamble sequences with N pr = 16 are peak power limited.However, it is reported in [22] that the supply voltage limits the transmit power in low-data-rate systems and the peak power limit cannot be exploited for low supply voltages.
Assuming a pulse with rectangular spectrum, the energy per pulse 2 , where B is the pulse bandwidth.Thus, the achievable preamble SNR can be calculated as shown in Figure 5.At N pr = 16, all preamble codes are limited by the peak power limit.The long preamble symbols contain approximately. 2 dB more energy in four times more pulses.Increasing the number of pulses does not necessarily lead to a preamble energy improvement, if T pr ≤ 1 ms, because the long preamble symbols and the short codes with spreading L = 16 are mean power limited between N pr = 64 and 1024.N pr = 4096 leads to an improvement, because T pr > 4 ms, which means the preamble is more than four times longer than T av .The short preamble codes with spreading 64 imply a four times longer preamble in contrast to the others, thus a gain of up to 6 dB can be achieved.

Link Budget
As mentioned before, E LOS /N 0 (1 m) is the input SNR of the receiver at 1 m which depends on the link budget.Table 2 shows an example link budget calculation for 802.15.4a channel (ch) 3, using N pr = 1024, N s = 31, L = 16, f c = 4.4928 GHz, and a bandwidth of 499.2 MHz.In that case, the average power limit of the FCC regulations applies and E p is calculated from (16), where also the antenna gain is included.E p is limited for 1006 sequences due to averaging over 1 ms (see Table 1).The preamble energy E pr = E p M 1 , the free space loss L fs at 1 m is given by 45.5 dB using Friis' equation [23], and the receiver antenna gain G RX is defined by 0 dBi.These values yield the received preamble energy without multipath components, meaning the energy of the line of sight component E LOS at 1 m.Assuming the input structure of the receiver is linear, the noise spectral density is given by N 0 = kT 0 F [23], where the Boltzmann constant k = 1.38 × 10 −23 Joule/Kelvin [J/K], the temperature of the environment T 0 = 293 K, and the noise figure of the receiver input structure F = 5 dB (cf.[24]).Implementation losses of 4 dB and a LOS fading margin of 3 dB are assumed.Thus, E LOS /N 0 (1 m) is obtained and can be used to calculate the maximal operating range according to (11) and (13).

Results
The maximal operating distance and the maximal acceptable pathloss are analyzed in this section.The maximal operating distance is based on the free-space link budget, because the LOS component is needed for accurate ranging.The maximal acceptable pathloss is shown as a more general value, which allows the implementer to analyze the effect of specific channel models, for example, NLOS scenarios, or specific system parameters, for example, lower noise figures.

Effect of Codes.
Figure 6 shows the maximal operating distance d max and the maximal allowed pathloss PL max with respect to the length N pr of the preamble sequences.The coherent receiver is directly proportional to E p /N 0 , which means that the operating distance is related to the preamble energy discussed in Figure 5.By contrast, the ED suffers from noncoherent combining losses, thus the noise dimensionality including the number of transmitted pulses is important for the final performance (see (13)).A change of E p /N 0 without changing the noise dimensionality, for example, using a different noise figure or pulse energy, leads to a shift of the curves along the dashed lines, but the shape of the curves does not change.Thus, the general conclusions are still valid, while d max and PL max need to be recalculated according to the new link budget.
In the overall performance there is a big gap between the CR and the ED.The CR achieves a maximal operating distance up to several thousand meters and the ED achieves only several hundred meters.However, an operating distance of several hundred meters is usually sufficient for (lowcomplexity) indoor localization systems and sensor networks.
As expected from Section 3, the best performance is achieved by the short preamble with long spreading (L = 64) which has the highest transmitted energy.A maximal operating distance of approximately 6000 m (PL max ≈ 82 dB) is achieved by the CR, and ≈430 m (PL max ≈ 60 dB) is achieved by the ED.The CR reaches approximately half of that distance (≈3000 m; PL max ≈ 76 dB) for the other two codes.As mentioned before, the energy detector shows a more specific behavior, which is discussed in detail in the rest of this paragraph.As observable, the increasing of N pr does not necessarily lead to a better performance.A performance degradation is seen at around E LOS /N 0 (d 0 ) ≈ 79 dB for increasing numbers of transmitted pulses due to constant transmitted energy (cf. Figure 5).This effect also harms the performance of the long preamble codes (N s = 127) significantly and leads to the lowest performance achieved.The performance of the short preamble sequences (N s = 31) with spreading L = 16 and the long preamble sequences (N s = 127) is best at N pr = 64, where a distance of ≈ 300 m (PL max ≈ 56 dB) and ≈200 m (PL max ≈ 53 dB) is reached, respectively.The preamble sequences with L = 64 show a local optimum for N pr = 64 with the same performance as the L = 16 sequence.This performance is also obtained for a much longer preamble with N pr = 1024 repetitions and slightly improved with N pr = 4096 at the cost of increased preamble energy (cf. Figure 5), much longer signals (see Table 1), and much higher processing effort.From these results, it seems inefficient for EDs to choose extremely long preambles with N pr ≥ 1024.
The IEEE 802.15.4a standard also defines different channels with specific bandwidths and carrier frequencies.An analysis of the various channels is given in the next section.

Effect of Frequency Channels.
The IEEE 802.15.4a standard defines 16 channels in three frequency bands, the subgigahertz band (<1 GHz), the low band (3.2-4.8GHz), and the high band (5.9−10.3GHz).The channel bandwidths B range from 499.2 to 1354.97 MHz.As mentioned in Section 3, keep in mind that the CEPT allows only the usage of the frequency bands 3.1-4.8and 6-8.5 GHz for UWB, where, for LDC, the signals have to be shorter than 5 ms.Thus, the short preamble symbol with spreading L = 64 and N pr = 4096 is not allowed for LDC transmission.It is well known that a higher carrier frequency f c causes higher losses and thus less received signal strength according to Friis' equation.A larger bandwidth leads to a higher allowed transmit power (see Section 3).To evaluate this tradeoff, six channels are analyzed in this paper, using the short preamble codes with L = 64.
Figure 7 shows the relation between input and output SNR for the specific channels.As seen from ( 9), the CR is again independent of the channel bandwidths.For the ED, variations occur due to the different pulse and receiver bandwidths.It can be observed that the channels with the large bandwidths need up to 1.5 dB more E p /N 0 in the working point to achieve the same LSNR.
Figure 8 shows the allowed preamble energies for the specific channels.The larger bandwidths of the preambles allow a gain of up to 4 dB, which is sufficient to compensate the SNR loss of the ED shown in Figure 7.This is also seen from (10), where the equivalent bandwidth W RRC influences LSNR linearly and the additional energy improves the SNR quadratically in the working point.Thus, a gain of up to 2.5 dB can be achieved.For the CR, the additional energy will directly improve the performance.
Figure 9 shows the maximal operating distance and the maximal allowed pathloss for the specific channels.It can   be observed that the low-band channels (Ch 3 and Ch 4) perform better than the high-band channels due to lower free-space losses.Only half the operating range is obtained when f c is increased from 4 to 8 GHz.A shift in the carrier frequency leads to a change of E LOS /N 0 , but it does not change the relation of input and output SNR (compare Ch 3 and Ch 9).A shift of the bandwidth changes this relation due to a change of ND, which is observable for Ch 9 and Ch 11.The operating range is doubled with the CR when the bandwidth is increased from 500 MHz to 1.33 GHz, while only the 1.3

Conclusions
A coherent receiver and an energy detector have been studied for ranging in IEEE 802.15.4a, in the sense of maximal allowed transmit energy, maximal operating distance, and maximum allowed pathloss.The maximal allowed transmit energy according to the FCC/CEPT regulations depends strongly on the parameters of the preamble.For most of the preamble code sequences, the average power limit applies.A longer spreading of the preamble symbols leads to a performance gain, because a larger preamble energy is obtained.As the FCC/CEPT limits the power spectral density, a higher bandwidth leads to an increased energy too.
The maximal operating distance is calculated from the link budget.The coherent receiver directly depends on the receiver input SNR, while the energy detector is also influenced strongly by the parameters of the preamble codes due to the noncoherent combining loss.A 64-symbol repetitions preamble is most efficient for the energy detector due to lower noncoherent combining losses and the short preamble symbols are preferable due to less despreading effort.The channels from the low-frequency band achieve longer ranges due to the lower pathloss.The mandatory lowfrequency channel ( f c = 4.5 GHz) achieves almost twice the range in comparison to the mandatory high-frequency channel ( f c = 8 GHz).A gain is obtained for the highbandwidth channels.The range is almost doubled with the coherent receiver, while the energy detector reaches only a gain of 30 percent.
The low-complexity energy detector achieves maximal operating distances of several hundred meters, while the coherent receiver reaches distances up to several thousand meters in free-space.Thus, both receiver architecture are appropriate for real-time locating systems and sensor networks in typical indoor scenarios.

Figure 3 :
Figure 3: Relation between input SNR (E LOS /N 0 ) and output SNR (LSNR) with respect to the noise dimensionality ND = N s N pr T I W RRC for the energy detector (ED) and the coherent receiver (CR).The fixed parameters are N s = 31, T I = 2.0032 ns, and W RRC = 1 GHz.

4 Figure 6 :
Figure 6: Code sequence analysis on the maximal operating distance and the maximal allowed pathloss, where the solid lines correspond to the energy detector, the dashed-dotted lines belong to the coherent receiver, and the dashed lines indicate constant noise dimensionality for the energy detector.The values are given for N pr = [16, 64, 256, 1024, 4096] (from left to right).

Figure 7 : 1 Ch 9 :
Figure 7: Relation between input SNR E LOS /N 0 and output SNR LSNR for the short preamble codes with a spreading L = 64 and N pr = 16 with respect to the IEEE 802.15.4a channels.The channel parameters in the legend are in GHz.

1 Ch 9 :Figure 9 :
Figure 9: Maximal operating distance and maximal allowed pathloss for the specific IEEE 802.15.4a channels.The dashed lines show the characteristic for a channel with B = 499.2MHz with the ND of Figure 6.