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A New Parameter for UWB Indoor Channel Profile Identification Lorenzo Mucchi and Patrizio Marcocci

Abstract—This paper proposes a new parameter for identifying the room typology when the receiver is in ultra wideband (UWB) indoor environments. The method proposed does not imply any estimation process at the received signal. The proposed parameter is not only able to clearly distinguish between LineOf-Sight (LOS) and Non-Line-Of-Sight (NLOS) conditions, but it is also capable of ordering the quality of the received signal in two different LOS or NLOS rooms, although the Signal-toNoise-Ratio (SNR) is the same. Moreover, this parameter is able to distinguish between LOS and NLOS macro groups clearly and, at the same time, to order conditions within these two macro groups (for example, clear LOS condition from QuasiLOS, i.e., when an object partially shadows the link, etc.). The method proposed in this paper is based on the calculation of the kurtosis index of the sampled received signal. The kurtosis index can be successfully applied to the received signal in order to identify the typology of the link between transmitter and receiver (LOS, Quasi-LOS, high-NLOS, low-NLOS, extreme-low-NLOS). Results are achieved by both real measurements and simulations with IEEE802.15.3a and 4a channel models. Index Terms—Channel identification, environment identification, UWB, kurtosis.

I. I NTRODUCTION

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NOWING the channel profile is very useful in order to maximize performance or minimize interferences in a wireless communication environment. There are several parameters which have to be properly set in the receiver depending on the link condition (LOS, Quasi-LOS, NLOS, extreme NLOS): for example the time delays and amplitudes of the channel multipath estimation algorithm, the number of fingers of the rake receiver, etc. The channel parameters (delay and amplitude of the receiving paths) estimation algorithm is particularly sensitive to the link condition [1]. This means that if a simpler algorithm is selected under LOS conditions, the algorithm under NLOS conditions must be more complex in order to guarantee the performance. Similarly, the number of fingers of the rake receiver has to be selected depending on the link condition in order to achieve quality with lowest complexity. Unfortunately it is not easy to identify the channel. In the literature there are few papers proposing parameters that allow to distinguish only between the LOS and the NLOS condition. Therefore, the present paper has a twofold aim: on the one hand, it intends to search for a new index that allows to distinguish more precisely between LOS and NLOS in

Manuscript received December 10, 2007; revised April 18, 2008; accepted December 11, 2008. The associate editor coordinating the review of this letter and approving it for publication was M. Win. L. Mucchi is with CNIT - Dept. of Electronics and Telecommunications, University of Florence, Italy (e-mail: [email protected]). P. Marcocci is with the Dept. of Electronics and Telecommunications, University of Florence, Italy (e-mail: [email protected]). Digital Object Identifier 10.1109/TWC.2009.070318

every environment, and, furthermore, between different LOS or NLOS conditions, creating a sub-set of LOS links and NLOS links ordered with an increasing quality; on the other hand it aims at defining a low complex parameter that allows the identification of the quality of the received signal in an UWB indoor environment. In [2] and [3], algorithms for NLOS identification are proposed. The Time-Of-Arrival (TOA) of the signal is studied in order to identify if a mobile station is experiencing LOS or NLOS condition. In particular, the TOA measured probability distribution function has been considered. In [4], a joint power envelope and TOA measured algorithms are proposed to distinguish between LOS and NLOS. All the algorithms mentioned above have quite high complexity and it is necessary to estimate the channel parameters in order to apply the algorithm. In particular, multipath time delays are needed in [2], whereas in [3] multipath amplitudes are needed. Moreover, both those algorithms can distinguish only LOS/NLOS condition. The kurtosis index was already used in [5], but only for TOA estimation. In particular, in [5] a normalized threshold selection technique for TOA estimation is proposed. The kurtosis index is used to decide which is the best path for TOA estimation. The threshold selection was arbitrary chosen and experimentally proven. Details about threshold-based TOA estimators in dense multipath channels can be found in [6]. The first work about the use of kurtosis for LOS-NLOS identification was [7], and recently a similar work was proposed in [8] and patented [9]. In the latter the kurtosis was used only to identify LOS-NLOS but not to distinguish different LOS or NLOS conditions. In other words, the main difference between the present paper and the method proposed in [8] [9] is that the technique employed in [8] [9] cannot identify the environment (e.g. Indoor Office, Residential, Industrial, etc.), but, basing on the knowledge of the environment typology, it can only determine if the link is LOS or NLOS. Moreover, the method proposed in [8] needs an estimation process before the application of the kurtosis index. This implies that the method proposed in [8] is characterized by a higher sensitivity to estimation errors in comparison to ours, and of course by a higher complexity. In this paper a very simple parameter, the kurtosis index, is used not only to find out more precisely if the transmitter and the receiver are under LOS or NLOS condition, but also to define the quality of the link in the specific receiver position under one of these two conditions (LOS/NLOS). In other words, the proposed parameter provides for a better granularity: this means that it is possible to decide if a LOS link is “better” than another. “Better” means that there is a high probability that the strongest path is the first (this is useful for

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the accuracy of the ranging in UWB systems) and that the main energy of the receiving signal is concentrated in the first arriving paths (this is useful to reduce the complexity of the receiver, i.e. to minimize the number of recombined paths in a rake receiver). This paper shows that it is possible to better distinguish a specified LOS or NLOS condition situation by using the kurtosis index. Moreover, the proposed index is able to order the received signals by quality at the same time. In order to explain this concept, it can be noted that by using the proposed index it is possible to determine if a receiver is placed in a room A (distance a, NLOS) rather than in a room B (distance b > a, extreme-NLOS) and to determine if a receiver is partially covered by a post (Quasi-LOS condition). At first, the cumulative distribution function (CDF) of the received signal amplitude was considered as candidate parameter. Unfortunately, the CDF function cannot distinguish between LOS and NLOS links in every condition and it has not a sufficient granularity to distinguish between different LOS or NLOS links. Moreover, the CDF method requires received signal amplitude estimation and the measure depends on the quality/complexity of the selected estimation algorithm: this fact can make it sometimes impossible to determine precisely if a link is LOS or NLOS. On the contrary, the kurtosis parameter is calculated directly on the received signal without any estimation of specific parameters (amplitude, phase, delay, etc.). Thanks to its high granularity in defining the quality of the channel profile of the link, the kurtosis index can be useful for a cognitive radio application for wireless communication. Knowing the channel profile, it is possible to make some particular decisions on the transmission side, or on the receiver side. For example, the waveform at the transmitter can be changed or the receiver architecture (number of RAKE fingers, estimation algorithms, etc.) can be properly selected to obtain a reliable radio communication. Regardless of the receiver position, the communication quality is always preserved with the lowest complexity. In this paper the performance is evaluated by using two set of measurements. The first is a set of real data deriving from an UWB experiment [10] [11] and the second is a set of data collected by simulating the IEEE 802.15.3a and 4a channel models [12] [13]. Fundamental papers on UWB can be found in [14] and [15]. The UWB high bandwidth nature and spectrum analysis can be found in [16] [17]. Our method does not need any estimation process on the received signal, but, of course, it still requires the synchronization. Details about synchronization issues on UWB can be found in [18] [19]. The comparison between the CDF and the kurtosis success percentage in determining the channel typology is reported in the results section. Moreover, the proposed index κ could help the localization systems to reach the error bound. For details see [20]. The following section (Section II) describes the system model of the UWB experiment (Subsection II-A) and the system model of the IEEE channel models (Subsection II-B and II-C). Section III presents the channel identification method proposed based on the kurtosis index. Simulation results are given in Section IV and are followed by concluding remarks in Section V.

II. S YSTEM MODEL In order to generate the channel which is to be subsequently identified, two different sets of data are considered. The first is a set of real measurements obtained from an UWB propagation experiment performed in a modern laboratory/office building [10] [11]. The second set is obtained from simulations of different channel models defined in the IEEE 802.15.3a and in the 4a standards that regulates the UWB indoor communications [12] [13]. A. UWB propagation experiment In the experiment [10] [11], a sub-nanosecond duration pulse was transmitted. The signal was a periodic probing pulse with a repetition rate of 2 · 106 pulses per second, so that successive multipath components spread up to 500 nanosecond (ns) can be measured unambiguously. The transmitter consists of a periodic impulse generator and an UWB antenna. The receiver is set up with a vertical polarized antenna and the channel response is recorded using a digital sampling oscilloscope (DSO). The sampling rate was 20.48 GHz which means that the time between samples TS = 48.828 ps and the measurements apparatus was set so that all the multipath profiles had the same absolute delay reference. During each channel profile measurements, both the transmitted and receiver were kept stationary. Multipath profiles data is collected in 14 rooms and along the hallways on one floor of the building (a detailed map is reported in [10] [11]). In each receiver location, impulse response measurements were made at 49 measurement points, arranged in a fixed-height, 7 × 7 square 15 cm spaced grid, covering a surface 90 cm × 90 cm. The transmitted pulse w(t) is measured 1 m apart from the antenna under LOS condition and used as a template pulse at the receiver. Five different channel conditions, depending on the position of the receiver inside the building, have been selected: Room F1: represents a typical Line-Of-Sight (LOS) UWB signal transmission environment, where transmitter and receiver are located in the same room (9.5 m far) with no obstacle between; Room F2: represents a Quasi-Line-Of-Sight (QLOS) condition, where transmitter and receiver are located in the same room (5.5 m far), but there is an obstacle (steel supporting column) that partially reduces the visibility; Room P: represents a high-SNR Non-Line-Of-Sight (NLOS) condition, where transmitter and receiver are not located in the same room and the distance between the transmitter and the receiver is 6 m; Room H: represents a Low-SNR NLOS (LNLOS) condition, where transmitter and receiver are not located in the same room and the distance is 10 m; Room B: represents an Extreme-Low-SNR NLOS (ELNLOS) condition, where transmitter and receiver are not located in the same room and the distance in this case is 17m. More details about this measurements are available in [10] [11]. B. IEEE 802.15.3a UWB channel model The multipath model of the standard is based on a large number of measurement campaigns. An UWB channel model

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derived by the Saleh-Valenzuela model with a couple of slight modifications was proposed in [12]. Four types of channel model are defined in this standard as follows: CM1 this model is based on LOS (0-4 m) channel measurements; CM2 this model is based on NLOS (0-4 m) channel measurements; CM3 this model is based on NLOS (4-10 m) channel measurements; CM4 this model was generated to fit a 25 nsec RMS (Root Mean Square) delay spread to represent an extreme NLOS multipath channel. For each Channel Model (CM), 100 independent realc izations are simulated by using a M atlab program. This program uses the best parameter values to approximate the four CM scenarios described above. More details about these parameters are shown in [12]. C. IEEE 802.15.4a UWB channel model The IEEE802.15.4a system model is detailed in [13]. It provides models for the following frequency ranges and environments: for UWB channels covering the frequency range from 2 to 10 GHz, it covers indoor residential, indoor office, industrial, outdoor, and open outdoor environments (usually with a distinction between LOS and NLOS properties). For our purpose we take into account only the residential and the indoor office environments in order to have a fair comparison with the real measurements: R IO

the model was extracted basing on measurements that cover a range from 7-20 m and it takes into account both LOS and NLOS conditions; the model was extracted basing on measurements that cover a range from 3-28 m and it takes into account both LOS and NLOS conditions.

For both the environments mentioned above, residential (R) and indoor office (IO), 100 independent realizations are simc program. This program uses the ulated by using a M atlab best parameter values to approximate the two environments described above. More details about these parameters are shown in [13]. III. PARAMETERS

FOR CHANNEL IDENTIFICATION

This work aims at finding a simple parameter that can classify the communication link quality. By analyzing the received signal we want to know from which room or scenario the signal is originated or passed. In the future wireless world it will be extremely important to identify quickly the channel typology and its degradation. In order to determine the link conditions (LOS corresponding to room F1, Quasi-LOS corresponding to room F2, High-SNR-NLOS corresponding to room P, Low-SNR-NLOS corresponding to room H and Extreme-low-SNR-NLOS corresponding to room B) two indexes have been considered and compared, the cumulative distribution function CDF and the kurtosis.

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A. Cumulative Distribution Function Let us consider the cumulative distribution function (CDF) of the estimated multipath amplitudes. The algorithms used to estimate the multipath amplitudes are described and discussed in [1]. The main purpose of that work was to investigate the effects of multipath propagation on ToA estimation using real measurement data by considering different algorithms with different levels of complexity. The trade-off between estimation accuracy, complexity and sensitivity to parameter choice for different propagation conditions was discussed. The performance of sub-optimal ToA algorithms with increasing levels of complexity derived from the Maximum Likelihood (ML) criterion and based on a simple peak detection process was evaluated. The performance of a conventional technique based on threshold detection was investigated as well, in order to better understand the conditions for which the adoption of more complex techniques proves to be convenient. The CDF of a variable X is defined as the probability that X assumed any value smaller than x, i.e., P (X < x) = F (x). One hundred paths are estimated in the received signal. Only four sets of multipath amplitudes were considered for CDF computation. The four sets are: first arriving path, first five arriving paths, strongest path and the five strongest paths. The results show that the CDF parameter is not able to discriminate a specific channel condition. For example, the standard deviations of the first arriving path or the strongest of all the rooms are very closed together (same order of greatness) (see Table I). Table I shows that by using the CDF index only a macro-identification is possible (LOS or NLOS) but it is difficult. Fig. 1 shows the CDF of the first and the strongest path of rooms F1 and F2 (LOS and QLOS cases), and Fig. 2 shows the CDF of the first and the strongest path of rooms H and B (low-SNR-NLOS and extreme-low-SNR-NLOS cases). As it can be seen, the CDF values are too close together: therefore it is not possible to distinguish these two conditions unambiguously. Moreover, all these solutions depend on the performance of the selected estimation algorithms. This means that the simpler the multipath profile estimation algorithm is, the harder it is to distinguish the rooms or link conditions by using the CDF. For an exhaustive discussion see [7]. TABLE I PARAMETERS FOR CHANNEL IDENTIFICATION OBSERVING THE CDF OF THE PATH AMPLITUDES ESTIMATED WITH S INGLE S EARCH ALGORITHM . Parameter Std. dev. First path Std. dev. Strongest Path CDF zero value First path CDF zero value Strongest path

Room F1 5.43e-03 9.60e-02 0.5102 0.3385

Room F2 4.62e-03 6.86e-02 0.3674 0.1940

Room H 2.30e-03 2.03e-02 0.5306 0.5410

Room B 1.91e-03 1.18e-02 0.4490 0.6230

B. Kurtosis index A low complexity parameter able to precisely discriminate channel conditions is proposed. The kurtosis is a statistical parameter that indicates the fourth order moment of the received signal amplitude. Kurtosis κ is mathematically defined as follows:  (xi − x)4 1 (1) κ(x) = 4 i σ N

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Estimation algorithm: Single Search

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Fig. 1. Cumulative distribution functions of the first path and the strongest path in the room F1 and F2.

IV. R ESULTS Estimation algorithm: Single Search 1 First path − H First path − B Strongest path − H Strongest path − B

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where σ is the standard deviation of the variable x and x is the mean value of x. N is the number of samples of x. The kurtosis index κ is supposed to be high in case of LOS conditions while it has low values for signals received under NLOS conditions. The parameter κ does not need any application of estimation algorithms on the received signal because it is calculated directly by the received signal samples. This makes κ more simple and efficient than CDF. Moreover, this makes the identification process easy, quick and immune to estimation errors. The results, shown in the following Section IV, highlight that the proposed identification method, based on the kurtosis calculation of the received discretetime signal, allows a sharp and exact identification of the channel link condition (LOS vs NLOS) independently of the estimation algorithm, and, moreover, it is able to identify different conditions within a macro-condition. For example, it can determine if the communication link is under a LOS condition or if there is a partial obscurement of the receiver (LOS vs QLOS).

In Fig. 3 the results achieved by the experimental data are presented. Dashed lines represent the mean value of the kurtosis index κ over the 49 grid locations in each room. Mean value allows to identify in which room (or channel condition) the receiver is, because the mean κ values are very different. Moreover, a deeper classification is possible, i.e., it is possible to identify the room inside a macro-group and to distinguish LOS from QLOS and NLOS from LNLOS or ELNLOS. The right half of Table II lists numerical values of mean kurtosis indexes κ for the real received signal in the experiment. Note that it is possible to carry out a “room classification”. In particular, high SNR rooms have a mean κ values above 10, while in the case of LOS condition (room F1) the value is nearly 50. Low SNR rooms show kurtosis indexes closer to each other and the range of identification is smaller, but still clearly applicable. In the same condition the CDF was not able to discriminate LOS from NLOS. In order to compare the CDF and kurtosis success percentage, we have generated 100 random channels and applied the CDF and the kurtosis to determine the room associated to that channel. As far as the standard deviation of the strongest path of the CDF is concerned, the thresholds of the two indexes can be set, for a first sample comparison, as follows: −3 ⇒ room B • from 0 to 16.0510 −3 • from 16.0510 to 31.2010−3 ⇒ room H −3 to 55.3510−3 ⇒ room P • from 31.2010 −3 to 82.3010−3 ⇒ room F2 • from 55.3510 −3 • from 82.3010 to ∞ ⇒ room F1 As far as kurtosis index κ is concerned, the thresholds of the two indexes can be set as follows: • from 0 to 5, 8955 ⇒ room B • from 5.8955 to 8, 964 ⇒ room H • from 8, 964 to 19, 598 ⇒ room P • from 19, 598 to 38, 927 ⇒ room F2 • from 38, 927 to ∞ ⇒ room F1 The thresholds were selected as the medium point of the segment between the two values of κ of two consecutive rooms. For example, since the mean value of the kurtosis for the room B is κB = 4.847 (see table II) and the one for the room H

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Kurtosis index CM1 Mean CM1 CM2 Mean CM2 CM3 Mean CM3 CM4 Mean CM4

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TABLE II T HE KURTOSIS INDEXES BY SIMULATION AND EXPERIMENT RESULTS ARE COMPARED IN THIS TABLE . Simulation CM1 (LOS, 0 ÷ 4m) CM2 (NLOS, 0 ÷ 4m) CM3 (NLOS, 4 ÷ 10m) CM4 (NLOS, > 10m)

Experiment F1 (LOS, 9.5m) F2 (NLOS, 5.5m) P (NLOS, 6m) H (NLOS, 10m) B (NLOS, 17m)

Kurtosis 49.642 28.212 10.984 6.944 4.847

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is κH = 6.944, the threshold which makes us to decide for room B can be chosen from 0 to 6.944+4.847 = 5.8955. Other 2 criteria to select the thresholds could be, of course, better than the one proposed here, but the main aim of this paper in only to suggest a new parameter which is able to easily recognize the room typology (LOS, QLOS and three different types of NLOS) without any estimation process on the received signal. The results show a percentage of success of the κ index higher than 74%, while the CDF only reaches the 33%. It is important to remember that the CDF is not applied directly to the received signal, as the kurtosis does, but it needs the estimation of the multipath amplitudes and delays. In this comparison the Single Search algorithm [1] is used for the multipath amplitudes and delays estimation. The result of the CDF is not significantly modified if another estimation algorithm is applied, as described in [1]. In order to prove the validity of the identification method proposed, the kurtosis κ has also been applied to the IEEE 802.15.3a standard channel models and the results have been compared. As described in section II, 100 realizations are simulated for each standard channel model and then the kurtosis indexes are calculated. The results are shown in Fig. 4. The mean κ is shown with dashed lines. In the left half of Table II the results of the simulation are listed and compared with those of the experiment. The results yielded by the experiment and by the simulation are numerically comparable. It is necessary to pay particular attention to the comparison of CM2 and F2 situations. CM2 represents a NLOS condition with 4 m distance link, while F2 is a NLOS condition with receiver about 6 m far away from transmitter. Thus, it is more reliable to compare F2 link to CM3. Finally, the results listed in Table II clearly show that rooms (from UWB experiment) and scenarios (from channel model simulations) that have similar physic characteristics have also similar mean kurtosis values. For the sake of completeness the kurtosis index κ is applied also to the IEEE802.15.4a channel models, in particular to the residential and the indoor office environments. The results are reported in Fig. 5. If one considers the considerable difference between the kurtosis indexes of the different environments (Office LOS, Residential LOS, Residential NLOS and Office

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NLOS), it is evident that the kurtosis is able to identify and discriminate the LOS and NLOS conditions as well as the room typologies. V. C ONCLUSION In this paper a new parameter for channel identification is presented. This parameter is the kurtosis index of the received signal. Initially, the cumulative distribution function (CDF) of the received signal estimated amplitude is considered. This work demonstrates that the CDF index can be used to distinguish LOS from NLOS rooms, but it is not able to discriminate rooms within each macro-group, i.e., it is not able to order two different LOS or NLOS rooms. On the contrary, a single channel identification is possible with the kurtosis index. This result has been achieved by using a real data set obtained from an UWB experiment and it has subsequently been confirmed by its application to the IEEE802.15.3a and 4a channel models. In conclusion, unlike other known parameters (which can only distinguish between LOS and NLOS conditions), the kurtosis index of the received signal can be used as an effective parameter to identify also a channel condition within the LOS or NLOS group. ACKNOWLEDGMENT The authors would like to thank Prof. Moe Z. Win and Dr. Henk Wymeersch from MIT for their precious help and suggestions. R EFERENCES [1] C. Falsi, D. Dardari, L. Mucchi, M. Z. Win, “Time of arrival estimation for UWB localizers in realistic environments," EURASIP J. Applied Signal Processing, Special Issue on Wireless Location Technologies Applications, vol. 2006 , article ID 32082, 13 pages.

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[2] S. Venkatraman and J. Caffery, “Statistical approach to non-line-of-sight BS identification," in Proc. 5th International Symposium on Wireless Personal Multimedia Commun., vol. 1, pp. 296-300, Oct. 2002. [3] S. Gezici, H. Kobayashi, and H. V. Poor, “Non-parametric non-line-ofsight identification," in Proc. Veh. Technol. Conf., vol. 4, pp. 2544-2548, Oct. 2003. [4] S. Al-Jazzar and J. Caffery Jr., “New algorithms for NLOS Identification," in Proc. IST Summit Conf., June 2003, Dresden, Germany. [5] I. Guvenc and Z. Sahinoglu, “Threshold selection for UWB TOA estimation based on kurtosis analysis," IEEE Commun. Lett., vol. 9, no. 12, pp. 1025-1027, 2005. [6] D. Dardari, C.-C. Chong, and M. Z. Win, “Threshold based timeof-arrival estimators in UWB dense multipath channels," IEEE Trans. Commun., vol. 56, 2008. [7] P. Marcocci, “UWB low complexity cognitive receiver design based on realistic measurements," Telecommunication Engineering Master Thesis, University of Florence, Florence, Italy, Dec. 2006. [8] I. Guvenc, C.-C. Chong, F. Watanabe, and H. Inamura, “NLOS identification and weighted least-squares localization for UWB systems using multipath channel statistics," EURASIP J. Advances Signal Processing, vol. 2008, article ID 271984. [9] I. Guvenc and C.-C. Chong, “Line-of-sight (LOS) or non-LOS (NLOS) identification method using multipath channel statistics," United States Patent 20080032709, 02/07/2008. [10] D. Cassioli, M. Z. Win, and A. F. Molisch, “The ultra-wide bandwidth indoor channel: from statistical model to simulations," IEEE J. Select. Areas Commun., vol. 20, no. 6, pp. 1247-1257, Aug. 2002. [11] M. Z. Win and R. A. Scholtz, “Characterization of ultra-wide bandwidth wireless indoor communications channel: a communication theoretic

view," IEEE J. Select. Areas. Commun., vol. 20, no. 9, pp. 1613-1627, Dec. 2002. [12] J. R. Foerster, M. Pendergrass, A. F. Molisch, “Channel models for ultrawideband personal area network," IEEE Wireless Commun., vol. 10, pp. 14-21, Dec. 2003. [13] A. F. Molisch et al., “A comprehensive standardized model for ultrawideband propagation channels," IEEE Trans. Antennas Propag., vol. 54, no. 11, part 1, pp. 3151-3166, Nov. 2006 [14] M. Z. Win and R. A. Scholtz, “Impulse radio: how it works," IEEE Commun. Lett., vol. 2, no. 2, pp. 36-38, Feb. 1998. [15] M. Z. Win and R. A. Scholtz, “Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications," IEEE Trans. Commun., vol. 48, no. 4, pp. 679-691, Apr. 2000. [16] M. Z. Win, “A unified spectral analysis of generalized time-hopping spread-spectrum signals in the presence of timing jitter," IEEE J. Select. Areas Commun., vol. 20, no. 9, pp. 1664-1676, Dec. 2002. [17] A. Ridolfi and M. Z. Win, “Ultrawide bandwidth signals as shot-noise: a unifying approach," IEEE J. Select. Areas Commun., vol. 24, no. 4, pp. 899-905, Apr. 2006. [18] W. Suwansantisuk, M. Z. Win, and L. A. Shepp, “On the performance of wide-bandwidth signal acquisition in dense multipath channels," IEEE Trans. Veh. Technol., vol. 54, no. 5, pp. 1584-1594, Sept. 2005. [19] W. Suwansantisuk and M. Z. Win, “Multipath aided rapid acquisition: optimal search strategies," IEEE Trans. Inform. Theory, vol. 52, no. 1, pp. 174-193, Jan. 2007. [20] D. B. Jourdan, D. Dardari, and M. Z. Win, “Position error bound for UWB localization in dense cluttered environments," IEEE Trans. Aerosp. Electron. Syst., vol. 43, 2007.