IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 56, NO. 5, MAY

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1 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 56, NO. 5, MAY An Integrated Overview of the Open Literature s Empirical Data on the Indoor Radiowave Channel s Delay Properties Mohamad Khattar Awad, Student Member, IEEE, Kainam Thomas Wong, Senior Member, IEEE, and Zheng-bin Li Abstract A comprehensive and integrative overview (excluding ultrawideband measurements) is given of all the empirical data available from the open literature on various temporal properties of the indoor radiowave communication channel. The concerned frequency range spans over GHz. Originally, these data were presented in about 70 papers in various journals, at diverse conferences, and in different books. Herein overviewed are the multipaths amplitude versus arrival delay, the probability of multipath arrival versus arrival delay, the multipath amplitude s temporal correlation, the power delay profile and associated time dispersion parameters (e.g., the RMS delay spread and the mean delay), the coherence bandwidth, and empirically tuned tapped-delayline models. Supported by the present authors new analysis, this paper discusses how these channel-fading metrics depend on the indoor radiowave propagation channel s various properties, (e.g., the physical environment, the floor layout, the construction materials, the furnishing s locations and electromagnetic properties) as well as the transmitted signal s carrier-frequency, the transmitting-antenna s location, the receiving-antenna s location, and the receiver s detection amplitude threshold. Index Terms Communication channels, dispersive channels, fading channels, microwave communication, mobile communication, multipath channels, scatter channels. I. INTRODUCTION THE wireless propagation channel constrains the capacity of information that can be communicated between a transmitter and a receiver. The transmitter and the receiver are usually surrounded by dense clutters of scatterers; this clustering is especially serious in indoor settings. The receiver s measured signal represents a constructive or destructive summation of multipaths, which have bounced off various scatterers and then arrive from diverse azimuth-elevation angles, at diverse polarization, with different arrival delays and, possibly, with frequency dispersion. The design of a wireless-communication system s coding, modulation, signal-processing algorithms and multiple-access scheme is predicated on the channel model. The wireless channel is generally time-varying, space-varying, frequency-varying, polarization-varying, dependent on the locations of the transmitter and the receiver, as well on the particular indoor environment. Each above variability presents Manuscript received April 22, 2006; revised December 11, M. K. Awad is with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada ( Mohamad@ieee.org). K. T. Wong is with the Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hung Hom, KLN, Hong Kong ( ktwong@ieee.org.). Z.-b. Li is with the Polaris Wireless, Santa Clara, CA USA. Digital Object Identifier /TAP not only unpredictability but also an opportunity for channel enhancement. A channel s impulse response (IR) may be represented by a linear time-invariant filter, if the channel is (or can be approximated as) temporally stationary [1] [5] where denotes the Dirac impulse function, symbolizes the number of temporally resolvable multipaths whose amplitudes exceed the detection threshold (of magnitude ). Moreover, and, respectively, refer to the th multipath s complex-valued arrival amplitude and the arrival excess delay. Subsequent sections will present a quantitative characterization of and rule-of-thumb insight into for each of a variety of channel metrics. These channel metrics are the number of time-resolvable multipaths, the path-occurrence probability, the power-delay profile (PDP) and the PDP taps amplitude distributions, the average delay and the root-meansquared-spread, the temporal autocorrelation coefficient, the coherence bandwidth, and finally, the tappeddelay-line (TDL) model taps. These characterizations and insight are deduced from the open literature s empirical data for a wide range of indoor environments. 1 Our key contributions to this work lie in the following: first, re-compute data under a uniform metric to contrast data presented in various references. Second, cross-check qualitative trends identified among the references and to explain any contradictions among various references. Third, analyze data presented but not investigated in references. Fourth, derive mathematical models to represent empirical data presented in different papers. This integrative survey will limit itself to the GHz frequency spectrum, covering most indoor radiowave wireless communication systems: GHz is used in wireless private branch exchange (PBX) systems, indoor portable phones, or wireless security systems. In the U.S., the ISM license-free bands at GHz, GHz, and GHz have motivated the development of indoor communication systems in these bands. Bluetooth operates at 2.4 GHz. Indoor Wimax operates at 3.5 GHz. The IEEE a,b,g operate at GHz. This GHz range covers the L band (1 1 Subsequently presented numerical data are read off from various references figures using the GetData V2.02 software. The data, as re-plotted in this survey, have been smoothed to enhance visualization. (1) X/$ IEEE

2 1452 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 56, NO. 5, MAY 2008 TABLE I OVERVIEW OF THE OPEN LITERATURE S EMPIRICAL DATA ON THE NUMBER N OF MULTIPATHS to 2 GHz), the S band (2 to 4 GHz), and the C band (4 to 8 GHz); excluded are the X band (8 to 12 GHz) and the Ku band (12 to 18 GHz). This GHz frequency-range coincides with the radiowave empirical measurement open-literature s near-exclusive focus on this band. II. NUMBER OF TIME-RESOLVABLE MULTIPATHS Table I overviews the empirical data available from the literature [4], [6] [12] on the number of time-resolvable multipaths 2 (i.e., resolvable multipaths whose amplitudes exceed the receiver s detection threshold), measured in various indoor environments (e.g., offices and factories) over the GHz frequencies. For all rows between consecutive horizontal lines in Table I, they correspond to measurements in the same overall building-complex. Each row in Table I is for data taken at different positions within the same compartment (e.g., room). The data in each row produce a histogram for. An entry under the column in Table I gives the maximum value in each histogram of the empirical data. 3 Each histogram (i.e., data set in each row in Table I) has been least-square fit in the analysis 2 Resolvable multipaths here refers to the measured data as subjected to the resolutions limit imposed by the instrumentation and data analysis. The resolvable multipaths incorporate all irresolvable multipaths. 3 Different references implicitly differently define the number of multipaths. In [7], [12], the impulse-response delay-axis is segmented into bins of 7.8 ns, within each of which the power of all arriving multipaths (which may be individually irresolvable by the instrumentation) is averaged. A multipath is said to be detected, if this average exceeds the above the received signal power at D=10. In [8] [11], no such averaging is performed; the number of multipath is said to equal the number of distinct peaks in the impulse-response with power exceeding. Although [10] and [11] define differently from [8] and [9], as will be discussed later in this section. references 4 to a pre-chosen distribution (e.g., the normal distribution in [10] and [11]). 5 Table I s and refer to this calibrated distribution s mean and standard deviation, respectively 6, 7. Fig. 1 shows how typically increases with a decreasing. At the higher detection thresholds (e.g., db) in the left side of the figure, only the dominant multipaths can be detected. At the lower detection thresholds, many weaker multipaths become detectable. Authors of this work observe these integrative qualitative trends underlying the empirical data in Table I and Fig. 1. More multipaths are detected at a greater receiver sensitivity [7], [10]. The more sensitive, the weaker a multipath can still be detected. Hence, a lower (relative to the power at ) increases the detected multipaths and mean amplitude, but decreases the variance, of the amplitude. For example, rises from 2 to 23 in [8] and [9] as the receiver s detection threshold drops from 4 In Table I, an empirical reference refers to a reference paper that presents original empirical data, whereas an analysis reference refers to a reference paper that presents no original empirical data but analyzes data presented in its corresponding empirical reference(s) in Table I. 5 This pre-chosen distribution is a priori chosen in the analysis references without stating any justification and without trying out other distributions. 6 Each row in Table I for [7] [9] consists of measurements at different sites but at an identical, whereas each row for [10] [12] consists of measurements at different sites but at a same and a same D. This additional D-sameness lowers in the rows corresponding to [10] [12], relative to those rows corresponding to [7] [9]. 7 Because the two analysis references [7] and [12] define differently the membership in their respective data groups (i.e., rows in Table I), [7] and [12] have different and values in Table I than for the NLOS data even though both analyze the same empirical data. For the LOS data in [7], is larger and the distribution is thus more dispersed from the mean.

3 AWAD et al.: AN INTEGRATED OVERVIEW OF THE OPEN LITERATURE S EMPIRICAL DATA 1453 Fig. 1. increases with increasing detection sensitivity (i.e., decreasing detection threshold ) in various LOS and NLOS settings. Data are taken from [7, Figs. 6 and 7]. db to db (relative to the received strongest multipath). As decreases, the histogram of flattens from being a Poisson distribution to approach a uniform distribution [7]. This is explained as follows: a more sensitive detection threshold produces more complete measurement data to better reveal the scatterers spatial continuity in the measurement setting [7]. If the histogram is approximated as Gaussian as in [10] [12], the histogram s flattening means a larger. appears to be largely independent, whether the environment is LOS or NLOS. and are comparable in either case [7] [9], [12]. A near-linear relationship is found by [12] to exist between the aforementioned calibrated distribution s and over various distances between the transmitting-antenna and the receiving-antenna. These linear formulas are listed under the column in Table I. The present authors own computations, which are listed under the column in Table I and are based on empirical data from [6], [4], suggest that a near-linear relationship also exist over various values. The NLOS case there has a that disperses the distribution slightly more than the LOS case does. increases with. This work s authors would explain this as follows: a larger would render reflection and scattering more likely, thereby increasing the number of indirect propagation routes and thus. Increasing can decrease [7], [12] or can increase [10], [11]. This apparent contradiction arises from these two series of papers different definitions for the receiver s detection threshold. In [7] and [12], one is used throughout with defined as a pre-set number of db below the received power at ; hence, a larger incurs more propagation loss and fewer arriving multipaths exceed the receiver s detection threshold. In [10] and [11], a variable is used so that the receiver becomes more sensitive at a larger. At each equals a pre-set number of db below the power of strongest multipath arriving at. Thus, for a constant decreases with increasing. III. PATH-OCCURRENCE PROBABILITY The number of multipaths cannot reveal the probability for any multipath to arrive at a particular excess delay (a.k.a., relative delay). This metric has, instead, been differently defined as follows. A) In [7] and [12], equals the probability that a multipath arrives at an 7.8 ns excess-delay interval centered around with an amplitude greater than the detection threshold. B) In [10], [11], [13], and [14], equals the probability that at least one multipath (regardless of the exact number) arrives at an 5 ns excess-delay interval centered around. Both definitions would generally produce. Table II overviews the literature s attainable empirical data on. The present authors have further computed the floor areas for Table II s data entries of [13] based on floor-plan diagrams in [13]. Fig. 2 shows typical curves of versus (not the absolute delay) under definition (A), and Fig. 3 shows typical curves of versus under definition (B). Analysis in [12] of measurements [6] and [4] (i.e., the top two curves in Fig. 3) inside factories at 1300 MHz gives [12, Eqs. (8) and (9)]. For LOS For NLOS (2a) (2b) (2c) (3a) (3b) under definition (A) for, with 7.8 ns being the time-sampling period in [12]. The following rules-of-thumb may be deduced from the measurements in Table II, and Figs. 2 and 3. increases with greater detection sensitivity [10] [14]. drops off exponentially with increasing for thresholds db below the reference power but linearly when over 48 db below the reference power [7]. At large decays more rapidly for a smaller than for a larger [7] (see Fig. 2). For a fixed detection threshold, the entire curve (of versus ) lowers with increasing. The present authors explain this observation as follows: a larger would incur a higher propagation loss, thereby weakening more multipaths to below the detection threshold. remains more substantial at a higher for a larger floor area than for a smaller floor area, a reading that the present authors explain as follows: a larger floor area means that the transmitted signal s multipaths would typically traverse over longer distances, thereby incurring longer propagation delays.

4 1454 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 56, NO. 5, MAY 2008 TABLE II OPEN LITERATURE S MEASUREMENTS OF P ( ) Fig. 3. P ( ) versus : Data for the LOS-factory and NLOS-factory curves are from [12]. Data for the LOS-NLOS-offices-partitioned curve are from [10]. Data for the LOS-factory-open area and NLOS-offices-partitioned curves are from [14]. Data for the NLOS2-offices-partitioned curve are from [13], where the suffix 2 in NLOS2 refers to the number of walls separating the transmitter and the receiver. Fig. 2. P ( ) versus : (a) at constant but various D, (b) LOS or NLOS but at various. Data are taken from [7, Figs. 1, 2, 4]. Referring to the drop in as increases, this drop is faster in open environments (e.g., the open-plan factories of [12]) than in cluttered environments (e.g., the office of [10]). The present authors explain this trend as follows: the more cluttered an environment, the more reflections will occur, and the larger will be. In environments with a larger path-loss exponent (e.g., [13, Eq. 4.5] versus [14, Eqs ]), is generally lower. The present authors explain this as follows: more multipaths are attenuated to below the receiver s detection threshold. Although both [12] and [14] presented measurements at factories of comparable path-loss exponents, is higher in [12] than in [14]. The present authors would explain this apparent discrepancy as due to these two references different definitions of. IV. POWER-DELAY PROFILE (PDP) AND THE PDP TAPS AMPLITUDE DISTRIBUTIONS The path-occurrence probability gives the likelihood of any multipath arriving at the specified, but no information on the power of such an arriving multipath. Instead, that information is given in the power-delay profile (PDP) [1] [5], denoted by, where (4)

5 AWAD et al.: AN INTEGRATED OVERVIEW OF THE OPEN LITERATURE S EMPIRICAL DATA 1455 TABLE III PRESENT AUTHORS CURVE-FIT BASED ON POWER-DELAY PROFILES BASED ON THE OPEN LITERATURE S EMPIRICAL DATA denotes a temporally stationary channel s impulse response. The channel s power-delay profile (PDP) is defined as the term-by-term magnitude-squared impulse response [15] (5) The would be deterministic constants for a specific measurement campaign with a specific transmitter and receiver, and at set locations in a particular indoor setting. For such a set of measurements, the data s histogram may be taken as the probability density function of a random variable. Such a set of power-delay-profile data may be collected over a local spatial area or a global spatial area. 8 Locally averaged power-delay-profile data collected at 1.3 GHz in factories [12] have been curve-fitted to the following mathematical form [12, Eq. (10)]: where is normalized to 0 db and is defined below (3) in Section III. Moreover, refers to a path-loss exponent, depends on, and is curve-fit to give [12, Eqs. (11) and (12)]. For LOS (6) (7a) (7b) (7c) 8 A local area means that the set of power-delay profiles is measured with the transmitter location varying by at most a few wavelengths (across different profiles) and the receiver location varying by at most a few wavelengths (across different profiles) [16]. In contrast, a global area could mean that the set of power-delay profiles correspond to either: (a) same D, but the transmitter s location and/or the receiver s location may vary by more than a few wavelength [10], [11] though in the same compartment of the same building; (b) different D but in the same type of environment (e.g., factories versus offices) but different specific environments (e.g., office #1 versus office #2 in the same building) [7], [13], [17]; (c) different D and in different environmental types (e.g., factories versus offices) [14], [16]. Fig. 4. Normalized jh( )j versus : The factory and college data are from [18, Figs. 11 and 12]. The office data are from [19, Fig. 5]. For NLOS (8a) (8b) The above equations indicate that the path-loss exponent (and thus the power loss over unit propagation-distance) is greater for NLOS than for LOS. An alternative and very common approximation to the power-delay profile is the exponential decay [20] where and are deterministic independent parameters to be evaluated by curve-fitting a specific set of empirical data. The deterministic scalar indicate the power of the decaying, whereas the deterministic scalar indicates the rapidity of decay in as increases. Indeed, equals the average value and the root-mean-squared value of according to (9). Extensive computations has been performed by the authors of this work to curve-fit various sets of power-delay-profile data from [18], [19], and [21] to evaluate for each data set its and. The present authors curve-fitting first normalizes the empirical data by converting (9)

6 1456 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 56, NO. 5, MAY 2008 TABLE IV OPEN LITERATURE S EMPIRICAL MEASUREMENTS OF THE POWER-DELAY PROFILE (PDP) AND OF THE PDP TAPS AMPLITUDE DISTRIBUTIONS at each to for ready comparison across data sets. The present authors curve-fitting results are presented in Table III, where RMSE refers to the least-squares curve-fitting s root-mean-squared error, and measures the goodness of fit. Fig. 4 plots the corresponding best-fit curves along with the corresponding raw data. The following rules-of-thumb from Table III and Fig. 4 have been observed by the present authors. is larger for LOS settings than for NLOS settings (with all else being equal, an LOS propagation path s amplitude at would exceed that of an NLOS propagation path, thereby affording a sharper decay). increases with an increasing floor area and decreasing scattering (e.g., the factory in [18] versus the school in [18]), wherein multipaths experiencing longer propagation delays would have diminished arrival power due to more distance-dependent propagation loss and less likelihood of reflection. increases with a decreasing wavelength, concurring with the empirical trend in [21, Fig. 4] that the received power decays faster with an increasing frequency. increases with an increasing wavelength, possibly due to a decrease in the multipaths penetration loss (which depends on frequency). This trend concurs with the empirical trend in [21, Fig. 4 ] that the received power increases with a decreasing frequency. To characterize the statistics of the coefficients, empirical data of have been least-square fitted to the well-known distributions of Rayleigh (Ray), Rician (Ric), Log-normal (Log), Nakagami (Nak), and Suzuki (Su). These curve-fitting results are summarized in Table IV. The following rules-of-thumb may be observed from Table IV. The Rician distribution best fits LOS data [16] at, but the Rayleigh distribution best fits the corresponding data for. This is expected because the LOS propagation path is (by definition) present at but not at any. Referring to Table IV s NLOS data [16] of at a fixed, the best-fit distribution is lognormal; and [16] speculates on the reason for the greater variability with global averaging than with local averaging. The identity of the best-fitting distribution depends on the receiver s detection sensitivity. At a higher detection threshold, the Rayleigh distribution is the best fit for [7] and [22]; the Rician distribution is the best fit for parts of the empirical data in [16]; the log-normal distribution is the best fit for other parts of the empirical data in [16]. At a lower detection threshold of db, the log-normal distribution fits best in [4], [6]. The present authors would explain the above as follows. A higher detection threshold at db partly de-noises the measured signal of its additive noise, but at the risk of missing the weakest multipaths. A lower detection threshold allows the weak multipaths to be counted, but is more susceptible to additive noise. Thus, removing the lognormal probability distribution s low end (i.e., by using a higher detection threshold) would change the distribution towards a Rayleigh or a Rician distribution. Moreover, [22] performs the following additional analysis to characterize the power-delay profile: at each, all member power-delay profiles values at are curve-fitted to the log-normal distribution, whose average at is defined as and whose standard deviation at is defined as. Then, [13] and [14] perform a second curve-fitting: the aforementioned sequence is curve-fitted to the a priori chosen mathematical form of and the sequence is curve-fitted to the a priori mathematical form. The numerical values and in Table IV have been computed in [7], [13], [14], [16], [18], and [22] based on the empirical data of the corresponding empirical references in Table IV. As expected, the decay parameters and decrease as obstruction severity increases from LOS to NLOS2.

7 AWAD et al.: AN INTEGRATED OVERVIEW OF THE OPEN LITERATURE S EMPIRICAL DATA 1457 TABLE V OPEN LITERATURE S EMPIRICAL MEASUREMENTS OF THE RMS DELAY SPREAD, V. AVERAGE DELAY AND THE ROOT-MEAN-SQUARED-SPREAD The channel s discrete-time power-delay profile is a mathematical function whose complete characterization necessitates a long bivariate waveform or a long sequence of ordered pairs. For those communications engineers who are interested primarily in the power-delay profile s temporal dispersion, these two following scalar metrics might suffice: the mean delay is [15] and the root-mean-squared (RMS) delay spread is [15] (10) (11) Tables V and VI, summarize the open literature s empirical measurements for the delay spread. In each measurement campaign, numerous delay profiles are collected at a site. Each delay profile may be construed as a statistical realization of a random variable, whose sample space contains all delay profiles measured at that site. The algebraic average, among all these measured realizations, is denoted as ; the median is symbolized as ; the maximum is denoted as max ; and the standard deviation is denoted as. Every row in Tables V or VI refers to a global set of such delay-profile realizations, except [23] and [24] which have local sets (see footnote for definitions of global versus local ). From the measurements cited in Tables V and VI, the following integrative rule-of-thumb may be observed. 9 and are generally larger for NLOS settings than for LOS ones, with all else being comparable [13], [21], [25] [27]. Additionally, is larger for NLOS settings than for LOS ones [13], [27], [28]. These trends are expected because an NLOS setting has more numerous multipaths at the larger values of. One exception is the 9 Because and show similar trends with respect to various measurement variables (e.g., (D=), the carrier frequency), the following discussion focuses on but can apply to as well.

8 1458 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 56, NO. 5, MAY 2008 TABLE VI OPEN LITERATURE S EMPIRICAL MEASUREMENTS OF THE RMS DELAY SPREAD, 4.75 GHz case of [21] and [29] with people occupying the room, where ns for LOS settings but 11.1 ns for NLOS settings. The present authors would explain this very slight discrepancy as people obstructing the LOS propagation to effectively become NLOS propagation. The only other apparent exception is in [30], where is smaller in NLOS settings than in LOS settings, though remains larger for NLOS settings than for LOS ones. [30] offers the explanation that the presence of many pulses [i.e., multipaths] makes the for heavily obstructed paths less sensitive to variations of the amplitude of any one pulse. As the carrier frequency increases, may increase slightly [31], [32], may decrease [21], [25], [29], [33], [34], or may remain unchanged [35]. The aforementioned decrease could be due to a higher absorption loss at a higher frequency, thereby resulting in fewer multipaths [33]. seems more sensitive to a change in the carrier frequency than is [31]. and increase with the floor area [21], [27], [30], and [31]. This increase is expected, as a larger room would allow more spatial dispersion among the scatterers [21]. increases with [21], [23], [27], [31], and [36] [40] for non-corridor environments; however, [4] and [20] suggest no such dependence. Moreover, [37] claims that for any particular environment, generally increases less with increasing when furnished, than when unfurnished [37, Fig. 16], a phenomenon that is explained in [37] as follows: increases with because each multipath would travel over a longer distance. This increase in would be more pronounced if the scatterers are distant from both the transmitter and the receiver. Nearby furniture, however, would produce dominant multipaths, thereby resulting in a smaller increase in as increases. For transmission and reception all within any same corridor, [23], [32], [33], [37], [41], [42], peaks at. This non-monotonic trend is explainable by the opposing trends in versus in (11) by [37] as follows. a) For a small, the propagation distances (traversed by the multipaths reflected off walls), would exceed the distances traversed by an LOS path. Hence, the multipaths would experience greater path loss and larger propagation delays, resulting in an increasing as increases.

9 AWAD et al.: AN INTEGRATED OVERVIEW OF THE OPEN LITERATURE S EMPIRICAL DATA 1459 TABLE VII PRESENT AUTHORS LEAST-SQUARES FITTING OF EMPIRICAL DATA Fig. 5. Empirical RMS delay-spread versus the normalized transmitterreceiver separation (D=). Data are taken from [21, Fig. 11] for measurements at 2.4 GHz in an NLOS setting. For the solid curve, the transmitter is at a fixed location in a particular room, and the receiver is at different locations in a neighboring corridor. For the dashed curve, the transmitter is at a fixed location in the above-mentioned corridor, and the receiver is at different locations in the above-mentioned room. b) However, at a certain limit, the propagation distances traversed by the multipaths reflected off walls are similar to the distances traversed by the LOS path, because of the rectangular structure of the corridors. Hence, the multipaths and the LOS path would experience similar path loss and similar propagation delay, thereby resulting in a decreasing as increases past. Fig. 5 plots versus, when one of the transmitting-antenna and the receiving-antenna is in a corridor, whereas the other is in a neighboring room. For the solid curve there, the transmitting-antenna is at a fixed location in a particular room, and the receiving-antenna is at different locations in a neighboring corridor. For the dashed curve, the transmitting antenna is at a fixed location in the above-mentioned corridor, and the receiving-antenna is at different locations in the above-mentioned room. The dependence of on an increasing is irregular, though generally increasing. There exists a standing wave behavior when the receiving-antenna is in a corridor and the transmitting-antenna is in a room. increases with detection sensitivity [24], [36], concurring with the discussion in Section II. Human presence in the environment has only an insignificant effect on [21], [29]. changes by ns among all open-literature measurements considered in this paper. To characterize the empirical distribution of, the authors of this survey paper least-squares (LS) fit various references empirical data to the well-known distributions of normal, lognormal, Rayleigh, Rician, Poisson, and Weibull. Table VII summarizes these results. The normal distribution best fits 70% of the empirical data sets, with the runner-ups Weibull distribution best fittings 20% and the log-normal distribution best fittings 8%. The normal distribution and the Weibull distribution represent the best or the second best fits, except for measurements in [18] and [23] where the log-normal and Poisson distributions are better. Fig. 6 shows the best-fitting distribution (i.e., the normal distribution in this case) plus the other candidate-distributions calibrated by a particular (but representative) set of empirical data from [43]. The normal distribution and the log-normal distribution generally 10 best fit those empirical measurements with a large variability in and/or environments (i.e., different particular environments, though within the same type of environments) as in [18] (Table VII, rows 6 11) and [23], [27], [31], 10 The only exception being [44], which consists of measurements in 23 houses but has the Weibull distribution as best fitting.

10 1460 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 56, NO. 5, MAY 2008 TABLE VIII OPEN LITERATURE S MEASUREMENTS OF THE TEMPORAL AUTOCORRELATION COEFFICIENT ( ; ) [43] compared to various (empirically cali- Fig. 6. Empirical data of brated) candidate distributions. [36], [43], [45], and [46]. Otherwise, Weibull best fits those empirical measurements with a smaller variability in and/or environments as in [18] (in Table VII, rows 12 and 13) and [26]. The present authors note that a tails-truncated normal or lognormal distribution (corresponding to removing outlying samples to reduce variability within the data set) would approach a Weibull distribution. VI. THE TEMPORAL AUTOCORRELATION COEFFICIENT If each measurement of a non-stationary channel s impulse response is considered to be a realization of a random process, the channel s temporal bivariate autocorrelation-coefficient function, shown in (12), at the bottom of the page, between multipath(s) arriving at the relative delay and multipath(s) arriving at the relative delay is given by [12, Eq. (19)] where denotes a statistical expectation and the superscript symbolizes complex conjugation. Any line-of-sight (LOS) propagation path must have, by definition. Table VIII summarizes the open literature s autocorrelationcoefficient data in various indoor environments. Each row in Table VIII is comprised of globally averaged 11 data at various values of. 12 decays faster for LOS settings than for NLOS settings, because the LOS path arriving at is stronger than all subsequent multipaths. For example, in LOS settings for temporal separation ns, the non-direct multipaths are uncorrelated with the direct path that arrives at ns [12], [22]. However, in NLOS settings, multipaths are uncorrelated for temporal separation of 25 ns [12] and up to 50 ns [16], [50]. 13 Work in [12] curve-fits empirical data collected at 1.3 GHz in a factory (see Table VIII) and obtains the following. For LOS, see (13a-13c) shown at the bottom of the next page. For NLOS (14) The above curve-fit models are plotted as solid curves in Fig. 7. These solid curves seem adequately descriptive of the empirical data, which are taken from [16] and [50] and are shown in Fig. 7(a) as icons even though the curves and icons are based on entirely different measurement settings. In both 11 Page 6 presents the definition of global averaging. 12 The relatively high value of ( ; ) = 0:74 for the corridor in [16], [50] could be attributed to waveguiding effects. In such a situation, the common wide-sense stationary uncorrelated scattering (WSSUS) model is inapplicable [16]. 13 In Table VIII s NLOS > 0 data, row #4 has ( ; ) 0 but rows #12 and #13 have ( ; ) 0. This apparent discrepancy might be due to the different spatial sizes of the scatterers in these references [16], [50]. (12)

11 AWAD et al.: AN INTEGRATED OVERVIEW OF THE OPEN LITERATURE S EMPIRICAL DATA 1461 channel frequency response s complex autocorrelation function equals [15], [52] (15) Fig. 7. Temporal autocorrelation coefficient at (a) =0, (b) > 0. The solid curves plot the curve-fit models [12, Eqs. (13c) and (14)]. The icons plot the empirical data from [50, Fig. 5]. Fig. 7(a) and (b), drops rapidly as increases from 0 to 20 ns. Thereafter, ns. For the LOS case of Fig. 7(a), anti-correlation occurs for certain values where, but no significant anti-correlation occurs in the NLOS case of Fig. 7(b). VII. COHERENCE BANDWIDTH Whereas the preceding channel-fading metrics are in the relative-delay domain, channel fading may also be characterized in the spectral domain. Specifically, the coherence bandwidth offers an alternative metric (versus the RMS-delay-spread ) to measure the channel s temporal dispersion. 14 The 14 B and are inversely related. The open literature offers various formulas to approximate this inverse relationship. In [3], [51], B (1= ) for some positive real number. In [41], [52], B, where > 0 and < 0. where denotes the Fourier transform of. The coherence bandwidth measures the spectral width of, given a set value for the channel s self-correlation coefficient. 15 Table IX overviews the open literature s various empirical measurements of. 16 Fig. 8 shows representative measurements [48] of how varies with the floor area and with the transmitting-antenna/receiving-antenna separation.to quantitatively relate to, the present authors use empirical data from [26], [30], and [48]. 17 References were also made in Table IX to calibrate the several candidate mathematical models listed in Table X. 18 Fig. 9 plots the best-fitting model (namely, ) along with the calibrating empirical data. The 4-parameter double exponential model offers better fits than the 5-parameter polynomial model in Table X, possibly due to the former s more rapid drop with increasing. From Table IX, Figs. 8 and 9, the present authors make the following rule-of-thumb observations. is generally larger for an LOS setting than for an NLOS one. This trend concurs with being smaller for an LOS setting than for an NLOS setting. 19 In every section of Table IX (i.e., all rows between a pair of consecutive horizontal lines in Table IX), the largest nonwaveguiding typically has a very small under an LOS setting (e.g., those entries marked with the superscript in Table IX). It agrees with Section V s observation that a smaller gives a smaller, and thus a larger 15 For example, at = 0:5; 0:7; 0:9;B equals the 3, 1.5, 0.45 db bandwidth in jr(1f )j, respectively. A larger would correspond to fewer dbs, as confirmed in Fig. 9 s best-fitting curves produced by the present authors (and will be further described below). As expected, the =0:7curve gives larger B than does the =0:9curve, with the former curve about 3 MHz above the latter curve. 16 For each of Table IX s (D=) entry from [3] and [48], the (D=) value has not been explicitly stated in the references but is measured by the present authors from the references diagrams. 17 This least-squares curve-fitting excludes Table IX s wave-guiding data sets (i.e., those superscripted with ). 18 This curve-fitting procedure first normalizes the data in each measurement group (i.e., data corresponding to a row in Table IX) such that its largest B becomes unity, so as to focus on the effects of (D=) on B. 19 This general rule-of-thumb has one exception when the receiver is located against a wall or in a corridor, whereby waveguiding effects produce a very small and a very high B. These are the entries in Table IX marked with the superscript. Each of these marked entries clearly has the largest B value within its respective measurement group (i.e., set of rows in Table IX). (13a) (13b) (13c)

12 1462 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 56, NO. 5, MAY 2008 TABLE IX OPEN LITERATURE S EMPIRICALLY MEASURED VALUES OF B IN VARIOUS INDOOR ENVIRONMENTS here. Fig. 8 concurs with this trend of a smaller for a larger. decreases with an increasing floor area. This is expected as a larger floor area allows the channel to experience a larger delay dispersion and hence a smaller, considering that and are inversely related. Furthermore, several references state the following rules-ofthumbs (but without justification). Reference [3] suggests that a small is under 4 MHz, if the power-delay profile has one predominant multipath. This, however, is contradicted by empirical measurements in [30, Fig. 11 (for site ke 1 )].

13 AWAD et al.: AN INTEGRATED OVERVIEW OF THE OPEN LITERATURE S EMPIRICAL DATA 1463 TABLE X AUTHORS CURVE-FITTING OF THE OPEN LITERATURES EMPIRICAL DATA TO REVEAL THE DEPENDENCE OF B ON D Reference [3] suggests that a large is over 10 MHz, if the power-delay profile has roughly equal-power multipaths arriving at similar delays. This, however, is contradicted by empirical measurements in [30, Fig. 11 (for site sw 1 )]. As a special case to (d) above, [53] suggests that would be large if the power-delay profile has a few multipaths arriving at small excess delays. This is supported by [30, Fig. 11 (for site east 1 )]; where Fig. 11 (for site sw 1 ) does not contradict (e). Fig. 8. Coherence bandwidth B empirical data versus the transmitter-receiver separation D and the floor area. The empirical data were collected at 5 GHz (Table V of [48]) and correspond to Table IX, rows 26 to 44. VIII. TAPPED-DELAY-LINE (TDL) MODEL Communications engineers often discretize the continuoustime impulse response of (4) to a very few discrete-time bins, for computational convenience in simulation studies. This results in the tapped-delay-line (TDL) model [15], [55], [56] (16) Fig. 9. The coherence bandwidth B empirical data versus the transmitter-receiver separation D. The empirical data were collected at 1.8 GHz (Fig. 5 of [41]) and correspond to Table IX, rows 44 to 47. Reference [3] suggests that a small is under 4 MHz, if the power-delay profile has only a few strong multipaths well separated in arrival delay. Reference [3] suggests that a large is over 10 MHz, if the power-delay profile has many multipaths. where denotes the total number of taps, symbolizes the th tap s propagation delay, and refers to the th tap s complex-valued stochastic time-varying amplitude and has a Doppler spectrum. A smaller would simplify the tapped-delay-line model but would compromise modeling accuracy. Tables XI and XII present seven tapped-delayed-line models whose and are evaluated from empirical data 20, 21, 22. No reference in Table XI explicitly justifies its choice of the value of. For comparison, Table XI s models #8 and #9 are the International Communications Union (ITU) models [58], [60] for the 20 Models #6 and #7 are stated in [57] with no explanation or justification. 21 For Table XI s models #1 to #5, a > 020dB because the empirical raw data were thresholded at = 020 db. 22 The classical (a.k.a. Jakes ) Doppler spectrum is S(f ) = (1=[1 0 (f=f )) ]) ;f 2 [0f ;f ] [58]. The uniform Doppler spectrum is S(f ) =(1=2f );f 2 [0f ;f ] [59]. The Rician Doppler spectrum is S(f ) = (0:41=2f [1 0 ((f=f )) ] +0:91(f 0 0:7f );f 2 [0f ;f ] [58]. Moreover, the receiver velocity is v; and the Doppler shift equals f = 0(v=)cos sin. Furthermore, and respectively denote the azimuth angle and the elevation angle between the incident signal s propagation direction and the receiver s velocity vector.

14 1464 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 56, NO. 5, MAY 2008 TABLE XI OPEN LITERATURES TAPPED-DELAY-LINE MODELS, DERIVED FROM EMPIRICAL DATA small-delay-spread case and the large-delay spread case, respectively. Fig. 10 contrasts Table XI s empirically based models #1 to #7 against these two ITU models. The following rules-of-thumb may be observed from Tables XI, XII, and Fig. 10. The present authors observe that is monotonically nonincreasing with respect to index in almost all models; the lone exception being model #7 for unknown reasons. Concurring with Section IV s observation that the power-delay profile decays faster (versus ) for LOS than for NLOS, the tap power decays faster (as the tap index increases) in LOS model #5 (with db at ns) than in NLOS model #3 (with db at ns). The taps amplitude distributions are Rayleigh or Rician, which (the present authors note) are exactly the best-fit distributions identified for Table IV s thresholded measurements in Section IV. The classical Doppler-spectrum holds where the transmitting-antenna/receiving-antenna separation,, exceeds the ceiling height, whereas the flat Doppler Dopplerspectrum holds when the transmitting-antenna is placed near the middle of the floor plan [61]. This is expected because the classical Doppler-spectrums correspond to the assumption that the multipaths angle-of-arrival is distributed in the azimuth plane, while the flat Dopplerspectrums correspond to the assumption that the multipaths angle-of-arrival is distributed in both azimuth and elevation planes. The present authors observe that all models considered here have inter-tap delay-separations from 36 ns to 120 ns. The inter-tap delay-separation needs be sufficiently long for low inter-tap cross-correlation to satisfy the uncorrelated-scattering model (discussed in Section VI). Each model s inter-tap cross-correlation coefficients between the first tap and subsequent taps are generally low. However, the cross-correlation coefficients become noticeably higher among taps #2, #3, and #4 - which would violate the uncorrelated-scattering assumption [61]. Models #4 and #5 each have a significant cross-correlation coefficient between the third and the fourth taps, even though ns. This finding might appear to contradict Fig. 7(b) of Section VI, which shows a near-zero correla-

15 AWAD et al.: AN INTEGRATED OVERVIEW OF THE OPEN LITERATURE S EMPIRICAL DATA 1465 TABLE XII CROSS-CORRELATION COEFFICIENTS ACROSS TAPS FOR TABLE XI S OPEN LITERATURE TAPPED-DELAY-LINE MODELS #1 TO #5 IX. CONCLUSION Each of the previous sections focus on one metric of the indoor radiowave wireless propagation channel overviewing empirical measurements from about 70 references, presenting integrative qualitative insights and rules of thumbs often with new analysis conducted by the present authors. The following subsections summarize the ways each independent channel-parameter of the channel would affect the channel overall. A. Detection Threshold As the detection threshold is lowered, the receiver becomes more sensitive towards the weaker multipaths and allows more multipaths to be detected. At higher detection thresholds of db, the measured signal is partly de-noised of its additive noise, though at the risk of missing the weakest multipaths. A lower allows the weak multipaths to be counted, but the receiver becomes more susceptible to additive noise. At a lower, mean amplitude, and will be larger; and the histogram of flattens from being a Poisson distribution to approach a uniform distribution. The above increases the channel s measured temporal dispersion, thereby increasing and. However, the variance of decreases with. The identity of the best-fitting distribution of the coefficient (for any specified ) thus depends on the receiver s detection sensitivity. At a higher detection threshold, the best-fit distributions of can be Rayleigh and Rician, but it is generally log-normal at db. This is because a higher threshold corresponds to truncating the lognormal probability distribution s low ends, thereby changing the distribution towards a Rayleigh or a Rician distribution. Fig. 10. (a) Table XI s empirically based TDL models #1, #6, and #7, compared to the two ITU TDL models. (b) The empirically based airport TDL model and the empirically based corridor TDL models from Table XI compared to the two ITU TDL models. tion coefficient for a delay difference over 25 ns. However, The present authors would note that there exists no real contradiction, as Fig. 7(b) involves the first arriving path, but and here do not. The present authors observe that the ITU models flat Doppler spectra mismatch most empirically based models non-flat spectra. The ITU model #9 s tap magnitudes generally exceed the empirical models tap magnitudes at comparable tap delays. B. Transmitter Receiver Separation With a very sensitive receiver, is independent of ; otherwise, at constant, a larger would generally give a smaller and would lower the entire curve of versus.however, a larger would increase (especially in furnished rooms). A larger would lead to a more rapid decay of with respect to at large. For a smaller decreases over at a faster rate than that for at a larger.a near-linear relationship exists between and at any value of. Where exceeds the ceiling height, the TDL model s coefficients would have the classical Doppler-spectrum; however the flat Doppler-spectrum holds when the transmitter is placed near the middle of the floor plan. C. Floor Area At high remains more substantial for a larger floor area than for a smaller floor area. A larger floor area gener-

16 1466 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 56, NO. 5, MAY 2008 TABLE XIII VARIOUS THEORETICAL DISTRIBUTIONS MATHEMATICAL FORMS ally increases as well as, and more rapidly renders the exponential decay of versus. D. Carrier Frequency A higher carrier-frequency increases penetration loss, and thus decreases the multipaths power. A higher carrier-frequency more rapidly renders the exponential decay of versus. E. Los Versus NLOS, and seem largely independent of whether NLOS or LOS. LOS settings, relative to NLOS settings, have smaller, and, but larger. The decay of and of versus is larger for LOS than for NLOS. For LOS situations, the Rician distribution best fits at, but the Rayleigh distribution best fits at any fixed. For NLOS data of at any fixed, the best-fit distribution is instead lognormal. Less clustering generally renders more rapid the decay in and in over, as less clustering produces fewer reflections and is thus less likely to have long delays. Human presence has little effect on the delay spread. Recall that a small implies low power loss, and a large implies large power loss. As increases, the multipaths attenuate to below, resulting in smaller. LOS situations might produce negative values in the temporal autocorrelation coefficient, but NLOS situations generally do not. The TDL models first taps (corresponding to the LOS path) have Rician doppler spectra for LOS situations, but a classical or flat doppler spectrum for NLOS. APPENDIX MATHEMATICAL FORMULAS OF CITED PROBABILITY DISTRIBUTIONS The mathematical formulas of cited probability distributions are tabulated in Table XIII. REFERENCES [1] G. Turin, F. Clapp, T. Johnston, S. Fine, and D. Lavry, A statistical model of urban multipath propagation, in Proc. IEEE Vehicular Technology Conf. (VTC 72), 1972, pp [2] T. Lo, J. Litva, and R. J. C., High-resolution spectral analysis techniques for estimating the impulse response of indoor radio channels, in Proc. IEEE Int. Conf. on Wireless Communication ICWC 92, Vancouver, BC, Canada, Jun. 1992, pp [3] W. Pietsch, Measurements of radio channels using an elastic convolver and spread spectrum modulation: Part II Results, IEEE Trans. Instrum. Meas., vol. 43, no. 5, pp , Oct [4] T. Rappaport, Characterization of UHF multipath radio propagation inside factory buildings, IEEE Trans. Antennas Propag., vol. 37, no. 8, pp , Aug [5] H. Hashemi, The indoor radio propagation channel, Proc. IEEE, vol. 81, no. 7, pp , Jul [6] T. Rappaport and C. McGillems, UHF fading in factories, IEEE J. Select. Areas Commun., vol. 7, no. 1, pp , Jan [7] K. Takamizawa, S. Seidel, and T. Rappaport, Indoor radio channel models of manufacturing environments, in Proc. IEEE Southeastern Conf. (Southeast 89), Columbia, SC, Apr. 1989, pp [8] P. Yegani and C. McGillem, A statistical model for the factory radio channel, IEEE Trans. Commun., vol. 39, no. 10, pp , Nov [9] P. Yegani and C. D. McGillem, A statistical model for the obstructed factory radio channel, in Proc. IEEE Global Telecommunications Conf. (GLOBCOM 89), Dallas, TX, Nov. 1989, pp [10] H. Hashemi, D. Lee, and D. Ehman, Statistical modeling of the indoor radio propagation channel Part II, in Proc. IEEE Vehicular Technology Conf. (VTC 92), Denver, CO, May 1992, pp [11] H. Hashemi, Impulse response modeling of indoor radio propagation channel, IEEE J. Select. Areas Commun., vol. 11, no. 7, pp , Sep [12] T. Rappaport, S. Seidel, and K. Takamizawa, Statistical channel impulse response models for factory and open plan building radio communication systems design, IEEE Trans. Commun., vol. 39, no. 5, pp , May 1991.

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18 1468 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 56, NO. 5, MAY 2008 [58] M. Jeruchim, P. Balaban, and K. S. Shanmugan, Simulation of Communication Systems Modeling Methodology and Techniques. New York: Kluwer Academic, [59] Y. Rosmansyah, S. Saunders, P. Sweeney, and R. Tafazolli, Equivalence of flat and classical doppler sample generators, IEE Electron. Lett., vol. 37, no. 4, pp , Feb [60] M. IbnKahla, Signal Processing for Mobile Communications Handbook. Boca Raton, FL: CRC Press, [61] J. Kivinen, X. Zhao, and P. Vainikainen, Empirical characterization of wideband indoor radio channel at 5.3 GHz, IEEE Trans. Antennas Propag., vol. 49, no. 8, pp , Aug [62] G. S. Prabhu and P. M. Shankar, Simulation of flat fading sing MATLAB for classroom instruction, IEEE Trans. Educ., vol. 45, no. 1, pp , Feb [63] A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, 2nd ed. Reading, MA: Addison-Wesley, [64] N. R. Diaz and J. E. J. Esquitino, Wideband channel characterization for wireless communications inside a short haul aircraft, in Proc. IEEE Vehicular Technology Conf. (VTC 04), May 2004, pp [65] S. Ross, A First Course in Probability. Upper Saddle River, NJ: Prentice Hall, Mohamad Khattar Awad (S 02) received the B.A.Sc. degree in electrical and computer engineering (communications option) from the University of Windsor, Windsor, ON, Canada, in 2004 and the M.A.Sc. degree in electrical and computer engineering from the University of Waterloo, Waterloo, ON, Canada, in 2006, where he is working toward the Ph.D. degree. Currently, he is a Research Assistant in the Broadband Communications Research Group (BBCR), University of Waterloo. His research interest includes wireless communications, wireless networks resource allocation and acoustic vector-sensor signal processing. Kainam Thomas Wong (SM 01) received the B.S.E. degree in chemical engineering from the University of California, Los Angeles, in 1985, the B.S.E.E. degree from the University of Colorado, Boulder, in 1987, the M.S.E.E. from the Michigan State University, East Lansing, in 1990, and the Ph.D. in electrical engineering from Purdue University, West Lafayette, IN, in He was a Manufacturing Engineer at the General Motors Technical Center, Warren, MI, from 1990 to 1991, and a Senior Professional Staff Member at The Johns Hopkins University Applied Physics Laboratory, Laurel, MD, from 1996 to Between 1998 and 2006, he had been a faculty member at Nanyang Technological University, Singapore, the Chinese University of Hong Kong, and the University of Waterloo, Waterloo, ON, Canada. Since 2006, he has been with the Hong Kong Polytechnic University as an Associate Professor. His research interest includes wireless communications and sensor-array signal processing. Dr. Wong received the Premier s Research Excellence Award from the Canadian province of Ontario in He has been an Associate Editor for the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, the IEEE SIGNAL PROCESSING LETTERS, and Circuits, Systems, and Signal Processing. Zheng-bin Li received the B.Eng. and M.Eng. degrees from the Beijing University of Posts and Telecommunications, Beijing, China, in 1988 and 1991, respectively, and the M.A.Sc. degree in electrical and computer engineering from the University of Waterloo, Waterloo, ON, Canada, in He had worked on GSM networks for China Unicom in the 1990s, and for Ericsson Research (Canada) from 2001 to He has been at Polaris Wireless, Santa Clara, CA, since His main technical interests are wireless systems design and wireless network planning.