Modeling the Statistical Time and Angle of Arrival Characteristics of an Indoor Multipath Channel

Modeling the Statistical Time and Angle of Arrival Characteristics of an Indoor Multipath Channel

Modeling the Statistical Time and Angle of ArrivalCharacteristics of an Indoor Multipath Channel

Michael D RiceMichael A Jensen

November 22, 1996

Most previously proposed statistical models for the indoor multipath channel clude only time of arrival characteristics However, in order to use statistical models insimulating or analyzing the performance of array processing or diversity combining, it alsonecessary to know the statistics of the angle of arrival and its correlation with time of arrival.In this paper, a system is described which was used to collect simultaneous time and angleof arrival data at 7 GHz Data processing methods are outlined, and results of data taken intwo different buildings are presented Based on the results, a model is proposed that employsthe clustered “double Poisson” time of arrival model proposed by Saleh and Valenzuela [1].The observed angular distribution is also clustered, with uniformly distributed clusters, andarrivals within clusters that have a Laplacian distribution.

in-Chapter 1

Radio has recently become an increasingly viable option for indoor tions applications The availability of higher frequency bands in the 900 MHz and 2.4 GHzrange has made wireless an attractive option for high bandwidth digital communications ap-plications such as local area networks Wireless networks can be particularly advantageousfor applications which require portability, or where installation of wiring is undesirable orimpractical.

communica-Multipath interference, or interference due to the reception of multiple copies of asignal due to reflections, is known to be a problem in many outdoor communication channels.However, multipath can also be particularly problematic in an indoor environment At UHFand microwave frequencies, the presence of walls and large objects in rooms makes the indoormultipath environment quite different from most outdoor scenarios As a result, the studyof indoor propagation characteristics has become an area of increased study.

In order to analyze or simulate the performance of a communications system, somekind of model for the channel is needed One of the first statistical models for the indoormultipath channel was proposed by Saleh and Valenzuela [1] Their data showed multipatharrivals which were grouped in clusters over time The relative delay between clusters wasrepresented by a Poisson distribution, and the separation between elements within clusterswas modeled by a second Poisson distribution with a different delay parameter.

There have been many different approaches to overcoming the problem of path interference, both in outdoor and indoor applications Some of them include channelequalization, directional antennas, and multiple antenna systems Each of these tends to bemore particularly suited to different applications This thesis will focus on multiple antennasystems The signals from different antennas can be combined in various ways, including di-versity combining, phased array processing, and adaptive array algorithms Adaptive arraysytems are becoming increasingly feasible for high bandwidth applications with continuingimprovements in digital signal processors The indoor multipath propagation model pre-sented in this thesis is intended as a tool to evaluate performance of these various multipleantenna systems.

multi-1.1 Problem Statement

Because array processing exploits the angular diversity of incoming signals, achannel model should include information about the angle of multipath arrivals in order toevaluate the performance of an array processing system The lack of angular dependence isa weakness of the Saleh-Valenzuela model Their model specifies amplitude and time of eacharrival, but makes no assumptions regarding the angular distribution of arrivals Saleh andValenzuela, as well as others who have studied the characteristics of indoor multipath prop-agation, have not addressed the area of angle of arrival for two reasons Measuring angle ofarrival simultaneously with time of arrival is much more complex than simply measuring thetime domain impulse response Secondly, for applications using only single antenna systems,the angle of arrival is often irrelevant However, applications now being considered whichperform spatial processing by using multiple antennas call for a more realistic representationof the angle of arrival.

The possibility that clustering occurs in angle as well as time seems probableas one considers the physical mechanisms which may create clustering Suppose a signalis transmitted in a building and the received signal contains two clusters The strongestarrival in each cluster would represent a major path to the receiver, either by line of sight, orwith very few reflections Subsequent arrivals within each cluster would likely follow similarpaths, but may be delayed in time and reduced in amplitude by reflecting off of more nearbyobjects en route Because they followed a similar path, there is a high likelihood that thearrivals are close in angle Generalizing this line of reasoning, it follows that clustering intime is likely associated with some kind of clustering in angle.

The nature of the angular clustering of indoor multipath arrivals has not ously been studied, nor has the correlation, if any, between time and angle of arrival Inorder to learn more about the indoor channel and to specify a complete model that includesangle of arrival, it is necessary to collect data that includes simultaneous measurements ofboth angle and time, from which their joint statistics can be computed This thesis presentsa data acquisition system that was built for this purpose, as well as a method of processingthe data to retrieve information on time and angle of arrival of multipath signals Datacollected using the system is presented, and a model for angle of arrival is proposed as anextension to the Saleh- Valenzuela model.

previ-1.2 Literature Review

Because of the similarities between the multipath channels in the indoor andurban environments, early research in modeling indoor multipath propagation was basedon previous research involving urban multipath propagation A seminal paper in this area,which has been a foundation for all subsequent research is that by Turin, et al [2] The firststatistical model specifically for the indoor multipath environment was proposed by Salehand Valenzuela [1] Their model, which will be explained in some detail in Chapter 2, isused as a basis for the extended model presented in this paper Other related models havealso been proposed more recently, such as that proposed by Ganesh and Pahlavan [3].

Since the paper by Saleh and Valenzuela, a number of various aspects of the indoorchannel have been addressed Bultitude, et al [4], compare the impulse reponse character-istics of frequency bands centered at 910 MHz and 1.75 GHz Tang and Sobol [5] studiedpropagation in buildings at 2 GHz for use in Personal Communications Services (PCS) Theymade various measurements, verified some models, and studied dynamic effects of movement.In a later paper by Ganesh and Pahlavan [6], variations in the indoor channel were studiedas the transmitter or receiver was moved short distances Todd et al [7] studied the indoorchannel using a multiple antenna system to evaluate antenna diversity performance Rap-paport and Hawbaker [8] compared the path loss and delay spread performance of severaldifferent types of antennas indoors.

Three recent articles survey the existing literature and provide very completereferences for further study of indoor radio propagation The article by Andersen, et al[9], discusses current work being done in modeling both outdoor and indoor propagation.Molkdar’s paper [10] addresses the existing literature specific to the indoor channel, withtables and comparisons of frequencies, etc The most complete survey of research in indoorcommunications is by Hashemi [11].

In most of the research that has been reported up to this point, the angle ofarrival has been addressed very little The first to address it were Lo and Litva [12] Theirvery preliminary findings indicated that multipath arrivals were in fact occuring at varyingangles in the indoor environment However, they were unable to arrive at any conclusionsfrom their limited data, and at this time they have not as yet published any additionalfindings Andersen [9], in his summary of channel models concluded that angle of arrival isan important area for future work.

Recently, a few other researchers have begun to examine the area of angle of arrivalin more detail Guerin [13] used a data acquisition system similar to the one used for thisthesis to collect narrowband angle of arrival data and wideband time of arrival data, but didnot collect any data in which the two were measured simultaneously Wang, et al [14], useda rectangular array to estimate both the elevation and azimuth angles of arrival for majormultipaths, but also did not measure the corresponding time of arrival Litva, et al [15], useda rectangular array to take simultaneous measurements of time and angle of arrival, similarto the format of the data presented here They came to the preliminary conclusion that itis possible to make accurate measurements of the type presented in this thesis, and fromthose measurements learn more about what is happening in the indoor multipath channel.However, their experiment was not extensive to make any conclusions about the channel.

This thesis expands on some of the more recent research The data gatheringapparatus presented here is a relatively simple system which enables accurate detection ofthe time, angle, and amplitude of all major multipath arrivals for a given transmit/receivescenario This system can easily be modified for channel analysis at other frequencies Thedata collected using this system was used to arrive at a statistical channel model based onthe Saleh-Valenzuela model, which was extended to include angle of arrival In addition, newparameters for the time and amplitude of arrival at a frequency of 7 GHz were found for theexisting model proposed by Saleh and Valenzuela, for two buildings of different construction.

reflection from rough surfaces, or a group of small, randomly oriented surfaces Plant foliageis an example of a cause of diffuse multipath This three part model (direct, specular, diffuse)is applicable to most outdoor channels, since the direct path is usually visible, and a singlespecular path is a good approximation even when there are multiple specular paths Thecorresponding simplified system impulse response for such a channel can be expressed as

h(t) = δ(t) + Γ(t)δ(t − ts) + ξ(t)δ(t − td) (1.1)

where the δ(t) term represents the direct path, tsis the specular path time delay, and tdis the diffuse path time delay Γ(t) is the specular path scaling factor, and ξ(t) is thediffuse path scaling factor Both Γ(t) and ξ(t) include the complex reflection coefficient of

the surface, the antenna gain in the direction of the reflected path, and path attenuation.

The time dependence of Γ(t) and ξ(t) is due to the fact that all of these properties, as

well as the location of the reflection point, change as either the transmitter or receiver

moves The amplitude of the diffuse component, ξ(t) is considered to be random When

ts= (2k + 1)π, the direct and specular paths have opposite phases, resulting in destructiveinterference When Γ(t) is large, this interference can cause the amplitude of the received

signal to approach zero, or “fade out” Multipath fading is a significant problem in bothoutdoor and indoor communications, but the indoor problem is very different from typicaloutdoor multipath environments.

In outdoor scenarios such as the one illustrated in figure 1.1, there is generallyone strong specular component In urban environments, and more especially in indoorenvironments, the number of significant specular multipaths increases dramatically Sincemost surfaces of reflection in a building are relatively smooth at the frequencies of interest,and scattered media that produce diffuse reflection are minimal indoors, we will considerdiffuse multipath to be negligible Figure 1.2 shows an example of a transmitter and receiverin neighboring rooms with some of the many possible propagation paths Note that mostof the paths involve propagation through walls, including the direct path As a result, thedirect path is attenuated, making the multipath components closer in amplitude and morelikely to cause destructive interference resulting in severe fades.

In this scenario, as is usually the case indoors, there are a very large number ofpossible multipaths, but obviously after a certain number of reflections and transmissionsthrough walls, the signal is sufficiently attenuated to be considered negligible For such a

Figure 1.1: Example of multipath in an outdoor channel

scenario, the impulse response h(t) can be expressed as an infinite sum:

where βkis the complex amplitude of the kth arrival, and tk is the associated time delay.

Note that βk has no time dependence because there is no moving transmitter or receiver asin figure 1.1.

As can be seen in figure 1.2, multipaths in an indoor environment can comefrom a wide range of different angles This can be an advantage because it allows forinterference rejection or coherent combining using various narrow beam antennas or spatialarray processing.

Conventional beamforming has been used as a means to reduce the effects of bothmultipath and co-channel interference Van Veen and Buckley [16] have written an excellenttutorial, which expands on the basic ideas presented here, and reviews some of the algorithmswhich are commonly used.

The basic principle of beamforming is that by adding the received signal fromseveral antennas with appropriate amplitude scaling and phase shifting, gains in signal powerand reduction in noise and interference power can be achieved This results in higher signalto noise ratios, and interferers can be nulled out A diagram of a 4 element linear array is

shown in figure 1.3 The desired signal arrives from an angle θ The distance d is the element

separation, usually about 1/2 wavelength If some reference point in the wavefront reaches

the first antenna at time t, the same wavefront reference point must travel a distance d sin θto reach the next adjacent antenna The propagation time is (d sin θ)/c, where c is the speed

of propagation Therefore, to maximize the desired signal, the output should be:

y(t) = x0(t) + ej2πd sin θ/cx1(t) + ej4πd sin θ/cx2(t) + ej6πd sin θ/cx3(t) (1.3)This summing of the signal will maximize the received signal power, and at the same timewill likely combine the interfering signal so as to cause destructive interference The receivedsignal to interference ratio after combining is thus increased dramatically.

Generalizing this for an array of n elements, the output of an array y(t) is given

Angle of

Desired Signal

x (t)

where w is the vector of weights, x(t) is the vector of received signals at time t, and wH

represents the Hermetian transpose of w.

Simple phase shifting as explained above gives a beam pattern with a main lobeand side lobes whose magnitude and width are determined by the number of elements andthe overall dimensions of the array In addition to phase shifting, the magnitudes of theweights in w can also be changed with different windowing functions, for example, to alterthe characteristics of this lobe structure.

In addition to simple beamforming, a variety of other algorithms have been oped, including statistically optimum array processing algorithms which take advantage ofany prior knowledge about the signal and its correlation structure when selecting weightingvalues for w These algorithms can effectively null out any undesired signals up to a limit,which is generally determined by the size and number of elements in the array.

devel-It has been shown that multipath interference is an important problem to be

have been presented as a method of combating this multipath interference However, in orderto adequately compare the performance of the available algorithms, information is needed tocharacterize the time delays and angles of arrival of the major multipath components in theindoor channel The angle of arrival has been largely ignored in the existing literature, butangular multipath structure is the focus of this paper due to its importance in evaluatingperformance of multiple antenna systems.

Chapter 2

EXISTING MODEL

Details of the the model proposed in [1] by Saleh and Valenzuela are presentedin this chapter In comparison to other multipath models found in the literature, the Saleh-Valenzuela model most closely reflects the characteristics of the data presented in this thesis,and their method will be extended in Chapter 5 to include the angle of arrival.

The model proposed by Saleh and Valenzuela is based on a clustering phenomenonobserved in their experimental data In all of their observations, the arrivals came in oneor two large groups within a 200 ns observation window It was observed that the secondclusters were attenuated in amplitude, and that rays, or arrivals within a single cluster,also decayed with time Their model proposes that both of these decaying patterns areexponential with time, and are controlled by two time constants: Γ, the cluster arrival decay

time constant, and γ, the ray arrival decay time constant Figure 2.1 illustrates this, showing

the mean envelope of a three cluster channel.

The impulse response of the channel is given by:

h(t) =

with each arrival, where φklis uniform on [0, 2π).

The amplitude of each arrival is given by βkl, which is a Rayleigh distributedrandom variable, whose mean square value is described by the double-exponential decayillustrated in figure 2.1 Mathematically it is given by:

where Λ is the cluster arrival rate, and λ is the ray arrival rate.

In [1], the parameters Γ and γ were estimated by superimposing clusters with

normalized amplitudes and time delays and selecting a mean decay rate The estimated

parameters from their data were Γ = 60 ns and γ = 20 ns.

The Poisson cluster arrival rate parameter, Λ, was estimated by solving for Λ suchthat the probabilities of the total number of clusters per random channel closely matched

the statistics of the observed data This produced an estimate of 1/Λ ≈ 300 ns The ray

arrival rate parameter was guessed at based on the average separation time between arrivals.

In this case the estimate was 1/λ ≈ 5 ns Both of these estimates were very rough, but the

best guesses that could be derived from the data.

In their data, Saleh and Valenzuela did not have any information on angle ofarrival, and therefore concluded that the angles of arrival were uniformly distributed over the

interval [0, 2π) For single antenna systems, time of arrival is generally sufficient information,

and angle of arrival not needed However, as suggested in the introduction to this paper,a need has arisen for a more accurate model as antenna array processors are considered forindoor wireless applications It will be shown later that the angle of arrival is not distributeduniformly, but exhibits some of the same clustering characteristics seen in the time domain.

Other models have been proposed since the Saleh-Valenzuela model Ganesh andPahlavan [3] revised Turin’s model [2] for urban multipath propagation, which is based ona modified Poisson process In this process, the time axis is divided into bins, and theprobability of an arrival in a bin is partially dependent on whether there was an arrival inthe previous bin Their model was used to simulate multipath indoor channels, and comparedelay spreads and received power levels The modified Poisson model fit their experimentaldata more closely than the clustered Poisson model However, the modified Poisson modeldoes not include the clustering effects which are very pronounced in the data presented inChapter 6 Furthermore, the clustered Poisson process is simpler for simulation and analysis.For these reasons, the extended model presented in this paper is based almost entirely onthe clustered Poisson model of Saleh and Valenzuela.

Chapter 3

DATA ACQUISITION SYSTEM

The time-of-arrival model proposed by Saleh and Valenzuela [1] was based ondata that specified arrivals by time only A system could be built that measured receivedpower as a function of angle in a manner similar to the systems used for measuring antennabeam patterns This approach would provide an indication of the statistics of the angle ofarrival, but would yield no information regarding the correlation between time and angle ofarrival In order to get an accurate picture of the time and angle of arrival and how they arecorrelated, it is necessary to measure them both simultaneously A system for doing this isoutlined in the following sections.

One way to measure time and angle of arrival simultaneously, is to keep eithertime or angle constant, while measuring the other, and repeat the procedure for a numberof different angles or times In this case, the easiest scenario would be to look at a narrowrange of angles using an antenna with a narrow angular resolution, measure the time domainimpulse response of the channel, rotate the antenna, and repeat this until the antenna hasrotated an entire 360◦ The most obvious way to measure the impulse response of the channelis to merely send a short pulse at the desired frequency and measure the received power asa function of time However, the problem with this approach is that there must be someabsolute time reference that is constant as the antenna is pointed in different directions.In other words, there must be some synchronization of the entire system The easiest wayto achieve this is to have some wired connection of known length between transmitter andreceiver For indoor measurements the separation of transmitter and receiver is limited,making this a practical option.

The system used for this thesis did not actually transmit a pulse, but simulatedthe impulse response using a chirp Using a chirp as opposed to a pulse achieves essentiallythe same results, but there are some significant advantages, as well as some disadvantagesto the chirp signal A chirp has a higher time-bandwidth product than a CW pulse of the

20 dB Signal Amplifier

MonitorAntenna Positioner

Figure 3.1: The Data Acquisition System

same duration In order to inject sufficient energy into the channel to achieve a high signalto noise ratio, it is essential to have a transmitted signal that has much longer durationthan the desired time resolution This is because practical transmitters have limited peakpower capability, and the 5 ns CW pulse required for direct time-of-arrival measurementswould simply be lost in the noise A much longer chirp signal injects more power, but canbe designed with the same bandwidth as the 5 ns pulse Since time resolution is inverselyproportional to bandwidth (when using the appropriate compression processing), the desiredtime resolution is achieved with a longer (and thus higher energy) signal.

The system used to collect the data presented in this thesis is illustrated in figure3.1 A network analyzer was used as a co-located transmitter and receiver, which sendsthe transmitted signal through coaxial cable to the remote transmit antenna The networkanalyzer, designed to measure transmission and reflection coefficients at its two ports, isconfigured to measure the transmission coefficient from the transmit antenna to the receiveantenna The HP network analyzer which was used makes measurements of the channelfrequency response across a specified range of frequencies It also has the capability of thengenerating a time domain impulse response by calculating an inverse Fourier transform.Because the timing is all done internally to the network analyzer, this method of generating

the impulse response provides a precise and consistent time reference when the antenna ispointed at different angles.

Recent allocations of bandwidth for purposes such as wireless indoor cations have been in the 900 MHz and 2.4 GHz ranges At this time some commerciallyavailable wireless products are available that use primarily the 900 MHz band, and in somecases the 2.4 GHz band Both of these bands, especially the 900 MHz band, have been thesubject of much research in indoor communications, but higher frequencies have had rela-tively little attention This is partly due to the fact that higher frequency bands have notyet been allocated for indoor use However, some recent researchers have begun to examinethe indoor applications of frequencies as high as 60 GHz [14].

communi-Obviously, it would be desirable to use a frequency band already allocated for usein indoor wireless applications, but the main factors influencing the choice of frequency inthis case were availability of hardware, portability of the system, and attenuation within thesystem The first two reasons both dictated a higher frequency Narrow angular resolutioncan be achieved with a smaller antenna at higher frequencies, allowing for more portabil-ity Furthermore, because of budget constraints, the system had to be built primarily withexisting hardware, and in this case, the most readily available equipment was designed forX-Band (8-12 GHz) On the other hand, minimizing attenuation in the system dictated alower frequency because of the significant amount of coaxial cable used in the setup Ul-timately, 6.75 to 7.25 GHz was chosen because it was the lowest possible frequency rangethat would work with the available dish antenna, which was fed by X-Band waveguide witha cutoff frequency of 6.625 GHz.

The choice of a band centered at 7 GHz, although not currently in use for indoorwireless communications, is justified for several reasons A higher frequency reduces thephysical size of antennas, and for array applications, increases the number of antennas thatcan be used in an array of given physical size Higher frequency bands also generally are ableto support higher data rates because of higher available bandwidths The main reason inthe past for keeping frequencies lower is reduced cost of hardware However, it is reasonableto assume that the cost of microwave equipment will decrease in the future, and buildingsystems which use high frequency bands will become more practical Most importantly,

the data acquisition system described in this chapter can be easily converted for use inother frequency bands by replacing the antennas with antennas suitable for the desiredband Furthermore, since data of the type presented in this paper has not previously beencollected, these measurements taken at 7 GHz will provide a general idea of the multipathproperties of a wider band of microwave frequencies for indoor applications.

It is likely that channel parameters will differ for other frequency bands (like the900 MHz and 2.4 GHz bands previously mentioned), but it is reasonable to assume that thegeneral multipath structure (i.e clustering patterns, statistical distributions) will be similar.For example, a channel from point A to point B such as the one shown in figure 1.2 willhave a certain impulse response with respect to time and angle at a given frequency Ata lower frequency, the transmission and reflection characteristics of the walls and objectswill be different, likely altering the amplitude characteristics of the channel However thetemporal and angular characteristics will remain unchanged As will be discussed later, theSaleh-Valenzuela model (generated from 1.5 GHz data) generated a reasonable fit to the 7GHz data presented here As a result, it can be assumed that the model presented hereshould apply to lower frequency bands, although the parameters may differ somewhat.

The antenna used for the data acquisition system is a dish antenna with a diameterof 60 cm At a frequency of 7 GHz, the antenna has a 3 dB beam width of about 6◦ (in boththe horizontal and vertical directions), and a null to null beam width of roughly 10◦ Thisprovides a very narrow angular resolution, but also presents another problem: it does notallow arrivals with a vertical angular spread component.

Since the data being collected is with respect to horizontal angle only, it wouldbe desirable for the receiving antenna to have a wide beam width in the vertical direction,so as to include all arrivals with any vertical component at a given horizontal angle Thiswould allow for reflections off floor and ceiling to be included, as well as reflections offwalls and other objects This would also be more representative of the beam pattern of anarray of vertical monopoles, a likely scenario for an indoor wireless communication system.As illustrated in 3.2, the circular dish provides a relatively narrow beam pattern, causingrejection of arrivals with any significant vertical component.

Horizontal Arrival

Arrival with Vertical Component

Main Lobe of Beam

Figure 3.2: Antenna Vertical Component Rejection

angle (degrees)

angle (degrees)

Figure 3.3: Data Collected with Original Antenna (left), and with Modified Antenna (right)In order to compare the data collected with the dish antenna with data that in-cluded more vertical components, the antenna was temporarily modified to widen its verticalbeam pattern The antenna was masked with microwave absorbent material so that its ef-fective physical shape was nearly rectangular This resulted in a vertical 3 dB beam width ofabout 30◦ and null to null beam width of nearly 60◦ Using the modified antenna, a numberof the sets of data were repeated A comparison of one of the data sets taken with bothantennas is shown in figure 3.3.

Comparing these two data sets, it is obvious that, while the relative amplitude ofsome of the arrivals has changed, most of the main arrivals are present in both experiments,and most importantly, the general structure of the clustering is unchanged For purposesof generating a statistical model, it appears that the statistics of the data have not beenappreciably affected As a result, all of the data presented in this thesis was collected with

the original, unmodified antenna Since masking the antenna caused gain losses of about5 dB, using the unmodified antenna provides measurements with a better overall signal tonoise ratio (somewhat evident in figure 3.3).

It is assumed that the indoor multipath channel is dominated by specular path This assumption is supported by the data, in that multipath arrivals appear highlylocalized in time and angle The arrivals due to multipath can be assumed to be reflectionsfrom walls, large furniture, and smaller objects which are highly conductive Diffuse multi-path in an outdoor environment is generally due to reflective surfaces that are not smooth,such as foliage Man-made objects, which comprise almost wholly the indoor environment,tend to be smooth, especially at microwave frequencies Diffuse multipath may exist indoors,but it is assumed that its presence is negligible in the data presented here.

multi-Because the multipath channel is assumed to be entirely specular, the image plotssuch as the one shown in figure 4.1 can be modeled as a collection of point sources blurredby a point spread function and corrupted by additive noise This assumption reduces theproblem of identifying exact time and angle of arrival to a simplified deconvolution, whichwould normally be very difficult in the diffuse source (or scattering) case.

The impulse response, or point spread function from an image processing point ofview, is shown in 4.2 This impulse response was generated by setting up the data acquisitionsystem in a line of sight environment with a high signal to noise ratio and no reflections inthe vicinity of the direct path Along the angular axis, the main lobe and side lobes of theantenna are visible, and along the time axis, the effects of windowing and pulse shaping intime can be seen In reality, there are side lobes in time, but the temporal side lobes aresmaller than the angular side lobes, and therefore not visible in the plot Because the pointspread function is known, this deconvolution problem lends itself very well to the CLEANalgorithm [17] The CLEAN algorithm was originally used for processing of astronomical

angle (degrees)

Figure 4.1: Raw Data Set

images, which are also often modeled as groups of point sources convolved with a blurringfunction The algorithm is essentially a recursive subtraction of the point spread functionfrom the image, with the point spread function positioned to correspond with the maximumvalue of the image The highest peak is found, its amplitude, time, and angle are stored, anda scaled copy of the impulse response is subtracted from the image This process is repeatedon the residual image until a predetermined threshold (usually corresponding to the noiselevel) is reached.

One problem faced in the processing of the data presented here is that since actualarrivals do not happen at discrete intervals, it is nearly impossible to perfectly line up theimpulse response with a peak in the image Even slight misalignment can lead to artifacts, orpoints that were taken as arrivals where there obviously weren’t any Furthermore, aroundvery strong arrivals, such as those in the middle of figure 4.1, the surrounding areas tendedto be significantly stronger than the noise floor This combined with point spread function(PSF) model error in the side lobes caused many points in those areas to be interpreted asarrivals Other sources of false detections may include volume reverberation or multiplicativenoise in the system.

To combat this problem, a scheme known as constant false alarm rate detection

angle (degrees)

delay (ns)

Figure 4.2: Impulse response of the data acquisition system

was used The noise floor threshold was adjusted at each point based on the average powerof the surrounding samples within a certain window This greatly reduced the number offalse arrivals that were detected, but did not eliminate all In this case the only other optionswere to go to more complex algorithms that would still not be perfect, or to pick out all ofthe major arrivals by manually looking at the image, which was not practical The CLEANalgorithm with constant false alarm level detection proved to be the simplest and overallmost reliable means of accurately identifying the time and angle of the major multipaths.

Once the arrivals were identified, an image plot of the processed data looks likefigure 4.3 This is the processed version of the raw data shown in figure 4.1 The next task isto identify clustering If the clustering effects found in [1] are present in the data, a channelmodel should include clustering In order to analyze the statistics of the clustering effects,the clusters in each data set must be identified.

Early analysis of the data showed clustering effects in both time and angle Theseclusters were obvious to the observer in most cases Some experimentation was done withcomputer algorithms for automatic cluster identification, but eventually it was decided thatthe overall amount of data was small enough that the clusters could just as easily and

angle (degrees)

Figure 4.3: The data set shown in figure 4.1 after processing

accurately be picked by hand This was done by a computer program that showed the imagegraphically and allowed the user to identify clusters using graphical input With the times,angles, and amplitudes of all major arrivals identified, as well as their clustering patterns,the data could be used to analyze the statistics and arrive at a model.

The time and amplitude of arrival portion of the combined model is represented

by h(t) in equation (2.1), where, as before, β2

klis the mean square value of the kth arrivalof the lth cluster This mean square value is described by the exponential decay given in

equation (2.3) and illustrated in figure 2.1.

As before, the ray arrival time within a cluster is given by the Poisson distribution

of equation (2.5), and the first arrival of each cluster is given by Tl, described by the Poisson

distribution of (2.4) The inter-ray arrival times, τkl, are dependent on the time of the

first arrival in the cluster Tl In the Saleh-Valenzuela model, the first cluster time T1 was

dependent on T0 which was assumed to be zero With the estimated parameter in [1] of

1/Λ ≈ 300 ns, the first arrival time will typically be in the range of 200 to 300 ns, which

is a reasonable figure However, a problem with this was found when the Λ parameter inthe new data was discovered to be very low, for reasons which will be discussed later Thismakes any long delays which would occur at larger separation distances between transmitter

and receiver highly improbable To remedy this problem, it is proposed that T0 be the lineof sight propagation time:

T0 = r

where c is the speed of light, and r is the separation distance This allows for the time of

the first arrival to be more directly dependent on the separation distance.

5.2 Correlation of Time and Angle

One of the most important reasons for collecting data with simultaneous mation on time and angle of arrival is to learn something about the correlation between thetwo The most desirable scenario, for the sake of simplicity, is for the two to be completelystatistically independent However, since we do not know whether this is a valid assumption,it is necessary to examine the correlation structure between time and angle, in order to eitherconclude that time and angle are independent, or to learn what the interdependence is.

infor-Correlation histograms were created in order to examine this characteristic in thearrival data Figure 5.1 is an example of such a histogram The picture contains a point for

every ∆t and ∆θ observed in the data set Note that the ∆t and ∆θ values are displayed

as absolute values (no negative times or angles) In this case there is a noticeable clustering

effect, with 3 well pronounced clusters There is an evident pattern in that most values of ∆θwere close to 0, 80 or 150 degrees The distribution of arrival differences (∆t) within a given

angular cluster appears quite invariant across the clusters This correlation structure shows adominant horizontal and vertically oriented banding effect which is characteristic of separablecorrelation functions [18] Separable correlation functions correspond to independent first

and second moment statistics between the horizontal (∆θ) and vertical (∆t) random variable

indices This supports an assumption of statistical independence between angle and time ofarrival.

This particular example was quite representative Most data collected showeda similar structure, with two or more clusters separated in angle, but with the averagerelative time delay being fairly constant Although this issue should probably be exploredin greater detail, the evidence we have presented will be deemed sufficient to proceed withthe simplifying assumption that there is no angle-time dependence.

The lack of correlation between time and angle has another consequence The

complete impulse response with respect to both time and angle, which we will call h(t, θ),

becomes a separable function

As a result, the functions h(t) and h(θ) can be discussed separately It is assumed that h(t)

is modeled by the Saleh-Valenzuela model outlined in Chapter 2, and therefore this chapter

deals with modeling h(θ).

|delta theta| (degrees)

Figure 5.1: Example of a correlation histogram

Since we are assuming that time and angle are statistically independent, we pose an independent angular impulse response of the system similar to the time impulseresponse of the channel given in 2.1:

pro-h(θ) =

βklδ(θ − Θl− ωkl), (5.3)

where, as before, βklis the ray amplitude for the kth arrival in the lth cluster, given in

equations (2.2) and (2.3) Θlis the mean angle of each cluster, which is distributed uniformly

on the interval [0, 2π) We propose that the ray angle within a cluster, ωkl, be modeled as a

zero mean Laplacian distribution with standard deviation σ:

5.4 Parameter Estimation

This section outlines methods of deriving the distributions and estimating the

parameter σ given in the previous section The distribution parameters of the cluster means,

Θl, is found by identifying each of the clusters in a given data set The mean angle of arrivalfor each cluster is calculated In order to remove the specific room geometry and orientation,the first arrival (in time) for each data set is taken as the reference The relative clustermeans are calculated by subtracting the mean of the reference cluster from all other clustermeans To estimate the distribution of cluster means over the ensemble of all data sets, ahistogram can be generated of all relative cluster means, disregarding the first clusters (sincetheir relative mean is always 0).

The procedure to estimate σ is similar The cluster mean is subtracted from the

absolute angle of each ray in the cluster to give a relative arrival angle with respect to thecluster mean The relative arrivals are collected over the ensemble of all data sets, and ahistogram can be generated Using a least mean square algorithm, the histogram is fit to the

closest Laplacian distribution, which gives the value for σ The results of these proceduresand the value of σ for the Clyde Building and Crabtree Building data are presented in

Chapter 6.

The extended model for h(t, θ) is useful for analysis or simulation of array

pro-cessing algorithms that might be used in an indoor environment In order, for example, toconduct a Monte Carlo simulation of an array antenna processor, it is necessary to generatea random channel using the statistical model This section outlines the procedure for doingso.

The first step is to choose the transmitter/receiver separation distance r, whichcan be chosen either randomly or arbitrarily Knowing r, the next step is to determine

β2(0, 0), the mean power of the first arrival, which is given by

where G(1m) is the channel gain at r = 1 meter, and α is a channel loss parameter γ and

θ are respectively the ray decay parameter and ray arrival rate in the model for h(t) In

general, assuming spherical spreading, G(r) is given by

Gtand Grare the antenna gains for the transmitter and receiver, and λ0 is the RF

wave-length Equation (5.5) is derived and the characteristics of α in the indoor environment are

discussed in greater detail in [1].

After β2(0, 0) is determined, the next step is to determine the cluster and array

arrival times The corresponding distributions are given in equations (2.4) and (2.5), where

T0 = r/c After the times are determined, the mean amplitudes βkl are determined by

equation 2.3 The actual amplitudes for each arrival, βkl, are determined by sampling a

Rayleigh distribution whose mean is βkl.

The angles are determined by first randomly choosing the cluster angles, which

are uniformly distributed from 0 to 2π Relative ray angles are then determined by sampling

a Laplacian distribution as given in equation (5.4).

The electrical phase associated with each arrival is assumed to be uniformly tributed and independent of all other variables Phase values can therefore be easily gen-erated in addition to the time and angle, if needed for a specific simulation application.Clusters and arrivals should continue to be generated until the amplitudes begin to fallbelow a predetermined threshold, or the specified channel noise floor The noise floor is

dis-dependent on the transmitter gain Gt, and the separation distance r, but may be influenced

by other factors in the indoor multipath environment, which have not been addressed here.Figure 5.2 shows a simulated channel response presented in the form of the datacollected by the data acquisition system Using the model, a random channel was generatedand the antenna beam pattern and noise were added to facilitate comparison with the originaldata.

angle (degrees)

Figure 5.2: Simulated Channel Response

Chapter 6RESULTS

This chapter presents the data collected using the data collection apparatus plained in Chapter 3 Data was collected in two different buildings, which had significantdifferences in their construction Although there are other building types that were notinvestigated, the two buildings studied are representative of the steel and concrete framebuildings which are very common in institutional and commercial settings In all of the datacollected, the transmitter and receiver had some kind of wall between them, and in mostcases they were in different rooms Separation distances ranged from approximately 20 feetto 100 feet Most doors in both buildings were wood, and were closed for all measurements.The following sections discuss general trends observed in the data, and the model parametersderived from the data for the two buildings.

This section outlines some of the general patterns and characteristics observed inthe data collected in the two buildings A total of 55 data sets were recorded on the fourthfloor of the Clyde Building (CB) on the Brigham Young University campus, and another 10data sets were collected in the Crabtree Building, a newer building also located on the BYUcampus The Clyde Building is constructed mostly of reinforced concrete and cinder block,with all internal walls being constructed of cinder block The building Saleh and Valenzuelaused for their measurements is similar to the Clyde Building in construction The CrabtreeBuilding is constructed with steel girders, and internal walls are gypsum board over a steelframe The next two sections discuss the model parameters estimated from the experimentaldata for each building More detailed information about the locations for collecting data,along with building maps, isincluded in Appendix B.

A clustering pattern in angle was immediately visible in the processed data images.Generally there were at least two or three clusters, except in rare cases with long propagationdistances and consequently low signal to noise ratios There were some extreme cases of morethan five clusters, especially in the Crabtree Building data In the Crabtree Building the

In both buildings, the line of sight path was generally observable in the data, butits attenuation was dependent on the number and type of walls between the transmitter andreceiver In the Crabtree Building, the line of sight through walls was stronger than in theClyde Building However, in the Clyde Building, in cases where there was only a single wallseparating the transmitter and receiver, the line of sight was generally the strongest arrival.

even with the doors closed Almost all strong clusters had corresponding strong back wallreflections offset by approximately 180◦, but this varied slightly with the geometry of thespecific situation.

In most respects, the data collected in the two buildings did not differ greatly.Both data sets exhibited similar clustering structures, as well as a decay over time of theamplitudes of the clusters and the rays within clusters The most pronounced difference wasa much slower decay rate in the Crabtree Building data, which produced a correspondingincrease in total number of arrivals, and a slight increase in the number of clusters Thenext two sections present the specific model parameter estimates for the Clyde and CrabtreeBuildings, respectively.

The cluster and ray decay time constants, Γ and γ, were estimated in the same

way that they were estimated in [1] The first cluster arrival in each set was normalizedto an amplitude of 1 and a time delay of 0 All arrivals were superimposed and plottedon a semilogarithmic plot as shown in figure 6.2 The estimate for Γ was found by curvefitting the line (representing an exponential curve) such that the mean squared error wasminimized For the Clyde Building data the mean squared error was 2.99, and Γ was foundto be 33.6, slightly more than half the figure found by Saleh and Valenzuela, who estimated60 for their data.

It is immediately noticeable that the fit in figure 6.2 is less than ideal This case

is worse than the other Γ and γ estimates, but shows a trend observed in all of the data In

their data, Saleh and Valenzuela did not have as accurate information about the specific timeand amplitude of arrival As a result, they made rough estimates for their decay parametersand did not attempt to generate a plot like figure 6.2 However, in their case, as well as inthis data, there is a definite trend of decay over time, which is most easily modeled by anexponential decay It will also be shown that an increase in the number of samples tendedto reduce the mean squared error, so that the poor fit in this first example may in fact bepartly due to the smaller number of samples than in other cases.

Figure 6.3 shows the estimate for γ using the same method The first arrival in

each cluster was set to a time of zero and amplitude of one, and all other arrivals were thenadjusted accordingly and superimposed In this case the number of samples was so large that

relative delay (ns)

Figure 6.2: Plot of normalized cluster amplitude vs relative delay for the Clyde Building,

with the curve for Γ = 33.6 ns superimposed.

the points on the graph would obscure the graph if all were present, so in the pictured graph,each plotted point represents the average of 5 points The superimposed curve represents

γ = 28.6 ns, which is quite close to the figure of 30 ns found by Saleh and Valenzuela The

mean squared error in this case was 1.59.

The rate of arrival parameters from the data were easily estimated, because ofthe fact that the precise time of arrival was known for each ray and cluster To estimate Λ,the cluster arrival rate, the first arrival in each cluster was considered to be the beginningof the cluster, regardless of whether or not it had the largest amplitude The arrival time ofeach cluster was subtracted from its successor, so that the conditional probability distribution

given in (2.4) could be estimated Estimates for Λ and λ were both done by fitting the sample

probability density function to the corresponding probablity for each bin The fitting wasdone using a least mean square criterion Figure 6.4 shows this cumulative density functionon a log scale and the closest fit This data does not include the first arrival in each data

set, for reasons which will be discussed in the next section In this case 1/Λ = 16.8 ns The

possible reasons for the large discrepancy between this estimate and the estimate of 300 nsgiven in [1] will also be discussed at the end of this chapter.

The second Poisson parameter, λ, representing the ray arrival rate, was estimated

relative delay (ns)

Figure 6.3: Plot of normalized ray amplitude vs relative delay for the Clyde Building, with

the curve for γ = 28.6 ns superimposed.

Figure 6.4: CDF of Relative Cluster Arrival Times for the Clyde Building (1/Λ = 16.8 ns)

Figure 6.5: CDF of Relative Arrival Times Within Clusters in the Clyde Building (1/λ =5.1ns)

in a similar fashion Each time of arrival was subtracted from the previous one to produce a

set of conditional arrival times p(τkl|τ(k−1)l) The probability distribution of these with the

best fitting pdf is shown in figure 6.5 In this case, 1/λ = 5.2 ns.

Figure 6.6 shows a CDF of the relative cluster angles Each plotted arrival angleis relative to the absolute angle of the first arrival in the data set The distribution looksvery uniform, with one exception There is a break between 50◦ and 310◦ (about 50◦ on eachside of zero), where there are very few arrivals The explanation for this is quite simple If acluster arrived at such a small angular separation, it would likely be counted as part of thestronger of the two clusters in almost any clustering algorithm Therefore, the conclusionthat the cluster mean angles are distributed uniformly over all angles is supported by thedata.

The distribution of the ray arrivals with respect to the cluster mean is shown infigure 6.7 The characteristic sharp peak of a Laplacian distribution is immediately obvious.The superimposed curve is a Laplacian distribution that was fit by integrating a LaplacianPDF over each bin, and matching the curves using a least mean square goodness of fitmeasure The Laplacian distribution turns out to be a very close fit In this case the angular

variance σ is 25.5◦ To examine the curve fit more closely, a log CDF of the absolute value of