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

73 509 0
Modeling the Statistical Time and Angle of Arrival Characteristics of an Indoor Multipath Channel

Đang tải... (xem toàn văn)

Tài liệu hạn chế xem trước, để xem đầy đủ mời bạn chọn Tải xuống

Thông tin tài liệu

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 Quentin H Spencer A Thesis Presented to The Department of Electrical and Computer Engineering Brigham Young University Provo, Utah, USA Committee Members: Brian D Jeffs, chair Michael D Rice Michael A Jensen November 22, 1996 Abstract Most previously proposed statistical models for the indoor multipath channel include only time of arrival characteristics However, in order to use statistical models in simulating or analyzing the performance of array processing or diversity combining, it also necessary 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 angle of arrival data at GHz Data processing methods are outlined, and results of data taken in two different buildings are presented Based on the results, a model is proposed that employs the clustered “double Poisson” time of arrival model proposed by Saleh and Valenzuela [1] The observed angular distribution is also clustered, with uniformly distributed clusters, and arrivals within clusters that have a Laplacian distribution Chapter INTRODUCTION Radio has recently become an increasingly viable option for indoor communications applications The availability of higher frequency bands in the 900 MHz and 2.4 GHz range has made wireless an attractive option for high bandwidth digital communications applications such as local area networks Wireless networks can be particularly advantageous for applications which require portability, or where installation of wiring is undesirable or impractical Multipath interference, or interference due to the reception of multiple copies of a signal 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 UHF and microwave frequencies, the presence of walls and large objects in rooms makes the indoor multipath environment quite different from most outdoor scenarios As a result, the study of indoor propagation characteristics has become an area of increased study In order to analyze or simulate the performance of a communications system, some kind of model for the channel is needed One of the first statistical models for the indoor multipath channel was proposed by Saleh and Valenzuela [1] Their data showed multipath arrivals which were grouped in clusters over time The relative delay between clusters was represented by a Poisson distribution, and the separation between elements within clusters was modeled by a second Poisson distribution with a different delay parameter There have been many different approaches to overcoming the problem of multipath interference, both in outdoor and indoor applications Some of them include channel equalization, directional antennas, and multiple antenna systems Each of these tends to be more particularly suited to different applications This thesis will focus on multiple antenna systems The signals from different antennas can be combined in various ways, including diversity combining, phased array processing, and adaptive array algorithms Adaptive array sytems are becoming increasingly feasible for high bandwidth applications with continuing improvements in digital signal processors The indoor multipath propagation model presented in this thesis is intended as a tool to evaluate performance of these various multiple antenna systems 1.1 Problem Statement Because array processing exploits the angular diversity of incoming signals, a channel model should include information about the angle of multipath arrivals in order to evaluate the performance of an array processing system The lack of angular dependence is a weakness of the Saleh-Valenzuela model Their model specifies amplitude and time of each arrival, but makes no assumptions regarding the angular distribution of arrivals Saleh and Valenzuela, as well as others who have studied the characteristics of indoor multipath propagation, have not addressed the area of angle of arrival for two reasons Measuring angle of arrival simultaneously with time of arrival is much more complex than simply measuring the time domain impulse response Secondly, for applications using only single antenna systems, the angle of arrival is often irrelevant However, applications now being considered which perform spatial processing by using multiple antennas call for a more realistic representation of the angle of arrival The possibility that clustering occurs in angle as well as time seems probable as one considers the physical mechanisms which may create clustering Suppose a signal is transmitted in a building and the received signal contains two clusters The strongest arrival in each cluster would represent a major path to the receiver, either by line of sight, or with very few reflections Subsequent arrivals within each cluster would likely follow similar paths, but may be delayed in time and reduced in amplitude by reflecting off of more nearby objects en route Because they followed a similar path, there is a high likelihood that the arrivals are close in angle Generalizing this line of reasoning, it follows that clustering in time is likely associated with some kind of clustering in angle The nature of the angular clustering of indoor multipath arrivals has not previously been studied, nor has the correlation, if any, between time and angle of arrival In order to learn more about the indoor channel and to specify a complete model that includes angle of arrival, it is necessary to collect data that includes simultaneous measurements of both angle and time, from which their joint statistics can be computed This thesis presents a data acquisition system that was built for this purpose, as well as a method of processing the data to retrieve information on time and angle of arrival of multipath signals Data collected using the system is presented, and a model for angle of arrival is proposed as an extension to the Saleh- Valenzuela model 1.2 Literature Review Because of the similarities between the multipath channels in the indoor and urban environments, early research in modeling indoor multipath propagation was based on 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 first statistical model specifically for the indoor multipath environment was proposed by Saleh and Valenzuela [1] Their model, which will be explained in some detail in Chapter 2, is used as a basis for the extended model presented in this paper Other related models have also 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 indoor channel have been addressed Bultitude, et al [4], compare the impulse reponse characteristics of frequency bands centered at 910 MHz and 1.75 GHz Tang and Sobol [5] studied propagation in buildings at GHz for use in Personal Communications Services (PCS) They made 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 studied as the transmitter or receiver was moved short distances Todd et al [7] studied the indoor channel using a multiple antenna system to evaluate antenna diversity performance Rappaport and Hawbaker [8] compared the path loss and delay spread performance of several different types of antennas indoors Three recent articles survey the existing literature and provide very complete references 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, with tables and comparisons of frequencies, etc The most complete survey of research in indoor communications is by Hashemi [11] In most of the research that has been reported up to this point, the angle of arrival has been addressed very little The first to address it were Lo and Litva [12] Their very preliminary findings indicated that multipath arrivals were in fact occuring at varying angles in the indoor environment However, they were unable to arrive at any conclusions from their limited data, and at this time they have not as yet published any additional findings Andersen [9], in his summary of channel models concluded that angle of arrival is an important area for future work Recently, a few other researchers have begun to examine the area of angle of arrival in more detail Guerin [13] used a data acquisition system similar to the one used for this thesis to collect narrowband angle of arrival data and wideband time of arrival data, but did not collect any data in which the two were measured simultaneously Wang, et al [14], used a rectangular array to estimate both the elevation and azimuth angles of arrival for major multipaths, but also did not measure the corresponding time of arrival Litva, et al [15], used a rectangular array to take simultaneous measurements of time and angle of arrival, similar to the format of the data presented here They came to the preliminary conclusion that it is possible to make accurate measurements of the type presented in this thesis, and from those 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 1.3 Contributions This thesis expands on some of the more recent research The data gathering apparatus presented here is a relatively simple system which enables accurate detection of the time, angle, and amplitude of all major multipath arrivals for a given transmit/receive scenario This system can easily be modified for channel analysis at other frequencies The data collected using this system was used to arrive at a statistical channel model based on the Saleh-Valenzuela model, which was extended to include angle of arrival In addition, new parameters for the time and amplitude of arrival at a frequency of GHz were found for the existing model proposed by Saleh and Valenzuela, for two buildings of different construction 1.4 Tutorial This section provides an introduction to the concepts of multipath interference and beamforming, which are used throughout this paper 1.4.1 Multipath Interference Multipath interference is the interference of a reflected signal with the direct path transmitted signal or another reflected signal An illustration of a communication channel with multipath is shown in figure 1.1 The direct path, specular multipath component, and diffuse multipath component are shown The specular component is generally due to reflection from a smooth or nearly smooth surface, while the diffuse component is due to reflection from rough surfaces, or a group of small, randomly oriented surfaces Plant foliage is 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 single specular path is a good approximation even when there are multiple specular paths The corresponding 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, ts is the specular path time delay, and td is the diffuse path time delay Γ(t) is the specular path scaling factor, and ξ(t) is the diffuse 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 destructive interference 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 both outdoor and indoor communications, but the indoor problem is very different from typical outdoor multipath environments In outdoor scenarios such as the one illustrated in figure 1.1, there is generally one strong specular component In urban environments, and more especially in indoor environments, the number of significant specular multipaths increases dramatically Since most 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 consider diffuse multipath to be negligible Figure 1.2 shows an example of a transmitter and receiver in neighboring rooms with some of the many possible propagation paths Note that most of the paths involve propagation through walls, including the direct path As a result, the direct path is attenuated, making the multipath components closer in amplitude and more likely to cause destructive interference resulting in severe fades In this scenario, as is usually the case indoors, there are a very large number of possible multipaths, but obviously after a certain number of reflections and transmissions through walls, the signal is sufficiently attenuated to be considered negligible For such a Figure 1.1: Example of multipath in an outdoor channel Hallway Transmitter Receiver Room A Room B Figure 1.2: Example of multipath in an indoor channel scenario, the impulse response h(t) can be expressed as an infinite sum: ∞ h(t) = βk δ(t − tk ) (1.2) k=0 where βk is 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 as in figure 1.1 As can be seen in figure 1.2, multipaths in an indoor environment can come from a wide range of different angles This can be an advantage because it allows for interference rejection or coherent combining using various narrow beam antennas or spatial array processing 1.4.2 Beamforming Conventional beamforming has been used as a means to reduce the effects of both multipath and co-channel interference Van Veen and Buckley [16] have written an excellent tutorial, which expands on the basic ideas presented here, and reviews some of the algorithms which are commonly used The basic principle of beamforming is that by adding the received signal from several antennas with appropriate amplitude scaling and phase shifting, gains in signal power and reduction in noise and interference power can be achieved This results in higher signal to noise ratios, and interferers can be nulled out A diagram of a 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 θ to 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/c x1 (t) + ej4πd sin θ/c x2 (t) + ej6πd sin θ/c x3 (t) (1.3) This summing of the signal will maximize the received signal power, and at the same time will likely combine the interfering signal so as to cause destructive interference The received signal 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 Desired Signal θ Interfering Signal Angle of Incidence d x (t) x (t) x (t) x (t) Antennas Figure 1.3: Illustration of a element linear antenna array with two received signals by: n wk xk (t) y(t) = (1.4) k=1 where wk is a “weight” which has a magnitude and phase component, and xk (t) is the received signal at the kth element This is often epressed in vector notation: y(t) = wH x(t) (1.5) 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 lobe and side lobes whose magnitude and width are determined by the number of elements and the overall dimensions of the array In addition to phase shifting, the magnitudes of the weights in w can also be changed with different windowing functions, for example, to alter the characteristics of this lobe structure In addition to simple beamforming, a variety of other algorithms have been developed, including statistically optimum array processing algorithms which take advantage of any prior knowledge about the signal and its correlation structure when selecting weighting values 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 It has been shown that multipath interference is an important problem to be addressed in the indoor environment Beamforming and other multiple antenna schemes Table B.1: Table of Data Transmit and Receive Locations File Name 00001 00002 00003 00004 00005 00006 00007 00008 00009 00010 00011 00012 00013 00014 00015 00016 00017 00018 00019 00020 Transmit Room # X 498 12 498 12 498 12 498 12 498 12 498 12 498 12 498 12 498 12 498 12 498 12 498 12 498 12 498 12 498 12 498 12 400 12 400 12 400 12 400 12 Y 10 10 10 10 10 10 10 10 29 29 29 29 29 29 29 29 8 8 Receive Room # X 495 495 495 495 495 14 495 14 495 13 495 495 495 13 495 495 495 495 495 14 495 14 495 14 495 14 495 495 58 Y 11 16 16 16 11 4 4 11 16 16 16 11 11 16 16 16 Date (all 1996) June June June June June June June June June June June June June June June June June June June June Table B.2: Continuation of Table B.1 File Transmit Name Room # X 00021 400 12 00022 400 12 00023 400 12 00024 400 12 00025 400 20 00026 400 20 00027 400 20 00028 400 20 00029 400 20 00030 400 20 00031 495 10 00032 495 10 00033 495 10 00034 495 10 00035 495 10 00036 495 10 00037 495 10 00038 495 10 00039 495 10 00040 495 10 00041 495 10 00042 494 11 00043 494 11 00044 494 11 00045 494 11 00046 494 11 00047 494 11 00048 494 11 00049 494 11 00050 494 11 00051 457 00052 445 00053 459 20 00054 440 00055 433 15 Receive Y Room # X 495 495 495 495 13 10 496 10 496 10 496 16 10 496 16 10 496 13 10 496 11 496 11 496 13 11 490 24 11 490 17 11 490 11 490 25 11 490 17 11 490 11 490 25 11 490 17 11 490 22 490 24 22 490 17 22 490 22 490 25 22 490 17 22 490 22 490 25 22 490 17 22 490 452 452 5 452 452 10 452 59 Date Y (all 1996) 11 June June June June 35 July 22 July 34 July 24 July July July June 11 June 11 22 July 22 July 22 July 14 July 14 July 14 July July July July 22 June 13 22 June 13 22 June 13 14 June 13 14 June 13 14 June 13 June 13 June 13 June 13 July July July July July Figure B.3: Map of the 4th floor of the Crabtree Building Table B.3: Data Gathered in the Crabtree Building (CTB) File Transmit Name Room # X Y 00056 415 50 00057 415 50 00058 450 100 00059 450 100 00060 250 30 10 00061 250 30 10 00062 250 25 30 00063 250 25 30 00064 Lobby A 15 35 00065 Lobby B 20 15 Receive Room # X 450 450 25 450 25 450 240 240 15 240 15 240 240 240 60 Date Y (all 1996) July 31 15 July 31 15 July 31 July 31 August 25 August 25 August August August August Appendix C PLOTS This chapter contains image plots of all the raw data sets The reference number is given at the top of each plot For tables of locations for each data set number, refer to Appendix B 61 00001 00002 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00003 300 350 250 300 350 250 300 350 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 250 00004 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00005 150 200 angle (degrees) 00006 20 20 40 40 60 60 80 80 delay (ns) delay (ns) 150 200 angle (degrees) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 350 200 50 Figure C.1: Plots 1-6 62 100 150 200 angle (degrees) 00007 00008 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00009 300 350 250 300 350 250 300 350 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 250 00010 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00011 150 200 angle (degrees) 00012 20 20 40 40 60 60 80 80 delay (ns) delay (ns) 150 200 angle (degrees) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 350 200 50 Figure C.2: Plots 7-12 63 100 150 200 angle (degrees) 00013 00014 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00015 300 350 250 300 350 250 300 350 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 250 00016 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00017 150 200 angle (degrees) 00018 20 20 40 40 60 60 80 80 delay (ns) delay (ns) 150 200 angle (degrees) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 350 200 50 Figure C.3: Plots 13-18 64 100 150 200 angle (degrees) 00019 00020 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00021 300 350 250 300 350 250 300 350 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 250 00022 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00023 150 200 angle (degrees) 00024 20 20 40 40 60 60 80 80 delay (ns) delay (ns) 150 200 angle (degrees) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 350 200 50 Figure C.4: Plots 19-24 65 100 150 200 angle (degrees) 00025 00026 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00027 300 350 250 300 350 250 300 350 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 250 00028 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00029 150 200 angle (degrees) 00030 20 20 40 40 60 60 80 80 delay (ns) delay (ns) 150 200 angle (degrees) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 350 200 50 Figure C.5: Plots 25-30 66 100 150 200 angle (degrees) 00031 00032 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00033 300 350 250 300 350 250 300 350 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 250 00034 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00035 150 200 angle (degrees) 00036 20 20 40 40 60 60 80 80 delay (ns) delay (ns) 150 200 angle (degrees) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 350 200 50 Figure C.6: Plots 31-36 67 100 150 200 angle (degrees) 00037 00038 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00039 300 350 250 300 350 250 300 350 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 250 00040 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00041 150 200 angle (degrees) 00042 20 20 40 40 60 60 80 80 delay (ns) delay (ns) 150 200 angle (degrees) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 350 200 50 Figure C.7: Plots 37-42 68 100 150 200 angle (degrees) 00043 00044 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00045 300 350 250 300 350 250 300 350 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 250 00046 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00047 150 200 angle (degrees) 00048 20 20 40 40 60 60 80 80 delay (ns) delay (ns) 150 200 angle (degrees) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 350 200 50 Figure C.8: Plots 43-48 69 100 150 200 angle (degrees) 00049 00050 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00051 300 350 250 300 350 250 300 350 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 250 00052 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00053 150 200 angle (degrees) 00054 20 20 40 40 60 60 80 80 delay (ns) delay (ns) 150 200 angle (degrees) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 350 200 50 Figure C.9: Plots 49-54 70 100 150 200 angle (degrees) 00055 00056 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00057 300 350 250 300 350 250 300 350 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 250 00058 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 00059 150 200 angle (degrees) 00060 20 20 40 40 60 60 80 80 delay (ns) delay (ns) 150 200 angle (degrees) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 350 200 50 Figure C.10: Plots 55-60 71 100 150 200 angle (degrees) 00061 00062 20 40 40 60 60 80 80 delay (ns) 20 delay (ns) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 150 200 angle (degrees) 00063 300 350 250 300 350 00064 20 20 40 40 60 60 80 80 delay (ns) 100 100 120 120 140 140 160 160 180 180 200 50 100 150 200 angle (degrees) 250 300 200 350 50 100 150 200 angle (degrees) 250 300 350 00065 20 40 60 80 delay (ns) delay (ns) 250 100 120 140 160 180 200 50 100 150 200 angle (degrees) Figure C.11: Plots 61-65 72 ... the performance of the available algorithms, information is needed to characterize the time delays and angles of arrival of the major multipath components in the indoor channel The angle of arrival. .. indication of the statistics of the angle of arrival, but would yield no information regarding the correlation between time and angle of arrival In order to get an accurate picture of the time and angle. .. arrival times of clusters and the arrival times of rays within clusters The time of arrival of each cluster is an exponentially distributed random variable conditioned on the time of arrival of the

Ngày đăng: 20/11/2012, 11:32

Từ khóa liên quan

Tài liệu cùng người dùng

  • Đang cập nhật ...

Tài liệu liên quan