WCDMA Radio Channel Classification

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(1)2007:013 CIV. MASTER'S THESIS. WCDMA Radio Channel Classification. Markus Andersson. Luleå University of Technology MSc Programmes in Engineering Media Technology Department of Computer Science and Electrical Engineering Division of Signal Processing 2007:013 CIV - ISSN: 1402-1617 - ISRN: LTU-EX--07/013--SE.

(2) WCDMA Radio Channel Classification Markus Andersson, Me January 19, 2007.

(3) Abstract When studying channel properties in cellular networks two key parameters are the delay spread and the type of fading. The delay spread holds information about the time dispersion the channel induces, whereas the effect the channel has on the power of propagating waves is reflected in the fading. Line-of-sight communications results in Rician fading whereas non-line-ofsight means Rayleigh fading. Measurements and classification of channel environments have, to the writer’s knowledge, so far only been done with the use of complex sounding devices. In this work, channel classification is performed using low-level data from a regular cell phone. Measurements were performed with a real cell phone in a controlled milieu where different radio environments were emulated. With the use of channel estimates from the cell phone, probability density function parameter estimations were performed with both maximum likelihood and method of moments techniques. The Rician K-factor, which expresses the ratio of line-of-sight components to scattered waves, was calculated with the results from the estimation. The K-factor calculations showed, as expected, obvious differences between various simulated environments. The K-factor increases with stronger line-of-sight component, which is in line with theory. For weak direct waves, the estimate often becomes zero which is due to the difficulty of detecting a weak direct wave in lots of scattered waves. To achieve better results, other estimation techniques might therefore be necessary. For repeated measurements with the same settings the variance of the K-factor estimates is quite high. Also, the variance increases with stronger direct wave. This might be due to additive noise during measurement. The mean of the K-factor estimates seems to be 3dB higher than expected. This offset is possibly due to the difference in the noise power between complex and real noise, which is exactly 3dB, or internal differences in the power level of the channel simulator. The reason for the difference is not clear but power measurements confirms it. With compensation for this, the calculated K-factors aligns much better to the expected K-factors. Although they are not exactly the same, they are so close that with further studies, classification of radio channels with the use of cell phone channel estimates should be possible..

(4) Preface This report is the result of a master thesis study carried out at Ericsson Research in Lule˚ a, Sweden. It has evolved from an idea of radio channel classification with the use of low-level cell phone data. As the writer, I would like to thank all of you that have supported me during this project. First of all Kjell Larsson at Ericsson Research for being my supervisor, Sven-Olof Jonsson, also at Ericsson Research, for giving me this opportunity. Anders Hedlund, Ericsson Skellefte˚ a, which have been more than helpful with his low-level coding. James LeBlanc and Magnus Lundberg at Lule˚ a University of Technology which have been extremely patient and answered at lot of questions. Also, thanks to all the coworkers at Ericsson Research that have helped me in troubled times..

(5) CONTENTS. CONTENTS. Contents 1 Background. 3. 2 Introduction 2.1 Wired networks . . . . . . . . . . 2.2 Cellular networks . . . . . . . . . 2.3 Impulse response and convolution 2.4 WCDMA basics . . . . . . . . . . 2.4.1 Radio access technologies 2.4.2 Direct sequence spreading 2.4.3 Rake receiver . . . . . . . 2.4.4 Physical channels . . . . . 2.4.5 Power control . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. 4 4 4 5 6 6 7 7 7 8. 3 Theory 3.1 Propagation of radio waves . . . . . . . . . . . 3.2 Delay . . . . . . . . . . . . . . . . . . . . . . . 3.3 Fading . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Frequency selective and flat fading . . . 3.3.2 Fast and slow fading . . . . . . . . . . . 3.4 Probability density function . . . . . . . . . . . 3.4.1 Rayleigh distribution . . . . . . . . . . . 3.4.2 Rician distribution . . . . . . . . . . . . 3.5 Channel types . . . . . . . . . . . . . . . . . . . 3.5.1 Typical urban . . . . . . . . . . . . . . . 3.5.2 Rural area . . . . . . . . . . . . . . . . . 3.5.3 Hilly terrain . . . . . . . . . . . . . . . . 3.6 Cell phone channel estimator and sample data 3.7 Parameter estimation . . . . . . . . . . . . . . 3.7.1 Method of moments . . . . . . . . . . . 3.7.2 Maximum likelihood estimation . . . . . 3.7.3 Cramér-Rao lower bound . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. 9 9 9 11 11 12 13 13 14 16 16 17 18 19 20 20 21 23. . . . .. 24 24 24 25 25. 4 Method 4.1 Simulating . . . 4.2 Measuring . . . 4.3 Post-processing 4.4 Estimating . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . . . . . . .. . . . .. . . . . . . . . .. . . . .. . . . . . . . . .. . . . .. . . . . . . . . .. . . . .. . . . . . . . . .. . . . .. . . . . . . . . .. . . . .. . . . . . . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 5 Results 26 5.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.3 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . 29. 1.

(6) CONTENTS. 5.4 5.5. CONTENTS. Modified K-factor estimates . . . . . . . . . . . . . . . . . . . Proposed presentation of results . . . . . . . . . . . . . . . . .. 33 35. 6 Discussion 36 6.1 Measurement difficulties . . . . . . . . . . . . . . . . . . . . . 36 6.2 Cell phone limitations . . . . . . . . . . . . . . . . . . . . . . 36 7 Conclusions. 37. 8 Further studies. 38. 2.

(7) 1. 1. BACKGROUND. Background. Cellular networks, such as GSM and 3G, are today available all over the world. Properly set, these networks have the capability of providing high performance wireless connectivity. To achieve that; planning, tuning, optimization and troubleshooting are done by the mobile operators. For the latter tasks, they use field test tools which are built for maintenance of wireless networks. An example of such tools is TEMS Investigation. In mobile networks, the radio channel characteristics differ depending on location of base stations and handheld devices, movement of the latter and also obstacles in the surrounding. Urban and rural areas will not have the same channel characteristics; neither will two different places within a building. Different channels could affect the performance for the end user. Therefore, information and knowledge about the radio channel characteristics would be very helpful and make it possible to better understand and troubleshoot new 3G services. The purpose of this project was to investigate if it is possible to characterize and classify different radio channels based on measurements from a modified cell phone. If possible and implemented in TEMS, such classification would give important information to the user regarding the radio channel properties. Information about how the cell phone perceives the channel could be useful during field tests. Areas in an environment can be tested to see if the radio channel characteristics in fact is what one expects them to be. Such information could also be useful as input during cell planning.. 3.

(8) 2. 2. INTRODUCTION. 2. Introduction. Communication systems in general, whether they are mobile or not, consist of at least one transmitter and one receiver. The path between these two, usually named channel, is the medium used for the transport of signals. The choice of medium to use, differs in various networks.. 3. 5. 6. 8. 9. 0. #. 2.1. Wired networks. In fixed systems, e.g. land line phones and computer networks, copper wires or fiber optic cables are often used as channels. As the purpose of transmission systems is to move information it is desirable that the received data is the same as the transmitted. In a perfect system, the channel would only transport the signal with no modifications, but in real world applications this is not the case. Every signal sent through a channel is to some extent distorted. The amount of channel induced distortion is highly dependent on the channel itself and techniques for undoing this distortion must be implemented in every communication system. Luckily, when it comes to channels like copper wires and fiber optic cables both have one important property which is invariance. Except for small changes in the properties of the copper due to, for example, temperature variations, the copper wire is regarded as an invariant medium. Hence, every signal sent through one copper wire will experience the same channel and be affected in the same way. Therefore, mitigation of the channel distortion is quite easy. Unfortunately, it is not as easy in cellular communication.. 2.2. Cellular networks. Figure 1: Example of wireless channels. One of the biggest differences between fixed and mobile networks is the channel itself. Instead of electrons moving in copper cables, mobile networks make use of electromagnetic waves which propagate in air, see Fig. 1 for a simple example of two mobile channels. The entire environment between transmitter and receiver is the channel and herein lays also the difficulty. All objects that make up the channel are not stationary. Cars and buses move, people are walking and trees are swaying in the wind. Besides, in a 4.

(9) 2. INTRODUCTION. 2.3. Impulse response and convolution. cellular network, transmitter and receiver are not usually on fixed locations, e.g. a person using a cell phone is not always sitting completely still. All this means that the transmission channel is variant, i.e. it changes in time. One signal sent through a mobile network at two different time instances will not experience the same channel. Remediation of the channel effects caused by a variant channel requires other methods than those for invariant channels.. 2.3. Impulse response and convolution. The distortion that different channels cause is highly correlated with their unique physical characteristics. Mathematically these properties are contained in the channel’s impulse response, IR. This is a time representation of the channel’s output, or response, when the input is an impulse. Herein lays a lot of information. The impulse response describes how the channel amplifies, attenuates and modifies the amplitude and phase of the input signal and also how the channel disperses the signal in time. x(t). y(t) = x(t)∗h(t). h(t). Figure 2: Block diagram of a transmission system. Transmission systems in time invariant channels are often described as in Fig. 2. The transmitted signal x(t) is being sent through a channel with IR h(t). This will result in the received signal y(t). If the input signal and the IR is known, the output of the system can be calculated as y(t) = x(t) ∗ h(t) where ∗ denotes convolution1 . In the one sided continuous time case it is defined according to Eq. 1. x(t) ∗ h(t) =. Z ∞. x(τ )h(t − τ )dτ. (1). 0. As the process of convolution may be invertible, this means that in transmission systems with known IRs, the sent signal can often be calculated from the received one. For this to work with wireless channels, which are time-variant, IR estimation has to be performed regularly. With the use of predetermined code sequences, so called pilot symbols, an estimate of the IR can be calculated. This, so called channel estimate, can then be used to counteract the channel induced distortion.. 1. For detailed information about convolution see [11] on page: 84-92. 5.

(10) 2. INTRODUCTION. 2.4. 2.4. WCDMA basics. WCDMA basics. Implementation of communication systems can be done in a number of ways. Regardless technique, optimization of performance and efficient use of the limited bandwidth is of great importance. The available bandwidth must be shared between multiple users and how to share it differs between various types of radio access technologies. 2.4.1. Radio access technologies. FDMA, Frequency Division Multiple Access, allows a portion of the total bandwidth to be used by each user during the entire transmission, see left part of Fig. 3. This technique is easy to implement, does not introduce ISI2 and makes synchronization easy. The drawbacks are that one must use a static spectrum allocation and frequency reuse is difficult. Also, users are assigned a part of the spectrum even if they don’t need it at all times. Another technique is TDMA, Time Division Multiple Access, seen in the middle of Fig. 3. Here each user is given a part of, or the entire bandwidth, for a short period of time. This means the users take turns using the channel. This gives an increase in capacity but requires at the same time, strict synchronization. The GSM system makes use of a combination of FDMA and TDMA. Users are assigned a part of the spectrum for a short time but the spectrum for each user can change between transmissions. This is knows as frequency hopping. TDMA. Time. Time. CDMA. Frequency. Frequency. Frequency. FDMA. Time. Figure 3: Radio access technologies Since the available bandwidth is constricted it is therefore very expensive and efficient use of the spectrum is of great importance. This, together with the demand for higher bitrates for new services, led to the use of CDMA, Code Division Multiple Access. CDMA is an old military technique, used among other things in the Global Positioning System, GPS. It makes use of spreading codes which make it possible to allow all users to communicate on all frequencies at all times, right part of Fig. 3. With the right codes the receiver can extract the sent signal belonging to a certain user. This 2. Inter-symbol interference. 6.

(11) 2. INTRODUCTION. 2.4. WCDMA basics. technique makes higher transfer rates possible and allows for more users than FDMA and TDMA. CDMA2000 and Wideband-CDMA, are radio access techniques that use CDMA technology. The difference between them is the width of the spectrum. WCDMA uses a 5 MHz wide signal whereas CDMA2000 uses 1.25MHz. A wider spectrum gives the advantage of even higher bit rates and is more robust against fading. 2.4.2. Direct sequence spreading. In WCDMA, simultaneous transmission for users is possible due to the utilization of direct sequence spreading codes. These codes are pseudo-random noise codes with a much higher rate than the information signal. Multiplication with these codes results in a spread spectrum signal which for WCDMA is 5 MHz wide. The rate of the resulting signal is referred to as chip rate rather than bit rate and the chip rate in WCDMA is 3.84 Mcps3 . Since each user has a unique code, separation between users is possible. After transmission through the channel, de-spreading is performed with the same code that was used in the spreading and the sent data is retained. More information about spreading and de-spreading can be found in [6] on page 27-30. 2.4.3. Rake receiver. The spread transmitted signals will, due to reasons explained in Chapter 3.1, be dispersed in time. The signals will arrive at the receiver after propagation on multiple paths. There the signal parts will add up either constructively or destructively, which means that the received energy will be changing in time. The Rake receiver, which is used in WCDMA, assigns one Rake finger at the delay positions that have significant energy. The channel estimate is then used to remove or at least reduce the channel induced distortion. Each finger will then contain a ”part” of the sent and time dispersed signal. The final step is to combine these parts of signal energy to maximize the useful energy. This is done with something called maximum ratio combining, see [6] on page 30-33. The steps that are performed in the Rake receiver are more or less like those in a matched filter. 2.4.4. Physical channels. The transmission of data between the base station, BS, and the user equipment, UE, is done on a number of different channels. These are not to be mistaken for the physical channel itself, i.e. the environment where the radio waves propagate. Some channels are for transport of actual data and 3. Mega chips per second. 7.

(12) 2. INTRODUCTION. 2.4. WCDMA basics. some are only needed for controlling the transmission system. An example of the latter is the Common PIlot CHannel, CPICH, which only sends pilot symbols for use in the channel estimate procedure, see Chapter 3.6. This channel is used by all users in the cell. As the purpose of the CPICH channel is to gain knowledge about how the radio channel affects the transmitted signals, there are no quality controls such as power control on the CPICH. Other channels like the Dedicated Physical CHannel, DPCH which is used for transmitting user data, must retain a constant quality. Measures that strive to counteract the channel induced distortion are therefore necessary and each user makes use of their own power controlled dedicated physical channel. 2.4.5. Power control. On the up link, i.e. communication from the UE to the BS, the goal with the power control is for the BS to receive equal signal quality from each user, regardless of the distance. If a user close to the BS transmits with too high power, signals from users transmitting at a greater distance might be overshadowed. The WCDMA BSs utilize a power control that measures the received signal quality, commands an increase or decrease in power from the UE, and does this 1500 times per second. As this is faster than any significant change in path loss, the signal quality can be controlled. From the UE point of view, i.e. the down link, the power control follows commands that the UE sends. If there is need for more power, e.g. at the edge of a cell, the UE demands it.. 8.

(13) 3. THEORY. 3 3.1. Theory Propagation of radio waves. Transmitted electromagnetic waves that propagate in air behave like waves in water in that they can change direction, are stopped etc. depending on which type of obstacle they encounter. There are three basic mechanisms that have impact on the propagation, i.e. reflection, diffraction, and scattering [13]. When radio waves impinge something that has a smooth surface and is very large compared to the wavelength of the wave itself, they are reflected. If the radio path is obstructed with a large dense object between the transmitter and the receiver, secondary waves can be formed after the object. This is named diffraction or shadowing since the waves actually can reach a receiver even though the line-of-sight propagation path is shadowed. With some obstacles, radio waves can also propagate through them, though this results in attenuation. Scattering is when radio waves hit obstacles with small dimensions or larger objects with a rough surface. If the dimension of the obstacle is in the order of one wavelength or less, the signal will be scattered in all directions.. 3.2. Delay Power Delay Profile. −85. RMS Delay spread Received Power [dB]. −90. Mean excess delay. −95. Maximum excess delay < 10 dB. −100. Noise threshold −105 0. 100. 200 300 Excess Delay [ns]. 400. 500. Figure 4: Power delay profile. Reflection, diffraction and scattering of electromagnetic waves will lead to a multipath propagation of the sent signal, i.e. each sent signal will be split in numerous rays that all travel on their own path to the receiver. Since these paths will have unequal distances, the received signal will be dispersed in time. A signal sent from a transceiver at some time instance will start 9.

(14) 3. THEORY. 3.2. Delay. to arrive at the receiver at time t0 . From that point on, the received energy will be the sum of all incoming rays as a function of the excess time τ . The amount of time dispersion that the channel induces affects the time it takes before the received energy fades away. The power delay profile in Fig. 4 shows an example of this. From this profile it is possible to calculate time dispersion measures such as mean excess delay and root mean square (RMS) delay spread. Mean excess delay is a measurement of the extra delay that the channel introduces after the first part of the signal arrives at t0 . RMS is the standard deviation of the delayed reflections, weighted by their respective energy. Both mean excess delay and delay spread differs widely between channel types which makes them important channel characteristics. Fig. 4 also show the maximum excess delay which is where the signal level has dropped 10 or 20 dB from the maximum received level. Basically, this is the time it takes to receive the ”whole” signal. There is also a noise threshold under which everything that is received is seen as noise. Power Delay Profile. 5. Mean excess delay: 2.81 µs Delay spread: 6.83 µs. 0 Received Power [dB]. −5 −10 −15 −20 −25 −30 −35 −40 −5. 0. 5. 10. 15 20 25 τ − Excess Delay [µs]. 30. 35. 40. 45. Figure 5: Discrete Power delay profile. Fig. 5 show a Power delay profile in the discrete case. Here calculation of mean excess delay, denoted τ¯ and root mean square (RMS) delay spread, denoted στ can be done according to Eq. 2, Eq. 3 and Eq. 4 where ak is the amplitude, P (τk ) the power and τk the time index. P P 2 P (τk )τk k ak τk τ¯ = P = Pk 2 k. τ¯2 =. ak. k. P (τk ). P P 2 2 2 k ak τk k P (τk )τk P P = 2 k. ak. στ =. k. q. τ¯2 − (¯ τ 2). 10. P (τk ). (2) (3) (4).

(15) 3. THEORY. 3.3. 3.3. Fading. Fading. The power delay profile shows how the received energy varies in time. This effect, caused by multipath propagation, is called fading. The instantaneous received power is the sum of many rays arriving with different amplitude and phase. Hence, a moving antenna will experience a strong signal where the superposition of the rays is constructive and, unfortunately, a very weak signal if it is destructive. This abrupt loss of signal strength, which can be as much as 30 dB, will unless mitigated, result in high bit error rate over the channel. The cause of these deep fades is actually very small position changes, those in the order of one wavelength. Changes in position will cause both time dispersion of the signal and time variance of the channel. Each resulting in two types of so called small-scale fading. Time dispersion of the signal leads to frequency selective or flat fading whereas time variance results in fast or slow fading. Besides this small-scale fading, motion over large areas results in largescale fading. This is an attenuation of the signal power as a function of distance. Hence, the instantaneous power is the combination of small-scale fading superimposed on large-scale fading. Though, it is the small-scale fading that causes the most severe problems. The sections below, which discuss various types of fading, talk about transmission of symbols. In WCDMA transmission of data is done in chips but the theory of fading applies to both. 3.3.1. Frequency selective and flat fading. Performance degradation due to time dispersion of the signal can be divided in two categories, frequency selective fading or flat fading. Both are dependent on the relationship between, Ts , the symbol time and Tm , the maximum excess delay. Ts is the time duration for each sent symbol and Tm is the maximum excess delay. Channels with Tm > Ts , will spread the symbols in time so that they interfere with each other, causing inter-symbol interference, ISI. Such a channel will be experiencing so called frequency selective fading. The opposite, with Tm < Ts , will result in flat fading. Frequency selective fading will cause serious performance degradation so mitigation is necessary [14]. Another way of looking at the degradation due to time dispersion is in the frequency domain. This gives a better understanding for the name frequency selective fading. In the frequency domain, the term coherence bandwidth, f0 , is used to denote the range of frequencies over which a channel affects passing signals with equal gain and linear phase. The coherence bandwidth is approximately the inverse of the maximum excess delay. This means that a channel will exhibit frequency selective fading if f0 < 1/Ts , i.e. all. 11.

(16) 3. THEORY. 3.3. Fading. the spectral components of the signal are not affected equally since the bandwidth of the signal is greater than the coherence bandwidth. Hence, to avoid ISI the channel must be flat fading with f0 > 1/Ts . 3.3.2. Fast and slow fading. Just like time dispersion reflects in two types of fading, so does the time variance of the channel. Movement of either the user equipment or objects in the propagation path will result in changes in the impulse response. In the time domain the coherence time, T0 , is the time over which the channel’s impulse response to a large extent is invariant. This means that channels with T0 < Ts will be fast fading since the channel’s response will be changing during the transmission of one symbol. Degradation caused by fast fading is very severe and can result in irreducible error rates [13]. If the channel state is invariant over the transmission time for one symbol, i.e. T0 > Ts , the channel will instead be slow fading. In the frequency domain the time variations of the channel will lead to a spectral broadening of the signal [13]. A channel with low coherence time is changing at a high rate. To understand the impact these changes have on the signal it is often useful to draw a parallel to the effect of signal keying. An infinitely long sinusoid at a certain frequency is in the frequency domain characterized by an impulse. As soon as this sinusoid is limited in time, e.g. switched on and off as in keying, a spectral broadening will occur. The rapid changes in the channel’s impulse response can, in some sense, be seen as keying and thus resulting in a spread of the signal. This effect is named Doppler spread or fading rate, and is approximately equal to the inverse of the coherence time fd ≈ 1/T0 . Hence, if the symbol rate, 1/Ts < fd the channel will change quicker than the symbols are sent, which will lead to fast fading. To avoid the problems with frequency selective and fast fading the signaling rate must be contained within the coherence bandwidth, f0 , and the Doppler spread. Too high symbol rate will introduce frequency selective fading since the coherence bandwidth will be smaller than the signal spectrum. A rate that is too low will result in fast fading since the channel’s response will change during the transmission of one symbol. Detailed information about fading can be found in [13] and mitigation techniques for the problems described above are discussed in [14].. 12.

(17) 3. THEORY. 3.4. 3.4. Probability density function. Probability density function. Multipath propagation, time dispersion and the type of fading one will experience highly depends on the physical properties of the channel. Densely built areas with a large amount of buildings, lampposts, street signs, etc., will produce a lot of scattered waves. The time dispersion in an environment like this is most certainly not minute. Neither is it likely that this environment allows for a line-of-sight, LOS, communication between transmitter and receiver. At least not with roof top mounted BSs. On the other hand, sparsely built cities and rural areas induce less scattering and line-of-sight communication is often possible. As the received signal consists of a mixture of delayed, reflected, and scattered waves, the physical differences in the radio channel will reflect in the amount of each type of wave the received signal contains. These variations will affect the statistics of the fading. 3.4.1. Rayleigh distribution. In 1889, John William Strutt the 3rd Baron Rayleigh, published the Rayleigh model [12]. This model assumes that a received multipath signal can be considered consisting of a large number of waves, possibly infinitely many, with independent and identically distributed, i.i.d., in-phase and quadrature components. The central limit theorem supports, that with sufficiently many arriving waves the IQ components will follow a Gaussian distribution as illustrated in Fig. 6(a). Amplitude PDF 0.6. 2 Density. Quadrature. In−phase and Quadrature−phase components 4. 0 −2 −4 −6. −4. −2. 0 2 In−phase. 4. 0.4 0.2 0. 6. 0. (a) Scattered waves.. 1. 2 3 Amplitude. 4. 5. (b) Amplitude PDF.. Figure 6: Scattered waves in IQ representation together with the amplitude PDF. If z = x + iy, where x and y are i.i.d. Gaussian with zero mean and variance σ 2 , the probability density function, PDF, for the amplitude, |z|, can be derived as in [9]. The result . x f (x|σ) = 2 exp σ 13. −. x2 2σ 2. . (5).

(18) 3. THEORY. 3.4. Probability density function. is the Rayleigh distribution and has the characteristic form displayed in Fig. 6(b). It has been shown that this model is in fact suitable for describing fading in areas with lots of scattered waves, such as densely built cities [4]. The σ in Eq. 5 is a function variable and is the standard deviation from the one dimensional Gaussian distribution. 3.4.2. Rician distribution. Radio waves propagating in sparsely built cities or rural areas are, just like those in densely areas, scattered and reflected. The big difference is that usually a line-of-sight, LOS, wave reach the receiver. Since this wave often is strong compared to the scattered waves, the PDF of the amplitude will change. The scattered waves will no longer have zero mean. This is displayed in 7(a). Amplitude PDF. In−phase and Quadrature−phase components 0.4 Density. Quadrature. 5 0. 0.3 0.2 0.1. −5 −5. 0 In−phase. 0. 5. 2. 4. 6. 8. Amplitude. (a) Scattered waves with LOS.. (b) Amplitude PDF with LOS.. Figure 7: Scattered waves in IQ representation with a LOS component together with the amplitude PDF. Due to this shift in mean, the amplitude PDF will change form, see 7(b). This new form is the Rician distribution defined as . x f (x|s, σ) = 2 exp σ. −. (x2 +s2 ) 2σ 2. . . I0. xs σ2. . x>0. (6). where the non-centrality parameter s ≥ 0 and the scale parameter σ > 0. As in the Rayleigh PDF, the function parameter σ is the local standard deviation of the one dimensional Gaussian distribution. I0 is the zero-order modified Bessel function of the first kind. The Rician K-factor which is defined as s2 K= 2 (7) 2σ expresses the ratio of dominant component to the scattered waves. In fact, as K → ∞ the Rician PDF → Gaussian and as K → 0 the Rician PDF → Rayleigh. That is, the stronger the line-of-sight component is, the greater will the shift of mean be for the scattered waves. Such a shift will make 14.

(19) 3. THEORY. 3.4. Probability density function. the Rician distribution approach Gaussian distribution. As the direct wave weakens the shift of mean will approach zero and the Rician PDF becomes Rayleigh. The representation in Fig. 7(a) is only valid in the stationary case. When there is relative movement between the transmitter and receiver the Doppler effect becomes an issue. This will lead to a phase shift in the received components, which results in a ”rotating” cloud in the IQ-plane, see Fig 8(a). However, the amplitude PDF will still be Rician as in Fig 8(b). In−phase and Quadrature−phase components. Amplitude PDF 0.4 Density. Quadrature. 5 0. 0.3 0.2 0.1. −5 −5. (a) Scattered Doppler.. 0 In−phase. waves. with. 0. 5. 2. 4. 6. 8. Amplitude. LOS. and (b) Amplitude PDF with LOS and Doppler.. Figure 8: Scattered waves in IQ representation with a LOS component together with the amplitude PDF, both with Doppler.. 15.

(20) 3. THEORY. 3.5. 3.5. Channel types. Channel types. The physics of multipath radio wave propagation makes the number of channels in mobile communication almost infinite. To be able to do simulations and calculations in 3G-networks, standardization organizations, such as ITU4 and 3GPP5 , have decided upon a few channel types to describe the most usual channel environments. Each channel model has its own characteristics regarding fading and delay. All data describing these channel models are available in [1]. The mean excess delay and the delay spread have been calculated with Eq. 2, 3 and 4. There are more channel models than the below mentioned but these are some of the most widely used. Also, observe the different scales on the x-axis. 3.5.1. Typical urban. In densely built cities the received signal usually consists of the sum of reflected, scattered and diffracted waves with no line-of-sight component. The radio channel will then be best described with the ”typical urban” model. The mean excess delay is moderate since the multipath propagation leads to some time dispersion of the signal. The delay spread is also noticeable. Since there is no line-of-sight component, this means that all channel taps will be Rayleigh distributed. Fig. 9 shows the impulse response for this channel model. Typical Urban Channel Model. 0. Filter taps Mean excess delay: 0.50 µs Delay spread: 0.50 µs. Average Relative Power [dB]. −5 −10 −15 −20 −25 −30 −35 −40. 0. 0.5. 1 Time Index [µs]. 1.5. 2. Figure 9: Impulse response for Typical Urban Channel Model. 4 5. International Telecommunication Union 3rd Generation Partnership Program. 16.

(21) 3. THEORY. 3.5. Rural Area Channel Model. 0. Filter taps Mean excess delay: 0.09 µs Delay spread: 0.10 µs. −5 Average Relative Power [dB]. Channel types. −10 −15 −20 −25 −30 −35 −40. 0. 0.1. 0.2. 0.3 Time Index [µs]. 0.4. 0.5. 0.6. Figure 10: Impulse response for Rural Area Channel Model. Hilly Terrain Channel Model. 0. Filter taps Mean excess delay: 0.89 µs Delay spread: 3.04 µs. Average Relative Power [dB]. −5 −10 −15 −20 −25 −30 −35 −40. −2. 0. 2. 4. 6. 8 10 Time Index [µs]. 12. 14. 16. 18. Figure 11: Impulse response for Hilly Terrain Channel Model. 3.5.2. Rural area. On the country-side there are usually less buildings that interfere with the propagation of radio waves. Therefore a dominant line-of-sight component will reach the receiver together with multipath reflections. The direct path between transceiver and receiver is always the shortest. Hence, the amplitude of the first channel tap in the Rural Area channel model will be Rician distributed. Since the traveled lengths of the multipath waves do not differ as much as they do in urban environments they arrive with relatively small delay. This, together with the dominant line-of-sight component, leads to small excess delay and delay spread. The channel model’s impulse response. 17.

(22) 3. THEORY. 3.5. Channel types. is depicted in Fig. 10. 3.5.3. Hilly terrain. Areas with large hills or mountains experience some reflected waves arriving very late. This leads to a high mean excess delay and, most significant, a very high delay spread. Large objects in the propagation path means no line-of-sight propagation, which equals Rayleigh fading channel taps. Fig. 11 shows the impulse response for this model.. 18.

(23) 3. THEORY. 3.6. 3.6. Cell phone channel estimator and sample data. Cell phone channel estimator and sample data. To mitigate the effects caused by multipath fading, cellular networks use pilot symbols to estimate the channel impulse response. These are known reference symbols that are transmitted through the channels. The purpose is to gain knowledge about the channel induced distortion that the transmitted data have been subjected to. With the use of pilot symbols, comparisons can be made between the received symbols and reference symbols. With some calculations a description of how the channel affects transmitted data is received in form of impulse response estimates. The estimates can then be used to counteract most of the channel distortion. The technique used for this and for calculating the estimates can differ between various mobile platforms and various receiver types, but the purpose is the same. In WCDMA, pilot symbols are sent primarily on two different channels. These are the CPICH and DPCH. The CPICH carries only pilot symbols whereas on the DPCH, pilot symbols are being transmitted interleaved between data and other signaling bits. The symbols from the channels are used during different parts of the estimation procedure, such as amplitude and phase estimation. The mobile hardware is, with special firmware, capable of delivering data from internal routines such as the channel estimation. Together with a computer with logging capabilities, i.e. the right software, the following log points and many others can be recorded: • DPCH symbols — The DPCH symbols as they arrive to the user after passing the channel. • CPICH symbols — The CPICH symbols as they arrive to the user after passing the channel. • FD — Finger delay, time between fingers in the Rake receiver. • AGC — In and output value of the Automatic Gain Control. All of these log points are directly related to the physical properties of the channel. The finger delay measurements should be possible to use together with the amplitude of the channel estimates to calculate the time delay and delay spread properties of the channel. To analyze the fading, other tools must be used.. 19.

(24) 3. THEORY. 3.7. 3.7. Parameter estimation. Parameter estimation. The cell phone channel estimator outputs are all samples from the calculated impulse response. As the probability density function (PDF) differs between various channel types, PDF parameter estimation could give important information about the experienced channel. Estimation can be done with numerous techniques. One way is to use the, in statistics well known, Kolmogorov-Smirnov test, [8], [3]. Though, it is more a goodness-of-fit technique than an actual estimation technique. Other alternatives for finding the parameter estimates are method of moments, [7], [2] and maximum likelihood estimation, [17], [16], [15], [10] and [7]. Method of moments make use of the moments of the PDF which often give simple expressions for the sought parameters. In maximum likelihood estimation the likelihood function of observing the given data set is maximized. 3.7.1. Method of moments. The method of moments estimator has the advantage of being easy to find and simple to implement. The disadvantage is that is has no optimality properties. Though, as long as the data set is large enough it is still useful since it is most often consistent.6 Its simplicity also gives the advantage of low calculation speed. As the name implies, this technique is based on the moments of a PDF. It is often possible to use the moments to set up equations and from these derive expressions for estimators to the function parameters in terms of moments. The theoretical moments can then be changed to the sample moments that gives the estimate. The general expression for the nth moment for the Rician PDF is given in [15] as n. 2 n/2. E[X ] = (2σ ). n Γ 1+ 2 . ". 1 F1. n s2 − ; 1; − 2 2 2σ. #. (8). where Γ is the gamma function and 1 F1 is a confluent hyper geometric function. Luckily, when n is even, the moments become simple polynomials in s and σ, e.g. E[X 2 ] = s2 + 2σ 2 4. 4. 2 2. E[X ] = s + 8s σ + 8σ. (9) 4. (10). Derivation of the estimators for s and σ in terms of E[X 2 ] and E[X 4 ] can be done using only Eq. 9 and Eq. 10 as follows 2 E 2 [X 2 ] = 2(s2 + 2σ 2 )2 = 2s4 + 8s2 σ 2 + 8σ 4 6. See [7] on page: 289-304. 20.

(25) 3. THEORY. 3.7. Parameter estimation. = E[X 4 ] + s4 ⇒ s4 = 2 E 2 [X 2 ] − E[X 4 ] =⇒ s =. q 4. 2 E[X 2 ]2 − E[X 4 ],. σ=. q. (11). (E[X 2 ] − s2 )/2. There are also other method of moments estimators that make use of lower order moments, such as the first and second moment that was used in [17]. Estimators based on lower order moments usually give better results but are not as easy to find as the estimators that are based on moments which are simple polynomials. 3.7.2. Maximum likelihood estimation. The most popular practical estimator is based on the maximum likelihood principle. It can be implemented even for complicated estimation problems and for large enough data sets it minimizes the variance of the estimation error to levels which makes its performance optimal7 The main idea with this estimation technique is to find the value of the unknown distribution parameter(s) that most likely have produced the observed data [10]. To solve this problem one has to maximize the joint density for the given data set. If we define the likelihood function as L(σ|x) = f (x|σ), where f (x|σ) is the PDF for the distribution we seek parameters to, this function represents the likelihood of the parameter σ given sample data x. Finding the global maximum of this function, something usually done by derivation, will give us the most likely distribution parameter. In the case with Rician distributed data the maximum likelihood estimators can be derived as described in [17]. Start with the Rician PDF, defined in Eq. 6. Let (x1 , x2 , . . . , xN ) be independent samples drawn from a Rician distribution with unknown parameters s and σ. Then the joint density for this outcome of N samples can be expressed as: J. = f (x1 ) . . . f (xN ) (x1 . . . xN ) −(x21 + . . . + x2N + N s2 ) exp = σ 2N 2σ 2 x1 s xN s . . . I0 ∗ I0 σ2 σ2. !. (12). Finding the parameters that are most likely for the given set of samples is done by finding the maximum of this likelihood function. To make the calculations easier we take the natural logarithm of J and get N N X N s2 X x2i xi s − + ln J = ln(xi ) − 2N ln σ − ln I0 2 2 2σ 2σ σ2 i=1 i=1 i=1 N X. 7. . See [7] on page: 157-199. 21. . . (13).

(26) 3. THEORY. 3.7. Parameter estimation. Log−likelihood surface for Rician distribution over s and σ 2. −2016 Rician σ−parameter. 2.05. −2018 2.1. −2020 2.15. −2022 2.2. −2024 2.25. −2026 2.3 3.1. 3.15. 3.2. 3.25 3.3 3.35 Rician s−parameter. 3.4. 3.45. 3.5. Figure 12: Log-likelihood surface for different combinations of s and σ. which is the log-likelihood function. To find the maxima of this function we have to solve the system in Eq. 14 while ensuring that the solution is a maximum, e.g. with the second derivative test.8 ∂ ln J = 0 ∂σ. ∂ ln J = 0, ∂s. (14). Since the expression for the Rician PDF is quite complicated no closed form solution exists [17], [15] and [2]. Finding the solution of the resulting nonlinear equation is usually done using numerical processes. Although the maximum likelihood estimate is difficult to find, Eq. 13 together with Eq. 14 lead to: N X ˆ 2 ] = s2 + 2σ 2 = 1 E[X (15) x2 N i=1 i which shows that the maximum likelihood estimate for the second moment is the ”sample second moment” [17]. This can be used to speed up the search for the global maxima. The search becomes one dimensional since the maxima lies somewhere on the ellipse defined by Eq. 15. The log-likelihood surface that lies on top of the parameter space [10] can be visualized as in Fig. 12. It has been calculated with Eq. 13 and the ”X” is the result of a search process for the maxima.. 8. 2nd derivative test ensures a maximum at x when f 00(x) < 0. 22.

(27) 3. THEORY. 3.7.3. 3.7. Parameter estimation. Cram´ er-Rao lower bound. Regardless the choice of estimation technique all estimates will include an estimation error. According to Harald Cramér and Calyampudi Radhakrishna Rao, the variance of estimator b for B is always equal to or greater than I −1 [B] where I[B] is the Fisher information for B. This limit, called Cramér-Rao lower bound, CRLB, is the lower limit for any unbiased estimator. As Rician distributed data are dependent on two parameters, the Fisher information matrix is defined as #. ". I [θ]i,j. ∂ ∂ ln f (x|θ) ln f (x|θ) =E ∂θi ∂θj. (16). where f (x|θ) is the joint density defined in Eq. 12 and θ = [s σ 2 ] is the parameter vector. The results from the derivations in Eq. 16 are presented in [16] as I(1, 1) =. N σ2. s2 Z− 2 σ. !. (17). Ns s2 I(1, 2) = I(2, 1) = 4 1 + 2 − Z σ σ I(2, 2) =. N σ4. s2 s4 1 + 2 (Z − 1) − 4 σ σ. !. (18). !. (19). which are the four elements in the Fisher information matrix with Z defined as   2 I12 sx2 x σ Z = E  2  (20) σ I 2 sx2 0. σ. I12. is the first order modified Bessel function squared. From this follows that the Cramér-Rao lower bound defined as I −1 [B] becomes 1 CRLB = det I. I(2, 2) −I(2, 1) −I(1, 2) I(1, 1). !. (21). where CRLB1,1 and CRLB2,2 are the lower limits for the variance of the estimation error for s and σ 2 , respectively. For fixed parameter values a numerical calculation of Z can be performed. This gives simple expressions for the CRLB which can be used as a yardstick in performance tests for various estimation techniques.. 23.

(28) 4. METHOD. 4. Method. The construction of a model for radio channel classification has been performed in a number of steps. First, a theoretical study was done on the subject and related work was investigated. After finishing the theoretical study, a radio network simulator in Matlab was used to check if classification would be possible based on channel estimates. Two different estimation techniques were used and evaluated, most importantly in terms of accuracy, but also, to some extent, calculation speed. The performance of the estimators was analyzed and compared using the Cramér-Rao lower bound. Measurements were then performed with a hardware channel emulator, a real UE and a BS emulator. The recorded data were post-processed and, finally, used in parameter estimation.. 4.1. Simulating. Part of an Ericsson in house Matlab based radio network simulator was used to investigate how the characteristics of different radio channels reflect in various types of fading. Estimation was performed on the first tap of simulated channel’s impulse responses as this is the one with direct wave contribution. Performance tests were also done on the different estimation techniques with Monte Carlo simulations.. 4.2. Measuring. In Skellefte˚ a, Sweden, Ericsson has a test lab, that is built for, amongst other things, radio channel simulations. The equipment there can be tuned for simulations on different radio channel environments and with the right cell phone software it is possible to record how a regular cell phone perceives these channels. Rohde & Schwarz CMU200 WCDMA Generator. Computer. DL. HP / Agilent 11759 RF Channel Simulator. UL. K600. SMIQ GPS Sync 10 MHz. Figure 13: Cell phone measurement setup.. 24.

(29) 4. METHOD. 4.3. Post-processing. Fig. 13 shows the setup and the equipment used for recording the cell phone channel estimates. The Rohde & Schwarz CMU200 WCDMA base station generator was used to set up a call from the cell phone. The down link from the generator was the input to the HP 11759 RF channel simulator which was set to use various types of fading, e.g. Rayleigh or direct waves. Different delays and various Doppler velocities could be set on each channel tap but this was not studied here. The output from the simulator was connected to the cell phone with use of external attenuation set to 30dB due to the fact that attenuation of the down link decreased the variance of the measurements. The cell phone was then monitored from a computer. With the use of modified cell phone software, data from a number of steps in the channel estimate procedure were written to log files. The measurements were done with the own cell registered in the neighbor cells list in the WCDMA BS generator. This was necessary to receive data with varying values. To clearly be able to decide whether or not it is possible to use the cell phone’s pilot symbols as ground for classification, one tap impulse responses were used. These were set to consist of different mixtures of line-of-sight and non-line-of-sight components, i.e. Rayleigh plus direct wave or only Rayleigh. The channel estimates were recorded and post-processed. The recording was done at a rate that allows for the assumption of independent samples.. 4.3. Post-processing. After the measurements, unwanted entries/log-points in the log files were removed with a Perl script and the remaining data were read into Matlab. There the data were cleaned and sorted. Duplicates were removed and only log points with the same time index were saved. The channel estimates were then scaled with the resolution of the quantizer, i.e. 16-bit. To remove the effect of the AGC, the estimates were also scaled with the relative amplification.. 4.4. Estimating. With the use of the post-processed channel estimates the PDF parameter estimation was performed. This was done primarily with maximum likelihood estimation but also, to some extent, with method of moments estimation. The estimated parameters were used to calculate the Rician K-factor.. 25.

(30) 5. RESULTS. 5. Results. 5.1. Simulations. The output from the Matlab radio network simulator shows obvious visual differences in the amplitude distribution of the channel estimates, see Fig. 14(a) and Fig. 14(b). With parameter estimation, these differences are reflected in the Rician K-factor. To study the performance of different estiTypical Urban − Simulated. 2. 1.5 Density. Density. 1.5 1 0.5 0. Rural Area − Simulated. 2. 1 0.5. 0. 0.5. 1 1.5 Amplitude. 2. 0. 2.5. 0. 0.5. (a) Without LOS.. 1 1.5 Amplitude. 2. 2.5. (b) With LOS.. Figure 14: Amplitude distribution of simulated channel estimates. mation techniques, repeated estimations were performed on simulated data. Fig. 15 shows the mean-square error for maximum likelihood and method of moments estimation after a large number of estimations on randomly generated data of various sample sizes. MSE as a function of samplesize Samples from Rician distribution with s=6 and σ=2. 4. MoM − s MoM − σ2 MLE −s MLE − σ2 CRLB. Mean Square Error. 3.5 3 2.5 2 1.5 1 0.5 0 10. 15. 20. 25. 30 N [samples]. 35. 40. 45. 50. Figure 15: Comparison of estimation techniques with CRLB.. 26.

(31) 5. RESULTS. 5.2. Measurements. The curves could be smother if the calculations were done with more simulations but that would be very time consuming. If we disregard the unevenness of the curves it is obvious that the maximum likelihood estimation is indeed asymptotically optimal as stated in [7]. It approaches the CramérRao lower bound for larger data sets. This can not be said about method of moments which has no optimality properties. Though, the simplicity and computational speed of method of moments can be of greater importance than the accuracy of maximum likelihood estimation. The calculation time has not been thoroughly tested, but the method of moments technique is roughly 100 times faster.. 5.2. Measurements. The differences in the physical properties of cellular environments should reflect in different types of fading. Fig. 16 shows some plots of the postprocessed CPICH channel estimates for various mixtures of direct wave components and scattered waves. These simulations was performed with a Doppler velocity of 3.6 km/h and the channel estimates are plotted in the IQ plane. The first figure, in the upper left corner, shows a mixture of scattered waves and a highly attenuated line-of-sight component. The scattered waves have, at least near, zero mean and equally distributed phase, just as in Fig. 6(a). R−0db + D−9dB. R−0db + D−6dB. R−0db + D−3dB. 0.2. 0.2. 0.2. 0. 0. 0. −0.2. −0.2. −0.2. −0.4 −0.4 −0.2. −0.4 −0.4 −0.2. 0. 0.2. R−3db + D−0dB. 0. 0.2. −0.4 −0.4 −0.2. R−6db + D−0dB. 0.2. 0.2. 0.2. 0. 0. 0. −0.2. −0.2. −0.2. −0.4 −0.4 −0.2. −0.4 −0.4 −0.2. 0. 0.2. 0. 0.2. 0. 0.2. R−9db + D−0dB. −0.4 −0.4 −0.2. 0. 0.2. Figure 16: IQ representation of measured and post-processed channel estimates for various mixtures of waves. R in the titles stand for Rayleigh fading and D for direct wave. The amount of attenuation is specified for each type. The bottom right figure, shows the opposite, a strong direct wave component. Here the shift in mean is clearly visible. The channel estimates also produce the characteristic ring shape due to movement between transceiver 27.

(32) 5. RESULTS. 5.2. Measurements. and receiver, remember Fig. 8(a). The additional figures describe various mixtures of scattered and direct waves. The titles use R to denote Rayleigh fading and D for direct wave. Each type is attenuated as specified, i.e. D-9dB means that the direct wave is attenuated 9dB. R−0db + D−9dB. 0. 0. 10 0. 0. 0.1 0.2 Amplitude R−3db + D−0dB. 0. 0.1 0.2 Amplitude. Density 0. 20 Density. Density. 20. 10. 0. 0. 0.1 0.2 Amplitude. 10 0. 0.1 0.2 Amplitude R−6db + D−0dB. 10. R−0db + D−3dB. 20. 0. 0.1 0.2 Amplitude R−9db + D−0dB. 0. 0.1 0.2 Amplitude. 20 Density. 10. R−0db + D−6dB. 20 Density. Density. 20. 10 0. Figure 17: Amplitude histograms for various mixtures of waves. Histograms over the amplitude for these channel estimates are shown in Fig. 17. Here it is easier to see the shift in mean for the non-extreme combinations of direct wave and scattered waves. The case with little lineof-sight has as expected the characteristic Rayleigh form. The stronger the direct wave component becomes the more will the distribution shift to the right and approach Gaussian, compare with Fig 7(b). All of this is in line with theory.. 28.

(33) 5. RESULTS. 5.3. 5.3. Parameter estimation. Parameter estimation Rayleigh−0dB + Direct wave−3dB Maximum likelihood estimation. 14. Data MLE | s≈0.05, σ≈0.05. 12. Density. 10 8 6 4 2 0. 0. 0.05. 0.1. 0.15. 0.2. 0.25. Amplitude. Figure 18: Maximum likelihood estimation on measured channel estimates with a mixture of Rayleigh-0dB + Direct wave-3dB. The results from the maximum likelihood estimation on the post-processed channel estimates differed greatly between different log files. With recorded data, based on settings in the channel simulator corresponding to a Rician K-factor of 0.5, the result after estimation can be visualized as in Fig. 18. The curve is the probability density function to which the estimated parameters, s ≈ 0.05 and σ ≈ 0.05, correspond. Fig. 19 and Fig. 20 show the spread of the estimations on measured data for various K-factors with different sample sizes. There seems to be an offset between expected and estimated K-factor. This is the case regardless of sample size, compare Fig. 19 and Fig. 20. With thorough analysis of the plots, the offset seems to be around 3 dB. As the amplitude of the scattered waves follows a Gaussian distribution, one solution for this could be the difference in calculating the variance of complex noise compared to the variance of real noise. A calculation of the real noise variance only takes the real part of our scattered waves into account and not the imaginary part, which makes the real noise variance smaller than the complex noise variance. This difference is exactly 3 dB. Another reason could of course be a badly calibrated channel simulator with an internal offset in the signal power. In fact, power measurements of the output from the channel simulator confirmed that the mean of the power of the Rayleigh fading signal is near 3dB lower than that of the direct wave. Whatever the reason for this is, if it is due to real/complex noise or an internal design issue is of minor importance. If it can be established that the offset is fixed at 3 dB, this can easily be compensated for. 29.

(34) 5. RESULTS. 5.3. K−factor estimates with samplesize ≈ 220. 16. Estimates Expected estimate Mean of estimates. 14 12 Estimated K−factor. Parameter estimation. 10 8 6 4 2 0 −10. −8. −6. −4 −2 0 2 4 Direct Wave Attenuation/Amplification [dB]. 6. 8. 10. Figure 19: K-factor estimation on log files with data sets of size ≈ 220. K−factor estimates with samplesize ≈ 450. 16. Estimates Expected estimate Mean of estimates. 14. Estimated K−factor. 12 10 8 6 4 2 0 −10. −8. −6. −4 −2 0 2 4 Direct Wave Attenuation/Amplification [dB]. 6. 8. 10. Figure 20: K-factor estimation on log files with data sets of size ≈ 450. Fig. 21 shows the variance and standard deviation of the estimates for two different sample sizes. As expected, the variance for larger data sets is lower than for small data sets. Higher variance as the direct wave becomes stronger was not expected, though it is not entirely unlikely that this is a result from additive noise during measurements. With large K-factors, i.e. strong direct waves, the denominator in the K-factor calculation will be small, at least compared to the nominator. If the noise then is independent from both the power of the direct wave and the power of the scattered waves, the effect of the noise will be greater, hence leading to high variance of K.. 30.

(35) 5. RESULTS. 5.3. Parameter estimation. Variance and Standard Deviation of K−factor Estimates. Variance/std of Estimated K−factors. 1.8. σ2 for samplesize ≈ 450 σ for samplesize ≈ 450. 1.6. σ2 for samplesize ≈ 220 σ for samplesize ≈ 220. 1.4 1.2 1 0.8 0.6 0.4 0.2 0 −10. −8. −6. −4 −2 0 2 4 Direct Wave Attenuation/Amplification [dB]. 6. 8. 10. Figure 21: Variance and standard deviation of K-factor estimates on log files with data sets of varying sizes.. 1.5. K−factor est. | Samplesize ≈ 220. 1 0.5 0. Estimated K−factor. Estimated K−factor. To better see the estimates in the region with weaker direct wave, Fig. 22(a) and Fig. 22(b) show the lower left part of Fig. 19 and Fig. 20 in greater detail. It is clear that many estimates equals zero, and that the number of zero estimates increases with weaker direct wave component.. −10 −8 −6 −4 −2 Direct Wave Attenuation/Amplification [dB]. 1.5. K−factor est. | Samplesize ≈ 450. 1 0.5 0 −10 −8 −6 −4 −2 Direct Wave Attenuation/Amplification [dB]. (a) Sample size ≈ 220. 20 estimates for (b) Sample size ≈ 450. 10 estimates for each setting each setting. Figure 22: K-factor estimation on multiple log files with data sets of varying sizes. Fig. 23, which shows an amplitude histogram of simulated data with a mixture of waves that corresponds to a K-factor equal to 0.5, clarifies this. One of the two probability density functions in the figure is from estimation. The other is the real PDF. The density functions are very similar and hard to distinguish from each other even though the differences between the real and estimated parameters are vast. The estimation resulted in s = 0.004, σ = 1.834 when the real parameters were s = 1.5, σ = 1.5. An s estimate so close to zero results in a very small K-factor, in this case 31.

(36) 5. RESULTS. 5.3. Parameter estimation. 2.38 ∗ 10e − 6 , which is far from the expected 0.5. MLE on Simulated Data with K−factor = 0.5. 0.4. Data Estimated PDF Real PDF. 0.35 0.3. Density. 0.25 0.2 0.15 0.1 0.05 0. 0. 1. 2. 3. 4. 5. 6. 7. Amplitude. Figure 23: MLE estimation error. Fortunately, this problem is only an issue for weak direct waves. A weak line-of-sight component easily disappears in the scattered waves and in those cases, the estimate for the s parameter often becomes zero. This occurs for both measured and simulated channel type estimates. K−factor dist. from MLE estimates with real K−factor = 0.125. K−factor dist. from MLE estimates with real K−factor = 0.25. 1500. 300. 1000. 200. 500. 100. 0. 0. 0.5. 0. 1. K−factor dist. from MLE estimates with real K−factor = 0.5. 300. 200. 200. 100. 100 0. 0.5. 0.5. 1. K−factor dist. from MLE estimates with real K−factor = 1. 300. 0. 0. 0. 1. 0. 0.5. 1. Figure 24: MLE estimation difficulties. Fig. 24 illustrates the distribution of the resulting K-factor after 5000 simulated estimations for a number of different K-factors. As the direct wave becomes stronger and the K-factor increases the estimation becomes more accurate.. 32.

(37) 5. RESULTS. 5.4. Modified K-factor estimates. Sadly, from an application perspective, the region with weaker direct wave components is of most interest. As the Rake receiver needs 1 chip spacing between assigned fingers, the ITU channel models has to be resampled to fit this time resolution. For the RA model this resampling results in a K-factor of 0.38 for the first channel tap. This value is a statistical mean that can be expected when performing repeated measurements and estimations in a RA channel environment. With instantaneous measurements and estimation, the K-factor can very well be over 0.38. Nonetheless, for classification between TU and RA, the most interesting interval for the Rician K-factor is low values up to, maybe 0.5. Estimation must therefore be accurate in this region which might require other estimation techniques. One solution could be Bayesian estimation [5], which could give better results for the difficult cases.. 5.4. Modified K-factor estimates. Modification of the results can be performed if the difficulty of estimating parameters in mixtures with weak direct wave is taken into account. If the zero estimates are interpreted solely as a result of the estimation procedure error they can be removed. This increases the mean of the K-factor estimates. This, together with compensation for the 3dB offset detected in the output power, leads to different results than before, see Fig. 25. Here the mean of the K-factor estimates align better to what was expected but there is still a deviation for some combinations of direct and scattered waves. 9. Compensated K−factor est. | Zero est. removed | Samplesize ≈220 Estimates Expected estimate Mean of estimates. 8. Estimated K−factor. 7 6 5 4 3 2 1 0 −1 −10. −8. −6. −4 −2 0 2 4 Direct Wave Attenuation/Amplification [dB]. 6. 8. 10. Figure 25: Compensated K-factor estimation on log files with data sets of size ≈ 220, zero estimates removed.. 33.

(38) 5. RESULTS. 5.4. Modified K-factor estimates. Fig. 26 shows the difference between the expected and estimated Kfactors for two different sample sizes. The offset is relatively small for all but two combinations of direct and scattered waves. With a 3dB amplification of the direct wave the deviation from expected K-factor is about +0.5. This is not large enough to raise any particular concerns. On the other hand, 9dB amplification results in an offset of -2. This is much higher than can be accepted and the exact reason for this is not clear. Difference between estimated and expected K−factors. 1. Sample size ≈ 450 Sample size ≈ 220. 0.5. Difference. 0 −0.5 −1 −1.5 −2 −2.5 −10. −8. −6. −4 −2 0 2 4 Direct Wave Attenuation/Amplification [dB]. 6. 8. 10. Figure 26: Difference between estimated and expected K-factors.. 34.

(39) 5. RESULTS. 5.5. 5.5. Proposed presentation of results. Proposed presentation of results. Based on calculations of mean excess delay and/or delay spread, which have not been performed but should be possible with use of channel estimates and finger delay, it is possible to compare the time dispersion characteristics of the physical channel to the ITU models. The difference between Typical Urban, TU, and Hilly Terrain, HT, are vast but the distinction between Typical Urban and Rural Area, RA, is more subtle. Since RA is the only ITU model with line-of-sight communication, hence the only model with Rician fading, an accurate estimation and calculation of the Rician K-factor can be used to separate this model from TU. To visualize the results from the calculations and estimations in comparison to, e.g. ITU channel models, a two dimensional image could be used. Fig. 27 shows one example of this. The pointer placement displays. Hilly Terrain. Typical Urban Rural Area. Low. Time dispersion. High. Radio Channel classification illustration. Low. Amount of line-of-sight. High. Figure 27: Radio channel classification illustration. the amount of line-of-sight and some type of time dispersion measure, e.g. the delay spread. As the calculated values most likely will fluctuate in time, low-pass filtering could be helpful. When the radio channel characteristics change, a buffer is used to display older samples. These are the faded marks in Fig. 27. The color gradient background specifies the areas where the combination of delay spread and Rician K-factor correspond to the specified channel models. The value of the K-factor typically varies from zero for the Typical Urban model to 0.38 for the 1 chip resampled Rural Area model. Though this is a statistical mean that very well might be exceeded. The time dispersion measures for TU and HT varies between [0 3µs] for the delay spread and [0 0.9µs] for the excess delay. Just as the interval for the K-factor, these are not absolute boundaries; rather intervals in which the mean excess delay and the delay spread most likely will lie.. 35.

(40) 6. DISCUSSION. 6 6.1. Discussion Measurement difficulties. The results in Fig. 19 and Fig. 20 show large variation between K-factor estimates of log files with the same mixtures of waves. Ideally, each estimate would be alike and close to the theoretical value. In the region with low Kfactor, the estimates are often close to zero due to reasons explained earlier. As this region is of importance in an application perspective, this issue must be resolved. Other estimation techniques might perform better [5]. During the measurements, too high signal power resulted in large variance in the AGC and in the final K-factor estimation. With the use of external attenuation, the variance of the AGC could be lowered and that seemed to lower the variance of the estimates. With additional measurements at different signal levels this error could be quantified and then hopefully also reduced. Another peculiar thing was the settings needed in the BS generator to be able to record data. The first recordings resulted in channel estimates with the exact same value. To received data that varies, the own cell has to be registered in the neighbor cells list. That means that the cell that the UE uses also has to be registered as a neighbor cell. The reason for this is at this point not clear.. 6.2. Cell phone limitations. Another issue that might affect the estimation is some limitations in the Rake receiver. The receiver often assigns two Rake fingers, even when the impulse response only should have one tap. The second, so called ghost finger, will contain parts of the signal energy. This could affect the estimation which is done on each finger separately. Unfortunately, this problem is not fixable until the receiver filter is exchanged.. 36.

(41) 7. 7. CONCLUSIONS. Conclusions. After performing theoretical studies, simulations in Matlab showed, as expected, obvious differences between the impulse responses amplitude distribution for various fading types. For estimation, method of moments and maximum likelihood estimation were identified as usable techniques and evaluated in terms of accuracy and speed. Maximum likelihood estimation turned out most accurate but method of moments is roughly 100 times faster computationally. With large enough data sets, method of moments should be ”good enough”. How large data sets that must be used has not been established. The use of real data recorded from a cell phone showed that the amplitude distributions of the channel estimates changes form with different mixtures of scattered and direct wave components. The stronger the direct wave, the more Gaussian-like distribution. The weaker, the more Rayleighlike. Combinations with nearly equal power means Rician distribution. All in line with theory. Parameter estimation and calculation of the Rician K-factor resulted in an increase of the K-factor with stronger direct wave. The mean values of the Rician K-factor estimates for various mixtures of waves are about 3 dB higher than expected, which could be due to the difference in noise variance between complex and real noise or due to that the channel simulator generates the power level of different signal components differently. Estimation performed on mixtures with weak direct waves often resulted in zero estimates due to difficulty of detecting the weak direct wave in the scattered waves. As the Rician K-factors statistically is 0 for Typical Urban and 0.38 for the 1 chip resampled Rural Area, the region with weak direct waves, i.e. K < 0.5, is of most interest from an application perspective. Other estimation techniques might therefore be necessary. With stronger direct waves the variance of the K-factor estimates increased. The exact reason for this has not been established. Though, it is not unlikely that the measurements are, to some extent, subjected to additive noise. Such noise would, if independent from the power in the signal components, have greater effect on the K-factor as the power of the scattered waves decrease. Although not investigated in this work, the mean excess delay and the delay spread should be possible to calculate from the cell phone channel estimates and the finger delay. This, together with the parameter estimates and the Rician K-factor, could be used for comparing the measured radio environment with channel models, such as, but not limited to, those specified by ITU. Even though an exact parallel between theoretical Rician K-factor, and practical Rician K-factor has been hard to establish, the results are in line with theory. Measurements on a real cell phone and PDF parameter estimation have shown that it should be possible to classify radio environments using cell phone measurement data. 37.

(42) 8. 8. FURTHER STUDIES. Further studies. Before the techniques in this report can be used for classification of radio channels, there are some issues that require further studies. • The variance of the estimated parameter for repeated simulations at the same settings is high. To be able to draw accurate conclusions about the radio channel environment the variance must be lowered. For each slot, the variance of the channel estimates can be calculated. This might be possible to use to weigh the channel estimates before estimation. Also, external attenuation of the down link signal seems to decrease the variance. Maybe the power of the output from the channel simulator is too high for optimal UE performance. • Overestimation of the Rician K-factor might be due to the dimensioning of the power in the scattered waves. Additional tests needs to be performed to ensure that the channel simulator output indeed is what is should be. The channel simulator might be dimensioning the power of the scattered waves with regard to complex noise instead of real noise which all calculation has been based on. Also, it might need to be re-calibrated. • Estimation of the parameters when the line-of-sight component is weak most likely requires other estimation techniques to avoid zero estimates. Bayesian estimation might improve the results. With these issues resolved, a product for classification of radio channels should be possible.. 38.

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