Comparison and Evaluation of Doppler Spread Estimation Algorithms in WCDMA

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Comparison and Evaluation of Doppler

Spread Estimation Algorithms in

WCDMA

HUI WEN

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Abstract

In a WCDMA transmission systems, the properties of the radio transmission channels can be strongly affected by the movement of User Equipment (UE) or the surrounding objects. The estimation of Doppler spread is therefore of great importance since it is closely related to the mobile speed, as it can also be used to characterize the fast fading in the radio channel. Thus the Doppler spread estimation can have wide range of applications and the relative research on this topic has drawn much attention. Many Doppler spread estimation algorithms has been proposed in the literature. In this report, these algorithms are divided into four categories, and the comparison is performed from both performance and implementation point of view to compare these four types of estimators.

During the investigation, the Rayleigh fading and Rician fading model with different mobile speed and SNR are simulated to analyze the performance of estimation algorithms under different conditions. The effect of Rician factor and angle of arrival of Line Of Sight (LOS) component is also taken into consid-eration in the evaluation. Furthermore, the computational complexity of each algorithm is calculated.

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Sammanfattning

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Acknowledgment

Firstly I would like to express my deepest gratitude to Ziqi Peng, my thesis work partner from KTH, for the cooperation, inspiration and encouragement throughout the thesis work.

I am also grateful to my supervisor Per L¨ofving and support team members Henrik Sahlin, Magnus Nilsson, Lu Li in Ericsson for their wonderful guidance and constant help during the entire thesis work. Without their help, my thesis work would have never been made.

And I would like to thank my examiner Prof. Tobias Oechtering from KTH for supervising me and giving me valuable suggestions.

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List of Figures

2.1 Example of the Channelization Code Tree . . . 6 2.2 Relation between Spreading and Scrambling . . . 6 2.3 Example of Parallel transmission of DPDCH and DPCCH . . . . 7 2.4 Example of Parallel transmission of DPDCH and DPCCH . . . . 7 2.5 WCDMA radio interface protocol . . . 7 2.6 Structure of WCDMA transmitter . . . 8 2.7 Structure of WCDMA uplink dedicated physical channels . . . . 8 2.8 Relation between Path Loss and Fast Fading . . . 10 2.9 Block diagram of the Rake receiver . . . 10 2.10 An example of relative movement between transmitter and receiver 11 2.11 The Jakes’ Spectrum (Clarke’s Spectrum) . . . 12 4.1 The Estimated Channel Response from BCL where Zero

Cross-ings are illustrated . . . 18 4.2 The Power Spectral Density of the received signal in ideal Rician

fading model. . . 22 4.3 The Theoretical Power Spectral Density Estimation by Using

Pe-riodogram . . . 24 4.4 The Estimated Power Spectral Density Estimation by Using

Pe-riodogram . . . 24 5.1 Comparison of computational complexity of four types of estimator 30 6.1 Comparison of simulated and theoretical value of Doppler spread

of three ZCR estimators . . . 33 6.2 Normalized mean square estimation error (NMSE) of three ZCR

estimators versus true maximum Doppler spread value . . . 34 6.3 Normalized mean square estimation error (NMSE) of ZCR

esti-mator versus SNR . . . 34 6.4 Comparison of simulated and theoretical value of Doppler spread

of covariance based estimators . . . 35 6.5 Normalized mean square estimation error (NMSE) of ZCR

esti-mator versus true maximum Doppler spread value . . . 36 6.6 Normalized mean square estimation error (NMSE) of covariance

based estimators versus SNR . . . 36 6.7 Comparison of simulated and theoretical value of Doppler spread

of PSD slope estimators . . . 37 6.8 Normalized mean square estimation error (NMSE) of PSD slope

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6.9 Normalized mean square estimation error (NMSE) of PSD slope estimators versus SNR . . . 38 6.10 Comparison of simulated and theoretical value of Doppler spread

of time domain ML estimators . . . 40 6.11 Normalized mean square estimation error (NMSE) of time

do-main ML estimators versus true maximum Doppler spread value 41 6.12 Normalized mean square estimation error (NMSE) of ML

estima-tors versus SNR . . . 41 6.13 Normalized mean square estimation error (NMSE) of ML

estima-tors with different detection resolutions versus SNR . . . 42 7.1 Performance comparison of eight types of Doppler spread

estima-tors in Rayleigh fading model . . . 44 7.2 Performance comparison of eight types of Doppler spread

estima-tors in Rayleigh fading model (Low velocity scenario) . . . 44 7.3 Normalized mean square estimation error (NMSE) of time

do-main ML estimators versus true maximum Doppler spread value 45 7.4 Performance comparison of eight types of Doppler spread

estima-tors in Rician fading model for fD= 20 with θ0= 0 . . . 46

7.5 Performance comparison of eight types of Doppler spread estima-tors in Rician fading model for fD= 120 with θ0= 0 . . . 47

7.6 Performance comparison of eight types of Doppler spread estima-tors in Rician fading model for fD= 20 with K = 2 . . . 47

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Chapter 1

Introduction

1.1 Introduction

Nowadays, the Wideband Code Division Multiple Access (WCDMA) technology is widely used throughout the world. From the perspective of operators, it is always important to make sure reliable transmission of data and at the same time reduce the transmission cost.

However, the performance of the radio transmission channels is strongly af-fected by the variations of channel properties. This is mainly due to the effect of multi-path fading, which can be characterized by the Doppler spread and the time delay spread. On the other hand, the mobile velocity or movements of sur-rounding objects is also closely related to the Doppler spread. The estimation of the Doppler spread is therefore of great importance to increase the performance of WCDMA baseband algorithms or reduce the complexity of these algorithms. It has a wide range of applications.

In the adaptive transmission systems, the information of the Doppler spread can be utilized to optimize the channel tracker step size, update the power control algorithms, adjust the interleaving length and measure the quality of CQI. In network control algorithms, such as the channel assignment and the handover [1], and some geolocation applications in the channel environment, the knowledge of the Doppler spread can also be applied.

For instance, if the knowledge of Doppler spread is available, the channel searcher is able to reduce the number of chips for correlation when the Doppler spread is high since the corresponding coherence time is small. This adjustment can result in higher estimation accuracy and lower computational cost.

Thus it becomes attractive to investigate the performance of various Doppler spread estimation algorithms in the literature, and evaluate the efficiency and the possibility to implement in applications of wireless communication systems, such as WCDMA.

1.2 Previous Work

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which can be classified into 4 major types: crossing rate based [2], [3], correla-tion based [4], [5], [6], Power Spectral Density (PSD) based [7], [8], [9], [10], and Maximum Likelihood (ML) based estimators [11], [12], [13].

However, most of these works have been focused on the development and the-oretical analysis of one single estimator. To the best of our knowledge, there has rarely been investigation that evaluate and compares different types of Doppler spread estimators. In [14], crossing based and covariance based estimators are analyzed and compared, but the performance has not been analyzed from the implementation point of view.

1.3 Problem Definition

The thesis is conducted by two persons (Hui Wen, Ziqi Peng) at Ericsson, Gothenburg. The scope of this thesis is to evaluate and compare the perfor-mance of different types of Doppler spread estimation algorithms in terms of estimation accuracy, and the possibility of implementation in a WCDMA sys-tems. More specifically, the Doppler spread estimation in the WCDMA uplink is considered.

1.4 Methodology

The thesis research is based on an investigation and comparison to the estima-tors proposed in the literature. Due to the time constraint, only few algorithms can be implemented and analyzed. Thus the methodology is to divide these algorithms into categorizes, and evaluate different types of algorithms in a same framework.

Based on our knowledge, the estimators are classified into four major types of estimation techniques: the crossing rate based estimators, the correlation based estimators, the PSD based estimators and the ML based estimators. Two esti-mators are chosen from each category. The selection criteria for the candidates algorithms are the possibility to be migrated into the WCDMA systems and the complexity for implementation.

The implementation and simulation of estimation algorithms will be com-pleted in the Baseband Core Library (BCL) of Ericsson by two person individu-ally. The specific task division is shown in Table 1.1. And the basic description and specific parameter settings of BCL can be found in the Section 6.1.

In order to migrate the estimators into WCDMA systems and implement the chosen algorithms in the simulation environment, some modifications are made and illustrated in detail in the following chapters. Therefore the implementation of algorithms is also an important part of the thesis work.

Four different estimators will be introduced and analyzed in this report, and the result will be used to compare with another four implemented estimators in BCL, which can be found in [15] or the corresponding literature.

Furthermore, the following research questions are considered to achieve the objective of this investigation:

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• Which algorithm is able to give reasonable estimation with lowest compu-tation complexity?

• Which algorithm is robust to the variation of channel properties? • What are the underlying reasons for these performances?

In order to answer these questions, the algorithms are evaluated in different channel models with different Doppler spread and Signal to Noise Ratio (SNR) by BCL simulation. The computational complexity for each algorithm will also be given to analyze the practical value.

Hui Wen (This Report) Ziqi Peng (Report [15]) Literature Investigation _X _X Algorithm Selection _X _X ZCR Estimator _X LCR Estimator _X Moser’s Estimator _X Hybrid Estimator _X PSD Slope Estimator _X

Power Integration Estimator _X

Time Domain ML Estimator _X

Frequency Domain ML Estimator _X

Complexity Analysis _X _X

Performance Comparison _X _X

Table 1.1: Task Division for the Thesis Research

1.5 Societal and Ethical Aspects

It is discussed in [16] that the new technologies can give previously unknown ethical problems to the society. Thus it is of importance to access the ethical implications of the newly developed technology.

The investigation of this report has been focusing on the estimation of Doppler spread, which gives information about mobile velocity. This infor-mation can be used to estimate the status of the user (walking, driving, etc.) and gives an indication of User’s behavior. It potentially gives rise to ethical issues if it is used inappropriately, thus the applications should be supervised.

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1.6 Thesis Outline

The report in organized as follows.

In Chapter 2, some background knowledge of WCDMA functionalities is explained, as well as the reception issues of WCDMA. The basic knowledge of Rake receiver and WCDMA physical channels is also addressed.

In Chapter 3, the two channel models used in the simulation and some relative properties of channel are presented. Some general calculations for the algorithms are also given.

In Chapter 4, the four chosen Doppler spread estimation algorithms are described.

In Chapter 5, the theoretical computational complexity for each algorithms is analyzed.

In Chapter 6, the evaluation and parameter selection of each algorithm are performed based on their simulation results in Rayleigh fading channel.

In Chapter 7, the algorithms are evaluated and compared based on their simulation results in both Rayleigh and Rician fading models. For a more comprehensive comparison, the simulation results of another four algorithms are also introduced.

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Chapter 2

Background

In this chapter, a brief discussion of the essential background needed throughout the thesis is presented.

2.1 WCDMA

2.1.1 General Description

WCDMA is a commonly used air interface to implement the Third Generation (3G) networks. Due to the rapid growing of user’s demand nowadays, the Sec-ond Generation (2G) networks cannot meet the requirements and expectations. While the 3G networks have been designed for high-speed data transmissions, it will be used as main framework for this thesis research.

WCDMA differs from other multiple access schemes in the way in which it shares the radio spectrum resource. The early analog cellular systems utilized Frequency Division Multiplex Access (FDMA), which splits available spectrum among subscribers over time. Time Division Multiplex Access (TDMA), which is used in the Global System for Mobile communication (GSM) standard, al-locates the spectrum to an individual subscriber but switches their access over time. Whereas the Code Division Multiple Access (CDMA) is based on the principle of the direct sequence spectrum spreading. The whole bandwidth is shared among multiple subscribers simultaneously. Their transmitted signal can be differentiated by unique spreading codes.

2.1.2 Spreading and Modulation

The bandwidth required to represent a signal is related to the data rate and available dynamic range. In the WCDMA air interface, the spreading technique is utilized to increase the resistance to the interference. Two kinds of codes are used in WCDMA: the channelization codes and the scrambling codes.

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Factor (OVSF) technique. The codes are generated from the code tree, which is shown in Fig.2.1. c1,1={1} c2,1={1,1} c_2,2={1,-1} c_4,1={1,1,1,1} c4,2={1,1,-1,-1} c4,3={1,-1,1,-1} c4,4={1,-1,-1,1}

Figure 2.1: Example of the Channelization Code Tree

The use of OVSF codes maintains the orthogonality between different spread-ing codes of different lengths and makes it possible to change the spreadspread-ing factor.

In addition to spreading, another part of the process in the transmitter is the scrambling. It can be used to separate the transmissions from different terminals. The scrambling is operated on top of spread, thus it does not change the bandwidth of the signal. The relation between spreading and scrambling is shown in the Fig.2.2.

Data

Channelization Codes Scrambling Codes

Bit rate Chip rate Chip rate

Figure 2.2: Relation between Spreading and Scrambling

Especially, in the uplink of WCDMA, the two dedicated physical channels are not time multiplexed, but instead the in-phase quadrature (I-Q) code mul-tiplexing is utilized [17]. The reason is to avoid the discontinuous transmission, which causes potential audible interference to the nearby audio equipment. And it can also be used to improve the peak-to-average ratio of transmitted signal. An example of continuous transmission achieved by applying I-Q code multi-plexing is shown in the Fig.2.3, and the spreading modulation process is shown in Fig.2.4.

2.1.3 Uplink Physical Channels

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Physical layer control information (DPCCH) Data (DPDCH) Data absent Data (DPDCH)

Figure 2.3: Example of Parallel transmission of DPDCH and DPCCH

Channelization Code cD Channelization Code cC DPDCH (data) DPCCH (control) *j I Q I+jQ Complex Scrambling code

Figure 2.4: Example of Parallel transmission of DPDCH and DPCCH

architecture of WCDMA is shown in Fig.2.5.

CTRL UserNData UserNData CTRL RRC RRC RLC RLC RLC RLC MAC MAC PHY PHY SignallingNRadioNBearer RadioNBearer LogicalNChannel TransportNChannel PhysicalNChannel UE WCDMANRAN

Figure 2.5: WCDMA radio interface protocol

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are mapped onto physical channels. The physical channels perform the actual transmission of data bits, which are distinguished by frequency, channelization code, scrambling code and modulation.

Considering only uplink, the structure of the transmitter is shown in Fig.2.6.

PRACH DPDCHd/1 DPDCHd/3 DPDCHd/5 DPDCHd/2 DPDCHd/4 DPDCHd/6 DPCCH ΣI ΣQ

Σ

Σ Σ RACHdControldPart j j UEdScramblingdcode j i Filter Filter I/Q Mod.

Figure 2.6: Structure of WCDMA transmitter

As one can see, three kinds of physical channels are used: PRACH, DPDCH, and DPCCH.

The Physical Random Access Channel is used to carry access requests. It uses only Open-loop power control therefore no pilot ot TPC bits are included. The Dedicated Physical Data Channel (DPDCH) is used to carry dedicated traf-fic and L3 signaling. And the Dedicated Physical Control Channel (DPCCH) is used to carry L1 signaling. It consists of pilot bits, Transmit Power Control (TPC) commands, Feedback Information (FBI) and Transport Format Combi-nation Indicator (TFCI).

According to the specification of [18], the structures of the uplink DPDCH and DPCCH are designed as shown in Fig.2.7.

DPCCH:8=5Kb.s8data8rate98totally8=Q8bits8per8DPCCH8slot Pilot:8Fixed8patters8B3949596978or888bitsk TFCI:8Transmit8Format8Combination8Indicator8BQ929398or848bitsk FBI:8Feedback8Information8BQ98=98or828bitsk TPC:8Transmit8Power8Control8bits8B=8or828bitsk = 2 3 4 5 6 7 8 9 =Q == =2 =3 =4 =5

Pilot TFCI FBI TPC

Coded8Data8B=Q8to864Q8bitsk Dedicated8Physical8Data8Channel8BDPDCHk8Slot8BQS666msk Dedicated8Physical8Control8Channel8BDPCCHk8Slot8BQS666msk I Q =8Frame8=8=58slots8=8=Qms

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2.2 Multipath Radio Channel and Rake

Recep-tion

2.2.1 Reception Issues

In the radio transmission channels, the transmitted signal is subject to three mutually independent propagation phenomena: path loss, shadowing, and mul-tipath propagation [19].

The path loss is used to describe the signal attenuation due to distance. It can be modeled by the log-distance path loss model, i.e. the signal power falls off proportional to at least the inverse of the square of the range (1/r2_).

Whereas the fading may vary with time, geographical position and frequency, it is often modeled as stochastic process.

In the radio system, the fading may either be due to the shadowing or the multipath propagation. The shadow fading, which is also called slow fading, describes the signal power loss due to the objects lie between the transmitter and receiver such that the transmission path is blocked.

Whereas the multipath propagation is used to describe the different paths a signal takes to reach the receiving antenna due to the reflections and diffractions of the transmission media. As a result, the received signal at receiver contains not only a direct LOS radio wave, but also a large amount of scattered waves.

According to [17], there are two possible effects resulting from the multipath propagation in WCDMA systems. If the arrival times of different multipath sig-nal are separated enough (larger than WCDMA chip duration), the receiver can identify the received multipath components with significant energy, and using certain algorithms to combine them. However, it is often that some signals from different paths arrive at almost the same time. For instance, paths with length different of half a wavelength (approximately 7cm at 2GHz) can result in almost same arrive time instant compared to the single chip duration. As a result, the constructive and destructive interference, which is also called fast fading or the Rayleigh fading, occurs at the received signal. In this case, the magnitudes of the received signal can normally described by the Rayleigh distribution [17].

The relation between the path loss and the fast fading is shown in the Fig.2.8. As can be seen, the received signal will fluctuate seriously due to the fast fading, which makes the error-free reception of data bits very difficult. Therefore, three countermeasures are used to overcome fading in WCDMA: The first one is to use strong coding (Turbo and convolutional coding) and interleaving to add redundancy and diversity to the signal thus help the receiver to recover the signal with fading. The second method to combat the effects of fading is to use a fast power control. Finally, the Rake receiver is used to combine the multipath components with significant energy and reduce the effect of fading.

2.2.2 The Rake Receiver

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0 200 400 600 800 1,000 −100 −80 −60 −40 −20 0 20 40 60 Distance(m) P o w er (dB) Path Loss Fading

Figure 2.8: Relation between Path Loss and Fast Fading

The Rake fingers containing correlators are used to track different multipath reflections from one scrambling code. To achieve this tracking, each finger cor-relates the signal with the same scrambling code but at different delay. And the finger can easily be used to track another terminal by changing a different code. According to [20], the block diagram of a Rake receiver is shown in the Fig.2.9. MatchedS Filter Correlator CodeS Generators Channel estimator Phase

rotator Delaysequalizer ΣI

ΣQ FingerS1 FingerS2 FingerS3 InputSSignal TimingS(FIngerSallocation) I Q Combiner I Q

Figure 2.9: Block diagram of the Rake receiver

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2.3 Doppler spread

The Doppler effect is the frequency change of the incoming received wave caused by the relative motion between transmitter and receiver. Considering the wire-less transmission scenario, the motion is mainly due to the relative motion between the mobile and base station, or the movement of objects in the trans-mission channel.

Considering only one transmission path, the Doppler shift can be given by ∆f = v

cfccos(θ), (2.1)

where v is the velocity of relative movement, c denotes the speed of light, fc is

the carrier frequency, and θ is the angle of received signal, i.e. the angle between the direction of motion of the mobile and the direction of signal transmission path, as illustrated in Fig.2.10.

Figure 2.10: An example of relative movement between transmitter and receiver Especially, when the transmitter is moving towards the position of receiver, the frequency shift will reach the maximum value, as given by

fD=

v

cfc, (2.2)

which is referred to as the maximum Doppler shift.

However, as discussed in the previous section, the transmitted signal is sub-ject to the multipath propagation due to reflections and refractions. According to the assumptions of Rayleigh or Rician fading model, each received wave ar-rives with its own random angle of arrival, which is uniformly distributed within [0, 2π] (i.e., isotropic scattering). The Doppler shift is therefore different for each incoming waves at receiver. As a result, when a pure sinusoidal signal with fre-quency fc is transmitted, the spectrum of received signal, which is also called

the Doppler spectrum, will be spread in to the range of fc− fD to fc+ fD.

Assuming the Rayleigh fading model, the ideal Doppler spectrum of received signal will have the shape as shown in Fig.2.11, which is called the Jakes’ spec-trum or the Clarke’s specspec-trum.

In this case, fDis referred to as the maximum Doppler spread or the Doppler

spread. The Doppler spectrum can have high density at the maximum Doppler spread, which can be detected to estimate the mobile velocity.

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Frequency

PSD

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Chapter 3

Channel Model

3.1 Basic Channel Model

As basic channel model, Rayleigh fading is chosen for simulation. Rayleigh dis-tribution is normally used to model multipath fading without LOS component. The channel response in the mobile environment can be seen as a sum of re-ceived path responses (fingers) due to reflection and scattering, and the delay spread for each received path can be neglected. Moreover, each received path is a result of constructive and destructive superposition of a large number of scattered waves coming from different directions. The channel response for one received path (finger) can be described as [21] [22]

hp(t) = lim N →∞ 1 √ N N X k=1 akej(wDt cos θk+φk) (3.1)

where N represents the number of independent scattered paths, and ak is the

path amplitude. The Doppler angular frequency is expressed by wD = 2πfD,

where fD is the maximum Doppler spread (maximum Doppler frequency), θk is

the arrival angle of the path and φk is the phase of the path.

Ideally, we can assume that the phases φk, the amplitudes ak and arrival

angles θk are independent stochastic variables. The phases are uniformly

dis-tributed over (−π, π], and the angles of arrival are uniformly disdis-tributed over (−π, π] in Rayleigh fading model.

The received, demodulated signal can thus be modeled as

y(t) = lim N →∞ σ2 h √ N N X k=1 akej(wDt cos θk+φk)+ w(t), (3.2) where σ2

his the power of the received signal, and w(t) is Additive White Gaussian

Noise (AWGN).

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where Nf is the finite number of received paths used to approximate the channel

response, hp,iis the impulse response of each received path (i.e., one Rake finger)

and δ(τ ) can be used to describe the delay experienced in each received path.

3.2 Extended Channel Model

To evaluate the effect of LOS component and some other properties of channel response, the basic channel model is extended in this section. The extended channel model includes a possible LOS component and directional scattering.

The LOS component can be seen as an additional path in the multi-path channel model. It can be expressed by [14]

hLOS(t) = ej(ωDt cos θ0+φ0), (3.4)

where θ0 and φ0 represents the arrival angle and the phase shift of the LOS

path, respectively.

It may contains high power compared to the other scattering components and have significant impact on the receive signal. Consequently, the channel response of one received path can be given by [14]

h(t) = √ 1 K + 1hp(t) + r K K + 1hLOS(t) = r 1 K + 1N →∞lim 1 √ N N X k=1 akej(wDt cos θk+φk)+ r K K + 1e j(ωDt cos θ0+φ0) (3.5) where K denotes the Rician factor, which describes the fraction of total power contained in the LOS component.

The received, demodulated signal in this case can thus be given by

y(t) = s σ2 h K + 1N →∞lim 1 √ N N X k=1 akej(wDt cos θk+φk)+ s Kσ2 h K + 1e j(ωDt cos θ0+φ0)_+w(t) (3.6) Another possible extension of the model is to include the influence of direc-tional scattering, which means the probability of the arrival path can be more likely from a certain direction. The distribution of Angle of Arrival Path (AOA) can be modeled by Von Mises distribution [23]

p(θ) = 1 2πI0(κ)

eκ cos(θ−α) (3.7)

where In(κ) is the n-th order modified Bessel function of the first kind, κ is the

beam width, and α represents the angle between the mobile direction and the average scattering direction, i.e. the directional scattering angle.

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3.3 Channel Properties

In this section, some properties of the radio channel that relate to this research subject will be described. Note that only the theoretical channel response is considered here.

3.3.1 Correlation function

According to the extended channel model Eq.(3.5), the correlation function can be given by rh(τ ) = E {h∗(t)h(t + τ )} = 1 K + 1rhp(τ ) + 1 K + 1rhLOS(τ ). (3.8) Note that the correlation function is complex valued and rh(−τ ) = r∗h(τ ).

For the scattering component hp, the correlation function can be represented

by [24] rhp(τ ) = J0 p−κ2_{+ ω}2 Dτ2− 2jκ cos(α)ωDτ I0(κ) , (3.9)

where J0(z) is the zero-th order Bessel function of the first kind, and I0(z) =

J0(iz) is the zero-th order modified Bessel function of the first kind. The Bessel

function is defined as J0(z) = 1 2π Z 2π 0 eiz cos φdφ = ∞ X k=0 (−1)k (k!)2 z 2 2k . (3.10)

Specifically, if assume the beam width κ = 0, the Eq.(3.9) can be simplified to

rhp(τ ) = J0(ωDτ ), (3.11) which means the Bessel function can be used to represent the autocorrelation function. This is also called Clarke’s or Jake’s model. Note that the correlation is a function of ωDτ , thus the shape is the same for different Doppler spreads,

but with different time scale.

For the LOS component, the correlation can be given by rhLOS(τ ) = e

jωDτ cos θ0_. _(3.12)

Note that the correlation function is periodic, and the frequency depends on the AOA of the LOS component θ0. When the LOS component arrives parallel

to the mobile velocity, i.e. θ0= 0, the frequency shift is maximized and equal

to the maximum Doppler spread. It is equal to zero if it is orthogonal to the mobile velocity, i.e. θ0= 90 degree.

3.3.2 Doppler spectrum

The Doppler spectrum of the channel response is the Fourier transformation of the correlation function, which can be given by

Sh(f ) =

1

K + 1Shp(f ) + K

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For the scattering component, the spectrum can be given by [21] Shp(f ) = cosh κ sin(α) r 1 −_ωω D 2 ! πI0(κ) r 1 −_ωω D 2 eκ cos(αωDω )_. _(3.14)

When κ = 0, it can be simplified to

Shp(f ) =    1 2πfD r 1− 1 fD 2 |f | ≤ fD 0 otherwise, (3.15)

which is the Clarke’s or Jakes’ Model.

Furthermore, the spectrum of the LOS component is given by

ShLOS(f ) = δ(f − fDcos θ0), (3.16) which means a peak in spectrum at the Doppler frequency.

Consequently, the Eq.(3.13) can be written as

Sh(f ) =    1 K+1· 1 2πfD r 1− 1 fD 2 + K K+1 1 2δ(f − fDcos θ0) |f | ≤ fD 0 otherwise. (3.17)

3.4 General Calculations

For digital transmission systems, the received symbols obtained from the Rake receiver can be seen as discrete-time samples from the time continuous channel, which is given by

yDP CCH[n] = y(nTs), (3.18)

where y(t) is the time continuous received signal, and Ts denotes the sample

period of the receiver.

Considering the WCDMA uplink scenario, the received, demodulated and despreaded signal from DPCCH can be modeled as

yDP CCH[n] = h[n] + w[n] (3.19)

where w[n] is white additive Gaussian noise in an idealized scenario. It can also be seen as an estimation of the channel response. Note that here the pilots are known to the receiver so they are removed after the demodulation.

In this report, the basic channel estimation based on pilot symbols is applied, which means the average values of the received despread pilot symbols of each slot from the DPCCH channel are calculated as the channel coefficients estimate for this slot. It is given by

ˆ h[n] = y[n] = 1 NP ilots NP ilots−1 X m=0 yDP CCH[10 · n + m], (3.20)

where Npilotsrepresents the number of pilot symbols in each slot. Note that the

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According to the standard parameter setting of WCDMA, the time period of one frame is 10ms, and one frame consists of 15 slots. In this case, the sampling interval of the channel estimate ˆh[n] in Eq.(3.20) is equal to the period of one slot, which is Ts= 1/1500 ≈ 6.67 × 10−4 second.

Assuming the signal property is stationary over the estimation duration, the time discrete representation of the autocorrelation functions of the channel estimation can be defined as

ry[k] = 1 M − k M −k X n=1 ˆ h∗[n]ˆh[n + k], (3.21)

where M is the number of slots used in the correlation estimation. It can also be written by

ry[k] = rh[k] + rw[k] = rh[k] + σw2δ[k], (3.22)

where σ2

w is the power of Gaussian additive noise and δ[k] denotes the Dirac

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Chapter 4

Doppler Spread Estimation

Algorithms

In this chapter, the four chosen Doppler spread estimation algorithms will be described individually.

4.1 Zero Crossing Rate Estimator

The Zero Crossing Rate (ZCR) estimation is a simple way to estimate the max-imum Doppler spread from the perspective of implementation. It is based on the zero crossing rate of estimated channel response given by Eq.(3.20), which is defined as the in-phase or the quadrature-phase (I/Q) components of the de-modulated received signal. A realization of channel response from BCL is shown in Fig. 4.1, where the zero crossings are illustrated.

0 0

Real

Im

ag

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According to [21], ZCR is given by ZCR = 1 π s −r00 y(0) ry(0) " e−ζI0(η) + b2 2ζ Z ζ 0 e−uI0 η ζu du # (4.1) where a = √2K, b =√2KωDcos θ0 q −ry(0)/r 00 y(0), ζ = (a2+ b2)/4 and η =

(a2_{− b}2_{)/4, K is the Rician factor in the Rician fading model.}

It can be proved that the value of b does not depend on the Doppler frequency ωD. As a result, the ZCR is proportional to the maximum Doppler spread and

it can be used as a Doppler spread estimator. Assuming the Rayleigh fading model, (4.1) can be further reduced to

ZCR = 1 π s −r00 y(0) ry(0) =√ωD 2π. (4.2)

The calculation of derivatives of correlation function can be found in [24]. Thus the ZCR estimator in the simulation is defined as

ˆ fD=

ZCR √

2 . (4.3)

4.2 Correlation Based Estimator

In the article [5], Mario Moser proposed a correlation based Doppler spread estimator. The estimator is based on the measurement of autocorrelation func-tion of channel estimates, and it is derived from the properties of the Doppler spectrum. Therefore the following two notations are defined and used in this estimator to characterize the spectrum.

1. The Doppler shift is defined as fshif t = R∞ −∞f Sh(f )df R∞ −∞Sh(f )df (4.4) where the Sh(f ) denotes the power spectrum density of channel response in

Eq(3.23). Note that this Doppler shift here does not characterize the frequency shift in one specific path, rather, it can be seen as the center of gravity of the Doppler spectrum of received signal.

2. The spread factor is defined as

σB = v u u t R∞ −∞(f − f 2 shif t)Sh(f )df R∞ −∞Sh(f )df . (4.5)

These two parameters are rather difficult to calculate. The reason is that they require the estimation of PSD and integration operation in the frequency domain. In [5] the author suggests to transform these calculations into time domain. As we know, the autocorrelation function rh(t) can be represented by

the inverse Fourier transformation of the power spectrum density Sh(f ) as

rh(t) =

Z ∞

−∞

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Calculation of the derivative of Eq.(4.6) with respect to t is given by r0_h(t) =

Z ∞

−∞

j2πf Sh(f )ej2πf tdf. (4.7)

The calculation of the derivative of Eq.(4.7) with respect to t is r00_h(t) =

Z ∞

−∞

j4π2f2Sh(f )ej2πf tdf (4.8)

Setting t = 0, and inserting Eq.(4.6) and (4.7) into (4.4) and (4.5), the calcula-tion for these two parameters can be transformed into time domain as

fshif t= 1 2πj r0_h(0) rh(0) (4.9) and σB= 1 2π s r0 h(0) rh(0) 2 −r 00 h(0) rh(0) . (4.10)

By doing this, the Doppler shift and the Doppler spread can be easily ob-tained if the autocorrelation function of the channel coefficients is available. In order to calculate the values of correlation function’s derivatives r0_h(0) and r00_h(0), Moser suggests following approximations [5]:

r0_h(0) = lim Ts→0 jIm {rh(Ts)} Ts ≈ jIm {ry[1]} Ts (4.11) and r00_h(0) = lim Ts→0 2Re {rh(Ts)} − rh(0) T2 s ≈ jIm {ry[1]} − rh[0] T2 s . (4.12)

Finally, the Doppler shift and Doppler spread can be calculated as fshif t= 1 2πTs Im {ry[1]} ry[0] (4.13) and σB= 1 2πTs s 1 − Im {ry[1]} ry[0] 2 −2Re {ry[1]} ry[0] , (4.14)

respectively. It means these two Doppler characteristics of the channel can be obtained from only two values of the autocorrelation function: ry[0] and ry[1].

Moreover, as shown in (3.22), the correlation at lag zero ry[0] should be

avoided in estimation since it contains the noise term, which has significant impact on the estimation results.

In order to reduce the influence of additive noise, another calculation can be used to avoid the using of ry[0]. If we estimate the slope of ry at lag zero

by approximating it linear between two points that are 3Ts apart (assuming

3Tsfc 1). The alternative estimators can be obtained as

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and σB= 1 2πTs s 2 3 − Im {ry[1]} Re {ry[1]} 2 −2Re {ry[2]} 3Re {ry[1]} . (4.16)

The derivation and assumptions required for this approximation process can be found in [5]. Calculating more general expressions for these two parameters, we can get fshif t= 1 2πT Im {ry[1]} Re {ry[1]} (4.17) and σB= 1 2πTs s 2 η2_{− 1} − Im {ry[1]} Re {ry[1]} 2 − 2Re {ry[η]} (η2_{− 1)Re {r} y[1]} , (4.18)

where ry[η] for η ≥ 2 represents the value of lag η of autocorrelation function.

In order to evaluate the accuracy of the estimators, it is desirable to trans-form these two parameters into the maximum Doppler spread fD (e.g., to

es-timate the mobile velocity). However, it requires the prior knowledge of the shape of Doppler power spectrum density. In this case, it is assumed the receive signal has a Jakes’ spectrum for simplicity. Then the maximum Doppler spread frequency can be calculated as [25]

ˆ fD=

√

2σB. (4.19)

4.3 PSD Slope Estimator

The third algorithm chosen for evaluation in this paper is described in [7], which can be seen as an algorithm based on the Doppler spectrum. It detects the first dominant peak slope of the received signal’s PSD, which is referred to as “PSD Slope Estimator” in the current report.

During the algorithm implementation process, the periodogram approach is chosen for the estimation of received PSD. It has the advantage of high effi-ciency from the perspective of computation and implementation by Fast Fourier Transform (FFT). It can be classified as a non-parametric estimation approach. Furthermore, several parametric approaches are also proposed in [9] [10] to im-prove the resolution and accuracy of estimation. However, the computational cost will be increased correspondingly. Thus these approaches are listed as future work to further improve the algorithm.

A periodogram estimate of power spectral density with length N is given by

ˆ S(f ) = Ts N N −1 X n=0 y[n]e−j2πf nTs 2 . (4.20)

In order to implement in practice, only finite number of frequency points are calculated. If y[n] is zero-padded to length M , the M-point periodogram estimator can be written by

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where fk= _{M T}k_s, k = 0, 1, . . . , M − 1 represents M estimated frequency points.

It can be efficiently computed by a M-point FFT.

In [7], the modulated received signal is used to estimate the PSD. However, considering the baseband scenario in this report, the PSD of received signal Sy(f ) can be given by Sy(f ) =      1 K+1· σ_h2 2πfD r 1− 1 fD 2 + K K+1 σ_h2 2 δ(f − fDcos θ0) + σ 2 w |f | ≤ fD σ2 w fD≤ |f | ≤ B (4.22) where the Doppler shift fshif t is set to zero for better illustration.

An example of the received signal PSD is shown in Fig.(4.2).

. . . .

Num. of Interval

₁

₂

_M

. . . .

_N

. . . .

M

. . . .

2

1 PSD

fLOS

-fD fD

Figure 4.2: The Power Spectral Density of the received signal in ideal Rician fading model.

Furthermore, by differentiating (4.22), its slope can be given by

dS(f ) df =            σ_h2f 4(K+1)πf3 D h 1−(_fDf )2i 3 2 , |f | ≤ fD, f 6= fLOS σ_h2f 4(K+1)πf3 D h 1−(_fDf )2i 3 2 + Kσh2 4(K+1)δ(f − fDcos θ0), f = fLOS 0, fD< |f | < f B (4.23) According to the shape of the Doppler spectrum, there should be three peaks in the slope of PSD: f = fm, f = −fm and f = fLOS. When the channel is

Rayleigh fading (no LOS component), it reduced to two peaks: f = fm and

f = −fm.

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of the received signal’s spectrum, and it is equal to the sampling frequency according to the Nyquist Sampling Theorem, i.e. B = Fs= 1/Ts= 1500 Hz.

The following calculation of the slope is suggested by the author:

s[k] = Pk+1 i=1 P [i] − Pk i=1P [i] 2∆B = P [k + 1] 2∆B (4.24)

where P [k] represents the sum of the power of i-th interval and its mirror interval as illustrated in Fig(4.2), and ∆B = B/2N is the bandwidth of one interval.

But we believe a mistake has been made by the author in [7], since the detection will give essentially the same result with detecting the shape of PSD when applying the calculation in Eq.(4.24). So the following slope calculation is proposed in the current report:

s[k] = P [k + 1] − P [k]

2∆B . (4.25)

The next step is to find out the interval that contains the frequencies f = fm

and f = −fm, which will be dominant in both Rayleigh fading and Rician fading

scenarios.

The detection procedure suggested in [7] is to calculate the slope from first interval by Eq.(4.24), i.e. s[1], s[2], . . ., until the first dominant slope is found. The choosing of threshold to determine which one is “dominant” will be dis-cussed later. Whereas the reason for finding the dominant slope of lowest order is to avoid the detection of the LOS component, which will be another dominant slope in the Rician fading scenario. The maximum Doppler spread can thus be calculated as

ˆ

fD= B − kmin(∆B) (4.26)

where kmin is the index of interval that contains the lowest order peak slope.

Due to the periodicity of periodogram estimation, the estimated power spec-tral density is shifted and will have the shape as shown in Fig(4.3).

An example of estimated PSD is shown in the Fig(4.4).

The tricky part of the algorithm is how to identify which peak is “dominant”. During the simulation in [7], it is assumed that the worst case signal-to-noise ratio (SNR) is known, and N0(worst) can be used as slope threshold to detect

the dominant peak, where N0(worst) is defined as the value of N0 corresponding

the worst case SNR.

After some basic tests, it turns out that the threshold values used in the simulation from [7] are not applicable for the implementation of this algorithm, since the simulation environment used for this thesis research (BCL) is not idealized. Thus in this research, the instant noise level calculated from the average power and estimated signal-to-interference ratio (SIR) of received signal is used as threshold. This detection approach is referred to as the “VEPSD Original” detection in the report for comparison

In order to improve the accuracy of detection, another method is proposed and tested in this report. The detection procedure contains the following two steps.

1). Calculate all the slopes and detect the maximum peak.

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Num. of Interval

PSD

M 2 1 1 2 M

fD B-f_D

Figure 4.3: The Theoretical Power Spectral Density Estimation by Using Peri-odogram 0 500 1000 1500 0 5 10 15x 10 7 Frequency [Hz]

Periodogram estimated spectrum

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times of previous peak, and it should also be larger than the maximum noise power calculated by using peak power amplitude divided by estimated SIR.

If there is no single point satisfying these requirements, the detection algo-rithm will find the maximum peak for the estimation.

The proposed detection method is applied to both slope calculation (4.24) and (4.25), the modified estimation approaches are referred to as “Modified PSD slope estimator 1” and “Modified PSD slope estimator 2” respectively in the rest of the report.

This detection method is based on empirical data from simulation. A the-oretical motivation will not be given in this report. It is believed that some statistical analysis based on receive signal distribution can be used to estimate an optimal threshold for detection. However, given the limited time for the thesis project, we decided to delegate it to the future work.

4.4 ML Estimator in Time Domain

The next chosen Doppler spread estimator is described in [11]. It can be clas-sified as a ML estimation approach in the time-domain. The basic idea is to calculate and evaluate the likelihood function based on the approximation of the correlation function. Furthermore, in order to migrate the algorithm into the WCDMA transmission system, some modifications are made to the algorithm, which are described in detail in this section.

Assuming the Doppler spread fD will remain constant during M slots, the

estimation of Doppler spread can be given by minimizing the log likelihood function [11] Fopt[fd] = ln [det(K[fd])] + Nm X i=1 Nm X l=1 ˆ K[i, l]K−1[i, l; fd], (4.27)

where ln [det(K[fd])] is the determinant of correlation matrix with the elements

K[i, l; fd] = σ2hJ0[2πfdm] + σ2w/Npilots· δ[i, l], (4.28)

where m is the lag of correlation function, fd is the hypothesis value of

normal-ized maximum Doppler spread, Nmis the size of correlation estimation matrix,

which is set to be the number of pilot symbols in each slot in [11] since pilots are used in the estimation directly, J0[z] is the first order modified Bessel function of

the first kind, δ[i, l] is the Kronecher symbol, σ2

his the power of received signal,

and σ2

wis the noise power. Thus the SNR can be represented by γ = σh2/σ 2 w.

It is assumed in [11] that the SNR is known, but the investigation also shows that the proposed algorithm is robust against errors between theoretical SNR and estimated SNR. However, in order to simulate a real world scenario, the output of SIR estimation from SIR estimator in BCL is used to estimate the signal energy and noise energy in the current investigation.

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where 0 ≤ i, l ≤ Npilot− 1, and M is number of slots used for simulation.

It means the estimation is based on the pilot symbols of M consecutive slots. However, considering the fact that only six to eight pilot symbols are available in each slot in the WCDMA uplink channel, it is more reasonable to use slot as unit to estimate the channel correlation (average over pilot symbols in each slot as shown in Eq.(3.20)). Thus the following estimation for the correlation is also proposed and tested in the following investigation:

ˆ K2[k] = 1 M − k M −k X n=1 ˆ h∗[n]ˆh[n + k] (4.30)

where ˆh is the channel estimates calculated from Eq.(3.20). In this case, the size of the correlation matrix is set to be 11 (i.e., including correlation from lag zero to lag 10).

The procedure to estimate the Doppler spread is to calculate the likelihood function (4.27) for each hypothesis value fd, compare all the values of likelihood

function, and find out the hypothesis that minimize the likelihood function as the estimate of maximum Doppler spread ˆfD.

A sub-optimal ML estimator is also proposed in [11]. It does not require the knowledge of SNR and also avoids the matrix inversion in ML estimator. This method can also be used to reduce the computational complexity.

The sub-optimal ML estimate of Doppler spread is given by minimizing the likelihood function Fsub= 1 Nm Nm X n=1 ˆ K2[n] ˆ K2[0] −σ 2 hJ0[2πfdn] σ_h2J0[0] 2 , (4.31)

which is a modification of the likelihood function proposed in [11] since the correlation estimation based on slot are applied in this research. Note that here the matrix calculation can be avoided, only the correlation vector is needed.

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Chapter 5

Computational Cost

Since the algorithms are intended to be evaluated for possible implementation in a real system, and not only as a theoretical analysis, the computational com-plexity of each algorithm is also an important factor that needs to be assessed. Thus in this chapter, the computational complexity for each algorithm will be evaluated and compared.

Since in a Digital Signal Processor (DSP), the multiplication operation and addition operation will be performed simultaneously in each clock cycling, one of them can be chosen as evaluation metric for the complexity evaluation. Nor-mally, the number of multiplications is the dominant factor in the computational cost. Therefore, in this report, the number of multiplications required for each algorithm will be used as a measurement for the computational complexity in real system. In order to narrow down the range of analysis to the estimation algorithms, the calculation of the input parameters of these algorithms is not taken into account, such as the average operation for the pilot symbols and the estimation of SIR of the received signal. The analysis for each algorithm is done in worst case scenario (i.e., the maximum possible computational cost).

5.1 ZCR Estimator

The channel estimates of each slot will serve as input for the ZCR estimator. Assuming the buffer length M is set to be 150 slots, the estimator simply com-pares the sign of two adjacent values (either the real part or the imaginary part of channel estimates) throughout the buffer, and count the number of times the sign flipped by comparing two adjacent estimates with zero. The final result can be given by using only one multiplication using Eq.(4.3). The computational cost for this estimator is shown in the Table 5.1.

Operation Multiplications Num.

Comparison* M 150

Doppler Spread Calcula-tion

1 1

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* Here one Comparison operation is considered to have the same computa-tional cost as one multiplication for comparison.

5.2 Correlation based Estimator

For the correlation based estimator, the first step is to calculate the correlation functions of the channel estimates using Eq.(3.21). In Moser’s estimator, only two points are needed from the autocorrelation function. One thing worth notic-ing is that in the follownotic-ing calculation, one multiplication between two complex values is equal to four real multiplications. The maximum Doppler spread then can be given from Eq.(4.14) and Eq.(4.19). The specific computational cost is shown in Table 5.2.

Correlation P2

k=1[4(M − k) + 2] 1192

Doppler Spread Calcula-tion*

4+(1 time square root) 5

Table 5.2: Complexity breakdown for the correlation based estimator * Here the square root operation is considered to have the same computa-tional cost as one multiplication for comparison.

5.3 PSD Slope Estimator

In order to obtain the PSD of the channel estimation, the FFT needs to be calcu-lated. The theoretical computational complexity of FFT is given byNF F T

2 log2NF F T,

where NF F T is the number of points for the FFT, which is set to be 512 in the

current investigation. Considering the fact that it is complex valued FFT, the complexity becomes 2NF F Tlog2NF F T in this case. However, considering the

fact that some DSPs can be used to calculate the FFT efficiently, the computa-tional cost for FFT operation will be listed separately in the analysis.

The PSD of the received signal can be calculated from Eq.(4.21), which requires 2NF F T times of multiplications. According to Eq.(4.24) and Eq.(4.25),

a maximum of NF F T

2Ns − 1 multiplications are required to calculate the slope of PSD, where Ns denotes the number of samples in one interval ∆B. We can

see that the calculation can be reduced with a sacrifice in resolution. However, Ns= 1 is used here to maintain the estimation quality.

Moreover, maximum NF F T

2Ns − 1 comparison operations are needed to detect the first dominant slope. If the modified detection proposed in Section4.3 is applied, at most NF F T

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Operation Multiplications Num. PSD Calculation 2NF F T + 2NF F Tlog2NF F T(512-FFT) 10240

Slope Calculation NF F T/(2Ns) − 1 255

First Dominant Slope De-tection*

NF F T/(2Ns) − 1[NF F T/(2Ns) + 19] 255 /275

Doppler Spread Calcula-tion

1 1

Table 5.3: Complexity breakdown for the PSD slope estimator

5.4 Time Domain ML Estimator

For both the optimal and the suboptimal approach, the elements of channel correlation estimation matrix can be calculated using Eq.(4.30). For the optimal ML estimator, the calculation of matrix determinant, matrix inversion, received signal energy and the multiplication between elements is required according to Eq.(4.27). Assuming the matrix size is set to be Nm (Maximum Lag of

correlation function Lm= Nm−1 ), the computational cost for these operations

are approximately N3

m, Nm2, 2M + 1 and Nm2 respectively. Note that here the

matrix are real valued. And the cost for the matrix inversion can be much lower since the correlation matrix is Hermitian matrix, but the upper bound is considered here for convenience. The computation also includes theoretical correlation matrix.

∆f = 20Hz ∆f = 5Hz Correlation Estimation

Matrix

PLm

k=0[4(M − k) + 2] 6402 6402

Receive Signal Power Es-timation

2M + 1 301 301

Noise Level Calculation 1 1 1

Matrix Inversion N3

m· (W/∆f ) 19965 79860

Matrix Determinant N3

m· (W/∆f ) 19965 79860

Correlation Matrix Calcu-lation

Nm· (W/∆f ) 165 660

Likelihood Function Cal-culation 2N2 m · (W/∆f ) + (W/∆f )(Logarithm operation) 3645 14580

Doppler Spread Estima-tion*

(W/∆f ) − 1 14 59

Table 5.4: Complexity breakdown for the time domain ML estimator For the suboptimal estimator (4.31), the matrix inversion and the calculation of determinant can be avoided. The information of the SNR is not required as well. From the perspective of implementation, these advantages can significantly reduce the complexity of the estimator.

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de-Operation Multiplications Num. ∆f = 20Hz ∆f = 5Hz Correlation Estimation Matrix PLm k=0[4(M − k) + 2] 6402 6402

Receive Signal Power Es-timation

2M + 1 301 301

Likelihood Function Cal-culation

(4Lm+ 1) · (W/∆f ) 615 2460

Doppler Spread Estima-tion*

(W/∆f ) − 1 14 59

Table 5.5: Complexity breakdown for the time domain sub-optimal ML estima-tor

tection range is W = 300 Hz, a Doppler spread estimate requires totally W/∆f times of likelihood function calculation (number of hypothesis values). Conse-quently, there is a trade-off between the estimation accuracy and computational cost. Obviously, the performance can be increased by using higher resolution, but the computational complexity will increase dramatically. It is illustrated in Table 5.4 and 5.5, where two different resolutions are used (∆f = 20 Hz and ∆f = 5 Hz respectively).

5.5 Summary

For comparison, the computational cost for these four estimators are presented in Fig.5.1.

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Chapter 6

Simulation Results

6.1 Simulation Environment

In this section, the simulation environment will be introduced briefly.

6.1.1 BCL

BCL stands for the Baseband Core Library, which is a reference model of WCDMA uplink baseband processing. The BCL is part of the simulation chain for the WCDMA transmission systems of Ericsson where the estimation algo-rithms are implemented. It is able to give a result that is close to the real world data, which makes the performance evaluation in this investigation more reliable and practical.

6.1.2 Simulation Parameters

The parameter settings for the simulations are presented in the Table6.1, where

Number of Simulation Frames 8000

Number of Slots in Each Frame 15

Number of Antennas 2

Slot Format 1

Number of Fingers Used 1

Number of channel estimates (Buffer Length) 150

TPC Off

AGC Off

Multipath Channel Type Pedestrian A

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Furthermore, the “Pedestrian A” is used for simulation in the basic channel model, which is an empirical channel model specified by International Telecom-munication Union (ITU) [26]. It is a tapped delay line model as given in Eq.(3.3) with the specified parameters as given in the Table 6.2.

Tap Relative delay (ns) Average power (dB)

1 0 0

2 110 -9.7

3 190 -19.2

4 410 -22.8

Table 6.2: Specified Parameters for ITU “Pedestrian A” Channel Model

6.2 Simulation Results

In this section, the four types of estimator introduced in this report are evaluated independently with respect to their performance in the basic channel model. Here, the effect of different velocities and different SNR values is evaluated. When testing different velocities, the SNR is set to 15 dB.

6.2.1 Crossing Rate

First the ZCR estimator is evaluated, which is a simple way to achieve basic Doppler spread estimation in terms of implementation.

0 50 100 150 200 250 300 50 100 150 200 250 300

True maximum doppler spread [Hz]

Mean estimate maxim um doppler spread [Hz] Average ZCR ZCR of Imaginary Part ZCR of Real Part

(a) Low Doppler and High Doppler

6 8 10 12 14 16 18 20 22 24 50 52 54 56 58 60 62 64

Mean estimate maxim um doppler spread [Hz] Average ZCR ZCR of Imaginary Part ZCR of Real Part

(b) Enlarged picture in low Doppler spread area

Figure 6.1: Comparison of simulated and theoretical value of Doppler spread of three ZCR estimators

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One can draw a similar conclusion from Fig.6.2, where the Normalized Mean Square Error (NMSE) is evaluated for different Doppler spread.

Note that the NMSE is calculated by (6.1)in this report, where E {·} repre-sents the mean operation.

N M SE (fD) = E_fˆ D      ˆ_f_D_{− f}_D2 f_D2      (6.1) 0 50 100 150 200 250 300 10−3 10−2 10−1 100 101 102 103

Normalized

MSE

Average ZCR ZCR of Imaginary Part

ZCR of Real Part

6 8 10 12 14 16 18 20 22 24 100

101

102

103

Normalized

MSE

Average ZCR ZCR of Imaginary Part ZCR of Real Part

Figure 6.2: Normalized mean square estimation error (NMSE) of three ZCR estimators versus true maximum Doppler spread value

0 2 4 6 8 10 12 14 10−3 10−2 10−1 100 101 102 103 SNR [dB] Normalized MSE fD= 10 Hz fD= 80 Hz fD= 160 Hz fD= 240 Hz

Figure 6.3: Normalized mean square estimation error (NMSE) of ZCR estimator versus SNR

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One can see that the gain in SNR improves the performance of the ZCR esti-mators, especially at low and middle speed.

Furthermore, as shown from the results, the performance for these three ZCR estimators are very close to each other. The estimator using the average ZCR can be slight more stable compared to the other to estimator. However, considering the computational cost, it is sufficient to calculate only real or imag-inary ZCR in practical implementation. In this report, the average ZCR will be used for comparison in order to get better performance.

6.2.2 Covariance Based Estimator

The simulation results of covariance based estimator proposed in [5] are pre-sented in this section. In order to find the optimum parameters for the estima-tor, different lags in autocorrelation function are simulated for comparison.

0 50 100 150 200 250 300 0 50 100 150 200 250 300

Mean estimate maxim um doppler spread [Hz] Original η = 2 η = 3 η = 4 η = 5

6 8 10 12 14 16 18 20 22 24 0 20 40 60 80

Mean estimate maxim um doppler spread [Hz] Original η = 2 η = 3 η = 4 η = 5

Figure 6.4: Comparison of simulated and theoretical value of Doppler spread of covariance based estimators

As shown in the Fig.6.4(a), in the wide range of Doppler spread, the co-variance estimator with η = 2 in the autocorrelation function demonstrates the best performance among all the estimators. But we can still observe the bias of this estimator at high velocities. According to the analysis in [5], this detection error is caused by noise and the linear approximation of derivatives of autocor-relation function. One de-biased algorithm is tested to battle this estimation error, which aims to compensate for the error introduced by the linear approx-imation. But there was no significant improvement on the performance. Thus the simulation result for the de-biased algorithm will not be presented in this report.

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An iterative algorithm can be applied to choose the optimum lag η based on the Doppler spread. However, in order to simplify the implementation, this algorithm is not included in the current investigation, and it is put into the future work of this thesis research.

0 50 100 150 200 250 300 10−3 10−2 10−1 100 101 102 103

Normalized MSE Original η = 2 η = 3 η = 4 η = 5

6 8 10 12 14 16 18 20 22 24 10−2 10−1 100 101 102 103

Normalized MSE Original η = 2 η = 3 η = 4 η = 5

Figure 6.5: Normalized mean square estimation error (NMSE) of ZCR estimator versus true maximum Doppler spread value

0 2 4 6 8 10 12 14 10−3 10−2 10−1 100 101 SNR [dB] Normalized MSE fD= 10 Hz (η=2) fD= 80 Hz (η=2) fD= 160 Hz (η=2) fD= 240 Hz (η=2) fD= 10 Hz (η=3) fD= 80 Hz (η=3) fD= 160 Hz (η=3) fD= 240 Hz (η=3)

Figure 6.6: Normalized mean square estimation error (NMSE) of covariance based estimators versus SNR

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In order to keep the estimation error at an acceptable level for the whole detection range, the estimator with η = 2 is chosen for further investigation.

6.2.3 PSD Slope Estimator

The simulation results of PSD slope estimators will be discussed in this sec-tion. For comparison, the original detection approach proposed in [7] and two modified detection approaches proposed in this report are analyzed.

Furthermore, for deeper investigation of this estimator, another two detec-tion approaches proposed in the previous literature are also included in the simulation, which are to detect the frequency point corresponding to the 3 dB fading level from the maximum peak on the received PSD and its slope. These two approaches will be referred to as “3 dB Detection on PSD” and “3 dB Detection on Slope” in this report, respectively.

0 50 100 150 200 250 300 0 50 100 150 200 250 300

Mean estimate maxim um doppler spread [Hz] Modified approach 1 Modified approach 2 VEPSD Original 3 dB Detection on PSD 3 dB Detection on Slope

6 8 10 12 14 16 18 20 22 24 5 10 15 20 25 30 35 40

Mean estimate maxim um doppler spread [Hz] Modified approach 1 Modified approach 2 VEPSD Original 3dB Detection on PSD 3dB Detection on Slope

Figure 6.7: Comparison of simulated and theoretical value of Doppler spread of PSD slope estimators

As one can observe from Fig.6.7, most of detection approaches suffer from the underestimation of Doppler spread. There are two possible reasons for this problem: First, as shown in Fig.4.4, the shape of estimated PSD of the received signal from BCL has significant difference from the ideal Jake’s spectrum due to serious fading and noise. It makes the detection process become very difficult to locate the correct position directly from the spectrum. The appearance of extra peaks resulting from noise will definitely bias the estimator. Second, the peak detector will end up with the maximum peak if no peak is found that can satisfy the searching conditions, which can make the index kmin larger than the

real value and thereby lower the estimate value of Doppler spread according to (4.3). This will also make the mean estimation value lower if large amount of simulation is executed.

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0 50 100 150 200 250 300 10−2

10−1

100

101

Normalized MSE Modified approach 1 Modified approach 2 VEPSD Original 3 dB Detection on PSD 3 dB Detection on Slope

6 8 10 12 14 16 18 20 22 24 10−2

10−1

100

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Normalized MSE modified approach 1 Modified approach 2 VEPSD Original 3dB Detection on PSD 3dB Detection on Slope

Figure 6.8: Normalized mean square estimation error (NMSE) of PSD slope estimators versus true maximum Doppler spread value

The reason for this improvement is that the simulation environment used in this research is far more realistic than the idealized signal and channel model from most research papers. Sometimes the expected result from these papers can not be given from the current simulator. Specifically, the threshold given from [7] is not applicable in this simulation. In this case, the empirical detection approaches can give a better performance than the original one, although we believe there is still potential to further increase the accuracy by using statistic analysis to the spectrum.

0 2 4 6 8 10 12 14 10−2 10−1 100 101 SNR [dB] Normalized MSE fD= 10 Hz (Modified 1) fD= 80 Hz (Modified 1) fD= 160 Hz (Modified 1) fD= 240 Hz (Modified 1) fD= 10 Hz (Modified 2) fD= 80 Hz (Modified 2) fD= 160 Hz (Modified 2) fD= 240 Hz (Modified 2)

Figure 6.9: Normalized mean square estimation error (NMSE) of PSD slope estimators versus SNR

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lower level of estimation error comparing to the first approach when SNR is above 2dB, except for low velocity when fD = 10 Hz. On the other hand, it

implies that the first approach is more robust to the variation of SNR than the second one. However, the second detection approach will be chosen since it has larger detection range.

Moreover, one can also see that the NMSE of two estimators shows an in-creasing trend when SNR is above 5 dB at low speed (fD= 10). The reason is

that the estimation is biased at these speeds. The estimation result can be more stable with higher SNR, but has larger bias compared to the real value. Thus the performance can not be improved with the increase of SNR in this range.

6.2.4 ML Estimator

In this section, the simulation results of time domain ML estimator with different parameters will be presented.

The first estimator chosen for simulation is the ML with correlation estima-tion based on slot, which is given by (4.30). The buffer length M = 150 is used. The second ML estimator reduces the length of buffer to M = 11 and removes the average operation. The purpose is to reduce the computational cost and to adapt to the fast variation of received signal energy. The original ML estima-tor in [11], which estimates the correlation matrix using pilot symbols (4.29), is also included in the simulation for reference. Furthermore, the first pilots from each slot are used to estimate the correlation matrix for the ML estimator. In this case, different buffer lengths are tested in the simulation. Finally, the suboptimal ML estimator (4.31) with buffer length M = 150 is included in the analysis.

Based on the simulation result shown in Fig.6.10, one can see that the orig-inal ML estimator is not able to give reasonable estimation of Doppler spread, and it can not be applied in this scenario. The reason is that in the uplink DPCCH channel of WCDMA transmission system, there are only 6 to 8 pilot symbols in each slot, which is not sufficient to give a reasonable estimation.

To fix this problem, the correlation matrix is estimated based on slot instead of pilot. In this report, we use either the averaged value over pilots or the first pilot of each slot. As shown in Fig.6.10, both of them have significant improve-ment on performance accuracy comparing to the original estimator. Further-more, if we consider the effect of buffer length, it is not difficult to observe that long buffer with averaging can give more accurate estimates comparing to short buffer.

Surprisingly, the suboptimal ML estimator gives best estimation among all the ML estimators. Here, one should notice that the SNR of received signal is unknown, and the signal power is not unified, which is different from the as-sumptions made in [11]. All of these parameters are estimated by implemented algorithm or channel estimator in BCL, thus the mismatch between the esti-mated and real value can introduce extra error to the estimation result of ML estimator. On the other hand, the suboptimal ML avoids the usage of these information. This is the reason why it can give more accurate result.

Comparison and Evaluation of Doppler Spread Estimation Algorithms in WCDMA