Performance evaluation of channel estimation techniques for an LTE downlink system

TABLE OF CONTENTS

Acknowledgments

Abstract

List of Figures

List of Tables

List of Acronyms

CHAPTER ONE Introduction
1.1 Introduction
1.2 Literature Review
1.3 Statement of the problem
1.4 Thesis contribution
1.5 Objectives
1.6 Methodology
1.7 Thesis Outline

CHAPTER TWO OVERVIEW OF LTE PHYSICAL LAYER
2.1. Air Interface of LTE
2.2. LTE Duplexing Methods
2.3. Allocation of Bandwidth and Time Framing
2.4. Time frequency representation
2.5. OFDM Multicarrier Transmission
2.6. The Cyclic Prefix
2.7. Subcarrier Spacing
2.8. Resource Block Size
2.9. Resource Grid Contents
2.10. OFDM Typical Transmitter Operation
2.11. OFDM Typical Receiver Operation
2.12 The general block diagram of the LTE downlink system
2.13. Types of Pilot Arrangements
2.13.1. Block Type Pilot Arrangement
2.13.2 Comb Type Pilot Arrangement
2.14. Wireless and mobile communication channel
2.15. Small scale fading
2.16. Propagation aspects and parameters
2.16.1 Delay spread
2.16.2. Maximum excess delay
2.16.3. Average delay
2.16.4. Root mean square delay
2.16.5. Coherence bandwidth
2.16.6. Doppler spread
2.16.7. Coherence time
2.17. Deep fade and diversity
2.17.1. The receive diversity
2.17.2. The transmit diversity
2.18. Multiple input multiple outputs (MIMO)
2.19. Diversity schemes

CHAPTER THREE CHANNEL ESTIMATION TECHNIQUES
3.1. Introduction
3.2. The LS channel Estimator
3.3. MMSE Channel Estimator
3.4. MLE Channel Estimator
3.5. The Linear Interpolation
3.6. Averaging Channel Estimator
3.7. The Hybrid Channel Estimation
3.8. Algorithm complexity

SYSTEM MODELING AND rESULT dISCUSSION
4.1 Introduction
4.2 System Model
4.2.1 Parameter Selection
4.2.2 CRC Generation and Channel Coding
4.2.3 Scrambling
4.2.4 Modulation
4.2.5 Layer mapping
4.2.6 Pre-coding
4.2.7 Mapping to resource elements
4.2.8 OFDMA Transmitter and Receiver
4.2.9 Channel Estimation Techniques
4.2.10 MIMO Receiver
4.3 Simulation Results
4.3.1 Performance of LS, MMSE and ML
4.3.2 Performance of LS with Averaging, Interpolation and Hybrid
4.3.3 Performance of MMSE with Averaging, Interpolation and Hybrid
4.3.4 Performance of ML with Averaging, Interpolation and Hybrid
4.3.5 Complexity Comparison of the Channel Estimation Techniques
4.3.6 Effect of Varying the Number of Antennas on the performance of the channel estimator

CHAPTER FIVE CONCLUSION AND FUTURE WORK
5.1. Conclusions
5.2. Future work

REFERENCES

List of Figures

Figure 2.1: LTE time domain structure for normal and extended cyclic prefix

Figure 2.2: LTE resource grid, resource blocks and Resource element

Figure 2.3: OFDM continuous time transmitter model using bank of oscillators of subcarriers

Figure 2.4: All contents of LTE resource grid

Figure2.5: The analog OFDM transmission system

Figure 2.6: OFDM continuous time receiver model using banks of oscillators

Figure 2.7: Block type pilot arrangement

Figure2.8: Comp type pilot arrangement

Figure 2.9: Classification of fading channels

Figure 2.10: Frequency flat fading

Figure 2.11: Frequency selective fading

Figure3.1: MMSE channel estimator

Figure4.1: the overall system model

Figure 4.2: LTE downlink system model for simulation used in this thesis

Figure 4.3: The structure of the turbo encoder

Figure 4.4: Downlink scrambling

Figure 4.5: Reference symbol position for a single antenna for LTE downlink

Figure 4.6: cell specific reference signals arrangement and spectral nulls

Figure 4.7: OFDMA transceiver block diagram

Figure 4.8: the channel Estimation procedures

Figure 4.9: The performance of channel estimation techniques

Figure 4.10: The performance of averaging, interpolation and hybrid based LS

Figure 4.11: The performance of averaging, interpolation and hybrid based MMSE

Figure 4.12: The performance of averaging, interpolation and hybrid based ML

Figure 4.13: Complexity comparison of ML and MMSE

Figure 4.14: Effect of varying the number of antennas

List of Tables

Table 2.1: Number of resource blocks, number of subcarriers, FF size and sampling frequency and cyclic prefix sizes for all LTE bandwidths

Table 4.1: LTE MIMO parameters selected

Table 4.2: The power delay profile of EVA standard channel model

Table 4.3: BER values for LS, ML and MMSE at some SNR values

Table 4.4: BER values for averaging, interpolation and hybrid based LS

Table 4.5: BER values for averaging, interpolation and hybrid based MMSE

Table 4.6: BER values for averaging, interpolation and hybrid based ML

List of Acronyms

illustration not visible in this excerpt

Acknowledgments

First of all I want to thank the creator of this complex world whose potential cannot be measured and who is invisible but its help and support can be felt by his creatures. Next to my GOD I want to thank to my mom who initiates me to learn my master’s degree in this new program in School of Electrical and Computer Engineering.

Next to this, I want to thank to my advisor Dr. Dilip Mali who helped me in the overall progress of the thesis work. He was not only as an advisor but as a friend we call each other at any time even at night time for academic and schedule of our next meeting in office. Finally, I need to rise my co-advisor Mr. Sinshaw Bekele for his valuable recommendation and giving me orientations how to write my thesis.

Abstract

In this thesis channel estimation techniques for LTE downlink named Least Square, Minimum Mean Square error and Maximum Likelihood estimation techniques are studied for the pilot symbol based channel estimation. In addition to this the performances of these three channel estimation techniques were also studied by introducing averaging, interpolation and hybrid methods.

This work also investigates the complexity of the channel estimation techniques in terms of the number of complex multiplications and by varying the FFT size and number of CP. furthermore, the effect of varying the number of antennas at the transmitter and receiver ends, where 2 x 2 and 4 x 4 antenna arrangements are considered as a case studies. The performance of these channel estimation techniques is also studied for EVA standard channel model in LTE. The considered channel model is EVA standard channel model with Doppler shift of 300HZ.

Simulation results in this thesis show that the ML channel estimation technique has the best performance. In terms of number of complex multiplications it is proved the ML has lower complexity. From the interpolating techniques it is shown the performance of the algorithm integrated with hybrid technique has the best performance. In addition to this it is shown that as the number of transmit and receive antennas increase from 2 x 2 to 4 x 4 the performance of the estimator increases.

CHAPTER ONE Introduction

1.1 Introduction

Long Term Evaluation (LTE) was intended by the alliance of national and regional telecommunications standardizing bodies known as the 3rd Generation Partnership Project (3GPP) since December 2004 [1].

This alliance was designed due to fabulous growth of wireless subscribers in the past decades with over four billion worldwide [2]. It was witnessed by the cellular wireless communications industry that more than one million new wireless subscribers per day have been added worldwide, this means more than ten new wireless subscribers are added in an average of every second [3].

This implies that, the user demand is high quality wireless communication with higher data rate. Thus high data rate can be achieved by either of the following noble technologies. The first technology is the use of wider bandwidth with multicarrier (OFDM) and the second one is the use of higher order modulation within a limited band width, the third one is the use of different transmission modes with multiple input multiple output (MIMO) technologies and so on. The bandwidth is very scares and expensive resource it may not be possible to obtain wider spectrum width to allow very wide band transmissions especially at lower frequency bands [4]. As can be seen in [1] the peak data rate of LTE is 300 Mbps in the downlink and 75 Mbps in the uplink.

There are two types of LTE with regard to the type of guard interval used, these are cyclic prefix LTE and zero pad LTE. As it is studied in [5], cyclic prefix LTE has better performance than Zero pad LTE in terms of BER. Therefore, in this thesis we will design everything with cyclic prefix based LTE.

To compensate between the cost of implementation and higher data rate LTE uses three technologies these are Orthogonal Frequency Division Multiple Access (OFDMA) which is used for downlink transmission, Single Carrier Frequency Division Multiple Access

(SCFDMA) which is used for uplink transmission and Multiple Input Multiple Output (MIMO).

In addition to this, LTE uses two types of duplexing technologies these are Frequency Division Duplexing (FDD) and Time Division Duplexing (TDD) [6].

Since this thesis is concerned about LTE downlink system and from that specifically the channel estimation block. There are three types of channel estimation techniques these are the pilot symbol based, blind or non-pilot symbol based and semi blind or combination of both pilot symbol and non-pilot symbol as studied in [6-12].

In any OFDM based communication system if the channel estimation is based on pilot symbol or reference data, it is possible to arrange the references in two ways. These are known as block type pilot arrangement, comb type pilot arrangement [7]. But LTE has its own special pilot arrangement according to the number of antennas.

1.2 Literature Review

Since LTE is a modern wireless communication technology and it has high throughput and allows mobility and have flexible bandwidth. There are a lot of researches regarding it. Especially for LTE downlink since secrete of high data rate and spectrum efficiency is due to its multiplexing system known as orthogonal frequency division multiple access (OFDMA).

The channel estimation can be done using reference symbols known as pilots as in [6-9]. It can be also performed with the data itself that is blind channel estimation as in [10]. The third one is the combination of the two known as semi blind channel estimation which uses both pilot symbols and received actual data to estimate the channel impulse response [11 12]. Different parameters are used to measure the performance of channel estimation techniques for LTE downlink system. In [13-19] channel estimation techniques for different channel environments are discussed.

S. Adegbite et.al. describes the interpolation techniques of the least square channel estimation technique for LTE downlink for three types of extended ITU channel environments and found the linear interpolation technique has best performance [13].

Asad Mehmood and Waqas Aslam Cheema [14] studied LTE downlink channel estimation for different channel environments such as ITU standardized environments and includes air interface possible combinations to visualize the performance difference and compare LS and Leaner Minimum Mean Square Error (LMMSE). The LMMSE channel estimation technique found to have better performance.

Jin Xinzhu [15] studied different channel estimation techniques for LTE uplink transmissions for different user equipment speeds and it was difficult to identify which estimator has best performance because each estimator has its own advantage and disadvantage. For example for lower mobile user equipment speed, the LMMSE channel estimator has better performance for lower SNR values and the Gauss Markov estimator also has better performance for higher SNR values. But for higher speed mobile user equipment’s, the LMMSE has the best performance in both high and low SNR values.

Mohammed H.M. et.al. carried out studies on different channel estimation techniques for LTE in different channel environments but using the SC FDMA or for uplink transmission and found that all channel estimation techniques degrade their performance with the increase of Doppler shift but variable step size linear mean square (VSS LMS) has better performance [16].

Md. Masud Rana et.al. carried out studies on different channel estimation techniques for LTE downlink system for different channel environments and found that proposed estimation technique has better performance than LS channel estimation technique when measured in mean square error (MSE) and symbol error rate (SER) for different signal to noise ratio (SNR) values. This channel estimation technique uses channel properties which is not the concern of LS channel estimator [17].

Abdel Hakim Khalifi and Ridha Boullegue [18] discussed different LTE channel estimation techniques for different channel lengths for LTE downlink transmission. They proposed a new hybrid of LS and LMMSE channel estimation technique which is a robust for channel length.

Mairo Bogdanovic and Alen Bazant [19] have shown that the LS channel estimation technique can be improved by using the comb type and block type pilot arrangement and their combination. On the other hand different interpolation methods such as linear and cubic are used and they found the linear interpolation technique has better performance than the cubic interpolation technique.

Spridon Zettas et.al.[20] studied the averaging channel estimation for different channel models such as frequency selective, AWGN, fast time varying. Finally it was shown that the averaging channel estimation technique performs best for AWGN channel and it can be perform acceptably for frequency selective fading channels but it fails to perform acceptably for fast time varying channels.

S. Adegbite et.al. [21] Studied least square channel estimation technique integrated with different interpolation techniques and found that linear interpolation technique is suitable. The performance of the interpolation techniques was evaluated at different extended ITU channels.

1.3 Statement of the problem

The channel estimation technique block in LTE downlink system is used to calculate the real channel parameters at the receiver. Since the channel can be affected by mobility of the user equipment and other factors of the communication environment. When any information signal is transmitted from the eNodeB to the UE it experiences different power attenuation and change of direction. When the power becomes very low the receiver will be an able to receive or sense the transmitted signal. If there is multiple change in direction the received signal will be multiple copies of the transmitted signal. Due to the reflection, diffraction and multipath fading occur during transmission the receiver obtains multiple copies of the transmitted signal at different time intervals. The arrival of signal difference results either in constructive or destructive signal addition at the receiver. For the recovery of the real channel the equalizer requires the estimated channel. Since the channel estimation technique has a great role in the performance and recovery of the signal it requires a great attention.

1.4 Thesis contribution

The main contributions of this work are to compare the performance of different channel estimation techniques for LTE downlink system, and study the effect of interpolation techniques on them.

In this thesis, performance of channel estimation techniques the LS, MMSE and MLE for LTE downlink is studied. The type of channel model simulated in this thesis is Extended Vehicular A (EVA) with Doppler shift of 300HZ. The three channel estimation techniques are the LS, MMSE and MLE with interpolation, averaging and hybrid. The performance of these channel estimation techniques will be evaluated to know the effect of adding the linear interpolation, averaging and hybrid method on their performance. The measuring parameters are the BER and complexity. This thesis hence helps to select an appropriate channel estimation technique for a specific application scenario.

1.5 Objectives

General objective:

The main objective of this work is to investigate the performance of different channel estimation techniques in 3GPP LTE standardized channel model EVA 300HZ.

Specific objectives:

The specific objectives of this work are:

- To compare the performance of LS, MMSE and ML channel estimation techniques for EVA 300HZ channel model.
- To investigate the effect of introducing interpolation, averaging and hybrid on the considered channel estimation techniques.
- To study the complexity of the MMSE and ML channel estimation techniques in 3GPP LTE.

1.6 Methodology

In this thesis, the channel estimation techniques LS, MMSE and MLE with interpolation, averaging and hybrid method are compared in performance using bit error rate (BER) and complexity. The simulation is done using Matlab software. It starts from the payload generation and goes to the downlink shared channel and to the physical downlink shared channel. The downlink shared channel contains the cyclic redundancy check, sub block segmentation, channel coding, rate matching and codeword concatenation or reconstruction.

The downlink physical shared channel contains the scrambler, the modulation mapping, the pre coder, layer mapping, resource element mapping and OFDM signal generator. This receiver processing starts from the OFDM signal reception and continuing through resource element de-mapping, channel estimation, Equalization, layer de-mapping, demodulation, descrambling, channel decoding and finally CRC detector.

Generally, the formal methodologies to be used to achieve objectives of the work are:

- Literature review: includes reading books, articles, researches, simulation tools and other resources related to the topic.
- System modeling and simulation: includes mathematical modeling of the channel estimation techniques and the standard channels used in 3GPP LTE and simulating the modeled communication system using MATLAB.
- Performance Comparison: includes comparing the performance of LS, MMSE and ML channel estimation techniques for EVA 300HZ, which is 3GPP LTE standardized channel model.
- Analysis and Interpretation of the results: the results of the modeling and simulation will be explained.

1.7 Thesis Outline

The first chapter is aimed to describe the introductory concepts related to the work done. The chapter included background of the study, literature review, statement of the problem, objectives of the study and methodologies implemented. In the second chapter details regarding the technologies involved in the system under consideration will be provided. Chapter three emphasizes on different types of existing channel estimation techniques in 3GPP LTE system. Chapter four includes the main part of this work. In this chapter system model, simulation parameters and assumptions of the simulation steps will be addressed. Furthermore; this chapter discusses the analysis and results of simulations obtained. Finally, chapter five summarizes the conclusions reached at the end of this work and recommendations for future work.

CHAPTER TWO OVERVIEW OF LTE PHYSICAL LAYER

2.1. Air Interface of LTE

The LTE was designed by having some technological improvements these are the dynamic allocation of variable bandwidth, new MIMO systems, multiple carrier transmission schemes, very low latency in the user and control plane [22].

The LTE has two transmission links, these are the uplink (from user equipment (UE) to evolved Node B (eNodeB)) and downlink (from the eNodeB to UE) and these transmission links use different multiple access techniques. The former uses SCFDMA and the later uses OFDMA [3].

The goal of LTE is to support higher data rate, low latency, flexible bandwidth deployments, low cost of implementation, higher spectrum efficiency and support mobility [1].

Higher data rates in LTE can be obtained using one or more of the following methods:

Method I: Using higher order modulation with in a limited bandwidth such as 16 Quadrature amplitude modulation (16QAM) which has 4 bits per OFDM symbol and 64 QAM which have 6 bits per OFDM symbol and so on.

Method II: Using multiple inputs multiple output (MIMO) antenna configurations with different transmission modes such as transmit diversity and special correlation and combining mechanisms at the receiver. Reducing the interference level since it means increasing the signal to noise ratio (SNR) level using larger bandwidth but it is not possible to increase the bandwidth to unlimited value since resource is limited [4]

The OFDM is done by dividing the available spectrum into several parallel small bands known as subcarriers. This minimizes the signaling rate since the data is transmitted through the parallel small bands. Its goal is to make all channels experience frequency flat fading which simplifies equalization at the receiver. The name OFDM

Implies that the frequency response of each subcarrier overlaps, and they are orthogonal with each other [2].

2.2. LTE Duplexing Methods

The two duplexing methods which are applied in LTE system are the Time Division Duplex (TDD) and the Frequency Division Duplex (FDD). In TDD communication is done using one frequency for both uplink and downlink, but the time for transmitting and receiving is different. In FDD the communication is done using different frequencies for uplink and downlink but at the same time or simultaneously [22-26]. In this thesis, the FDD is selected for downlink transmission to see the effect of frequency selectivity of different channel environments on the LTE system model and channel estimation techniques.

2.3. Allocation of Bandwidth and Time Framing

As mentioned earlier, the LTE system own flexible band width ranging from 1.4MHZ to 20MHZ. To use the specified bandwidth efficiently and to share the resource among users, LTE divides the bandwidth by a difference of 12 subcarriers with a subcarrier spacing of 15KHZ (12x15KHZ=180KHZ). The subcarrier spacing is used to keep the orthogonality of the small band subcarriers or to avoid the inter carrier interference. The resource which can be found by dividing the LTE bandwidth by 180KHZ is known as a Resource Block (RB) and the total bandwidth is obtained by concatenating the RB in frequency domain [22-24].

Figure 2.1 shows the LTE time domain structure for normal and extended cyclic prefix. In this figure, it is clearly shown that each frame has 10 sub frames with period of 1ms each. This indicates that one frame requires total time period of 10ms. Furthermore each sub frame has two slots with time period of 0.5ms.

illustration not visible in this excerpt

Figure 2.1: LTE time domain structure for normal and extended cyclic prefix

2.4. Time frequency representation

From the above topics that are the allocation of bandwidth and time framing, we can guess that LTE is represented as a time and frequency grid. This is the most attractive part of OFDMA because after certain steps, the LTE data and signal are mapped to the time frequency grid known as resource grid. The resource grid has x and y axis. The x coordinate of the resource grid is time and the y coordinate is frequency as shown in figure 2.2. The smallest resource in a resource grid which is made up of one subcarrier and one OFDM symbol is known as Resource Element (RE). The time domain of a RE is an OFDM symbol and the frequency domain of the resource element is a subcarrier.

The resource element is located at the intersection of OFDM symbol in time domain and subcarrier in frequency domain. A resource block is a group of resource elements. 12 subcarriers in frequency domain and 7 or 6 OFDM symbols are arranged to make a resource block. This means if the cyclic prefix is normal cyclic prefix there are 7 OFDM symbols in time domain and 12 subcarriers in frequency domain which implies 12x7=84 resource elements in a single resource block. If the cyclic prefix length used is extended, the number of OFDM symbols reduces to 6 but the numbers of subcarriers remain the same which indicates 12x6=72 resource elements in a single resource block.

As we can see from figure 2.2, resource element is made up of a single OFDM symbol in time domain and a subcarrier in frequency domain. The resource elements unite to form a resource block that is 12x7=84 resource elements. And these resource blocks also add up to make the frequency time resource grid. The size of the resource grid depends on the size of the bandwidth. This means as the bandwidth gets larger and larger from 1.4 to 20 Mega Hertz (MHZ) the size of the resource grid increases proportionally.

The size of the spacing between the subcarriers is 15KHZ. The size of the resource block for any bandwidth is 12x15=180KHZ. But the size of the resource block depends on the size of the system bandwidth. For example let’s take 10MHZ bandwidth LTE system, the number of resource blocks are as indicated in table 2.1, is 50. Which means 50x180KHZ= 9MHZ it is not off course equal to the bandwidth but the remaining 1MHZ is used for subcarrier spacing. It is possible to calculate the amount of frequency wasted for subcarrier spacing 50x15KHZ=0.75MHZ which is approximately 1MHZ [25 26].

2.5. OFDM Multicarrier Transmission

In LTE communication system, the downlink transmission is based on OFDMA and the uplink transmission is SC-FDMA. The OFDM transmission system reduces the inter symbol interference and bit error rate at the receiver. There are two types of OFDM multi carrier transmissions, which are analog and discrete [1 2]. First, the OFDM transmitter divides the information signal in to several parts and the bandwidth is also divided accordingly then the smaller information signals are carried by different smaller frequency bands known as sub carriers [1].

illustration not visible in this excerpt

Figure 2.2: LTE resource grid, resource blocks and Resource element

There are several steps in LTE OFDM generation and transmission. First the modulated data are mapped to the resource grid, where they are analyzed and aligned in the frequency domain. This means each modulated symbol is mapped to a separate subcarrier at the frequency axis of the resource grid. Since as described earlier, the numbers of sub carriers depend on the size of the selected bandwidth with a subcarrier spacing of 15KHZ. These data streams are distributed and mixed to the number of OFDM subcarriers.

The bandwidth is divided in to several resource blocks means we can calculate it by the following relation

[illustration not visible in this excerpt](2.1) where

=number of resource blocks

= the subcarrier spacing and each subcarrier frequency can be calculated using the presiding formula:

[illustration not visible in this excerpt] (2.2)

Where k= 0 to Number of subcarriers=

From this point of view, the OFDM system requires N number of modulators for each subcarrier. And the OFDM modulated signal can be found as follows

[illustration not visible in this excerpt] (2.3)

Where = the OFDM symbol

illustration not visible in this excerpt

Figure 2.3: OFDM continuous time transmitter model using bank of oscillators of subcarriers [4]

To implement this transmission system, a bank of oscillators are required to generate the subcarriers for each symbol to be transmitted. But the OFDM system has a more simplified and fast technique to avoid these bank of oscillators.

This technique is used with a discrete OFDM transmission and is known as fast Fourier transforms (FFT). Assuming the channel sampling rate is Fs and the channel sampling time is the inverse of Fs which is Ts= 1/Fs. The discrete time representation of equation 2.3 is given as:

[illustration not visible in this excerpt] (2.4)

After generation of OFDM symbol, a cyclic prefix is added at the beginning of the symbol which is a copy of the end or tail of an OFDM symbol. This repetition of a copy of an OFDM symbol is used to protect the transmission system from delay spread of the wireless and mobile communication channel. For more information on the relations and OFDM multicarrier transmission systems it is possible to see [1-5].

2.6. The Cyclic Prefix

As we have seen earlier, the OFDM transmission system divides and parallelizes an information signal and modulates with smaller bands known as sub carriers. When doing this, there might be inter symbol interference (ISI) which is the interference between adjacent symbols. ISI is a result of multipath propagation [3].

Especially when the phases and amplitudes of the sub carries are equal, the interference will be worst. To avoid this ISI, the OFDM multi carrier system uses cyclic prefix which is a copy of the tail of an OFDM symbol. The cyclic prefix does not add any additional information, rather it is a repetition of a part of an information or symbol. From this point of view, the cyclic prefix is useless and costs transmission power when it is inserted.

But it has several purposes when it is applied in OFDM multi carrier transmission. These aims are:

- To avoid or reduce the effect of delay spread [1- 4]
- To remove the ISI [3]
- To maintain orthogonality between adjacent subcarriers in the receiver [4]

Therefore the length of the cyclic prefix is the most important factor in designing the OFDM multi carrier transmission systems. If we make the cyclic prefix too short to minimize overhead and power used to transmit, it can’t with stand the delay spread due to different propagation types. And if we make too long, it will clear the delay spread and the ISI caused by multipath fading. But it has several drawbacks such as increasing over head or repetition of information and power consumption [1-4].

Therefore due to these advantages and disadvantages of the length of cyclic prefix, LTE has its own standard of length of cyclic prefix to design its OFDM multicarrier transmission. These standards consider the delay spread of different propagation types and different channel models.

Considering this into account, LTE standardized cyclic prefix lengths are of three types. These are:

- Normal cyclic prefix length with 4.7 µS
- Extended cyclic prefix length with 16.6 µs for subcarrier spacing of 15KHZ
- Extended cyclic prefix length with 33us for subcarrier spacing of 7.5KHZ

The functions of these cyclic prefix lengths are also specified. The extended cyclic prefix length used with subcarrier spacing of 7.5KHZ is used for broadcast or multicast context. The normal cyclic prefix length 4.7µs is used for most urban and sub urban environments [25].

2.7. Subcarrier Spacing

From the above discussions, we can say that the subcarrier spacing should be small. If we make the subcarrier spacing very small, the channel becomes non frequency selective or flat and we are saving enough resource. But since we are dealing about mobile and wireless communication system specifically LTE, when a user moves with certain speed, the frequency of the transmission channel varies or offsets by the Doppler shift frequency. Therefore the subcarrier spacing should be as large as possible to avoid the Doppler shift and implementation imperfection.

To minimize the effect of Doppler shift of motion of a mobile terminal LTE uses standardized subcarrier spacing of 15KHZ.

Having this in mind, the number of subcarriers can be calculated from the given spectrum size or bandwidth as described in [4], the 10% of the bandwidth is used for guard interval. For example a 10MHZ bandwidth use 1MHz as its guard interval and the number of subcarriers is calculated by dividing to the subcarrier spacing, which is equal to 600 subcarriers. Table2.1 shows the number of subcarriers for each bandwidth of LTE system [4]. All the parameters of LTE downlink system are described below ones we select the channel bandwidth and the required parameters for the specified channel bandwidth should be taken.

Table 2.1: Number of resource blocks, number of subcarriers, FFT size and sampling frequency and cyclic prefix sizes for all LTE bandwidths after [4]

illustration not visible in this excerpt

2.8. Resource Block Size

As can be seen in figure2.2 the total resource of an eNodeB is known as a resource grid and the 12 subcarriers by 6 0r 7 OFDM symbols is known as a resource block. The smallest resource that a UE can access in a resource grid is called a resource element. The resource block is a resource which is available at an eNodeB to be transmitted to mobile user equipments. The eNodeB schedules the resource block according to the feedback obtained from the user equipment terminal. The feedback is channel characteristics and properties. If the channel characteristic is good, the scheduler schedules to that user equipment. If the channel parameter is bad, it will not schedule to that resource block it change to another resource block.

Therefore LTE resource block size should be as small as possible to increase the gain in frequency selective scheduling (scheduling of data transmission for good subcarriers should be large). The smaller resource block size ensures the frequency response for all resource blocks is similar and this helps the scheduler to assign good resource blocks only. But to avoid successive feedback overheads, the resource block size should be as large as possible since LTE sub frame size is 1ms to minimize latency. Considering these into account, LTE standardizes the size of the resource block to be 12 subcarriers or 12x15KHZ=180KHZ [25 26].

2.9. Resource Grid Contents

The resource grid is made up of several resource blocks and these are in turn made from resource elements. Even the resource element is made up of one OFDM subcarrier in frequency domain and one OFDM symbol in time domain.

As can be seen from figure 2.4 the resource grid contains control and data information signals. These control signals are the user data, data control indicator (DCI), primary synchronization symbol (PSS), secondary synchronization symbol (SSS), primary matrix indicator (PMI), and cell specific reference symbol (CSR).

The user data Physical Downlink Shared Channel (PDSCH), the Physical Downlink Control Channel (PDCCH) and CSR are placed in every sub frame of a resource grid. The PSS and SSS are placed in frames 0 and 5 at specific OFDM symbol and OFDM subcarrier indices that is SSS at 5th symbol and PSS at 6th symbol. The Broadcast Control Channel (BCCH) is found only on frame 0.

illustration not visible in this excerpt

Figure 2.4: All contents of LTE resource grid

Generally, the resource grid contains different sources of data for each sub frame.

- For sub frame 0: all source of data are placed
- For sub frame 5: user data, CSR, DCI, PSS and SSS are present
- For sub frames: (1,2,3,4,6,7,8,9,10) user data ,CSR and DCI are placed

The placement of these data and control signals in a resource grid for LTE system has an effect on the performance of the system as a whole or a particular block. For example the position of pilot symbols or CSRs in a sub frame has an effect on channel response estimation at the receiver of the LTE system [25].

2.10. OFDM Typical Transmitter Operation

OFDM transmission is done by dividing a large given band in to smaller bands known as subcarriers and map to them the bits or the data to be transmitted.

If we want to divide a large band for example 10MHZ in to 300 smaller bands and each subcarrier carries 16 bits. The data rate is standard of LTE but as we can see from its advantage, we may need to divide the large band in to smaller bands by reducing the gap between these bands. But if we do so, there will be subcarrier interference. To avoid this we use a spectrum gap known as subcarrier spacing. For LTE as mentioned in earlier sections, it is 15KHZ. This is all in frequency domain. If we see in time domain the following concept will happen.

The OFDM symbols when transmitted through physical medium or channel, they arrive at the receiver at different times. This arrival of OFDM symbols at different times means if one OFDM signal arrives delayed, there will be interference between consecutive OFDM symbols which is known as Inter Symbol Interference (ISI). To avoid ISI, we use a time gap between OFDM symbols. This time gap between consecutive OFDM symbols is known as cyclic prefix and used to avoid the effect of delay spread of the channel. This technique is used by copping the head of an OFDM symbol and placing it at the tail of it. This technique helps to avoid transmission break during the spectral gap.

When we divide a large given band into smaller bands, the input bits are first converted from serial to parallel and map each group of bits to its own subcarrier, then we add cyclic prefix and finally by changing them to serial we transmit them.

illustration not visible in this excerpt

Figure2.5: The analog OFDM transmission system [4]

As we can see from Figure 2.5, the input bit or data sequences are serial and the serial to parallel convertor changes to parallel data. Then the parallel bit sequence are modulated or mixed with smaller sub bands called subcarriers and finally converted to serial and goes to transmission channel. The mathematical model for figure 2.5 as in [4] is given in equation 2.5.

The term orthogonality is defined as when two modulated OFDM subcarriers are mutually orthogonal over the time interval ( ) .

This means

[illustration not visible in this excerpt] (2.5)

For

m= OFDM symbol index

From this relationship it is seen that the OFDM transmission is defined as the modulation of a set of orthogonal functions or signals .

Where

[illustration not visible in this excerpt] (2.6)

2.11. OFDM Typical Receiver Operation

The OFDM transmitter generates signal and modulates it and mix it with multiple bands known as subcarriers. To the modulated symbols the transmitter adds cyclic prefix and transmit it to the mobile and wireless channel.

The OFDM receiver performs the opposite of the OFDM transmitter. It receives the OFDM signal from the mobile and wireless channel and demodulates it and removes the cyclic prefix. As we have seen earlier, since the cyclic prefix does not add new information on the symbol, rather it is a repetition of the tail of the OFDM symbol. In addition to this, the cyclic prefix is used to protect or remove the delay spread of the mobile and wireless channel therefore the distorted and interfered channel parameters are also found and removed with the cyclic prefix together. As we can see in the Figure 2.4, the OFDM receiver receives the signal and adds white Gaussian noise and mixed with the subcarriers and finally integrates it at the OFDM symbol duration by ignoring the cyclic prefix duration [2].

As we can understand from figures 2.3 and 2.4, we need several numbers of oscillators to generate each subcarrier at the transmitter for modulation and at the receiver for demodulation purpose. But this can’t be implemented in practice because the size of the equipment and cost will be much expensive and the equipment is very complex. Considering this into account, scientists create a new modulation and demodulation technique for multi carrier transceiver.

illustration not visible in this excerpt

Figure 2.6: OFDM continuous time receiver model using banks of oscillators [5]

As we can understand from figure 2.6 the input signal is the received OFDM signal and an AWGN is added and it is converted to parallel. These parallel sequences of signals are mixed with the small band generated at the oscillator. The integrator is used as a detection technique in this case.

But in this thesis we do not use the analogue OFDM system rather we will discuss and use in our design discrete and digital OFDM transmit and receive systems which use Inverse Fast Furrier Transform (IFFT) as their modulation and mixing technique and Fast Fourier Transform (FFT) as their demodulation and integration technique [4].

2.12 The general block diagram of the LTE downlink system

After generation of the input signal the LTE block diagram contains the CRC generator. The CRC is used for detection of error in digital communication system but not for error correction. It detects whether or not an error exists or not and finally requests retransmission of data. According to [29 31] CRC is used for channel coding in the modeling of LTE downlink shared channel. There are two CRC generator polynomials these are GCRC24A and GCRC24B. The GCRC24A is used for transport block while the GCRC24B is used with cod block. This is used when the size of the transport block is larger than the maximum size (6144) bits.

Next to the CRC generation and attachment the channel coding is followed. The turbo coding is used as a coding scheme for physical downlink shared channel. When a turbo coder is used with normalized additive white Gaussian noise its performance approaches the Shannon capacity limits. According to [32] the turbo encoder is a parallel concatenated convolutional code (PCCC) with two convolutional encoders and one turbo internal inter leaver according [29 31 32].

It has only one input but three outputs. The outputs are the systematic bit stream, the parity bit stream and interleaved parity bit stream. The systematic parity bits are equivalent to the input bit stream that is why it is called systematic recursive convolutional codes are used for turbo coding on LTE channel coding [31].

The output code words of the first encoder and the second encoder are different because of the internal turbo inter leaver between them. The inter leavers which are positioned between the convolutional codes make the output code words uncorrelated. There are two types of inter leaver these are the block inter leaver and random inter leaver.

Note that the channel coding the turbo coding is used to reduce the BER and increase reliability of the system [32]. The block inter leaver writes the bit streams in column wise and reads row wise. The random inter leaver uses fixed random position for bits to be placed at the output of the inter leaver [33].

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