國 立 交 通 大 學
電信工程學系碩士班
碩士論文
適用於移動式 WiMAX 系統之疊代式通道估
計與載波間干擾消除技術
Iterative Channel Estimation and ICI Cancellation
for Mobile WiMAX Systems
研 究 生：蔡嘉航 Student:
Chia-Hang
Tsai
指導教授：李大嵩 博士 Advisor:
Dr.
Ta-Sung
Lee
適用於移動式 WiMAX 系統之疊代式通道估計與載波
間干擾消除技術
Iterative Channel Estimation and ICI Cancellation for
Mobile WiMAX Systems
研 究 生：蔡嘉航 Student: Chia-Hang Tsai
指導教授：李大嵩 博士 Advisor:
Dr. Ta-Sung Lee
國立交通大學
電信工程學系碩士班
碩士論文
A Thesis
Submitted to Institute of Communication Engineering
College of Electrical Engineering and Computer Science
National Chiao Tung University
in Partial Fulfillment of the Requirements
for the Degree of
Master of Science
in
Communication Engineering
June 2007
適用於移動式 WiMAX 系統之疊代式通道估計
與載波間干擾消除技術
學生：蔡嘉航
指導教授：李大嵩 博士
國立交通大學電信工程學系碩士班
摘要
正 交 分 頻 多 工 系 統 為 新 一 代 無 線 通 訊 系 統 最 常 使 用 的 技 術 ， 如 IEEE 802.11a/g/n、 IEEE 802.16、IEEE 802.20、數位電視、數位廣播等許多系統均採 用此技術。傳統的正交分頻多工系統並不適用在高速移動的環境中，然而移動傳 輸是未來無線通訊系統的趨勢之一，如 IEEE 802.16-2005 可支援到車速 120 km/hour，而 IEEE 802.20 更可支援到車速 250 km/hour。傳統的正交分頻多工系 統可以有效率地使用在非時變通道中，且僅需簡單的等化器，即可修正通道效 應，但在移動的環境中，通道隨著時間改變，使得接收端的子載波失去正交性， 因而導致子載波之間的相互干擾，使得解調變後的效能降低。在本論文中，吾人 設計出一個疊代式通道估計與載波間干擾消除技術，其利用通道估計結果將 ICI 以數學模型趨近表示之，使接收端得以有效併行地消去子載波間的干擾，而能在 移動的環境下運作。吾人藉由電腦模擬驗證此一新演算法在移動的環境中並使用 IEEE 802.16-2005 的規格下，可有效改善位元錯誤率。Iterative Channel Estimation and ICI Cancellation
for Mobile WiMAX Systems
Student:
Chia-Hang
Tsai
Advisor:
Dr.
Ta-Sung
Lee
Department of Communication Engineering
National Chiao Tung University
Abstract
Orthogonal Frequency Division Multiplexing (OFDM) is a popular technique in modern wireless communications. There are many systems adopting the OFDM technique, such as IEEE 802.11 a/g/n, IEEE 802.16, Digital Video Broadcasting, etc. On the other hand, mobile transmission is a trend in future wireless communications. For example, IEEE 802.16-2005 supports vehicle speed up to 120 km/hour. OFDM systems can be used efficiently in time invariant environments with one-tap equalizers. However, subcarriers are no longer orthogonal to each other in time-varying channels, and this causes the intercarrier interference (ICI) and degrades the system performance. To alleviate this problem, we propose an iterative ICI mitigation and time-varying channel estimation scheme, which can obtain the ICI information from the channel estimate using piece-wise linear or Taylor series approximate and then cancel it in parallel fashion. The proposed PIC structure and the
Acknowledgement
I would like to express my deepest gratitude to my advisor, Dr. Ta-Sung Lee, for his enthusiastic guidance and great patience. I also wish to thank my friends for their encouragement and help. Finally, I would like to show my sincere thanks to my parents for their inspiration and love.
Contents
Chinese Abstract
I
English Abstract
II
Acknowledgement III
Contents IV
List of Figures
VII
List of Tables
IX
Acronym Glossary
X
Notations
XII
Chapter 1 Introduction ... 1
Chapter 2 Overview of Mobile WiMAX System ... 4
2.1 Physical Layer Description ...5
2.1.1 Randomizer ...6
2.1.4.1 Pilot Modulation ...9
2.1.4.2 Preamble Structure...10
2.2 Key Features of Scalable OFDMA ... 11
2.2.1 Scalable Channel Bandwidth ... 11
2.2.2 Sub-channelization and Permutation ...12
2.2.3 Fractional Frequency Reuse...17
2.3 Transmit Techniques ...18
2.3.1 Transmit Diversity: Space-Time Coding ...19
2.3.2 Transmit Beamforming: Adaptive Antenna System ...22
2.4 Summary ...24
Chapter 3
Channel Estimation for Mobile WiMAX System .. 26
3.1 Channel Model...27
3.1.1 SUI Channel Model for Fixed Wireless Application ...27
3.1.2 ITU Channel Model for Mobile Wireless Application ...32
3.1.3 SCM Channel Model for Mobile MIMO Wireless Application ...34
3.2 Channel Estimation...36
3.2.1 LS and MMSE Channel Estimation...39
3.2.2 Interpolation Techniques...41
3.2.3 Time Domain LS Channel Estimation ...42
3.3 Summary ...46
Chapter 4
ICI Mitigation for Mobile WiMAX Systems... 47
4.2 ICI Modeling...51
4.2.1 Piece-wise Linear Model ...51
4.2.2 Taylor Series Modeling...55
4.3 Combined Channel Estimation and ICI Mitigation ...59
4.3.1 Data Detection Techniques ...59
4.3.2 PIC Equalizer ...60 4.3.3 Complexity Issue ...63 4.4 Computer Simulations ...64 4.5 Summary ...72
Chapter 5
Conclusion ... 73
Bibliography ... 75
List of Figures
Figure 2-1 PRBS generator for randomizer ...6
Figure 2-2 OFDMA randomizer DL initialization vector ...7
Figure 2-3 Convolutional encoder ...8
Figure 2-4 PRBS generator for pilot modulation...10
Figure 2-5 Example of DL preamble for segment 1 ... 11
Figure 2-6 Cluster structure ...13
Figure 2-7 Allocated subcarriers into subchannels for PUSC ...14
Figure 2-8 Example of mapping OFDMA slots to subchannels and symbols in DL PUSC ...15
Figure 2-9 Description of a UL PUSC tile...15
Figure 2-10 Allocated subcarriers into subchannels for FUSC ...16
Figure 2-11 AMC bin structure ...17
Figure 2-12 Description of fractional frequency reuse ...18
Figure 2-13 Block diagram of STC...20
Figure 2-14 Illustration of Alamouti scheme ...20
Figure 2-15 Cluster structure for STC PUSC using 2 Antennas...22
Figure 2-16 Illustration of AAS ...23
Figure 2-17 Generalized AAS zone allocation...24
Figure 2-18 AAS zone structure in OFDMA mode ...24
Figure 3-1 Doppler spectrum of SUI channel models ...30
Figure 3-2 Doppler spectrum of ITU channel models ...34
Figure 3-3 BS and MS angular parameters in SCM specification ...35
Figure 3-4 Baseband model of a typical pilot-based system ...36
Figure 3-5 Pilot-aided channel estimation scheme ...41
Figure 3-6 Comparison with two channel estimation methods...46
Figure 4-1 Plot of channel matrix ...50
Figure 4-2 Piece-wise linear model ...52
Figure 4-3 Piece-wise linear model using symbols nearby...52 Figure 4-4 Mean square error of different approximations to the varying channel
...58
Figure 4-5 Magnitude of different approximations to the varying channel ...58
Figure 4-6 Nearest point data detection method ...60
Figure 4-7 PIC structure...61
Figure 4-8 System Structure...63
Figure 4-9 Comparison of schemes without and with ICI compensation in second-order varying channel ...67
Figure 4-10 Comparison with different blocks with different SNR...68
Figure 4-11 Comparison with different blocks with different velocity...68
Figure 4-12 BER performance of different d in 150 km/hr ...69
Figure 4-13 BER performance for different modulation schemes in 120 km/hr ...70
Figure 4-14 BER performance for different methods of 512-FFT in 100 km/hr ...71
List of Tables
Table 2-1 Data rate for different modulations and code rates ...5
Table 2-2 Puncturing patterns and orders to realize different code rates ...8
Table 2-3 Useful data payload for a slot...8
Table 2-4 OFDMA scalability parameters for different bandwidth ...12
Table 3-1 Parameters of SUI-3 channel models ...28
Table 3-2 Parameters of ITU channel models ...33
Table 4-1 Iterative ICI cancellation procedure...63
Table 4-2 parameters of the simulated system ...65
Acronym Glossary
3GPP third generation partnership project AAS Adaptive Antenna System AMC Adaptive Modulation and Coding AOA angle of receptionAOD angle of departure
AWGN additive white Gaussian noise BS base station
CCIR co-channel interference rejection CINR carrier-to-interference-and-noise ratio
DL downlink
DFT discrete fourier transform FFT fast fourier transform FUSC Full Usage of Subchannels
IEEE institute of electrical and electronics engineers ICI inter-carrier interference
IDFT inverse discrete fourier transform IFFT inverse fast fourier transform ISI inter-symbol interference
LS least square
MMSE minimum mean square error MS mobile station
NLOS non-line-of-sight
OFDM orthogonal frequency division multiplexing OFDMA orthogonal frequency division multiple access PIC parallel interference cancellation
PUSC Partial Usage of Subchannels QAM quadrature amplitude modulation QOS quality of service
QPSK quadrature phase shift keying SCM spatial channel model
SNR signal-to-noise ratio STC space time coding
SVD singular value decomposition
UL uplink
Notations
BW bandwidth
N FFT size
L maximum length of the channel
G maximum delay of the channel
H channel frequency response
h channel time response
g multipath channel tap gain τ multipath delay
x time domain transmit signal
X frequency domain transmit signal
y time domain receive signal
Y frequency domain receive signal
P pilot magnitude
f pilot subcarrier index
d number of neighboring points to generate the ICI estimate
q number of subcarriers used for data transmission
w time domain AWGN noise
Chapter 1
Introduction
Wireless communication systems have been in use for quite a long time. Many standards are available based on which user devices communicate, but the present standards fail to provide sufficient data rate, when the user is moving at high speed. Broadband wireless access is an appealing way to provide flexible and easily-to-deploy solution for high speed communications. In view of this requirement for future mobile wireless communication systems, the 802.16 standard has been proposed by Institute of Electrical and Electronic Engineers (IEEE) [1], [2].
The WiMAX (Worldwide Interoperability for Microwave Access) Forum is committed to providing optimized solutions for fixed, nomadic, portable and mobile broadband wireless access. Two versions of WiMAX address the demand for these different types of access:
• IEEE 802.16-2004: This is based on the 802.16-2004 version of the IEEE 802.16 standard. It uses Orthogonal Frequency Division Multiplexing (OFDM) and supports fixed and nomadic access in Line of Sight (LOS) and Non Line of Sight (NLOS) environments. For LOS environment, the frequency range in 802.16d is from 2GHz to 66GHz and Single Carrier (SC) is mainly adopted as the transmission scheme. For NLOS environment, it focuses on the Broadband Wireless Access (BWA), where the frequency band ranges from 2GHz to 10GHz. In physical layer (PHY),
NLOS temps to adopt OFDM and OFDMA techniques.
• IEEE 802.16-2005: Optimized for dynamic mobile radio channels. This version is based on the IEEE 802.16-2005 amendment and provides support for handoffs and roaming. The choice of the subcarrier number becomes more flexible since it provides four options, 128, 512, 1024, and 2048, in contrast to the single choice of 2048 in IEEE 802.16-2004. The frequency band ranges from 2GHz to 6GHz.
Orthogonal Frequency Division Multiplexing (OFDM) is a popular technique in modern wireless communication systems. In an OFDM system, the bandwidth is divided into several orthogonal subchannels for transmission. A cyclic prefix (CP) is inserted before each symbol. Therefore, if the delay spread of the channel is shorter than the length of the cyclic prefix, the intercarrier symbol interference (ISI) can be eliminated due to the cyclic prefix. On the other hand, subcarriers in OFDM are orthogonal to each other over time-invariant channels, so the conventional OFDM system only requires one-tap equalizers [3] to compensate the channel response. This characteristic simplifies the design of the OFDM receiver, and for this reason, the OFDM technique is widely used in wireless communication systems.
The mobile transmission is a trend in future wireless communications. Many systems support the mobile transmission. However, while OFDM system is applied in mobile environments, the reliability of OFDM is limited because of the time-varying nature of the channel. This leads to the loss of subcarrier orthogonality , which, in turn, yields intercarrier interference (ICI) and increases inaccuracies in channel tracking. The effect of channel variations for the ICI has been addressed in [4]. Therefore, the
are not practical due to the complexity of reducing the ICI effect and the incompatibility with the 802.16 standards. For example, the precoding solution for self-cancellation [5] requires a modification of the transmit format such that it is incompatible with the existing transmit schemes. If ICI is modeled as an additional Gaussian random process [4] and not adequately compensated, the ICI will result in a severe error floor. Robust channel estimation using time and frequency domain correlation with H∞ approach [6] results in a large computation delay in adopting the singular value decomposition (SVD) and the H∞ estimation algorithms. The ML iterative estimator [7] and adaptive matrix equalizer [8] require a large computation load and thus lose their feasibility at high speeds or become too complex for commercial products. In this thesis, an iterative ICI mitigation and time-varying channel estimation scheme are proposed to solve the problem, which include the time domain channel estimator, ICI modeling using derivatives of the channel variation based on [7], [9], and the parallel interference cancellation (PIC) equalizer similar to [10], which consists of a set of one-tap equalizers and a set of ICI cancellation filters to both compensate for the multiplicative distortion and cancel the ICI.
The rest of this thesis is organized as follows. In Chapter 2, an overview of WiMAX system is given. The transmit techniques such as Space-Time Coding (STC) and Adaptive Antenna System (AAS) are also introduced. In Chapter 3, channel models being used are introduced and several channel estimation approaches that fit the IEEE 802.16 standard are discussed. In Chapter 4, we propose a PIC equalizer to suppress the channel effect in mobile concern, several computer simulation results are also given to show the performance improvement of the proposed ICI cancellation system structure in IEEE 802.16-2005 system. In Chapter 5, we conclude this thesis.
Chapter 2
Overview of Mobile WiMAX System
WiMAX is a broadband wireless technology that supports fixed, nomadic, portable and mobile access. To meet the requirements of different types of access, two versions of WiMAX have been defined. The first is based on IEEE 802.16-2004 and is optimized for fixed and nomadic access. The second version is designed to support portability and mobility, and will be based on the IEEE 802.16-2005 amendment to the standard. In this chapter, we will focus on the physical layer of orthogonal frequency division multiple access (OFDMA) structure in IEEE 802.16-2005 and provide a detail introduction of Scalable OFDMA (SOFDMA) technology. Finally, the transmit techniques such as STC and AAS adopted in the system will be introduced.2.1 Physical Layer Description
Worldwide Interoperability of Microwave Access (WiMAX) is a technology based on the IEEE 802.16 specifications to enable the delivery of last mile wireless broadband access as an alternative to cable and DSL. WiMAX will provide fixed, nomadic, and portable mobile wireless broadband connectivity without the requirement for direct line-of-sight (LOS) with a base station. WiMAX provides metropolitan area network connectivity at speeds of up to 75 Mb/sec. WiMAX systems can be used to transmit signal as far as 30 miles. However, on the average a WiMAX base-station installation will likely cover between three to five miles [11].
WiMAX covers both LOS and NLOS applications in the 2-66 GHz frequencies. The PHY layer contains several forms of modulation and multiplexing to support different frequency range and application. Data rates determined by exact modulation and encoding schemes are shown in Table 2.1. The IEEE 802.16 standard was originally written to support several physical medium interfaces and it is expected that it will continue to develop and extend to support other PHY specifications. Hence, the modular nature of the standard is helpful in this aspect. For example, the first version of the standard only supported single carrier modulation. Since that time, OFDM has been added [12].
Table 2-1: Data rate for different modulations and code rates
73.2 48.8 24.4 20 Bandwidth (MHz) 26.1 17.5 8.7 7 22.5 15 7.5 6 73.2 48.8 24.4 20 Bandwidth (MHz) 26.1 17.5 8.7 7 22.5 15 7.5 6
Raw bit rate (Mb/s)
In IEEE 802.16-2005, its applications are focused on mobile applications in the 2-6 GHz. Two multi-carrier modulation techniques are supported in 802.16-2005: OFDM with 256 carriers and OFDMA with 128, 512, 1024, or 2048 carriers.
In the following sections, we will introduce the main block diagrams of the transmitter architecture. We will put emphasis on physical layer description on OFDMA mode in IEEE 802.16-2005.
2.1.1 Randomizer
The randomization is performed on each burst of data on the DL and UL, which means that for each allocation of a data block, the randomizer shall be used independently. For RS and CC encoded data, padding will be added to the end of the transmission block, up to the amount of data allocated minus one byte, which shall be reserved for the introduction of a 0x00 tail byte by the FEC. The PRBS generator shall be 1 X+ 14 +X15 as shown in Figure 2-1. Each data byte to be transmitted shall enter sequentially into the randomizer. Preambles are not randomized.
LSB MSB
On the downlink, the randomizer shall be re-initialized at the start of each frame. In OFDMA mode, the randomizer shall be re-initialized with the sequence: [LSB]011011100010101[MSB]. At the start of subsequent bursts, the randomizer shall be initialized with the vector shown in Figure 2-2. The frame number used for initialization refers to the frame in which the DL burst is transmitted. The subchannel offset used for initialization refers to the allocated subchannels in which the DL burst is transmitted.
Figure 2-2: OFDMA randomizer DL initialization vector
2.1.2 Forward Error Correction
In OFDMA mode, the encoding is performed by passing the data in block format through a convolutional encoder. A single 0xFF tail byte is appended to the end of each burst after randomization. Each data block is encoded by the binary convolutional encoder, which shall have native rate of 1/2, a constraint length equal to 7, and shall use the generator depicted in Figure 2-3. Puncturing patterns and serialization order that shall be used to realize different code rates are defined in Table 2-2. Table 2-3 gives the data payload sizes and the code rates used for the different modulations.
Figure 2-3: Convolutional encoder
Table 2-2: Puncturing patterns and orders to realize different code rates
Code rates Rate 1/2 2/3 3/4 dfree 10 6 5 X 1 10 101 Y 1 11 110 XY X1Y1 X1Y1Y2 X1Y1Y2X3
2.1.3 Interleaver
All encoded data bits shall be interleaved by a block interleaver with a block size corresponding to the number of coded bits over the allocated subchannels per OFDM symbol. The interleaver is defined by two step permutation. The first permutation ensures that adjacent coded bits are mapped onto nonadjacent subcarriers. The second permutation ensures that adjacent coded bits are mapped alternately onto less or more significant bits of the constellation, thus avoiding long runs of lowly reliable bits.
2.1.4 Modulator
After bit interleaving, the data are entered serially to the constellation mapper. For OFDMA mode, Gray-mapped QPSK, 16QAM, and 64QAM shall be supported. The constellation-mapped data shall be subsequently modulated onto all allocated data subcarriers and each subcarrier multiplied by the factor 2 * (1/ 2−wk) according the subcarrier index, k.
2.1.4.1 Pilot Modulation
Pilot subcarriers shall be inserted into each data burst in order to constitute the symbol and they shall be modulated according to their carrier location within the symbol. The PRBS generator depicted in Figure 2.4 shall be used to produce a sequence, w . The polynomial for the PRBS generator shall be k 1 X+ 9+X11. For OFDMA mode, each pilot shall be transmitted with a boosting of 2.5 dB over the average power of each data tone. The pilot subcarriers shall be modulated according to (2-1):
{ }
8 1 Re ( ) 3 2 = − k k c w and Im{ }
ck =0. (2-1)The pilot in DL preamble shall be modulated according to (2-2):
{
}
{
}
1 Re 4 2 ( ) 2 Im 0 = ⋅ ⋅ − = k premablePilotsModulated w premablePilotsModulated (2-2)Figure 2-4: PRBS generator for pilot modulation
2.1.4.2 Preamble Structure
For OFDMA mode, the first symbol of the DL transmission is the preamble and the preamble subcarriers are divided into three carrier-sets. Those subcarriers are modulated using a boosted BPSK modulation with a specific PN code. There are three possible groups consisting of a carrier-set each that may be used by any segment. Each segment uses a preamble composed of a carrier-set out of the three available carrier-sets in the following manner: (In the case of segment 0 under 2048-FFT, the DC carrier will not be modulated at all and the appropriate PN will be discarded; therefore, DC carrier shall be always zero. For the preamble symbol of 2048-FFT, there will be 172 guard band subcarriers on the left side and the right side of the spectrum). For example, Figure 2-8 depicts the preamble of segment 1 for 2048-FFT.
Figure 2-5: Example of DL preamble for segment 1
2.2 Key Features of Scalable OFDMA
Although IEEE 802.16-2005 is generally perceived as the mobile version of the standard, in reality it serves the dual purpose of adding extensions for mobility and including new enhancements to the OFDMA physical layer. This new enhanced IEEE 802.16-2005 physical layer is now being referred as Scalable OFDMA (SOFDMA) and includes a number of important features for fixed, nomadic, and mobile networks. Because of these advantages, most of the industry will build their IEEE 802.16-2005 products using SOFDMA technology. However, the IEEE 802.16-2005 standard is not just for mobility. There are also many compelling reasons for using SOFDMA in fixed broadband wireless access (BWA) networks. In this section, we will focus on some key features of SOFDMA for mobile wireless applications [13], [14].
2.2.1 Scalable Channel Bandwidth
Scalability is one of the most important advantages of OFDMA. Spectrum resources for wireless broadband worldwide are still quite different in its allocation. With OFDMA subcarrier structure, it is designed to be able to scale to work in different channelization from 1.25 to 20 MHz to cope with varied worldwide requirements as efforts proceed to achieve spectrum harmonization in the longer term. The scalability is supported by adjusting FFT size according to the different channel bandwidth to fix the subcarrier frequency spacing. By fixing the subcarrier spacing
and symbol duration, the basic unit of physical resource is fixed. Therefore, the impact to higher layers is minimal when scaling the bandwidth.
The significant advantage from scalability is the flexibility of deployment. With the little modification to different air interfaces, OFDMA system can be deployed in various frequency bands to flexibly address the requirement for various spectrum allocation and usage model requirements. The OFDMA scalability parameters used in the thesis are listed in Table 2-4. The subcarrier spacing is fixed to 11.16 kHz and the symbol time is fixed to 89.6 sμ . With the flexibility to support wider range bandwidth, OFDMA also enjoys high sector throughput, which allows more efficient multiplexing of data traffic, lower latency and better quality of service (QoS).
Table 2-4: OFDMA scalability parameters for different bandwidth
22.4 us (Tb/4) 89.6 us 11.16 KHz 128 1.43 1.25 256 2.86 2.5 512 5.71 5 1024 11.4 10 Values Parameters CP duration Useful symbol time (Tb) Subcarrier spacing 2048 FFT size 22.8 Sampling frequency (MHz) 20 Bandwidth (MHz) 22.4 us (Tb/4) 89.6 us 11.16 KHz 128 1.43 1.25 256 2.86 2.5 512 5.71 5 1024 11.4 10 Values Parameters CP duration Useful symbol time (Tb) Subcarrier spacing 2048 FFT size 22.8 Sampling frequency (MHz) 20 Bandwidth (MHz)
2.2.2 Sub-channelization and Permutation
subchannelization: diversity and contiguous. The diversity permutation takes subcarriers pseudo-randomly to form a subchannel. The diversity permutations include DL & UL PUSC (Partial Usage of Subchannels), DL FUSC (Full Usage of Subchannels), and additional optional permutations. The contiguous permutation groups a block of adjacent sub-carriers to form a subchannel. The contiguous permutations include DL & UL AMC (Adaptive Modulation and Coding). With DL PUSC, for each pair of OFDM symbols, the usable subcarriers are grouped into
clusters containing 14 adjacent subcarriers per symbol, with pilot and data allocations
in each cluster in the even and odd symbols as shown in Figure 2-6. Other definitions of the PUSC subcarrier allocation are: one subchannel contains two clusters by one OFDMA symbol and one slot is one subchannel by two OFDMA symbols.
Figure 2-6: Cluster structure
Divide these clusters into several Major Groups. The allocation algorithm varies with FFT sizes. For each subchannel, subcarriers are distributed in some clusters that belong to its major group as shown in Figure 2.7. A subchannel contains 2 clusters and is comprised of 48 data subcarriers and 8 pilot subcarriers. Allocating subcarriers to subchannel in each major group is performed separately for each OFDMA symbol by first allocating the pilot carriers within each cluster, and then taking all remaining data carriers within the symbol and using the procedure described in (2-3):
even symbols odd symbols
{
}
( , )[ mod ] _ mod
=
⋅ + +
subchannels k s k subchannels subchannels
subcarrier k s
N n p n N DL PermBase N (2-3)
where
( , )
subcarrier k s is the subcarrier index k in subchannel s
subchannels
N is the number of subchannels in current partitioned major group ( 13 ) mod
k subccarriers
n = k+ ⋅s N
subccarriers
N is the number of data subcarriers allocated to a subchannel [ ]
s
p j is the series obtained by rotating basic permutation sequence cyclically to
the left s times
The parameters vary with FFT sizes. Figure 2-8 shows an example of mapping OFDMA slots into subchannels and symbols in the DL PUSC.
subcarriers Ngguard subcarriers Ng-1 guard subcarriers Group 0 Sub-channel 1 Sub-channel 0 Group 0 Group 0 … … … … … … … subcarriers Ngguard subcarriers Ng-1 guard subcarriers Group 0 Sub-channel 1 Sub-channel 0 Group 0 Group 0 … … … … … … …
Subchannel number
OFDMA symbol index
Spanning two OFDMA symbols
Subchannel number
OFDMA symbol index
Spanning two OFDMA symbols
Figure 2-8: Example of mapping OFDMA slots to subchannels and symbols in DL PUSC
Compared with the cluster structure for DL PUSC, a tile structure is defined for the UL PUSC whose format is shown in Figure 2-9. The slot is comprised of 48 data subcarriers and 24 pilot subcarriers in 3 OFDM symbols.
Figure 2-9: Description of a UL PUSC tile
FUSC achieves full diversity by spreading tones over entire band. The symbol structure is constructed using pilots, data, and zero subcarriers. The symbol is first allocated with the appropriate pilots and with zero subcarriers, and then all the
remaining subcarriers are used as data subcarriers. To allocate the data subchannels, the remaining subcarriers are partitioned into groups of contiguous subcarriers. Each subchannel consists of one subcarrier from each of these groups as shown in Figure 2-10. The number of groups is therefore equal to the number of subcarriers per subchannel. The exact partitioning into subchannels is according to the same procedure as (2-3).
subcarriers
Group 0 Group 1 Group 2 Group 3
Sub-channel 1
Sub-channel 0 Ngguard
subcarriers Ng-1 guardsubcarriers
Group N
subcarriers
Group 0 Group 1 Group 2 Group 3
Sub-channel 1
Sub-channel 0 Ngguard
subcarriers Ng-1 guardsubcarriers
Group N
Figure 2-10: Allocated subcarriers into subchannels for FUSC
The contiguous permutation groups a block of adjacent subcarriers to form a subchannel, such as DL AMC and UL AMC. As shown in Figure 2-11, a bin consists of 9 adjacent subcarriers in a symbol, with 8 tones for data and one assigned for a pilot. A slot in AMC is defined as a collection of bins of the type (N x M = 6), where
N is the number of adjacent bins and M is the number of adjacent symbols. Thus 4
different ways of defining a slot are (6 bins, 1 symbol), (3 bins, 2 symbols), (2 bins, 3 symbols), (1 bin, 6 symbols). AMC permutation enables multi-user diversity by choosing the sub-channel with the best channel frequency response.
Figure 2-11: AMC bin structure
In general, diversity subcarrier permutations perform well in mobile applications while contiguous subcarrier permutations are well suited for fixed, portable, or low mobility environments. These options enable the system designer to trade-off mobility for throughput.
2.2.3 Fractional Frequency Reuse
In OFDMA mode, users operate on subchannels which only occupy a small fraction of the channel bandwidth and the cell edge interference problem can be easily solved by reconfiguration of the subchannel usage without resorting to traditional frequency planning. In mobile applications, the flexible subchannel reuse is facilitated by subchannel segmentation and permutation zone. A segment is a subdivision of the available OFDMA subchannels (one segment may include all subchannels). Permutation Zone is a number of contiguous OFDMA symbols in DL or UL that use the same permutation. The DL or UL subframe may contain more than one permutation zone.
The subchannel reuse pattern can be configured so that users close to the base station operate on the zone with all subchannels available. While for the edge users, each cell and sector operates on the zone with a fraction of all subchannels available.
In Figure 2-11, F1, F2 and F3 are different sets of subchannels in the same frequency channel. With this configuration, the full load frequency reuse of one is maintained for center users to maximize spectral efficiency while fractional frequency reuse is achieved for edge users to improve edge user connection quality and throughput. The subchannel reuse planning can be dynamically optimized across sectors or cells based on network load and interference conditions on a frame by frame basis. All the cells and sectors therefore, can operate on the same frequency channel without the requirement for frequency planning.
Figure 2-12: Description of fractional frequency reuse
2.3 Transmit Techniques
In order to increase the range and reliability of WiMAX systems, the WiMAX standard supports optional multiple-antenna techniques such as Alamouti Space-Time Coding (STC), Adaptive Antenna Systems (AAS) and Multiple-Input
single-antenna technology:
• Array Gain: This is the gain achieved by using multiple antennas so that the signal adds coherently.
• Diversity Gain: This is the gain achieved by utilizing multiple paths so that the probability that any one path is bad does not limit performance. Effectively, diversity gain refers to techniques at the transmitter or receiver to achieve multiple “looks” at the fading channel. These schemes improve performance by increasing the stability of the received signal strength in the presence of wireless signal fading. Diversity may be exploited in the spatial (antenna), temporal (time), or spectral (frequency) dimensions.
• Co-channel Interference Rejection (CCIR): This is the rejection of signals by making use of the different channel response of the interferers.
2.3.1 Transmit Diversity: Space-Time Coding
In order to increase the rate and range of the modem, there are several considerations. Generally, BS can bear more cost and complexity than SS, so multiple-antenna techniques are a good option at BS, also called transmit diversity. Among various transmit diversity schemes, STC is the most popular scheme with the feature of open loop (i.e., no feedback signaling is required) as channel information is not required at the transmitter. Therefore we will focus on the scheme of STC with 2 transmit antennas in this section as shown in Figure 2-13.
Sub-channel Modulation Sub-channel Modulation IFFT Input Packing IFFT Input Packing Space-Time Encoder Space-Time Encoder IFFT IFFT IFFT IFFT Filter Filter Filter Filter DAC DAC DAC DAC RF RF RF RF
#
BS RFRF ADCADC FilterFilter FFTFFT
#
EqualizerEqualizerSub-channel Demod. Sub-channel Demod.
#
Space-Time Decoder Space-Time Decoder SSFigure 2-13: Block diagram of STC
The space-time block coding scheme was first discovered by Alamouti for two transmit antennas. Symbols transmitted from those antennas are encoded in both space and time in a simple manner to ensure that transmissions from both the antennas are orthogonal to each other. This would allow the receiver to decode the transmitted information with a slight increment in the computational complexity.
Figure 2-14: Illustration of Alamouti scheme
Figure 2-14 shows the operation of Alamouti scheme. The input symbols to the space-time block encoder are divided into groups of two symbols. At a given symbol
ST Decoder
+
Hs
n
H y
H=
H Hs
H+
H n
H(
2 2)
1 2 2 2(
H H
H=
h
+
h
I
=
ρ
I
)
y
ST Encoder 1 1 2 2 2 1s
s
s
s
s
s
∗ ∗⎡
−
⎤
⎡ ⎤
⎢
⎥
⎢ ⎥
⎢
⎥
⎢ ⎥
⎢
⎥
⎣ ⎦
6
⎣
⎦
s
A Allaammoouutti isscchheemme e* 1 2 * 2 1 s s s s ⎡ − ⎤ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ s . (2-4)
The encoder outputs are transmitted in two consecutive transmission periods from two transmit antennas. Let h1 and h2 be the channel gains from the first and second transmit antennas to the only one receiver antenna. Assume that h1 and h2 are scalar and constant over two consecutive symbol periods. The received signals in two consecutive symbol periods, denoted as r1 and r2, can be expressed as
1 1 1 2 2 1 * * 2 1 2 2 1 2 r h s h s n r h s h s n = + + = − + + , (2-5)
where n1 and n2 are AWGN noise modeled as identical independent distributed (i.i.d.) complex Gaussian random variables with zero mean and power spectral density N0/2 for each dimension. The above equation can be rewritten in a matrix form as
( )
( )
N N 1 1 2 1 1 * * * * 2 2 2 1 2 r h h s n s r h h n ⎡ ⎤ ⎡ ⎤ ⎢ ⎥⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ =⎢ ⎥ =⎢ ⎥⎢ ⎥+⎢ ⎥ = ⋅ + − ⎢ ⎥ ⎣ ⎦ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ s n H r H s n . (2-6)Since the channel matrix H is unitary, i.e. HH H = ρ·I2, where ρ = h12 + h22, the ML decoder can perform an MRC operation on the modified signal vector r given by H H = ⋅ = ⋅ + ⋅ = ⋅ + n r H r s H n s n ρ ρ . (2-7)
Therefore, we can obtain the space-time decoded vector s .
For OFDMA mode, STC coding is done on all data subcarriers that belong to an STC coded burst in the two consecutive OFDMA symbols. Pilot subcarriers are not encoded and are transmitted from either antenna 0 or antenna 1. In PUSC, the pilot
allocation to cluster is changed as shown in Figure 2-15. The pilot locations change in period of 4 symbols to accommodate two antennas transmission with the same estimation capability.
Figure 2-15: Cluster structure for STC PUSC using 2 Antennas
2.3.2 Transmit Beamforming: Adaptive Antenna
System
Future wireless communication systems aim at providing higher data rates with better link quality subject to being interference limited. Smart antenna technology is one of the most promising technologies for increasing both system coverage and capacity as shown in Figure 2-16. AAS, although an optional feature, through the use of more than one antenna elements at BS, can significantly improve range and capacity by adapting the antenna pattern and concentrating its radiation to each individual user. There are several advantages of using beamforming:
• Increase SNR of certain subscribers and steer nulls to others that can enable bursts to be concurrently transmitted to spatially separated users.
Figure 2-16: Illustration of AAS
First, the generalized AAS zone allocation is introduced as shown in Figure 2-17. The frame is divided into two parts: the fist part is allocated to the non-AAS users and the second part (called AAS zone) is allocated to the AAS users. This allows a mixture of non-AAS and AAS users to be supported by the same BS. The BS can dynamically allocate capacity to non-AAS and AAS traffic. The SS without AAS capability will ignore the traffic in the AAS zone.
Figure 2.18 shows the AAS zone structure in OFDMA mode. AAS_DLFP in an AAS zone is preceded by an AAS DL preamble of one symbol duration. All other data bursts within an AAS zone have a preamble whose duration is specified in AAS_DL_IE. AAS_DLFP provides a robust transmission of required BS parameters to enable SS access allocation. Each AAS_DLFP requires not carry the same information. Different beams may be used within the AAS diversity map zone. For
OFDMA mode, REP-RSP MAC message shall be sent by SS in response to a REP-REQ message from the BS to report estimation of the mean DL CINR (carrier-to-interference-and-noise ratio).
Regular DL Bursts Regular UL Bursts
DL
UL
Regular DL Bursts
Regular UL Bursts FDD
TDD
Regular DL Bursts Regular UL Bursts
DL
UL
Regular DL Bursts
Regular UL Bursts FDD
TDD
Figure 2-17: Generalized AAS zone allocation
…
2 OFDMA subchannelsAAS portion
AAS_DLFP
AAS Diversity Map Zone
AAS DL preamble Frequency Time SS #1 SS #2 SS #3 SS #4 SS #5 Non AAS portion
…
2 OFDMA subchannelsAAS portion
AAS_DLFP
AAS Diversity Map Zone
AAS DL preamble Frequency Time SS #1 SS #2 SS #3 SS #4 SS #5 Non AAS portion
The key features of scalable OFDMA in IEEE 802.16-2005 is also described to see the enhanced structure in mobile environment. We also introduce some key transmit techniques and their operations. By using these transmit techniques, the capacity and range of the system can be improved significantly.
Chapter 3
Channel Estimation for Mobile
WiMAX System
The use of multi-amplitude schemes in wireless OFDM systems requires the tracking of the fading radio channel. In real situations, channel estimation should be done before data detection to avoid bad distortion of the channel. In this chapter, channel estimation and interpolation schemes are introduced. First, three channel models corresponding to static or mobile environments are introduced in Section 3.1. Then, in Section 3.2, conventional least square (LS) and minimum mean square error (MMSE) channel estimation schemes [15] with several interpolation approaches [16] are introduced. In mobile environment, the need for the estimate of channel impulse response in time domain leads us to the time domain LS channel estimator [17]. The channel estimates can be further adopted to do the ICI mitigation in Chapter 4.
3.1 Channel Model
Wireless propagation channels have been studied for more than 50 years, and a large number of channel models are already available. The signal that has propagated through a wireless channel consists of multiple echoes of the originally transmitted signals; this phenomenon is known as multipath propagation. The different multipath components are characterized by different attenuations and delays. The correct modeling of the parameters describing the multipath components is the key point of channel modeling.
In first generation systems, a super-cell architecture is used where the base station and subscriber station are in LOS condition and the system uses a single cell with no co-channel interference. For second generation systems, a scalable multi-cell architecture with NLOS conditions becomes necessary. In WiMAX system, the wireless channel is characterized by:
¾ Path loss (including shadowing) ¾ Multipath delay spread
¾ Fading characteristics ¾ Doppler spread
The main channel models were considered here: Stanford University Interim (SUI) channel models [18], International Telecommunication Union (ITU) channel models [19] and Spatial Channel Model (SCM) channel models [20]. Each channel model was parameterized in order to best fit the particular channel characteristics.
3.1.1 SUI Channel Model for Fixed Wireless
Application
IEEE 802.16-2004. There are many possible combinations of parameters to obtain different channel descriptions. A set of 6 typical channels were selected for the three terrain types that are typical of the continental US. The channel parameters are related to terrain type, delay spread, and antenna directionality and each channel model has three taps with distinct K-factor and average power. Table 3-1 shows an example of time domain attribute of the SUI-3 channel, which is chosen to evaluate the proposed algorithm.
Table 3-1: Parameters of SUI-3 channel models
Multipath Delay Profile
Due to the scattering environment, the channel has a multipath delay profile. It is characterized by τrms (RMS delay spread of the entire delay profile) which is defined
as
(
)
2 2 2 rms jPj j avg τ =∑
τ − τ (3-1) wherej
P = (power in the jth delay component) / (total power in all components)
RMS delay spread
A delay spread model was based on a large body of published reports. It was found that the RMS delay spread follows lognormal distribution and that the median of this distribution grows as some power of distance. The model was developed for rural, suburban, urban, and mountainous environments. The model is of the following form
1
rms T d yε
τ = (3-2)
where τrms is the RMS delay spread, d is the distance in km, T1 is the median value of τrms at d = 1 km, ε is an exponent that lies between 0.5 ~ 1.0, and y is a lognormal variant. Depending on the terrain, distance, antenna directivity and other factors, the RMS delay spread values can span from very small values (tens of nanoseconds) to large values (microseconds).
Fading distribution, K-factor
The narrow band received signal fading can be characterized by a Ricean fading. The key parameter of this distribution is the K-factor, defined as the ratio of the “fixed” component power and the “scatter” component power. The narrow band K-factor distribution was found to be lognormal, with the median as a simple function of season, antenna height, antenna beamwidth and distance. The model for the K-factor (in linear scale) is as follows:
s h b o
K =F F F K d uγ (3-3)
where
s
F is a season factor; F =1.0 in summer; 2.5 in winter s
h
F is the received antenna height factor
b
o
K and γ are regression coefficients
u is a lognormal variable which has 0 dB mean and a standard deviation of 8 dB. Using this model, one can observe that the K-factor decreases as the distance increases and as antenna beamwidth increases.
Doppler spectrum
The random components of the coefficients generated in the previous paragraph have a white spectrum since they are independent of each other. The SUI channel model defines a specific power spectral density (PSD) function for these scatter component channel coefficients called “rounded” PSD which is given as
2 4 0 0 1 1.72 0.785 ( ) 0 f f S f = ⎨⎧⎪ −⎪⎪ + ⎪⎪⎪⎩ 0 0 1 1 f f ≤ > (3-4) where 0 m f f f
= . In fixed wireless channels the shape of the spectrum is therefore different than the classical Jake’s spectrum for mobile channels. Figure 3-1 shows that its shape of Doppler spectrum is convex.
considered if multiple transmit or receive elements, i.e. multiple channels, are being simulated. Antenna correlation is commonly defined as the envelope correlation coefficient between signals transmitted at two antenna elements. The received baseband signals are modeled as two complex random processes X(t) and Y(t) with an
envelope correlation coefficient of
{ }
(
)
(
{ })
{
}
{ }{
2}
{
{ }2}
env E X E X Y E Y E X E X E Y E Y ρ ∗ − − = − − (3-5)Note that this is not equal to the correlation of the envelopes of two signals, a measure that is also used frequently in cases where no complex data is available.
Antenna gain reduction factor
The use of directional antennas requires to be considered carefully. The gain due to the directivity can be reduced because of the scattering. The effective gain is less than the actual gain. This factor should be considered in the link budget of a specific receiver antenna configuration.
Denote ΔGBW as the Gain Reduction Factor. This parameter is a random quantity which dB value is Gaussian distributed with a mean μgrf and a standard deviation σgrf given by 2 )( ) (0.53 0.1 ) ln( / 360) (0.5 0.04 ln( / 360) grf I I μ = − + β + + β (3-6) (0.93 0.02 ) ln( / 360) grf I σ = − + β (3-7) where
β is the beamwidth in degrees
I = 1 for winter and I = -1 for summer
gain of the antenna equals G− ΔGBW. For example, if a 20-degree antenna is used, the mean value of ΔGBW would be closed to 7 dB.
3.1.2 ITU Channel Model for Mobile Wireless
Application
As we know, for fixed wireless application such as IEEE 802.16-2004, the SUI channel models are recommended for simulation. However, for mobile wireless application like IEEE 802.16-2005, the recommendatory channel model is not proposed at present. Here we choose International Telecommunication Union (ITU) channel model [19] for mobile and fixed use.
ITU channel model is a measurement based channel model proposed for the 3GPP WCDMA system. Delay and average power of each multipath for the ITU channel models are summarized in Table 3-2. Four or six multipath signals are generated in the wireless channel depending on the channel type as shown in Table 3-2 respectively. The ITU channel model can be modeled as
( )
(
)
1 ( ) N n n n n w t p g t z t τ = =∑
− (3-8)where z(t) and w(t) denote the complex low pass representations of the channel input and output respectively, p is the strength of the nth weight and n g t is the n( ) complex Gaussian process weighting the nth replica.
Table 3-2: Parameters of ITU channel models
As shown in Table 3-2, ITU channel model includes two environments. For the pedestrian test environment, this environment is characterized by small cells and low transmit power. Base stations with low antenna height are located outdoors, and pedestrian users are located on streets, inside buildings or residences. Its path loss is defined by
(dB)
10 10
40 log 30 log 49
L = R+ f + , (3-9)
where R denotes the separation (km) between the base station and the mobile station and f is carrier frequency.
For vehicular environment, it is characterized by large cells and higher transmit power. The model is applicable for in urban and suburban areas outside the high rise core where the buildings are of nearly uniform height. Its path loss is written as
(
3)
10 10 10
40 1 4 10 b log 18 log b 21 log 80
L = − × − Δh R− Δh + f + (3-10)
where
R is the separation (km) between base station and mobile station f is carrier frequency
b
h
Δ is base station antenna height (m), measured from the average rooftop level The path loss model is valid for a range of Δ from 0 to 50 m. hb
The ITU channel model uses Doppler spectrum of classical Jake’s spectrum. As shown in Figure 3-2, the Doppler spectrum is concave.
Figure 3-2: Doppler spectrum of ITU channel models
3.1.3 SCM Channel Model for Mobile MIMO
Wireless Application
Spatial Channel Model (SCM) channel model [20] is the channel model of third Generation Partnership Project (3GPP), which focuses on fixed and mobile MIMO wireless application. It is a detailed system level model for simulating urban micro-cell, urban macro-cell and suburban macro-cell fading environments. The SCM model considers N cluster of scatterers. Each cluster corresponds to a resolvable path.
Figure 3-3: BS and MS angular parameters in SCM specification
For a NT element linear BS array and a NR element linear MS array, the channel
coefficients of one of the N multipath components are given by a NR ×NT matrix of
complex amplitudes. Assuming omnidirectional antenna elements are employed at the BS and MS and neglecting pathloss and shadowing, the channel impulse response for the lth path between the sth transmit and uth receive antenna can be written as
( )
(
)
(
)
(
)
(
)
, , , , , , , 1 , , exp sin exp sin exp cos s n m AOD n m M n u s n u n m AOA m n m AOA v j kd P h t jkd M jk t θ φ θ θ θ = ⎧ ⎡ ⎤ ⎫ ⎪ + ×⎪ ⎪ ⎢ ⎥ ⎪ ⎪ ⎣ ⎦ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎡ ⎤ ⎪ = ⎨⎪ ⎢⎣ ⎥⎦× ⎬⎪ ⎪ ⎪ ⎪ ⎡ ⎤ ⎪ ⎪ − ⎪ ⎪ ⎢⎣ ⎥⎦ ⎪ ⎪ ⎪ ⎩ ⎭∑
v . (3-11)where j = − , k is the wave number 2 /1 π λ, λ is the carrier wavelength in meters, Pn is the power of the nth path, M is the number of subpaths per-path, ds is the distance in meters from BS antenna element s to the reference (s = 1) antenna, du is the distance in meters from MS antenna element u to the reference (u = 1) antenna,
(AOA) for the mth subpath of the nth path with respect to the MS broadside and
, ,
n m AOD
θ is the Angle of Departure (AOD) for the mth subpath of the nth path with respect to the BS broadside. The details of the generation of relevant parameters are given in [20].
3.2 Channel Estimation
This section describes channel estimation schemes to recover the channel frequency response. Recall that the frame structure of OFDMA in IEEE-802.16 is described as with certain pilot subcarriers in subbands for the both preamble and the data frames, as described in 2.1.4. We have to develop the pilot-based channel estimation which is introduced in [21] with the system structure shown in Figure 3-4.
Figure 3-4: Baseband model of a typical pilot-based system
For the discrete baseband equivalent system shown in Figure 3-4, we assume perfect timing synchronization in this thesis. The binary information data are grouped
Figure 2-6, the modulated data X= ⎣⎢⎡X(0), X(1), , X N( −1)⎤⎥⎦T are transformed and multiplexed into time domain response
(0), (1), , ( 1)T
x x x N
⎡ ⎤
= ⎢⎣ − ⎥⎦
x using the inverse discrete fourier transform
(IDFT):
H =
x F X , (3-12)
where N is the number of subcarriers and F is the DFT matrix
0( 1) 00 ( 1)0 ( 1)( 1) N N N N N N N N W W W W − − − − ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ F (3-13) with 2 1 j nk nk N N W e N π − = . (3-14)
The guard interval is then inserted to prevent possible inter-symbol interference (ISI) in OFDM systems, and the resultant samples
{
x n are g ( )}
( ) ( ) ( ) , , , 1 , 0,1, , 1 g x N n n G x n x n n N ⎧ + = − − ⎪⎪⎪ = ⎨⎪ = − ⎪⎪⎩ , (3-15)
where G is the number of samples in the guard interval. The transmitted signal is then sent to a multi-path fading channel. The received signal can be represented by
( ) ( ) ( ) ( )
g g
y k =x k ⊗h k +n k , (3-16)
where h k is the impulse response of channel and ( )( ) n k is the additive white Gaussian noise (AWGN). The channel impulse response h k can be expressed as: ( )
( ) 1
(
)
0 L i i i h k − g δ k τ = =∑
× − , (3-17)response of the ith path, and τi is the ith-path delay time normalized by sampling time.
After removing the guard interval from y k , the received signal g ( ) (0), (1), , ( 1)T
y y y N
⎡ ⎤
= ⎢⎣ − ⎥⎦
y can be expressed in matrix form
H = + y hF X w , (3-18) where ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 1 1 0 0 h h G h h h h G h G h ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ 0 0 h 0 0 (3-19)
is the channel matrix which represents the circular convolution of (3.16). Then, the signals are sent to the DFT block to demultiplex the multicarrier signals:
H = = + Y Fy FhF X Fw . (3-20) Set ( )0 , ( )1 , , ( 1)T H H H N = ⎡ ⎤ = ⎢⎣ − ⎥⎦ H Fh , (3-21)
since the channel matrix h is Toeplitz and F is unitary, FhF can be simplified H [22] , [23] as
( ) ( )
H =diag =diag
FhF Fh H . (3-22)
Then, the received signal Y can be seen as the multiplication of the transmitted signal
3.2.1 LS and MMSE Channel Estimation
If the time domain channel vector h= ⎣⎢⎡h(0), h(1), , h N( −1)⎤⎥⎦T is Gaussian and uncorrelated with the channel noise vecotor n and set X=diag( )X , the MMSE estimate [15] of h aims at minimizing E ⎡⎢
(
(
−)
)
2⎤⎥⎢ ⎥ ⎣ Y XFh ⎦ becomes 1 ˆMMSE = hY YY− h R R Y , (3-24) where { H} H H hY =E = hh R hY R F X (3-25) 2 { H} H H YY =E = hh +σn n R YY XFR F X I . (3-26)
are the cross covariance matrix between h and Y and the auto-covariance matrix of Y. Further, R is the auto-covariance matrix of h and hh σn2 =E
{ }
n2 denotes the noise variance. By using (A+BCD)-1 =A-1 -A B DA B-1 ( -1 +C-1 -1) DA in [22], -1 the MMSE estimate can be formulated asˆMMSE H =FhˆMMSE = ×F
(
QMMSEF X Y . (3-27) H H)
where(
H H)
1 2 1(
H H)
1 MMSE hh σn hh − − − ⎡ ⎤ = ⎢⎢ + ⎥⎥ ⎣ ⎦ Q R F X XF R F X XF . (3-28) After some computation, the estimator can be computed asˆ MMSE
H =Rhh(Rhh +σn2(XXH) )− −1 1HˆLS (3-29) Besides, the LS estimator for h which minimizes
(
y−XFh) (
H y−XFh can)
be represented as [22]:
LS LS
ˆ = H H
H FQ F X Y, (3-30) where
(
)
LS 1 H H − = Q F X XF (3-31)After some matrix computation, the estimator can be computed as
( )
(
)
= 1 (0) (1) ( 1) ˆ (0) (1) ( 1) T LS Y Y Y N X X X N diag − ⎡ − ⎤ ⎢ ⎥ = ⎢⎣ − ⎥⎦ H X Y . (3-32)For pilot-aided channel estimation using subcarrier allocation of IEEE 802.16 described in (2.2.2), only the pilot subcarriers are known at first, and thus the LS and MMSE schemes shall use the pilot information to estimate the channel frequency response at the pilot subcarriers first. The information contains two parameters, pilot magnitude P=[ ,P0 P1, , PNp−1]T and pilot subcarrier index
0 1 1
[ ,f f, , fNp− ]T =
f , where P stands for the magnitude of the kth pilot k with subcarrier index f and Nk p is the total number of pilot subcarriers. Thus, we can extract the received signal vector at the pilot subcarriers:
0 1 1
[ ( ), ( ), , ( Np )]T
p = Y f Y f Y f −
Y . (3-33)
Then, the LS channel estimate in (3-32) can be modified as
( )
(
)
1 0 1 0 1 1 1 ( ) ( ) ( ) ˆ p p T N P LS N P Y f Y f Y f P P P diag − − − ⎡ ⎤ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ = H P Y , (3-34)and the MMSE channel estimation in (3-29) would be modified as ˆP
MMSE
H ( 2( ( ) ( )H) )1 1ˆP hh hh σn diag diag − − LS
= R R + P P H (3-35)
Afterwards, the interpolation method can be adopted to obtain the overall channel frequency response, which will be described in 3.2.2. The overall channel estimation
Pilot subcarrier extraction Pilot subcarrier channel estimation Channel interpolation
Known pilot data Ps
Received signals after FFT Estimated channel frequency response , P ilo t s H s R Hin terp s, Pilot subcarrier extraction Pilot subcarrier channel estimation Channel interpolation
Known pilot data Ps
Received signals after FFT Estimated channel frequency response , P ilo t s H s R Hin terp s,
Figure 3-5: Pilot-aided channel estimation scheme
After the channel is estimated, a conventional equalization method using a one-tap equalizer can be employed to equalize the distorted received signals. Thus the decision output is
ˆ
X=dec diag
(
( )
Hˆ −1Y (3-36))
3.2.2 Interpolation Techniques
After the estimation of the channel frequency response of pilot subcarriers, the channel response at the data subcarriers can be interpolated by adjacent pilot subcarriers. Several techniques described in [16] and [24] can be adopted to get the overall frequency response.
z Linear interpolation: Two successive pilot subcarriers are used to determine the channel response in between the pilot subcarriers. For data subcarrier k,
1 − < ≤
j j
f k f , the estimated channel response is given by
1 int 1 1 1 ( ) ( − ) − ( ( ) ( − )) − − = + − − j P P P erpl j j j j j k f H k H f H f H f f f . (3-37)
z Lagrange polynomial interpolation: The linear interpolation can be further represented as 1 int 1 1 1 ( ) j P( ) j P( ) erpl j j j j j j k f k f H k H f H f f f f f − − − − − − = + − − . (3-38) Y Yp Hˆp
H
ˆ
Thus, we can further increase the order of the interpolation function as the number of channel estimates at the pilot subcarriers used to estimate the channel response at one data subcarrier increases (not just the adjacent two pilot subcarriers) int 1 1 1 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) u u u u u u P P erpl j N j N j N j N j N j N H k L k H f L k H f L k x t − − − + − + + − + − = + + + (3-39) where 1 1 1 1 1 1 1 ( ) ( )( ) ( ) ( ) ( ) ( )( ) ( ) u u u u u u j N i i j N i i j N i i i i i j N j N n n j N i n n i k f k f k f k f L k f f f f f f f f k f f f − − + + − − − + + − + − = − ≠ − − − − = − − − − − = −
∏
(3-40)and the kth data subcarrier estimate uses 2Nu adjacent pilot subcarrier estimates,
{
fj N− u, fj N− u+1, , fj N+ u−1}
, for fj−1 < ≤k fj.It is obvious that the linear interpolation uses the order of two of the Lagrange interpolation function and requires 2 multiplications for each desired subcarrier. If we extend the order to 2Nu, the requirement in doing the Lagrange interpolation increases to 2Nu multiplications per subcarrier since the scaling term L k in (3-40) remains constant for fixed subcarrier allocation. i( )
