Contribution

In this thesis, several channel estimation techniques are discussed. We combine and apply them to the Orthogonal Frequency Division Multiplexing (OFDM) system. In Chapter 3, the channel environments and Decision directed Channel Estimation are introduced. We choose SUI-3, SUI-3 and Vehicular A to run the computer simulations. In Chapter 4, the Expectation Maximization algorithm based Channel Estimation is considered.

Finally, we compare and analyse the SER performance of the proposed estimators. For the result, the EM-AR can work on time and does not use any buffer to save data. The EM-Linear Interpolation can work as well as EM-AR, but it has to use some buffer, which is

not desirable in real-time applications. No mater in high speed or low speed, the Expectation Maximization Channel Estimation can work very well.

Chapter 2 Overview of WiMAX System

2.1 Introduction to OFDM

The material in this Chapter is largely taken from [6], [7], and [13].

2.1.1 Concept and Brief Mathematical Expression of OFDM

In a single carrier system, a single fade or interference can cause the entire link to fail, but in a multicarrier system, only a small percentage of subcarriers will be affected. Error correction coding can then be used to correct for the few erroneous subcarriers. And OFDM is a special case of multicarrier transmission.

In a classical parallel data system, the total signal frequency band is divided into nonoverlapping frequency channels. It seems good to avoid spectral overlap of channels to eliminate inter-channel interference. However, this leads to inefficient use of the available spectrum. To cope with the inefficiency, the concept of using parallel data transmission by means of frequency division multiplexing (FDM) was published in mid-1960s. The concept of FDM was to use parallel data streams with overlapping carriers. The basic idea of OFDM is to divide the available spectrum into several subchannels (subcarriers). By making all subchannels narrowband, they experience almost flat fading, which makes equalization and channel estimation easier. To obtain a high spectral efficiency, the frequency response of the subchannels are overlapping and orthogonal, hence the name OFDM. This orthogonality can

Cyclic prefix

Time

Fig. 2-1 Cyclic prefix is a copy of the last part of the OFDM symbol.

be completely maintained, even though the signal passes through a time-dispersive channel, by introducting a cyclic prefix.

A cyclic prefix is a copy of the last part of the OFDM symbol which is prepended to the transmitted symbol, see Fig. 2-1. This makes the transmitted signal periodic, which plays an important roll in avoiding intersymbol and intercarrier interference [14]. Although the cyclic prefix introduces a loss in signal-to-noise ration (SNR), it is usually a small price to pay to mitigate interference. For this system we employ the following assumptions:

z The channel impulse response is shorter than the cyclic prefix.

z Transmitter and receiver are perfectly synchronized.

z The fading is slow enough for the channel to be considered constant during one OFDM symbol interval.

z Channel noise is additive, white, and complex Gaussian.

The brief mathematical description of the OFDM system allows us to see how the signal is generated. Mathematically, each carrier can be described as a complex wave:

( ) ( )

^{j w tc c( )t}

c c

S t = A t e

^{⎡⎣ +φ ⎤⎦ (2.1)}

The real signal is the real part of S tc

( )

. Both A tc

( )

and φc

( )

t , the amplitude and phase of one carrier, can vary on a symbol-by-symbol basis. But the values of the parameters are constant over the symbol duration τ

An OFDM signal consists of many carriers. Thus the complex signal S ts

( )

can be on the frequency of a particular carrier are fixed values over one symbol period, thus can be rewritten as constants:

If the signal is sampled with a sampling frequency of 1 T , then the sampled signal can be represented by

Besides, the symbol time is restricted to be longer than what the signal can be analyzed to N samples. It is convenient to sample over the period of one data symbol, thus

τ =NT

To simplify the signals, let w₀ = . Then the signal becomes0

( )

^{1 ( )}

As we know, the form of the inverse discrete Fourier transform (IDFT) is

( )

¹

( )

²

Fig. 2-2 A symbolic picture of the individual subchannels for an OFDM system with N tones over a bandwidth W

which is equivalent to the condition for “orthogonality” discussed before. Thus as a conclusion, using DFT to define the OFDM signal can maintain the orthogonality. Fig. 2-2 displays a schematic picture of the frequency response of the individual subchannels in an OFDM symbol. In this figure, the individual subchannels of the system are separated and orthogonal from each other.

2.1.2 Continous-Time Model of OFDM Including The Concept of Cyclic

The continuous-time OFDM model presented in the Fig. 2-3 can be considered as the ideal baseband OFDM system model, which in practice is digitally synthesized and will be discussed in the next section. We start to introduce the continuous model with the waveforms used in the transmitter and proceed all the way to the receiver.

z Transmitter

Assumeing an OFDM system with N subcariers, a bandwidth of WHz and a symbol length of T seconds, of which T seconds is the length of the cyclic _g

Transmitter Channel Receiver

Fig. 2-3 Baseband OFDM system model

prefix, the transmitter uses the following waveforms

( )

frequency k W N , the common interpretation of OFDM is that it uses N subcarriers, each carrying a low bit-rate. The waveforms φk

( )

t are used in the modulation and the transmitted baseband signal for OFDM symbol number l as

( )

¹ ,

( )

points. When an infinite sequence of OFDM symbols is transmitted, the output from the transmitter is a juxtaposition of individual OFDM symbols as

( ) ( )

¹ ,

( )

z Physical channel

We assume that the support of the (possibly time variant) impulse response ^g

( )

^τ,t

of the physical channel is restricted to the interval τ∈ ⎣⎡0,T_g⎤⎦ , i.e., to the length of

the cyclic prefix. The received signal becomes

( ) ( )( ) ( ) ( ) ( )

0

;

Tg

r t = g s t× =

∫

g τ t s t−τ τd +n t ^(2.10)

Where n is additive, white, and complex Gaussian channel noise.

z Receiver

Effectively this means that the cyclic prefix is removed in the receiver. Since the cyclic prefix contains all ISI from the precious symbol, the sampled output from the

receiver filter bank contains no ISI. Hence we can ignore the time index l when calculating the sampled output at the ^_ th matched filter. By using (2.9), (2.10), and (2.11), we get

We consider the channel to be fixed over the OFDM symbol interval and denote it by ^g

( )

^τ , which gives

The latter part of this expression is the sampled frequency response of the channel from the receiver filter bank can be simplified to

( ) the following equation is thus obtained.

( ) ( )

According to (2.16), we know that

k k k

y = h + n

^(2.18)

x

0,l

Fig. 2-4 Continuous-time OFDM system interpreted as parallel Gaussian channels.

The benefit of a cyclic prefix is twofold: it avoids both ISI (since it acts as a guard space) and ICI (since it maintains the orthogonality of the subcarriers). By re-introducing the time index

l, we may now view the OFDM system as a set of parallel Gaussian channels, according to Fig. 2-4.

2.1.3 Discrete-Time Model

An entirely discrete-time model of and OFDM systme is displayed in Fig. 2-5.

Compared to the continous-time model, the modulation and demodulation are replaced by an inverse DFT (IDFT) and a DFT respectively and the channel is a discrete-time convolution.

The cyclic prefix operates in the same fashion in this system and the calculations can be performed in essentially the same way. The main difference is that all integrals are replaced by sums.

Fig. 2-5 Discrete-time OFDM system

As far as the receiver is concerned, the use of a cyclic prefix longer than the channel response will transform the linear convolution in the channel into a cyclic convolution.

Denoting cyclic convolution by “⊗”, we can write the whole OFDM system as

( ( ) )

points, g is the channel impulse response of the channel (padded with zeros to obtain a length of N), and n is the channel noise. Since the channel noise is assumed to be white _l Gaussian, the term nl =DFT

( )

nl represents uncorrelated Gaussian noise. Furthermore, we use the fact that the DFT of two cyclically convolved signals is equivalent to the product of their individual DFTs. Denoting element-by-element multiplication by “ i ”, the above expression can thus be written as

( )

l l l l l l l

y = x i DFT g + n =x h +n i

^(2.20)

Where hl =DFT

( )

gl is the frequency response of the channel. Therefore we have obtained the same type of parallel Gaussian channels as the continuous-time model. The only difference is that the channel attenuations h are given by the _l N -point DFT of the discrete-time channel, instead of the sampled frequency response as in (2.15).

2.1.4 Imperfections of OFDM

Depending on the mathematical analyzed situation disscused before, imperfections in a real OFDM system may be ignored or explicitly included in the model. Below we mention of the imperfections and their corresponding effects.

z Dispersion

Both time and frequency dispersion of the channel can destroy the orthogonality of the system, i.e., introduce both ISI and ICI. If these effects are not sufficiently mitigated by e.g., a cyclic prefix and a large inter-carrier spacing, they have to be included in the model. One way of modelling these effects is an increase of the additive noise.

z Nonlinearities and clipping distortion

OFDM systems have high peak-to-average power ratios and high demands on linear amplifiers. Nonlinearities in amplifiers may cause both ISI and ICI in the system.

Especially, if the amplifiers are not designed with proper output back-off (OBO), the clipping distortion may cause severe degradation.

z External interference

In wireless systems, the external interference usually stems from radio transmitters and other types of electronic equipment in the vinciniy of the receiver.

2.2 Introduction to OFDMA

OFDMA is a multiple access method based on OFDM signaling that allows simultaneous

Table 2-1 OFDM Advantages and Disadvantages

Advantages Disadvantages

Bandwidth efficiency

Immunity to multipath effect

Robust against narrowband interference

Sensitive to frequency offset Sensitive to timing offset Sensitive to phase noise

Large peak-to-average power ratio

transmissions to and from multiple users along with the other advantages of OFDM. In OFDM, a channel is divided into carriers which is used by one user at any time. In OFDMA, the carriers are divided into subchannels. Each subchannel has multiple carriers that form one unit in frequency allocation. In this way, the bandwidth can be allocated dynamically to the users according to their needs. A simple comparison of the subcarrier allocation of OFDM

Fig. 2-6 Comparison of subcarrier allocatins in OFDM and OFDMA (from [8]).

and OFDMA is shown in Fig. 2-6.

An additional advantage of OFDMA is the following. Due to the large variance in a mobile system’s path loss, inter-cell interference is a common issue in mobile wireless systems. An OFDMA system can be designed such that subchannels can be composed from several distinct permutations of subcarriers. This enables significant reduction in inter-cell interference when the system is not fully loaded, because even on occasions where the same subchannel is used at the same time in two different cells, there is only a partial collision on

Fig. 2-7 Subcarrier allocation in an OFDMA symbol (from [9]).

the active sub-carriers.

Fig. 2-7 shows an example subcarrier allocation in an OFDMA symbol. The frequency response of a typical broadband wireless channel is also depicted. In this example, the deep-fading condition and narrowband interference are considered. In the top plot, we see that when the channel is in deep fade, the subcarriers are not sufficiently energy efficient to carry information. These wasted subcarriers can be utilized by there uses in OFDMA, thus achieving higher efficiency and capacity. Very few, if any, subcarriers are likely to be wasted in OFDMA, since no particular subcarrier is likely to be bad for all users.

In order to support multiple users, the control mechanism becomes more complex.

Besides, the OFDMA system has some implementation issues which are more complicated to handle. For example, power control is needed for the uplink to make signals from different users have equal power at the receiver, and all users have to adjust their transmitting time to be aligned. We shall address some issues in the context of IEEE 802.16e.

2.3 Introduction to IEEE 802.16e

Since the publication of the IEEE 802.16 standard for fixed broadband wireless access in 2001, a number of revision and amendments have taken place. Like other IEEE 802 standards, the 802.16 standards are primarily concerned with physical (PHY) layer and medium access control (MAC) layer functionalities. The idea originally was to provide broadband wireless access to buildings through external antennas communicating with radio base stations (BSs).

To overcome the disadvantage of the line-of-sight (LOS) requirement between

transmitters and receivers in the 802.16 standard, the 802.16a standard was approved in 2003 to support nonline-of-sight (NLOS) links, operational in both licensed and unlicensed frequency bands from 2 to 11 GHz, and subsequently revised to create the 802.16d standard (now code-named 802.16-2004). With such enhancements, the 802.16-2004 standard has been viewed as a promising alternative for providing the last-mile connectivity by radio link.

However, the 802.16-2004 specifications were devised primarily for fixed wireless users. The 802.16e task group was subsequently formed with the goal of extending the 802.16-2004 standard to support mobile terminals.

The IEEE 802.16e has been published in Febuary 2006. It specifies four air interfaces:

WirelessMAN-SC PHY, WirelessMAN-SCa PHY, WirelessMAN-OFDM PHY, and WirelessMAN-OFDMA PHY. This study is concerned with WirelessMAN-OFDMA PHY in a mobile communication environment.

Some glossary we will often use in the following is as follows. The direction of transmission from the base station (BS) to the subscriber station (SS) is called downlink (DL), and the opposite direction is uplink (UL). The SS is considered synonymous as the mobile station (MS). It is sometimes termed the user. The BS is a generalized equipment set providing connectivity, management, and control of the SS.

2.3.1 OFDMA Basic Terms

In the OFDMA mode, the active subcarriers are divided into subsets of subcarriers, where each subset is termed a subchannel. The subcarriers forming one subchannel may, but need

Fig. 2-8 OFDMA frequency description (3-channel schematic example, from [4]).

not be, adjacent. The concept is shown in Fig. 2-8.

Three basic types subchannel organization are defined: partial usage of subchannels (PUSC), full usage of subchannels (FUSC), and adaptive modulation and coding (AMC); among which the PUSC is mandatory and the other two are optional. In PUSC DL, the entire channel bandwidth is divided into three segments to be used separately. The FUSC is employed only in the DL and it uses the full set of available subcarriers so as to maximize the throughput.

Slot and Data Region

The definition of an OFDMA slot depends on the OFDMA symbol structure, which varies for uplink and downlink, for FUSC and PUSC, and for the distributed subcarrier permutations and the adjacent subcarrier permutation.

z For downlink PUSC using the distributed subcarrier permutation, one slot is one subchannel by two OFDMA symbols.

z For uplink PUSC using either of the distributed subcarrier permutations, one slot is one subchannel by three OFDMA symbols.

z For downlink FUSC and downlink optional FUSC using the distributed subcarrier permutation, one slot is one subchannel by one OFDMA symbol.

In OFDMA, a data region is a two-dimensional allocation of a group of contiguous

Fig. 2-9 Example of the data region which defines the OFDMA allocation (from [4]).

subchannels, in a group of contiguous OFDMA symbols. All the allocations refer to logical subchannels. This two-dimensional allocation may be visualized as a rectangle, such as the

4 3× rectangle shown in Fig. 2-9 Segment

A segment is a subdivision of the set of available OFDMA subchannels (that may include all available subchannels). One segment is used for deploying a single instance of the MAC.

Permutation Zone

A permutation zone is a number of contiguous OFDMA symbols, in the DL or the UL, that use the same permutation formula. The DL subframe or the UL subframe may contain more than one permutation zone. The concept of permutation zone will be further elaborate later.

2.3.2 OFDMA Symbol Parameters

z Some OFDMA symbol parameters are listed below.

z BW: Nominal channel bandwidth.

z N_used: Number of used subcarriers.

z n: Sampling factor. This parameter, in conjunction with BW and N_used, determines the subcarrier spacing and the useful symbol time.

z G: Ratio of cyclic prefix (CP) time to useful time.

z N_FFT : Smallest power of two greater than N_used. z Sampling frequency: Fs = ⋅

[

n BW ^{8000 800}

]

× .

z Subcarrier spacing: Δ =f F N_{s FFT} .

z Useful symbol time: T_b = Δ .1 f

z Cyclic prefix (CP) time: T_g = ⋅ .G T_b

z OFDM symbol time: T_s = + .T_b T_g

z Sampling time: T N_{b FFT} .

2.3.3 Scalable OFDMA [9]

One feature of the IEEE 802.16e OFDMA is the selectable FFT size, from 128 to 2048 in multiples of 2, excluding 256 to be used with OFDM. This has been termed scalable OFDMA (S-OFDMA). One use of S-OFDMA is that if the channel bandwidths are allocated based on integer power of 2 times a base bandwidth, then one may consider making the FFT size proportional to the allocated bandwidth so that all systems are based on the same subcarrier spacing and the same OFDMA symbol duration, which may simplify system design. For example, Table 2-2 lists some S-OFDMA parameters proposed by the WiMAX Forum [10].

S-OFDMA supports a wide range of bandwidth to flexibly address the need for various spectrum allocation and usage model requirements.

When designing OFDMA wireless systems the optimal choice of the number of subcarriers per channel bandwidth is a tradeoff between protection against multipath, Doppler shift, and design cost/coplexity. Increasing the number of subcarriers leads to better immunity to the ISI

Table 2-2 S–OFDMA Parameters Proposed by WiMAX Forum

Parameters Values

System Channel Bandwidth (MHz) 1.25 5 10 20

Sampling Frequency (MHz) 1.4 5.6 11.2 22.4

FFT Size 128 512 1024 2048

Subcarrier Spacing ( fΔ ) 10.94 kHz

Useful Symbol Time(T_b = Δ )1 f 91.4 μ sec

Guard Time(T_g =T_b 8) 11.4 μ sec

OFDMA Symbol Duration(T_s = + )T_b T_g 102.9 μsec

caused by multipath; on the other hand it increases the cost and complexity of the system (it leads to higher requirements for signal processing power and power amplifiers with the capability of handling higher peak-to-average power ratios). Having more subcarriers also results in narrower subcarrier spacing and therefore the system becomes more sensitive to Doppler shift and phase noise. Calculations show that the optimum tradeoff for mobile systems is achieved when subcarrier spacing is about 11 kHz [11] .

2.4 OFDMA Frame Structure

Duplexing Modes

In licensed bands, the duplexing method shall be either frequency-division duplex (FDD) or time-division duplex(TDD). FDD SSs may be half-duplex FDD (H-FDD). In license exempt bands, the duplexing method shall be TDD.

Point-to-Multipoint (PMP) Frame Structure

When implementing a TDD system, the frame is composed of BS and SS transmissions. Fig.

2-10 shows an example. Each frame in the downlink transmission begins with a preamble

Fig. 2-10 Example of an OFDMA frame (with only mandatory zone) in TDD mode (from [2]).

followed by a DL transmission period and an UL transmission period. In each frame, time gaps, denoted transmit/receive transition gap (TTG) and receive/transmit gap (RTG), are between the downlink and uplink subframes and at the end of each frame, respectively placed.

They allow transitions between transmission and reception functions.

Subchannel allocation in the downlink may be performed with PUSC where some of the subchannels are allocated to the transmitter or FUSC where all subchannels are allocated to the transmitter. The downlink frame shall start in PUSC mode with no transmit diversity. The FCH shall be transmitted using QPSK rate 1/2 with four repetitions using the mandatory coding scheme (i.e., the FCH information will be sent on four subchannels with successive logical subchannel numbers) in a PUSC zone. The FCH contains the DL Frame Prefix which specifies the length of the DL-MAP message that immediately follows the DL Frame Prefix

Fig. 2-11 Illustration of OFDMA with multiple zones (from [2]).

and the repetition coding used for the DL-MAP message.

The transitions between modulations and coding take place on slot boundaries in time domain

The transitions between modulations and coding take place on slot boundaries in time domain

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