Decoupled maximum likelihood carrier frequency offset estimator for MIMO OFDM systems

1.1 Advantage of OFDM Systems Frequency division multiplexing FDM is a technology that transmits multiple signals simultaneously over a single transmission path, such as a cable or wire

Chapter 1 Introduction

Wireless communications technologies are now prevalent throughout today's society and growing in demand The whole world are planning and installing radio networks to support communications requirements, the success of these networks may be driven by the availability of the radio frequency spectrum The radio frequency spectrum, a finite natural resource, has greater demands placed on it every day In an effort to make the most efficient use of this resource, various technologies have been developed so that multiple, simultaneous users can be supported in a finite amount of spectrum This concept is called "multiple access." To ensure profit grows parallel with the demand for wireless technologies, manufacturers have had to develop methods of putting more users

in the same spectrum space In this thesis, we focus on the discussion of Orthogonal Frequency Division Multiplex (OFDM), a multiple access technology which has drawn increasing attention recently

1.1 Advantage of OFDM Systems

Frequency division multiplexing (FDM) is a technology that transmits multiple signals simultaneously over a single transmission path, such as a cable or wireless system Each signal travels within its own unique frequency range (carrier), which is modulated by the data (text, voice, video, etc.)

OFDM spread spectrum technique distributes the data over a large number of carriers that are spaced apart at precise frequencies This spacing provides the "orthogonality" in this

technique which prevents the demodulators from seeing frequencies other than their own

In a typical terrestrial broadcasting scenario, there are multipath-channels (i.e the transmitted signal arrives at the receiver using various paths of different length) Since multiple versions of the signal interfere with each other (inter symbol interference (ISI)),

it becomes very hard to extract the original information The “orthogonality” between sub-carrier makes OFDM outperform other wireless systems in terms of high spectral efficiency, resiliency to RF interference, and lower multi-path distortion Due to these benefits, OFDM systems have received increasing attention There is a great interest in using OFDM for high-speed wireless local area network applications Development is ongoing for wireless point-to-point and point-to-multipoint configurations using OFDM technology In a supplement to the IEEE 802.11 standard, the working group published IEEE 802.11a, which outlines the use of OFDM in the 5.8 GHz band[42] OFDM forms the basis for the Digital Audio Broadcasting (DAB) and Digital Video Broadcasting (DVB) standard in the European market OFDM also forms the basis for the global ADSL (asymmetric digital subscriber line) standard

1.2 Advantage of MIMO-OFDM Systems

The major challenges in future wireless communications system design are increased spectral efficiency and improved link reliability The wireless channel constitutes a hostile propagation medium, which suffers from fading (caused by destructive addition of multipath components) and interference from other users Diversity provides the receiver with several (ideally independent) replicas of the transmitted signal and is therefore a

powerful means to combat fading and interference and thereby improve link reliability Common forms of diversity are time diversity (due to Doppler spread) and frequency diversity (due to delay spread) In recent years the use of spatial (or antenna) diversity has become very popular, which is mostly due to the fact that it can be provided without loss

in spectral efficiency Receive diversity, that is, the use of multiple antennas on the receive side of a wireless link, is a well-studied subject [4] Driven by mobile wireless applications, where it is difficult to deploy multiple antennas in the handset, the use of multiple antennas on the transmit side combined with signal processing and coding has become known under the name of space-time coding and is currently an active area of research The use of multiple antennas at both ends of a wireless link (multiple-input multiple-output (MIMO) technology) has recently been demonstrated to have the potential of achieving extraordinary data rates The corresponding technology is known

as spatial multiplexing and yields an impressive increase in spectral efficiency

The main motivation for using OFDM in a MIMO channel is the fact that OFDM modulation turns a frequency-selective MIMO channel into a set of parallel frequency MIMO channels Besides spatial diversity, broadband MIMO channels offer higher capacity and frequency diversity due to delay spread Orthogonal frequency division multiplexing significantly reduces receiver complexity in wireless broadband systems The use of MIMO technology in combination with OFDM, i.e., MIMO-OFDM [5,6,7], therefore becomes an attractive solution for future broadband wireless systems

MIMO-OFDM is a technology that uses multiple antennas to transmit and receive radio signals It allows service providers to deploy a Broadband Wireless Access (BWA) system that has Non-Line-of-Sight (NLOS) functionality Specifically, MIMO-OFDM takes advantage of the multipath properties of environments using base station antennas that do not have LOS

The MIMO systems use multiple antennas to simultaneously transmit data, in small pieces to the receiver, which can process the data flows and put them back together This process, called spatial multiplexing, proportionally boosts the data-transmission speed by

a factor equal to the number of transmitting antennas In addition, since all data is transmitted both in the same frequency band and with separate spatial signatures, this technique utilizes spectrum very efficiently

1.3 Problem in OFDM Systems

One of the arguments against OFDM is that, it is sensitive to synchronization errors There are two main kinds of synchronization errors: time symbol error and Carrier Frequency Offset (CFO) In this thesis, only the effect of CFO is studied

CFO is the difference between the carrier frequency of the received signal and the frequency of the receiver oscillator It is caused by the Doppler shift and oscillator

instabilities There are two types of carrier frequency offset: Integer CFO and fractional

CFO Carrier frequency errors result in a shift of the received signal’s spectrum in the

frequency domain With the frequency errors as an integer multiple of the subcarrier

spacing, the subcarriers are still mutually orthogonal But the received data symbols, which are mapped to the OFDM spectrum, are in the wrong position in the demodulated spectrum Fractional CFO spills the energy over the subcarriers, resulting in loss of their mutual orthogonality and hence causes inter-carrier interference(ICI)

Both SISO-OFDM and MIMO-OFDM systems suffer from the loss of orthogonality between the sub-carriers due to CFO CFO attenuates the desired signal, adds phase, and reduces the signal to noise ratio (SNR)[8] As a result, performance of the systems is severely downgraded Accurate carrier offset estimation and compensation is more critical in OFDM communication systems than other modulation schemes

In this dissertation the author develop a decoupled maximum likelihood blind carrier offset estimator The performance of the estimator will be analyzed and compared with other estimators (ESPRIT, CP and hopping pilot approach) in the literature for both SISO-OFDM and MIMO-OFDM systems Compared to the existing methods, the advantage of the proposed CFO estimator is that

1) It has better spectrum efficiency as it does not require any additional training sequence or pilot symbol

2) The proposed scheme has better BER performance especially when SNR is low

1.4 Thesis Outline

The intention of this chapter is to outline the simulated system environment and highlight the subject matters that are pertinent to the dissertation Chapter 1 of this dissertation has provided a concise coverage of the relevant materials that are required for the understanding of the subject matter of this dissertation A more in-depth study of SISO-OFDM and MIMO-OFDM communication systems are covered in Chapter 2 In Chapter

3, the effect of CFO to OFDM systems is analyzed The two main types of CFO estimation schemes in the literature, the data-aided and non-data aided schemes[9], are introduced and compared Performance of the proposed DEML (Decoupled Maximum Likelihood) blind carrier offset estimator for SISO-OFDM and MIMO-OFDM systems is analyzed in Chapter 4 and Chapter 5, respectively Finally, Chapter 6 concludes the report with a summary of the results that are obtained and recapitulates the objective of this dissertation

Chapter 2 OFDM Systems

In this chapter, OFDM is first compared with other multiple access techniques in order to analyze the benefits of the system The advantage of OFDM systems over multipath frequency selective fading channel is then addressed The last part of this chapter gives

an overview of OFDM and MIMO-OFDM systems

2.1 Comparison of OFDM With Other Multiple Access Techniques

Multiple access schemes are used to allow many simultaneous users to use the same fixed bandwidth radio spectrum The bandwidth allocated to any communication system is always limited For mobile phone systems, the total bandwidth is typically 50 MHz, which is split in half to provide the forward and reverse links of the system Sharing of the spectrum is required in order to increase the user capacity Frequency Division Multiple Access (FDMA), Time Division Multiple Access (TDMA) and Code Division Multiple Access (CDMA) are the three major methods of sharing the available bandwidth

to multiple users in wireless communication system

2.1.1 FDMA

The first generation of multiple access technique is the analog FDMA systems such as AMPS (Advanced Mobile Phone Services) For a system of FDMA, the available bandwidth is subdivided into a number of sub-channels with narrower bandwidth Each user is allocated a unique frequency band in which to transmit and receive on During a call, no other user can share the same frequency band

The main shortcoming of FDMA systems is the bandwidth inefficiency In FDMA systems, the bandwidth of each channel allocated to each user is typically 10 kHz-30 kHz for voice communications However, the minimum required bandwidth for speech is only

3 kHz The extra bandwidth between adjacent signal spectra is called guard band, which

is maintained in order to prevent sub-channels from interfering with each other In a typical FDMA system, up to 50% of the total spectrum is wasted due to the extra spacing between sub-channels Moreover, precise narrowband filters are necessary for FDMA systems to filter out interference signals from neighboring sub-channels

2.1.2 TDMA

The second generation consists of the first mobile digital communication systems such as the TDMA based GSM (Global System for Mobile Communication) Unlike FDMA system, one user in TDMA system takes all the frequency bandwidth but during a precise interval of time TDMA divides the available spectrum into multiple time slots, by giving each user a time slot in which they can transmit or receive In reality, only one person is actually using the channel at any given moment, but he or she only uses it for short bursts

He then gives up the channel momentarily to allow the other users to have their turn

TDMA partly overcomes the problem of low bandwidth inefficiency in FDMA system by using wider bandwidth channels, which are shared by several users Multiple users access the same channel by transmitting their data in different time slots TDMA systems are more bandwidth efficient as compared to FDMA systems, since no extra guard band is needed

There are however, two main problems with TDMA There is an overhead associated with the change-over between users due to time slotting on the channel A change-over time must be allocated to allow for any tolerance in the start time of each user, due to propagation delay variations and synchronization errors This limits the number of users

in each channel, results in lower system capacity

Another problem in TDMA systems is the multipath delay spread, which is an important

parameter to access the performance capabilities of wireless systems Because there are obstacles and reflectors in the wireless propagation channel, the transmitted signal arrivals at the receiver from various directions over a multiplicity of paths Such

a phenomenon is called multipath Multiple reflections of the transmitted signal may

arrive at the receiver at different time, the time dispersion of the channel is called

multipath delay spread For a reliable communication without using adaptive equalization

or other anti-multipath techniuques, the transmitted data rate should be much smaller than the inverse of multipath delay spread[10] Otherwise, the multipath delay spread will result in Inter Symbol Interference (ISI) (or bits "crashing" into one another) which the

receiver cannot sort out The symbol rate of each channel is high in TDMA systems (as

the channel handles the information from multiple users) resulting in problems with multipath delay spead

2.1.3 CDMA

Code Division Multiple Access (CDMA) is a spread spectrum technique that uses neither frequency channels nor time slots With CDMA, the narrow band message (typically digitized voice data) is multiplied by a large bandwidth signal that is a pseudo random noise code (PN code) All users in a CDMA system use the same frequency band and transmit simultaneously This is possible because the signal of each user is modulated by

a unique PN code It is like everybody is talking at the same time but using different languages, there is no interference between each other because none of the listeners understand any language other than that of the individual to whom they are listening

One of the main advantages of CDMA systems is the capability of using multipath signals that arrive in the receivers with different time delays FDMA and TDMA, which are narrow band systems, cannot discriminate between the multipath arrivals, and resort

to equalization to mitigate the negative effects of multipath While CDMA systems can make use of the multipath signals and combine them to make an even stronger signal at the receivers by using different technologies, e.g RAKE receiver [11]

2.1.4 OFDM

Similar to FDMA, OFDM systems achieve multiple user access by subdividing the available bandwidth into multiple channels However, OFDM uses the spectrum much more efficiently by spacing the channels much closer together This is achieved by

making all the carriers orthogonal to one another, preventing interference between the closely spaced carriers

OFDM overcomes most of the problems with both FDMA and TDMA It splits the available bandwidth into many narrow band channels (typically 64-4096) The carriers for each channel are made orthogonal to one another, allowing them to be spaced very close together, without guard band as required in the FDMA systems There is no overhead associated with switching between users, since users in OFDM systems do not need to be time multiplexed as in TDMA systems

Fig 2.1 Spectrum of a single OFDM sub-carrier and OFDM symbol

Figure 2.1 shows the spectrum of a single OFDM sub-channel and the spectrum of an OFDM symbol, which are characterized by the fact that spectrum of different sub-carriers overlaps As shown in the figure, at the centre frequency of each carrier, the amplitude of all other carriers’ signals are zero This is called the “orthogonality” between sub-carriers Although the spectrum of different sub-carriers is overlapping with each other, there is no interference caused by other sub-carriers as long as the OFDM signal is transmitted and received at the precise center frequency of each sub-carrier The orthogonality between

sub-carriers allows them to be spaced as close as theoretically possible This overcomes the problem of large carrier spacing required in FDMA

Each carrier in an OFDM signal has a very narrow bandwidth (i.e 1 kHz), thus the resulting symbol rate is low As mentioned in the previous section, signal with low symbol rate has a high tolerance to multipath delay spread, as the delay spread must be very long to cause significant inter-symbol interference

Compared to CDMA, OFDM is more resistant to frequency selective fading since its parallel nature allows errors in sub-carriers to be corrected OFDM performs much better than CDMA in a multipath environment since it is better at overcoming Inter Symbol Interference (ISI), which happens when reflected signals overlap with the transmitted signal However, OFDM is more sensitive to frequency offset, which results in Inter Carrier Interference (ICI)

2.2 Multipath Frequency Selective Fading Channel

Before getting into the structure of OFDM systems, we would like to discuss the performance of OFDM systems over a multipath frequency selective fading channel In

an ideal radio channel, the received signal would consist of only a single direct path signal, which would be a perfect reconstruction of the transmitted signal However in a real channel, the signal is modified during transmission in the channel The received signal consists of a combination of attenuated, reflected, refracted, and diffracted replicas

of the transmitted signal On top of all this, the channel adds noise to the signal and can cause a shift in the carrier frequency if the transmitter, or receiver is moving (Doppler

effect) In a radio link, the RF signal from the transmitter may be reflected from objects such as hills, buildings, or vehicles This gives rise to multiple transmission paths at the receiver

2.2.1 Advantage of OFDM Systems in Frequency Selective Fading Channel

In any radio transmission, the channel spectral response is not flat It has dips or fades in the response due to reflections causing cancellation of certain frequencies at the receiver Reflections of near-by objects (e.g ground, buildings, trees, etc) can lead to multipath signals which have comparable signal power as the direct signal This can result in deep nulls in the received signal power due to the strong interference signal

For narrow bandwidth transmissions if the null in the frequency response occurs at the transmission frequency then the entire signal can be lost This can be partly overcome in two ways By transmitting a wide bandwidth signal or spread spectrum as CDMA system

do, any dips in the spectrum only result in a small loss of signal power, rather than a complete loss Another method is to split the total transmission bandwidth into many narrow-bandwidth carriers This is exactly what is done in OFDM systems The original signal is spread over a wide bandwidth, so most likely nulls in the spectrum only affect a small number of carriers rather than the entire signal The information carried by those lost carriers can be recovered by using some error correction techniques such as Forward Error Correction (FEC) [12]

2.2.2 Guard Interval in OFDM Systems

In order to overcome the effect of mulitpath fading channel, guard interval is necessary in OFDM sytems One of the most important properties of OFDM transmissions is its high level of robustness against multipath delay spread [13][14] This is a result of the long symbol period used, which minimizes the inter-symbol interference The level of multipath robustness can be further increased by the addition of a guard period between transmitted symbols The guard period allows time for multipath signals from the pervious symbol to die away before the information from the current symbol is gathered The most effective guard period to use is a cyclic extension of the symbol Part of the end

of the symbol waveform is put at the start of the symbol as the guard period, this effectively extends the length of the symbol, while maintaining the orthogonality of the waveform The cyclic extension of the symbol is called Cyclic Prefix (CP) Figure 2.2 shows the example of CP in OFDM systems

Timecyclic prefix

Fig 2.2 Cyclic prefix – a copy of the last part of OFDM symbol

CP enables cyclic convolution for each symbol, thus orthogonality is preserved even with imperfect timing and channel impairment In wireless environment, sub-carriers are still

orthogonal as long as the length of CP exceeds the time dispersion of wireless channels (no ISI) This provides multipath immunity as well as symbol time synchronization tolerance

As long as the multipath delay echoes stay within the guard-period duration, there is strictly no limitation regarding the signal level of the echoes: they may even exceed the signal level of the shorter path! The signal from all paths is combined at the input of the receiver and result in a stronger combined signal Since the FFT is energy conservative, the energy of the combined signal is the summation of all the signal energy from different paths On the other hand, the delay spread begins to cause inter-symbol interference when it is longer than the guard interval However, they do not cause significant problems as long as the echoed signal is sufficiently weak This is true most of the time

as multipath echoes delayed longer than the guard period will have been reflected of very distant objects

Other variations of guard periods are possible One possible variation is to insert zero- amplitude signal into adjacednt OFDM systems The OFDM symbols can be easily identified by using this method It also allows for symbol timing to be recovered from the signal, simply by applying envelop detection The disadvantage of using this guard period method is that the zero period does not give any multipath tolerance Throughout this work, the CP based guard interval is adopted

2.3 Generation of OFDM Systems

In this section, it is introduced that how data is modulated and demodulated in OFDM systems Details are given on how data is modulated and transmitted and then recovered

at the receiver in a digital approach of the OFDM scheme

2.3.1 FFT and IFFT in OFDM Systems

In order to achieve a high spectral efficiency, the frequency response of the sub-channels are overlapping and orthogonal to each other, which gives the name of OFDM To generate OFDM symbols successfully, the relationship between all the carriers must be carefully controlled to maintain the orthogonality of the carriers OFDM is generated by firstly choosing the spectrum required, based on the input data, and modulation scheme used Each carrier to be produced is assigned some data to transmit The required amplitude and phase of the carrier is then calculated based on the modulation scheme (typically differential BPSK, QPSK, or QAM) The required spectrum is then converted back to its time domain signal using an Inverse Fourier Transform In most applications,

an Inverse Fast Fourier Transform (IFFT) is used The IFFT performs the transformation very efficiently, and provides a simple way of ensuring the carrier signals produced are orthogonal

The FFT transforms a cyclic time domain signal into its equivalent frequency spectrum This is done by finding the equivalent waveform, generated by a sum of orthogonal sinusoidal components The amplitude and phase of the sinusoidal components represent the frequency spectrum of the time domain signal The IFFT performs the reverse process, transforming a spectrum (amplitude and phase of each component) into a time domain

signal An IFFT converts a number of complex data points, of length that is a power of 2, into the time domain signal of the same number of points Each data point in frequency spectrum used for an FFT or IFFT is called a bin

The orthogonal carriers required for the OFDM signal can be easily generated by setting the amplitude and phase of each frequency bin, then performing the IFFT Since each bin

of an IFFT corresponds to the amplitude and phase of a set of orthogonal sinusoids, the reverse process guarantees that the carriers generated are orthogonal

2.3.2 Digital Approach of OFDM

A possible realization of an OFDM scheme can be dramatically simplified if a digital approach is used The approach is based on the use of FFT to generate and to demodulate the transmitted signal The flowing figure shows the digital implementation of OFDM systems

P / S

P

/

S

QAM Decoder N c-FFT

S / P

) 2 cos( πf c t

) 2 sin( πf c t

) 2 sin( πf c t

−

) 2 cos( πf c t k

Consider a sequence of N symbols, each symbol being represented by a point in a 2-D

constellation These symbols can be written as:

k

j

where a b are the coordinates of the point that represents the symbol k k, k

Then an inverse fast Fourier transform is computed on this set of symbols

where / , f k =k T 0≤ ≤ and T is the symbol duration t T

Then the signal is converted to radio frequency and transmitted through channel

()()

=+

exp[

)2

sin(

)2

cos(

)()

k k k

k k k

Q I

t f j

r

t f jr

t f r

t jS t

S

t

U

ϕπ

ϕπϕ

sin(

As shown in equation (2.8) and (2.9), the transmiited signal, sk = ak + jbk, is finally

recovered at the receiver

2.4 Generation of MIMO-OFDM Systems

Various schemes that employ multiple antennas at the transmitter and receiver are being considered to improve the range and performance of communication systems By far the most promising multiple antenna technology today is called multiple-input multiple-output (MIMO) system MIMO systems employ multiple antennas at both the transmitter and receiver

MIMO-OFDM combines OFDM and MIMO techniques thereby achieving spectral efficiency and increased throughput A MIMO-OFDM system transmits independent OFDM modulated data from multiple antennas simultaneously At the receiver, after OFDM demodulation, MIMO decoding on each of the subchannels extracts the data from all the transmit antennas on all the subchannels The block diagram of a MIMO-OFDM systems is shown in Figure 2.4

Figure 2.4 Block diagram of MIMO-OFDM

Define the transmitted vector x [ 1, 2, ]T

and in the same frequency band Assuming N receive antennas and representing the signal received by each antenna as r i,we have:

As can be seen from the above set of equations, in making their way from the transmitter

to the receiver, the independent signals {x x1, 2, x M} are all combined Traditionally this

“combination” has been treated as interference However, by treating the channel as a matrix, we can in fact recover the independent transmitted streams {x i} To recover the transmitted data stream {x i } from the { r i }, we must estimate the individual channel

weights h ij, construct the channel matrix H Several approaches have been developed to for channel estimation in OFDM systems [15][16] Having estimated H, multiplication

of the vector r with the inverse of H produces the estimate of the transmitted vector x

Because multiple data streams are transmitted in parallel from different antennas, there is

a linear increase in throughput with every pair of antennas added into the system [17] An important fact to note is that unlike traditional means of increasing throughput, MIMO systems do not increase bandwidth in order to increase throughput They simply exploit the spatial dimension by increasing the number of unique spatial paths between the transmitter and receiver

As a result, without increasing bandwidth (a very expensive commodity) or total transmit

power, we can achieve substantial throughput improvement by using MIMO-OFDM This has significant ramifications as it suggests that operators can provide broadband services within the current spectrum that they have purchased Staying at the current carrier frequencies implies that: (a) Signals can propagate further thus reducing the cost

of overall network deployment; (b) RF subsystems can be built using today’s well understood and inexpensive processes

Chapter 3 Carrier Frequency Offset

As mentioned, the OFDM systems are more sensitive to CFO than other communication systems In this chapter, the effect of CFO on Signal to Noise Ratio (SNR) and Bit Error Rate (BER) of OFDM systems is analyzed in detail Then, methods to estimate and compensate the CFO available in the literature are introduced and compared

3.1 Effect of CFO in OFDM Systems

It has been demonstrated that OFDM systems is much more sensitive to Carrier Frequency Offset than other single carrier systems [18][19] As introduced in the first chapter, CFO can be normalized with respect to the subcarrier bandwidth and divided into the integer part and fractional part for convenience Integer CFO need to be corrected

perfectly since it causes a cyclic shift of subcarriers and a phase change proportional to the OFDM symbol number In this thesis, we assume that the integer part of CFO has

been estimated and compensated Our study focuses on the effect of fractional CFO Fractional CFO attenuates the desired signal, adds phase, and causes an inter-carrier interference (ICI) Fig 3.1 shows the relationship between CFO and ICI

Figure 3.1 The relationship between CFO and ICI

Carrier frequency offset also reduces the signal to noise ratio (SNR) and hence increases the bit error rate (BER) Unlike the integer CFO, the fractional CFO cannot be corrected perfectly in practice How fractional CFO affects the SNR and BER of OFDM systems is discussed in the following section

3.1.1 Effect of CFO on SNR for AWGN Channel

For an Additive White Gaussian Noise (AWGN) channel, all the elements of channel impulse response in frequency domain are equal to one Denote the channel impulse response in frequency domain as H k( ), H k( ) 1= for all AWGN channels In the absence

of carrier frequency offset, the received data frame in the frequency domain is

( ) ( ) ( ) ( ) = ( ) ( ) 0,1, , c 1

Y k X k H k N k

+ = − (3.1) where, N cis the number of sub-carriers in one OFDM symbol

As proved in [8], in the presence of a carrier frequency offset, the received data frame after discarding the cyclic prefix and performing IFFT is

( 1)sin

c

c c c

c

j N

N N

N

j N

N N

N

⎡ π − ε⎤πε

Where, ε is the carrier frequency offset normalized by sub-carrier spacing The total

occupied bandwidth in an OFDM system, f OFDM 1

T

≈ , where T is symbol duration So,

the normalized carrier frequency offset ε is

c

j N C

N N

N

⎡ π − ε⎤πε

sin

x

x c

The SNR of the system is also affected by the CFO

( )

1 ( )

x x

x o

SNR

η

σ

=

σ , the relationship between the actual SNR

and SNR can be represented by o

2 2

( )SNR( )

o o

( )SNR( )

< ( ) <

o o

o o

C SNR

C SNR SNR

ε

ε =

ε (3.9)

Equation (3.9) proves that the actual SNR is reduced when carrier frequency offset exists

In [8], it is also proved that the Bit Error Rate of OFDM systems is increased when carrier frequency offset presents

3.1.2 Effect of CFO on SNR for a Multipath Fading Channel

For a multipath fading channel, H k( ) is no longer a constant Instead, it is a random variable The received data frame is

sin

sin = ( ) ( ) ( ) ( ) ( )

c c c

c

j N

N N

N

C X k H k ICI k N k

⎡ π − ε⎤πε

( ) ( ) ( )SNR( , )

( ) ( )

2 2

( , )

( ) ( )

( ) ( )

( ) =

SNR E SNR k

C H k E

3.2 Literature Survey

In last section, it is proved that the actual signal to noise ratio is reduced when carrier frequency offset exsists Hence the performance of the OFDM systems is degraded In order to improve the performance of OFDM systems, the carrier frequency offset must be estimated and compensated before performing the FFT demodulation There are mainly

two types of carrier frequency offset estimator available in the Literature: Data-aided scheme and Non-data-aided scheme

3.2.1 Data-aided Scheme

Data-aided scheme employ well-designed training sequence or pilot symbols to estimate carrier frequency offset Data-aided scheme is capable of achieving rapid and reliable frequency synchronization, so it is often used by packet-oriented systems

One of the most popular methods in data-aided scheme is to employ the known relation between training sequences or pilot symbols Moose proposed a correlation-based technique that uses two consecutive identical training symbols to estimate CFO in [20] The acquisition range of this algorithm is ony ½ subcarrier spacing, although it is a maximum-lilelihood (ML) estimation Following Moose’s algorithm, several techniques were proposed to increase the estimation range of CFO by using multiple identical pilot symbols with a smaller symbol period Schmidl and Cox [21] used two well-designed training symbols, which were defined in the IEEE standard 802.11a As defined in the standard, the first training symbol consists two identical parts, which could be used to estimate the fractional part of the CFO using the method proposed in [20] The second

full-period training symbol has a special correlated relation with the first one Schmidl and Cox employed the special correlated relation to estimate the integer part of CFO A similar method was proposed by Lim in [22] In this method, only two identical half-period symbols were used to estimate both integer and fractional part of CFO The CFO acquisition range was extended in [23] by using one training symbol with more than two identical parts Their algorithm has been proved to be better than the Schmidl and Cox’s scheme in terms of smaller minimum mean-squared error (MMSE) Song [24] suggested

a multistage correlation method to acquire CFO, but the performance of the system was worse as compared to the results in [21] and [23] A simplified version of Song’s estimation method that requires only two correlation steps was proposed by Patel [25]

As mentioned in the first chapter, diversity provides the receiver with several (ideally independent) replicas of the transmitted signal and is therefore a powerful means to combat fading and interference and thereby improve link reliability In recent years, the use of spatial or antenna diversity has become very popular, which is mostly due to the fact that it can be provided without loss in spectral efficiency The use of multiple antennas at transmitter and multiple antennas at receiver (MIMO) technology in combination with OFDM, i.e., MIMO-OFDM, therefore becomes an attractive solution for future broadband wireless systems Similar to SISO-OFDM systems, MIMO-OFDM systems exhibits great sensitivity to CFO

Several data-aided schemes were proposed in the literature Optimal training for MIMO channel estimation was considered in [26] It was incorporated with sparse-training

sequence in [3] to estimate CFO and MIMO channels Several blocks were collected for estimating CFO so that the number of training symbols carried per block was less

The data-aided schemes achieve the frequency synchronization at the expense of bandwidth and power In recent years, the non-data-aided or blind schemes have received

increasing attention

3.2.2 Non-Data-aided Schemes

Non-data-aided schemes or the blind schemes, do not need any additional training sequence or pilot symbols On the other hand, non-data-aided schemes only rely on the received OFDM symbols The scheme exploits the structural and statistical properties of the transmitted OFDM signals Since no training symbols are required, blind methods are attractive for saving bandwidth and having higher throughput and are more suitable for circuit-switched transmissions

Several non-data-aided algorithms exploiting null subcarriers were proposed in the literature [27][28], but the effect of frequency selectivity on the performance is not addressed These methods do not assure identifiability and consistency of the resulting CFO estimators regardless of the underlying channel nulls Hopping null subcarriers were exploited to render the performance independency of the channel zero locations [29] Identifiability of null carrier based CFO estimation has been studied in [9], wherein a null subcarrier hopping scheme was proposed which guarantees identifiability and improves performance Null subcarriers are incorporated in several wireless OFDM standards, but

their placement is fixed as in [27][28] and does not guarantee identifiability Subcarrier hopping restores identifiability, but also gives up the adjacent channel interference protection afforded by fixed guard null subcarriers The estimators based on null subcarriers needs sufficiently many null subcarriers to achieve satisfactory high resolution CFO estimation Null subcarrier methods are not really blind, in the sense that null subcarriers are equivalent to zero-padding and hence suffer roughly the same rate loss as training

The structural and statistical properties of OFDM signals such as cyclic prefix or constant modulus were exploited in some other non-data-aided schemes In [2], a joint time and frequency offset method based on ML criterion has been proposed In this method, the redundancy of the cyclic prefix (CP) is exploited Hence, no additional pilots or training sequence are required However, CP-based algorithms hinge on the availability of an excess CP, i.e., the CP is chosen beyond the length of the fading channel In this case, the bandwidth efficiency of the system is still affected since the extra CP acts like pilots [1]

Schmidl and Cox introduced a blind approach in [30] This estimator, in addition to being bandwidth efficient, also provides certain robustness or self-starting capability against channel breakdowns and drastic environmental changes However, this approach requires the constellation on each sub-carrier to have points equally spaced in phase In addition, the length of the guard interval must be chosen from a subset of allowed values In [1], a blind sub-space based estimation algorithm exploiting the inherent structure of OFDM signals has been proposed The salient feature of this sub-space based algorithm is that it

can offer the performance of a super-resolution subspace algorithm, via ESPRIT (estimation of signal parameters via rotational invariance techniques) [31]

The literature on non-data-aided CFO estimator for MIMO-OFDM systems is relatively scarce Antennal diversity was exploited to estimate the carrier frequency offset in [32]

by using a single input multi-output (SIMO) system This method is extended to a MIMO-OFDM systems in [33] By exploiting MIMO diversity, significant gains over single transmit diversity at low SNR can be achieved

Chapter 4 DEML Blind CFO Estimator for OFDM systems

As discussed in the last chapter, a few carrier frequency estimation algorithm have been proposed in the literature However, the estimation procedure based on the traditional maximum likelihood (ML) criterion usually relies on the excess cyclic prefix (CP) symbols of OFDM systems, hence reduces the bandwidth efficiency of the system when multipath channel is involved In this chapter, we present a decoupled maximum likelihood blind estimation method, which doesn’t rely on the structure of CP

Standard notations are used in this chapter: Bold lowercase non-italics letters denote vectors while bold uppercase non-italics letters denote matrices E[ ]i is the expectation of the random variable in the brackets; ( )H

i denotes matrix Hermitian and ( )ˆi denotes estimation of ( )i ; i represents the Euclidean norm; A B stands for the Hadamard •

Product of two matrices A and B; I is the N c N c×N c identity matrix

4.1 OFDM Systems Model

Baseband equivalent representation of an OFDM systems is shown in Figure 4.1 The input binary data is fed into a serial to parallel converter Each data stream then modulates the corresponding sub-carrier by MPSK or MQAM Modulations can vary

from one sub-carrier to another to achieve the maximum capacity In this work, for simplicity, we use

Remove CP

P/S

S/PTransmitter

systems The modulated data symbols for the k th block, represented

bysk =[s k(0), (s N k c−1)]T , are then transformed by inverse fast Fourier transform (IFFT) The output symbols are denoted as xk =[x k(0), x N k( c−1)]T Using matrix representation, the N point time domain signal for the c k block is given by th

− ω ω

is the N c×N c inverse DFT (IDFT) matrix A cyclic prefix is added to the output of the IDFT before it is sent to a fading channel The channel model is assumed to be slowly time varying and have a finite impulse response h , l l∈[1, ]L , where L is the length of

the channel impulse response As mentioned in Chapter 2 section 2.3.2, in wireless environment, sub-carriers are still orthogonal as long as the length of CP exceeds the time dispersion of wireless channels The length of the cyclic prefix,N , has to be greater than g

L to avoid inter symbol interference (ISI) and to preserve the orthogonality between

subchannels The baseband signal is upconverted to radio frequency (RF) before being transmitted over a frequency selective fading channel At the receiver, the received RF signal is downconverted using a receiver local oscillator The receiver input is the convolution of channel impulse response and transmitted signals, which can be described

by

1 0

k block input, can be written as

where ∆ is the absolute frequency difference between transmit-receive oscillator and f T s

is symbol duration In the presence of φ , the receiver input is modulated by

Since W EW I , the E matrix destroys the orthogonality among sub-carriers and thus H ≠introduces inter-channel interference (ICI) In order to recover the transmitted signal,s , k

the carrier offset, φ must be estimated and compensated before performing the DFT

4.2 DEML Blind Carrier Offset Estimator

In this section, we derive the cost function for estimating the carrier frequency offset φ

As mentioned above, the channel is slowly time varying So the channel response matrix

H remains unchanged for several time intervals The noise is assumed to be additive,

white and Gaussian (AWGN)

Lemma 1: The transmitted OFDM time samples ( ) x k j excluding cyclic prefix are

orthogonal provided the frequency domain data ( )s k j are independently identically

* 0

1

2 0