OFDM and Its Applications_Report

OFDM And Its Wireless Applications : A Survey

1. Introduction

The OFDM , a multicarrier system , addresses both the problems of single-carrier

system. The basic idea of OFDM is to divide the available spectrum into several

subchannels (or subcarriers) [1]. By making all subchannels narrowband, they experience

almost flat fading , which makes equalization very simple. The OFDM provides a DSP-

based technique allowing the bandwidths of modulated carriers to overlap without

interference. Bandwidth and spectral efficiency is achieved compared to single-carrier

system. To Obtain a high spectral efficiency, the frequency responses of the subchannels

are overlapping and orthogonal. This orthogonality can be completely maintained , even

though the signal passes through the time-dispersive channel, by introducing cyclic

prefix. It also supports a high data rate due to serial-to-parallel conversion of symbols

acquiring long symbol duration, thus helping eliminate ISI . Time and frequency

synchronization is the main limitation of multicarrier systems.

1.1 OFDM Block Diagram with Explanation:

There are two types of OFDM system models- continuous time and discrete time

models. The continuous time models are simple MPSK/MFSK diagrams in which the

modulated carriers are orthogonal to each other and summed up directly without IDFT

stage. Phases are generated according to symbols read by modulator stage input.

Assumptions in Discrete time model [1]

The digital implementation of OFDM system is achieved through DFT and its

Inverse IDFT to transform from time to frequency and frequency to time domain.

A cyclic prefix is added in two different ways , in first after IFFT samples are

padded at the end in the form of circular shift . The additional block is without

any useful information and acts as a guard interval in time domain to eliminate the

effect of multipath delay spread. In second method guard interval is added at the

end of each OFDM symbol in terms of copy of part of OFDM symbol. Due to this

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spectrum is not much affected and guard interval Tg will be removed immediately

after demodulation stage.

Fig.1 OFDM transmitting system with increased symbol rate.

To generate OFDM successfully, the relationship between all the subcarriers must

be carefully controlled to maintain the orthogonality of the carriers . For this reason ,

OFDM is generated by firstly choosing the spectrum required based on the input data

and the modulation scheme used. Each subcarriers to be produced is assigned some data

to transmit. The required amplitude and phase of the subcarriers is calculated based on

modulation scheme (BPSK,QPSK or QAM) . The modulated subcarriers spectrum setting

acts as sampled IDFT bin setting. In order to perform frequency domain data into time

domain data. Before RF upconversion , the cyclic prefix is added to remove the ISI

effect. Also the output of the IFFT stage is in the form of discrete samples. So D-to-A

conversion is required before RF conversion stage. At the receiver after A-to-D

conversion, the FFT transforms a time domain signal into its equivalent frequency

spectrum. The amplitude and phase of the sinusoidal components represent the frequency

spectrum of the time domain signal. For subcarrier offset removal, pilot signals are

considered which may have slightly higher power than the data subcarriers .

A. Serial-to-parallel Conversion and Symbol mapping :

The input serial data stream is read into the word size e.g. 2bits/word for QPSK,

8bits/word for 256-PSK and converted into a parallel format just like conventional M-

PSK method. The OFDM is a high data rate communication. So a high probability of ISI

Antennai/p Data

[Forward error correction (FEC) & Channel Coding]

Digital OFDM Transmitter

Channel Coding

OFDM modulation

D/A

Up-Conversion

RF-Amplifier

ScramblerConvolutional PuncturerEncoder

InterleaverMapper Pilot InsertionIFFTCyclic Prefix

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is expected as the symbol time duration may become less than the maximum delay of the

RF channel; but here reading the data in the form of word is advantageous.

B. Modulation of Data:

After reading data in terms of bits/symbol, apply differential coding to each

symbol sequence (optional) and convert the serial symbol stream into parallel segments

according to the number of carriers and symbols per carrier. Assign OFDM block to the

appropriate subcarrier in IFFT bin. Taking the FFT of the result will give the discrete

time domain signal.

Let {Sn,k} where k=0 to N-1 with E|Sn,k|2=σ2s be the complex symbols to be

transmitted at the nth OFDM block, then the OFDM modulated signal can be

represented by

(1)

Where Ts,Δf and N are the symbol duration , the subchannel space and the

number of subchannels of OFDM signals, respectively [2]. For the receiver to

demodulate the OFDM signal, the symbol duration should be long enough such that Ts

Δf=1 which is also called the orthogonal condition since it makes e -j2πkΔft orthogonal to

each other for different k. With the orthogonal condition, the transmitted symbols Sn,k

can be detected at the receiver by

(2)If there is no channel distortion.

The sampled version f the baseband OFDM signal S(t) in (1) can be expressed as

(3)

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Which is actually the inverse discrete Fourier transform (IDFT) of the transmitted

symbols {Sn,k} k=0 to N-1 and can efficiently be calculated by fast Fourier Transform

(FFT). It can easily be seen that demodulation at the receiver can be performed using

DFT instead of the integral in (2)

A cyclic prefix (CP) or guard interval is critical for OFDM to avoid interblock

interference (IBI) caused by the delay spread of wireless channels. They are usually

inserted between adjacent OFDM blocks. Fig 2. shows the function of the CP. Without

the CP, the length of the OFDM symbol is Ts, as shown in (1). With the CP, the

transmitted signal is extended to T=Tg+Ts and can be expressed as

(4)

It is obvious that Sn(t)=Sn(t+Ts) for -Tg≤t≤0, which is why it is called the CP.

The impulse response of a wireless channel can be expressed by h(t) and received signal

can be expressed by xn(t) and nk is the impact of AWGN and is defined as

(5)

It can be proved that nk are independent identically distributed complex circular

Gaussian with zero mean and variance σn2. With Hk, transmitted symbols can be

estimated. For single carrier systems, the received signal is the convolution of the

transmitted sequences or symbols and the impulse response of wireless channels in

addition to AWGN, whereas the impact of the channel is only a multiplicative distortion

at each subchannel for OFDM systems, which makes the signal detection in OFDM

systems very simple and is also one of the reasons why OFDM is very popular

nowadays[2][3]. A pulse shaping filter for the OFDM systems is proposed in [3] to

remove the constraint of CP.

Also, transmit and receive filters in OFDM system suffer from poor frequency

response because of the use of rectangular window function. The non-rectangular

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window based prototype filters are proposed for the transmitter and receiver end. The

comparison of performance of OFDM system and the suggested filter bank based

multicarrier systems is provided in terms of BER and the stop band attenuation of the

constituent filters. The constraint of CP can be removed by transmitting the data at higher

rate than the symbol rate. The upsampling factor depends upon the characteristics of the

channel. The experimental results shown in [3] show that the upsampling factor of 4

sufficesto attain satisfactory BER performance for the adopted channel models.

Apparently , the upsampling and downsampling process call for certain filtering

operation.

From the aforementioned discussion , channel state information (CSI) is required

for coherent detection. Various channel estimation approaches have been developed for

OFDM communications. Similar to single carrier modulation , time and frequency

varying wireless channels affect the performance of OFDM systems. Time-varying

impairments may come from the carriers frequency offset (CFO) caused by the mismatch

of frequencies between the oscillators at the transmitter and the receiver, or from the

Doppler spread due to the relative movement between the transmitter and the receiver.

Frequency varying impairments are from the timing offset or the delay spread of wireless

channels. Since the duration of the OFDM symbol is longer and its bandwidth is

narrower compared with single-carrier modulation, OFDM systems are more robust to

frequency-selective fading but more sensitive to the time-varying impairment of

channels.

2. Channel Estimation

In OFDM systems , CSI can be estimated using training symbols known at both

the transmitter and the receiver . The training symbols may be inserted at different

subchannels of different OFDM blocks as shown in Fig.2

These training symbols are more often called pilots. The CSI corresponding to the

pilot subchannels is first estimated, and then, that corresponding to the data-bearing

subchannels is obtained by interpolation. This is called pilot-aided channel estimation. In

addition to interleaving the training symbols and the informative symbols by such

frequency-division multiplexing, they may also be superimposed,which can be regarded

as a special form of pilots. This kind of training symbols are usually called superimposed

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Fig.2. Typical training blocks and comb pilots. (a) Comb Pilots. (b) Preamble.

as a special form of pilots. This kind of training symbols are usually called superimposed

pilots , which were first proposed to phase synchronization and originally called spread-

spectrum pilots. And were later applied for channel estimation. On the other hand, all

training symbols may be arranged at the first (or couple of) OFDM blocks. The training

blocks in this case are sometimes called preamble. The CSI corresponding to the training

blocks are first estimated, and that corresponding to the training blocks are first

estimated, and that corresponding to the subsequent data blocks can be tracked and

further improved with the help of the demodulated data. This is called decision-directed

channel estimation (DDCE). When channel statistics are unknown and CSI is treated as a

deterministic parameter, maximum-likelihood (ML) channel estimation will be optimal

and will approach the Cramer-Rao bound(CRB). For channels with AWGN, ML

estimation of channel parameters is equivalent to finding channel parameters to minimize

Where x and H are the received signal vector and channel frequency response

vector, respectively, which are defined as the index that indicates the OFDM block is

omitted in the subsequent discussion of Report.

||x-SpH||2

(6)

And Sp is the pilot symbol matrix , which is defined as

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Pilot-Aided Channel Estimation: Using pilot tones to estimate channel

coefficients was proposed in [2] . The two major issues of pilot-aided channel estimation

are pilot design and interpolation. The optimal design for the pilot pattern, power

allocation, and number of pilots has extensively been studied , which critically depends

on a proper criterion and the channel model. The impact of pilots on system performance

for time-varying channels has first been analyzed in [2]. The optimal pilot design for

frequency-selective channels has been investigated in a n d , whereas that for doubly

selective channels has been investigated in. The pilots have been designed to minimize

the MSE of channel estimation or CRB, maximizing the channel capacity and

minimizing the symbol error rate . As indicated before , LMMSE estimation can be

applied for joint channel estimation .

Can be applied for joint channel estimation and interpolation. However , it

requires channel statistics and high computational complexity. This motivates us to

develop low-complexity interpolation algorithms. In addition to the linear and high-order

polynomial-based interpolation, pilot –aided channel estimation can also be based on

FFT. FFT-based channel estimation essentially uses a low-pass filter as an interpolator,

and the filter is implemented in a transform domain. Instead of using a low-pass filter ,

we may catch significant taps in the transform domain and turn off those trivial taps,

which can improve the performance of channel estimation, particularly when the SNR of

the system is low. However, when turning off trivial taps of using a low-pass filter , a

useful component may also be removed, which will cause a large estimation error for

those subchannels on the edge.

2.1 DDCE:

For DDCE, CSI at the preamble block is first estimated and then used to

demodulate and detect the symbols at the next data block. CSI can be tracked by using

detected symbols or data, either hard decision or soft decision. For systems with error-

correction coding, redundancy in coding can be exploited by iteratively performing soft

symbol decision and channel estimation. A major problem of DDCE is error propagation,

which is particularly severe for a system with a large Doppler frequency. This can be

solved by periodically inserting training blocks. Comb pilots may also be applied instead

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of training blocks and channel tracking or prediction can be used for further performance

improvement. For coded OFDM systems, expectation-maximization algorithms can

improve estimation performance by exploiting the error probability information available

at the decoder. Theory of robust statistics is applied to alleviate the error propagation of

DDCE in fast fading channels.

Comparison of DDCE methods fit in systems operating in static or quasi-static

channels. It particularly fits in systems in a slot transmission mode , such as wireless

cellular systems. Initial channel estimation is provided with the training blocks and is

then followed by tracking or prediction. Their major advantage is that they are able to

provide high spectrum efficiency by using detected data as pilots. However, error

propagation will be induced in fast fading channels.

PACE methods can reliably estimate channels both in static and time-varying

channels by appropriately designing pilot patterns. It is desired for systems in a

continuous transmission mode, such as digital TV. For the same percentage of overhead,

the comb-pilot-aided estimation outperforms the training block-aided methods,

particularly for a system with high mobility. When a superimposed pilot sequence is

considered, bandwidth efficiency can be improved at the expense of an increase of

transmit power. Although the superimposed training may not be the optimal approach for

channel estimation, it will lead to a low-complexity estimator.

2.2 Channel Estimators and Pilot Schemes:

Some improvements are made in [4] in two major aspects : i) the channel will not

be assumed constant within one OFDM symbol and the ICI will be more effectively

addressed by employing a best linear unbiased estimator (BLUE) . ii) we will adopt a

general basis expansion model (BEM) to fit to the channel time-variation over all the

considered OFDM symbols. In [4] the channel estimator and BEM will be devised to be

independent of the channel statistics, in order to avoid the influence of a possible

mismatch. In [4] frequency-domain multiplexed pilots are considered. For the i th OFDM

symbol i.e. T(i) to denote the set that contains the indices of the pilot-carrying subcarriers

and D(i) to denote the set that contains the indices of the data-carrying subcarriers.

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Fig.3. Three different pilot schemes. The horizontal axis corresponds to the time; Vertical axis to the subcarrier positions. The pilot position is represented by a dot.

In [7] a robust spectrum sensing algorithm for OFDM modulated signals is highly

desired to implement cognitive radio (CR) when the primary signal uses OFDM

modulation. Motivated by this demand, a Time-Domain Symbol Cross-correlation based

spectrum sensing algorithm (TDSC method) is proposed in [7]. If lth and mth OFDM

symbols have the same pilot tone positions and define

(7)

Which is the Time-Domain symbol Cross-Correlation (TDSC) function of two OFDM

symbols. After some straightforward calculations, is can be shown than

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(8)

TDSC method needs only to compute correlations and a small number of

amplitude comparison and a small number of amplitude comparison operations to

perform spectrum sensing. Hence it is very low complexity and easy to apply in practice.

In [8] comparison of diverse frequency-domain multiplexed pilot arrangement schemes

for time-varying channel estimation in OFDM systems is proposed. In first scheme, the

comb-type, only a fraction of the subcarriers is dedicated to the pilots, but the pilots are

carried by each OFDM symbol. In the second scheme, the block-type, the pilots occupy

all subcarriers, but such pilot OFDM symbols are interleaved with data OFDM symbols.

In third scheme, the mixed-type, is a combination of the first two schemes. Pilot aided

channel estimators are applied, which take into account the channel variation within one

OFDM symbol. The performance of the three pilot schemes is compared for different

carriers situations. It is shown that comb-type scheme can be opted for estimating short

but fast channels, while the block-type scheme is promising for long but slow channels.

The mixed-type scheme yields a good tradeoff between these two channel situations.

In [9] the PAPR reduction technique is initially presented where the pilot tone

positions still follow a frequency hopping pattern known to the receiver, as in

conventional systems. However, in [9] relaxation maintain in constraint that the pilot

symbols have a fixed amplitude and phase. Specifically, author allow the pilot symbols to

be represented with multiple signaling points equispaced on the circle with a carefully

chosen radius. In first PAPR reduction scheme based on multiple-point pilot

representations, valid pilot symbols on specific subcarriers are generated first and the

corresponding PAPRs are calculated. Then, the OFDM frame with the minimum PAPR

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is chosen for transmission into the channel in a similar fashion as in the TR method. In

second approach [9] author relieve the assumption that the pilot tones are located at pre-

arranged positions. This creates a new degree of freedom for the pilot tone application to

reduce the PAPR similar to the TI approach. Essentially, in addition to changing the

phase of pilot symbols, by varying the positions of pilot subcarriers across all available

subcarriers in the OFDM system, and sending the OFDM frame corresponding to the

pilots on subcarriers and phases achieving the lowest PAPR, further reduction in the

PAPR is achieved in comparison to the first approach. In second method as positions of

pilot tones are chosen “blindly” to the receiver (receiver does not know the pilot

locations), the modification to the receiver is introduced, forcing it to estimate the pilot

locations first based on the increased pilot carrier power levels.

Fig.4. Pilot tone grid configurations

In addition, in order to meet the condition that pilot ones should be transmitted

equi-probably on all subcarriers, an adjustment at the transmitter is introduced to the

assignment of power distribution on the pilot tones at different positions. In Fig. pilot

arrangement is such that pilots are distributed regularly on frequency bins and across all

time indices to enhance channel estimation capabilities. As example of the pilot grid

structure adopted in [9] for P=2. The number of pilot tones chosen serves the purpose of

PAPR reduction, in addition to aiding channel estimation, and keeps the data rate at a

reasonable level. Since, in general pilots have higher power than the data subcarriers,

increasing P, the number of pilots in an OFDM frame, does not prove very beneficial

beyond a certain point.

In [10] pilot symbol assisted channel estimation in OFDM system is investigated.

To obtain the consistent estimation of communication channel, it is necessary to perform

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filtration or interpolation on pilot symbols scattered in an OFDM frame. Different

techniques on pilot symbols are investigated in[10] concretely linear interpolation, Spline

Interpolation, Cubic interpolation, Bezier curve interpolation and Larange barycentric

interpolation. The performance of studied methods is then evaluated and compared by

measuring the bit error rate (BER), mean squared error (MSE), mean absolute error

(MAE) and root mean square error (RMSE) in frequency selective multipath Rayleigh

fading channel. Compared results are shown in Fig. 5

Fig.5. Bit error rate at different signal to noise ratios of 8-QAM in frequency selective multipath Rayleigh fading channel.

Table I. Estimation Errors for different types of channel Estimation

The resulting bit error rate for different interpolation methods is presented in Fig.

5. The bit error rate is degraded both by imperfect channel estimates and noise

disturbances. The estimation errors calculated as Mean Squared Error (MSE), Root Mean

Squared Error (RMSE) and Mean Absolute Error (MAE) for examined channel

estimation methods are presented in Table 1. As can be seen from the table , the FFT

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interpolation performs the best, with the lowest MSE, RMSE and MAE error from all

other compared methods[10].

3. Role of Digital Signal Processing in OFDM Systems

3.1 Performance Evaluation of Wavelet OFDM :

Power line communication (PLC) is one of the most attractive communication

methods for in-home networks. However, the emissions of unwanted electric waves from

PLC system cause harmful interference to other radio communication systems with the

same frequency band. Wavelet OFDM is expected to be an efficient modulation for PLC

because it can make steep and deep notch for any frequency band in the transmit signal

power spectrum. However, wavelet OFDM cannot implement the equalization by guard

interval(GI) like OFDM and causes performance degradation in multipath channels

including power line channels. In [15] ASCET (Adaptive Sine modulated/Cosine

modulated filter bank Equalizer for Transmultiplexers) to wavelet OFDM and evaluate its

performance over a multipath power line channel . In particular, we propose an

estimation scheme of equalizer coefficients for ASCET that the required preamble

becomes short. We compare the performance of OFDM with GI to that of wavelet

OFDM with ASCET over the multipath power line channel by computer simulations. In

[15] it is shown that proposed scheme can achieve the approximately equivalent

performance of OFDM with GI by using the shorter preamble as compared to the

original scheme.

Fig.6. The baseband communication model by using transmultiplexers.

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Fig illustrates communication systems by using synthesis/analysis transmultiplexers. The

channel transfer function is represented by Hch(z) in this figure. The synthesis filter banks

are expressed as

(9)

And the analysis filter banks are expressed as

(10)

Wavelet OFDM is composed of critically sampled PRCMFB (Perfect Reconstruction

CMFB). In PR-CMFB, the synthesis filters Fm(z)=Fmc(z) and the analysis filters

Hm(z)=Hmc(z) are obtained by cosine modulation of a proto-type filter.

(11)

In [15] it is pointed out that MMSE based estimation for equalizer coefficients requires

much preamble symbols and proposed an estimation scheme of equalizer coefficients for

ASCET that the required preamble symbols becomes short. Results showed that scheme

proposed in [15] can achieve the approximately equivalent performance of OFDM with

GI by using short preamble as compared to the original scheme.

3.2 Asymmetric OFDM Systems Based on Layered FFT Structure:

In [15] extension is proposed to convolutional theory of layered fast Fourier

Transform (FFT). Based on this framework, novel asymmetric OFDM systems that

bridge general OFDM and single carrier systems. Adaptive to the capability of the

transceiver, asymmetric OFDM systems provide significant flexibility in system design

and operation. It is shown in [15] how effects of noise enhancement and frequency

diversity counteract each other in asymmetric OFDM systems. Performance comparison

with general OFDM and single carrier systems also given. Single Carrier Frequency-

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domain equalized (SC-FDE ) systems has one problem that the complexity in the

transmitter and receiver is very unbalanced. In [15] asymmetric OFDM systems that

bridge the gap between general OFDM and SC-FDE systems. The systems are developed

based on a novel “layered” fast Fourier transform (FFT) structure that is an extension of

the convolution property of the discrete Fourier transform (DFT). The proposed

asymmetric OFDM systems provide flexibility in system design and operation by

adapting to the capability of the transceiver, such as the dynamic range of power

amplifier and battery status, and duplex requirements. Divide and Conquer (D & C)

algorithm is used to calculate an N-point DFT of the signal.

As shown in Fig. below at the transmitter , input data are first coded, interleaved, and

modulated and then arranged into an P x Q array. The data in the qth column of the array

are denoted as vector xq. A Q-point IFFT is then applied to each row. Under the

assumption that the IFFT outputs are stored in the same array, then the outputs are read

out column-wise. In particular systems, this can be realized by a P x Q rectangular

interleaver. The output of the interleaver is appended with a cyclic prefix or zero padding.

The signal is transmitted over a channel with a digital tap-delayed line (TDL) model

h=(h0,h1,……,hL-1). The channel is assumed to be quasi-static, being constant over at least

one OFDM symbol period. At the receiver, after removing the cyclic prefix, the samples

are input column-wise to a P x Q array. A Q-point FFT is applied to each row. Assume

the FFT outputs are stored in the same array, and denote the FFT outputs in the qth

column as yq. Now yq and xq have relationship of

yq=Hqxq+nq.

(12)

Here Hq is the channel matrix. Nq contain AWGN samples, each having zero mean and

variance σ2n . Note that the samples in nq have the same mean and variance as the noise

samples introduced in the received time-domain signals, because the FFT does not

change the statistical property of the AWGN. Based on novel three-layered FFT

structure, [15] developed asymmetric OFDM systems that bridge between OFDM and

SC-FDE systems. The asymmetric OFDM systems have reduced PAPR and improved

CFO (Carrier Frequency Offset) sensitivity and frequency diversity , compared to OFDM

systems, and less unbalanced complexity compared to SC-FDE systems.

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Fig.7. Block diagram of the proposed asymmetric OFDM systems.

The asymmetric OFDM scheme provides significant flexibility in system design

and operation, and it is particularly promising for distributed networks where transceivers

can negotiate link parameters according to their hardware capability and battery status.

In [16] comparative study on Fourier-based OFDM (FFT-OFDM) and Wavelet-

based (DWT-OFDM) in DVB-T system been proposed. It is found that the DWT-OFDM

in AWGN and Rayleigh fading channels. For AWGN channel, the gain in term of energy

per bit to noise ratio Eb/No was improved by about 5dB when the system used Haar

wavelet compared to FFT-OFDM with a cyclic prefix (CP) of ¼-th the total OFDM

symbol period, for the same BER of 0.001. Other members of Daubechies families such

as dB8,dB16 and dB32 also outperformed by the gains of 7dB,10dB and 11dB

respectively, at the same BER. Daubechies db8 and db1 outperform FFT-OFDM in

Rayleigh fading, both in multipath flat fading and multipath frequency selective fading.

The DWT-OFDM ‘s with db8 and Haar outperformed FFT-OFDM by 7 and 2dB

respectively, at BER of 0.01 in the flat fading channel. DWT-OFDM and FFT-OFDM

showed about the same performance below 10dB of Eb/No in frequency selective fading.

However, the wavelet-based OFDM showed significant improvement of performance at

higher than 10dB of Eb/No.

Various FFT architectures such as single-memory architecture, dual-memory

architecture, pipelined architecture, array architecture and cached-memory architecture,

have been proposed in the last three decades. The pipelined architecture should be the

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best choice for UWB (Ultra Wideband) systems since it can provide high throughput rate

with acceptable hardware cost [17]. Modified “radix-24 SDF algorithm” is proposed to

achieve the calculation of 128-point IFFT. The order of twiddle factor sequence is

different compared to the earlier radix-24 SDF algorithm. The change in twiddle factor

sequence achieves easier implementation of the CSD multiplier used for IFFT

calculation. It is also proposed that the required speed can be achieved on FPGA itself

without using parallel processing architectures. It is verified that the OFDM module

achieves a maximum clock speed of 528MSamples/s. In general ASICs are three times

faster than FPGA, operating the ASIC based OFDM module in 528MHz with the

proposed modified radix-24 SDF pipelined algorithm is very much easier [17].

Performance of Wavelet OFDM in underground Coal Mine PLCs is proposed in

[19] . The channel of the underground coal mine (UCM) PLCs is analysis, which

indicates the UCM PLCs is more complex than home PLCs and this channel can be

described with multipath characteristics and strong noise interference characteristics.

Accurate modulation should be adopted. Conventional OFDM and Wavelet OFDM are

compared by focusing on two important aspects: transmission efficiency and spectral

leakage. It will be shown that, for the case of the UCM power line channel. Wavelet

OFDM offers substantial advantages over conventional OFDM . Wavelet OFDM is

proposed to use in UCM PLCs in [19].

Fig.8. Traditional OFDM system and D4,D6,D8,D10 represents the two rand, three rank, four rank, and five rank wavelet of Daubenhenics wavelet group.

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An Interference Cancellation Algoritm (ICA) for both Fourier and wavelet based

OFDM is proposed in [21]. Both ideal and non-ideal case is been compared. In the ideal

case assumption is made as an unwanted sinusoidal signal and in non-ideal case

assumption is made that the received OFDM signal is contaminated with sinusoidal

interference. Simulation results are shown below.

Fig.9. Performance of an OFDM system with and without interference And Performance of Fourier and wavelet-based OFDM : a non-ideal case.

For non-ideal case, the wavelet-based OFDM has to outperformed Fourier-based OFDM .

At SNR=5dB, an error of 0.01817 was obtained as compared to 0.03167. The difference

of about 1.35 percent was due to the fact that wavelet transform has the property. In both

cases wavelet-OFDM outperformed Fourier-OFDM [21] .

4. MIMO Technique In OFDM

MIMO techniques or space-time processing can be used in wireless

communications for diversity gain and capacity improvement. Recent books have given a

comprehensive introduction of MIMO techniques. Here, we focus on special when

MIMO techniques are used with OFDM .

Most of MIMO techniques are developed for flat fading channels. However,

multipath will cause frequency selectivity of broadband wireless channels. Therefore,

MIMO-OFDM which has originally been proposed to exploit OFDM to mitigate ISI in

MIMO systems, turns out to be a very promising choice for future high-data-rate

transmission over broadband wireless channels. The earliest work in MIMO-OFDM has

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become a very popular area in wireless communications, particularly in the past several

years. In this section we only very briefly provide an introduction of the topic.

4.1 Basic MIMO-OFDM

A MIMO-OFDM system with Mt transmit antennas and Mr receive antennas is

shown in fig. 10 . Space-time processing in the figure may exploit any space-time

techniques developed for flat fading channels. Although it is still called space-time

processing, it actually signal in the space and frequency domains in MIMO-OFDM .

As shown in fig space-time processing converts the transmitted symbol or data stream

{Sn} into Mt substreams {S(m)k}, through simple multiplexing or STC, for OFDM

modulation and transmission through different antennas. If only a multipath of wireless

channels is considered and the CP is long enough, the demodulated signal at each receive

antenna is a superposition of those from different transmit antennas and can be express as

(13)For i=1,…..,Mr , where denotes the frequency response at the kth subchannel

corresponding to the mth transmit and the ith receive antenna, and is the impact of

channel noise at the kth subchannel of the ith receive antenna, which is usually

independent for different k or I, Gaussian , and with zero mean. Equation (11) can also be

written in matrix form as

xk=Hksk+nk

(14)where xk, sk, nk and Hk are the received signal vector, transmitted signal vector, noise

vector, and channel matrix at the kth subchannel, respectively, and are defined as

(15)

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The MIMO-OFDM system model can easily be generalized into an MU MIMO-

OFDM system model by combining various multiple-access technologies, such as

OFDMA, TDMA, CDMA , or space-division multiple access. For MU MIMO-OFDM

system , MU interface (MUI) also degrades performance.

In the previous discussion, we have not taken into count the effect of ICI caused

by the frequency offset or high Doppler spread. Similar to SISO-OFDM systems. MIMO-

OFDM could be impaired by ICI. For MIMO-OFDM systems, ICI due to the Doppler

shift is analyzed in [35] , and a time-domain filtering-based ICI mitigation technique is

also developed for fast fading wireless channels, where the channel cannot anymore be

assumed to be constant within an OFDM symbol. ICI due to the frequency offset is

investigated in [36]. Approaches to mitigate both MUI and ICI in MU MIMO-OFDM is

developed in [37], which exploit TH precoding and iterative equalization.

CSI is required for signal detection of most of MIMO-OFDM systems, which can

be obtained by channel estimation. Similar to SISO-OFDM systems, the accuracy of

channel estimation directly affects the performance of MIMO-OFDM systems.

Therefore, channel estimation is an important topic to facilitate MIMO-OFDM for

wireless communications. Channel estimation techniques for SISO-OFDM systems have

been addressed in previous section. The challenge of channel estimation in MIMO-

OFDM systems from that each receive signal corresponds to several channel parameters,

which we also need to take into consideration when designing training or pilot sequences.

By exploiting the correlation of channel parameters at different subchannels and OFDM

blocks , channel estimation for MIMO-OFDM has been developed in [173]. The details

Fig.10. MIMO-OFDM

20

on approach development , performance analysis, and enhanced approaches can

be found in previous papers.

(16)

4.2 Performance optimization

Bell Laboratories layered space-time architecture (BLAST) , including vertical

BLAST (V-BLAST) and diagonal BLAST can directly be used in OFDM for SM.

Compared to SISO-OFDM systems, SM-based MIMO-OFDM approaches can achieve

high data rates over wideband channels. For SM-based MIMO-OFDM systems,

performance and complexity tradeoff is one of the critical issues. In addition, link

adaptation by utilizing CSI and/or channel quality information (CQI) at the transmitter

and CSI or CQI feedback are also important to SM-based MIMO-OFDM systems. We

will address these issues in the following sections.

1. Performance and complexity tradeoff: To support high-data-rate wireless access

with required quality-of-service , turbo codes and turbo detection have been

introduced in SM-based MIMO-OFDM systems. However, the complexity of soft

demapping/decoding for turbo techniques exponentially increases with the

number of transmit antennas and modulation order. To reduce the complexity ,

nonlinear interference cancellation with linear demapper and hard decision are

used in [37]. In [38] a decision-feedback receiver , which takes decision errors

into consideration for equalization formulation and soft-bit demapper , is

developed to mitigate the effect of error propagation in V-BLAST OFDM

systems.

By exploiting the correlation of frequency response at different

subchannels, detection complexity in SM-based MIMO-OFDM systems can be

reduced through subchannel grouping or interpolation, where Gram-Schmidt

operation or QR decomposition is used instead of direct matrix inversion to

calculate the nulling vectors.

2. Link adaptation and CSI feedback: Link adaptation including transmission power

21

5. Fading in Multipath Channels

In wireless communications, fading is deviation of the attenuation that a carrier-

modulated telecommunication signal experiences over certain propagation media. The

fading may vary with time, geographical position and/or radio frequency, and is often

modelled as a random process. A fading channel is a communication channel that

experiences fading. In wireless systems, fading may either be due to multipath

propagation, referred to as multipath induced fading, or due to shadowing from obstacles

affecting the wave propagation, sometimes referred to as shadow fading.

Digital broadcasting systems in Europe are the OFDM SFN networks. Information in

OFDM systems is carried out on signal subcarriers. Distributions of the OFDM

subcarriers in points of SFN coverage area reveal channel distortions and are thus of

meaning for system evaluation. Superposition of signals from different transmitters in

SFN network depends on relative gains, time delays and phase differences. These

parameters are connected with receiver position within SFN. Applying the phasor

representation of OFDM unmodulated signal in multipath environment to SFN signals

allows to evaluate resulting signals in OFDM baseband channel. In this way the OFDM

phasor model connects OFDM subcarrier distributions with receiver position. The spots

of most risky signal reception are evaluated in the coverage area in simple models of SFN

network.[23]

Application of the phasor representation of the OFDM signal to the SFN network

allows investigating baseband channel distortions in correlation with receiver position

within coverage area. The lines of constant relations between parameters of different

signal paths are of help to this aim. The grid of circles of constant relations between

amplitudes and hyperbolas of constant difference between paths time delays allows

unanimously describe amplitude of resulting signal in case of two transmitter SFN

network and realise simulations of estimates in general case .Presented models in[23]

neglect the influence of terrain and directivity of antennas. Neverthless concept of grid of

lines connecting points of equal time delays and relative gains remains valid in real

situations and could be included in frequency planning with the help of digital maps. The

22

time delay and possibly- the change of phase along every path- could be estimated

parallel with the loss of the path gain calculations. These data allow estimating the

number of minima in resulting OFDM signal and its relative depth. It can lead to

appointing spots of less certain signal reception within SFN network and reveal

singularities in the signal coverage. The method of OFDM phasor representation applied

to SFN coverage could allow also indicating directions of fastest channel changes during

mobile reception. In case when reflected signals are present every source of reflection

could be treated as independent additional transmitter with its specific directivity. Time

delays from these source should be increased by signal delay on a way from transmitter

to point of reflection.

In [24] alamouti coded wavelet based OFDM for multipath fading channels is

proposed. Performance of conventional DFT based OFDM and wavelet based OFDM

(WOFDM) with and without Alamouti coding over multipath Rayleigh fading channels

with exponential power delay profile. Results shown in [24] shows that WOFDM has

slightly better bit error rate performance than the conventional OFDM with and without

Alamouti code. Besides the performance improvement of WOFDM as compared to

conventional OFDM increases by the use of Alamouti coding. In addition to having

better performance , WOFDM might be an alternative to conventional OFDM since it has

better bandwidth efficiency.

Channel variation destroys the orthogonality among the subcarriers and

leads to intercarrier interference (ICI). ICI poses a significant limitation on wireless

OFDM systems. In [25] an efficient method of providing reliable communications using

OFDM in fast time-varying fading channels. It is observed that ICI power arises from a

few adjacent subcarriers. This observation motivates us to designing low-complexity Q-

tap ICI equalizers. To employ these equalizers, channel state information is also required.

In [25] design a pilot-aided minimum mean square error (MMSE) channel estimation

scheme for a time-varying wide-sense stationary uncorrelated scatters channel model.

The MMSE channel estimator utilizes the statistical channel properties to achieve

computational efficiency. The performance degradation due to ICI becomes significant as

the carrier frequency, symbol duration, and vehicular velocity increase. An equalizer is

23

effective for ICI mitigation. However the traditional MMSE and ZF equalizers for

OFDM systems , process N subcarrier signals simultaneously using N available received

signals in one OFDM symbol block and therefore , these schemes require a large matrix

inversion [26-34].

6. Smart Antennas

Smart antennas (also known as adaptive array antennas, multiple antennas and

recently MIMO) are antenna arrays with smart signal processing algorithms used to

identify spatial signal signature such as the direction of arrival (DOA) of the signal, and

use it to calculate beamforming vectors, to track and locate the antenna beam on the

mobile/target. The antenna could optionally be any sensor. Smart antenna techniques are

used notably in acoustic signal processing, track and scan RADAR, radio astronomy and

radio telescopes, and mostly in cellular systems like W-CDMA and UMTS .

Orthogonal frequency division multiplexing (OFDM) has become one of the most

popular air-link technologies for future broadband wireless communications. To further

improve its bandwidth efficiency and system performance, adaptive resource allocation

and smart antenna techniques have been widely used in the OFDM system. However, the

use of fully adaptive beamforming in an OFDM system significantly increases the

complexity of the medium access control layer design and thus affects the

implementation of adaptive resource allocation. A novel cross-layer adaptive resource

allocation strategy with hybrid adaptive array and switched-beam smart antennas suitable

for the OFDM systems has been proposed. With the help of different smart antennas

schemes based on different users’ quality of service requirements, the strategy effectively

reduces the complexity of adaptive resource allocation in an OFDM system, while still

maintaining a satisfactory system performance [39].

To implement transmit beamforming, the channel state information on each

individual subcarrier has to be conveyed from the receiver to transmitter. In order to

reduce the channel feedback requirement in the OFDM system. In [40] the time and

frequency domain correlations of the channel fading into consideration. Based on our

successive beamforming (SBF) technique, we develop several classes of feedback

algorithms for the OFDM systems. These new algorithms use the knowledge from the

24

previous frame or neighboring subcarrier to aid the beamforming codebook design for the

current subcarrier [40].

Algorithms implemented in [40] are:

4.3 time domain round robin successive beamforming (TDRSBF)

4.4 frequency domain round robin successive beamforming(FDRSBF)

4.5 frequency domain clustered successive beamforming(FDCSBF)

7. Applications

During the past decade, OFDM has been adopted in many wireless

communication standards , including European digital audio broadcasting, terrestrial

digital video broadcasting and satellite-terrestrial digital video broadcasting, and satellite-

terrestrial interactive multi service infrastructure in China. In addition, OFDM has been

considered or approved by many IEEE standard working groups, such as IEEE

802.11a/g/n, IEEE 802.15.3a , and IEEE 802.16d/e.

The applications include wireless personal area networks, wireless local area

networks, and wireless metropolitan networks. Currently, OFDMA is being investigated

as one of the most promising radio transmission techniques for LTE of the 3rd Generation

Partnership Project (3GPP) , International Mobile Telecommunications- Advanced

Systems. Before introducing the major features of several OFDM applications, we briefly

describe the design guideline of OFDM for wireless communications.

7.1 Design Guideline

When OFDM is used for wireless communications, its parameters depend on the

Doppler shift and delay spread of wireless channels, in addition to complexity

consideration. From the discussion in Introduction to reduce the effect of Doppler shift ,

the symbol duration of OFDM should be chosen such that

25

which implies that the symbol duration is constrained by the Doppler frequency of

wireless channels, and symbol duration should be short to ensure small ICI. On the other

hand, to deal with the delay spread of wireless channels, the length of the CP Tg must be

larger than the delay span Ts. The modulation efficiency of OFDM depends on the ratio

of the length of the CP and the symbol duration. Therefore, the symbol duration of

OFDM should be as large as possible from the efficiency point of view. A state-of-the-

art design should take both the Doppler shift and delay spread of wireless channels into

consideration and balance their impacts.

Once the symbol duration Ts is determined, the subchannel space Δf will be determined

using the orthogonal principal i.e. TsΔf=1. If the available bandwidth of an OFDM signal

is Bw, the number of subchannles will be determined by

(17)

Where |x| denotes the largest integer less than or equal to x. If FFT is used for OFDM

modulation and demodulation , the length of FFT will usually be

Modulation=2k and k=[log2N]

(18)

Where |x| denotes the smallest integer larger than or equal to x. From the length of the

FFT and symbol duration.

(19)

7.2 Mobile and Fixed Wireless Systems

OFDM has been adopted in IEEE 802.16 standards [219] to support peak data rate

up to 75Mb/subcarriers at the frequency bands under 11GHz. OFDMA in IEEE 802.16-

2004 fixes the size of FFT to be 256 and varies the subchannel space according to the

bandwidth of the system. Different from IEEE 802.16-2004, OFDMA in IEEE 802.16e-

2005 maintains the same subchannel space, i.e. Δf=10.94KHz, and changes the sizes of

26

FFT according to the bandwidth of the system. Table compares the parameters for (a)

IEEE 802.16-2004 and (b) IEEE 802.16-2005 , respectively.

Table-IISome Parameters Of IEEE 802.16, (a) IEEE 802.16-2004. (b) IEEE 802.16e-2005

(a)Bandwidth, Bw, (MHz) 1.75 3.5 5.5 7Subchannel space, Δf , (KHz) 7.81 16.6 25.0 31.3Symbol Duration, Ts , (µs) 128 64 40 32Sampling frequency, fs, (MHz) 2 4 6.32 8FFT size, Modulation 256 256 256 256

Table-II (b)Parameters Of MB-OFDM-UWB

Bandwidth, Bw, (MHz) 1.75 3.5 5.5 7Subchannel space, Δf , (KHz) 10.9 10.9 10.9 10.9Symbol Duration, Ts , (µs) 91.4 91.4 91.4 91.4Sampling frequency, fs, (MHz) 1.40 5.60 11.2 22.4FFT size, Modulation 128 512 1024 2048

Table-IIIParameters Of MB-OFDM-BASED UWB

Bandwidth, Bw, (MHz) 528MHzSubchannel No., N 128Subchannel Space,Δf 3.2MHzSymbol Duration, Ts 312.5nsecLength of CP,Tg 60.6nsecLength of Gi, TGI 9.5nsec

In both OFDM and OFDMA modes, the ratio of the length of the CP to the

symbol duration may be ¼, 1/8, 1/16 or 1/32, and the modulation scheme may be QPSK,

16 quadratic amplitude modulation (16QAM) or 64QAM, depending on the channel

environments and the targeted data rate. In addition, antenna arrays may be used for

diversity and interference suppression. STC is also optional in IEEE 802.16 to increase

the data rates and extend the coverage.

In the downlink of 3GPP LTE, OFDMA is a basic modulation scheme, which is with the

length of the CP Tg=4.7/16.74 µs (short/long CP) and the subchannel space Δf=15kHz.

27

7.3 MB-OFDM for UWB Systems

Multiband OFDM (MB-OFDM) was once a standard candidate for the IEEE

802.15.3a working group [220-229] for ultrawideband (UWB) systems. The basic idea of

MB-OFDM is to divide the spectrum into several subbands, and a data stream is

transmitted over each band by OFDM . The parameters of OFDM are listed in Table III.

It should be noted that the actual bandwidth of the OFDM signal is 409.6 MHz, although

the bandwidth of each subband is 528MHz. Interleaving is used to exploit frequency

diversity. The MB-OFDM-based UWB system achieves data rates ranging from 55 to

480MB/s over distances up to 10m.

The combination of MIMO and MB-OFDM has also been investigated , for high-

data-rate transmission. However, there is some argument on whether we need multiple

antennas in a UWB system because it should be with low complexity and low cost,

whereas multiple antennas required by MIMO increase the cost of transceivers and

obviously contradict them.

7.4 Cognitive Radio

Cognitive Radio [4] has emerged as a promising technology to solve the current

spectrum scarcity problem. Dynamic spectrum management and access is one of the key

functions of cognitive radio. OFDM can be used to construct the transceiver of cognitive

radio. OFDM can be used to construct the transceiver of cognitive radio by virtue of its

flexibility for subchannel assignment and power allocation.

Secondary (unlicenced) users in cognitive radio exploit spectrum holes, which are bands

that are not used by primary (licenced) users, and should not interfere with the operation

of primary users. Therefore , the available spectrum for the secondary users is usually

disjoint bands. Furthermore, the available bands change with the activities of the primary

users, which require the secondary users to flexibly adjust the frequency bands of their

modulated signals. Moreover, geographic separation introduces discrepancies of the

available spectrum between the transmitter and the receiver, particularly at the initial link

establishment stage. Motivated by these demands, interleaved OFDM-based transform

domain communication system (TDCS) has been proposed for cognitive radio, the

performance of OFDM-based TDCS has been investigated, and bit-error-rate formulas

28

have been obtained. However, there are many unsolved issues for OFDM-based cognitive

radio networks, such as spectrum sensing [4], interference identification, and transceiver

design [4]. Due to the attractive advantages of MIMO-OFDM, a generalized design of

MIMO-OFDM-based cognitive radio has been proposed in.

29

Conclusion and Further Research

In this report I briefly describe OFDM for wireless communications. Report starts

with basic principle of OFDM and techniques to deal with impairments in wireless

systems, including channel estimation, timing and frequency offset estimation, ICI

mitigation , and PAPR reduction. Then , we introduced related modulation and access

schemes , such as OFDM SC-FDE , EST-based modulation, OFDMA. Report also

summarizes the MIMO techniques for OFDM and the wireless applications of

OFDM .

The OFDM related technique has been invented over 40 years ago. OFDM for

wireless communication has intensively been an active research area in the past 10

years due to implementation of DSP based algorithm using VLSI.

However there are many unsolved issues OFDM –based cognitive radio networks,

such as spectrum sensing , interference identification and transceiver design.

Still some of the open issues and remaining hurdles on the way to a full-scale

commercialization of MIMO systems are antenna issues , receiver complexity ,

system integration and signaling and CSI at transmitter although MIMO is going to

be the 4G technology.

Mobile WiMAX uses OFDMA in its physical layer, we can effectively use Scalable

OFDM (SOFDM/SOFDMA) scheme in almost all Wireless systems due to its

advantages like combating ISI and ICI, spectral efficiency. There is much scope in

WiMAX mobile systems using Scalable OFDM [41].

30

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