# The Overview Of OFDM Computer Science Essay

Published:

This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.

First proposals for OFDM were made in the 60s and the 70s. It has taken more than a quarter of a century for this technology to move from the research domain to the industry. The concept of OFDM is quite simple but the practicality of implementing it has many complexities. So, it is a fully software project. OFDM is the latest technique which is used for the future generation wireless communication systems.

OFDM depends on principle of Orthogonality. This means, it allows the sub carriers, subcarriers are orthogonal to each other, meaning that cross talk between co-channels is eliminated and inter-carrier guard bands are not required. This greatly simplifies the design of both the transmitter and receiver, unlike conventional FDM; a separate filter for each sub channel is not required.

Orthogonal Frequency Division Multiplexing (OFDM) is a digital multi carrier modulation scheme, which uses a large number of closely spaced orthogonal sub-carriers.

A single stream of data is split into parallel streams each of which is coded and modulated on to a subcarrier, a term commonly used in OFDM systems.

Each sub-carrier is modulated with a conventional modulation scheme (such as quadrature amplitude modulation) at a low symbol rate, maintaining data rates similar to conventional single carrier modulation schemes in the same bandwidth. Thus the high bit rates seen before on a single carrier is reduced to lower bit rates on the subcarrier.

In practice, OFDM signals are generated and detected using the Fast Fourier Transform algorithm. OFDM has developed into a popular scheme for wideband digital communication, wireless as well as copper wires.

Actually, FDM systems have been common for many decades. However, in FDM, the carriers are all independent of each other. There is a guard period in between them and no overlap whatsoever. This works well because in FDM system each carrier carries data meant for a different user or application. FM radio is an FDM system. FDM systems are not ideal for what we want for wideband systems. Using FDM would waste too much bandwidth. This is where OFDM makes sense.

In OFDM, subcarriers overlap. They are orthogonal because the peak of one subcarrier occurs when other subcarriers are at zero. This is achieved by realizing all the subcarriers together using Inverse Fast Fourier Transform (IFFT). The demodulator at the receiver parallel channels from an FFT block. Note that each subcarrier can still be modulated independently.

Since orthogonality is important for OFDM systems, synchronization in frequency and time must be extremely good. Once orthogonality is lost we experience inter-carrier interference (ICI). This is the interference from one subcarrier to another. There is another reason for ICI. Adding the guard time with no transmission causes problems for IFFT and FFT, which results in ICI. A delayed version of one subcarrier can interfere with another subcarrier in the next symbol period. This is avoided by extending the symbol into the guard period that precedes it. This is known as a cyclic prefix. It ensures that delayed symbols will have integer number of cycles within the FFT integration interval. This removes ICI so long as the delay spread is less than the guard period.

## Objective:

The aim of this project is to investigate the OFDM scheme, and realize a fully functional system in software and analyzing how it is reducing the inter-symbol interference caused by the multipath fading channels and different effects and estimating, evaluating the performance of it.

## Background:

Most first generations systems were introduced in the mid 1980's, and can be characterized by the use of analog transmission techniques and the use of simple multiple access techniques such as Frequency Division Multiple Access (FDMA). First generation telecommunications systems such as Advanced Mobile Phone Service (AMPS) only provided voice communications. They also suffered from a low user capacity, and security problems due to the simple radio interface used. Second generation systems were introduced in the early 1990's, and all use digital technology. This provided an increase in the user capacity of around three times. This was achieved by compressing the voice waveforms before transmission.

Third generation systems are an extension on the complexity of second-generation systems and are expected to be introduced after the year 2000. The system capacity is expected to be increased to over ten times original first generation systems. This is going to be achieved by using complex multiple access techniques such as Code Division Multiple Access (CDMA), or an extension of TDMA, and by improving flexibility of services available.

The telecommunications industry faces the problem of providing telephone services to rural areas, where the customer base is small, but the cost of installing a wired phone network is very high. One method of reducing the high infrastructure cost of a wired system is to use a fixed wireless radio network. The problem with this is that for rural and urban areas, large cell sizes are required to get sufficient coverage.

## Chapter 2

## OFDM:

The orthogonal Frequency Division Multiplexing (OFDM) is a very effective technique for achieving the data in high rate and tackling the issues in a multipath fading in wireless communication. OFDM can be considered as hybrid version of frequency shift keying modulation and multi-carrier modulations. This multi carrier modulation defines one principle for transmitting data where as the stream is divided into several numbers of parallel bit streams, and then these streams are modulated into subcarriers or carriers. Separating these carriers by an integer multiple of inverse of the symbol it achieves duration of parallel bit orthogonality. It can be stated from the above context that the orthogonal Frequency Division Multiplexing (OFDM) is the technique to achieve the data in high rate. Hybrid version of the modulation techniques achieves orthogonality by separating the carriers and applying the appropriate steps to the carriers.

The OFDM modulation deals with multiplexing QAM data over a very large number of carriers. The QAM symbols are of OFDM type and are sent through an Inverse Fourier Transformation. At the beginning of every OFDM symbol a cyclic prefix is added to hold the orthogonality between the carriers in the presence of time dispersive channel. To use time and frequency correlation the OFDM signaling structure allows a channel estimator. For real time implementation, this channel estimator is too complex .To bring down these complicated issues the use of frequency correlation and time is separated. It can be stated from the above context that OFDM deals with multiplexing the data and is sent through aÂ inverse Fourier transformation. There after in order to achieve the orthogonality prefixing and separation are done. To implement the real time applications the frequency correlation and time are separated

In the multi user OFDM the antennas which receive signal, is formed by superposition of the signal contributions associated with several user or transmit antennas. In OFDM systems while designing the subcarriers utmost care has to be given so that each subcarrier suffers from flat fading only. Maximum subcarrier spacing is determined by the extent of channel coherence. Due to the parallel transmission on the numerous subcarriers (Tzi-Dar Chiueh and Pei-Yun Tsai, 2007, pp.26) the OFDM symbol length increased than that of the single carrier symbols. It can be stated from the above context during the design aspects of subcarriers care has to be taken to allow flat fading only. The subcarrier spacing can be determined by the external coherence. Due to the parallel transmission the length of OFDM symbols are increased.

## OFDM System Architecture:

## Orthogonal Frequency Division Multiplexing

In OFDM the subcarrier pulse used for transmission is chosen to be rectangular. This has the advantage that the task of pulse forming and modulation can be performed by a simple Inverse Discrete Fourier Transform (IDFT) which can be implemented very efficiently as a I Fast Fourier Transform (IFFT). Accordingly in the receiver we only need a FFT to reverse this operation. According to the theorems of the Fourier Transform the rectangular pulse shape will lead to a sin(x)/x type of spectrum of the subcarriers

Obviously the spectrums of the subcarriers are not separated but overlap. The reason why the information transmitted over the carriers can still be separated is the so called orthogonality relation giving the method its name. By using an IFFT for modulation we implicitly chose the spacing of the subcarriers in such a way that at the frequency where we evaluate the received signal (indicated as arrows) all other signals are zero. In order for this orthogonality to be preserved the following must be true:

1. The receiver and the transmitter must be perfectly synchronized. This means they both must assume exactly the same modulation frequency and the same time-scale for transmission (which usually is not the case).

2. The analog components, part of transmitter and receiver, must be of very high quality.

3. There should be no multipath channel.

In particular the last point is quite a pity, since we have chosen this approach to combat the multipath channel. Fortunately there's an easy solution for this problem: The OFDM symbols are artificially prolonged by periodically repeating the 'tail' of the symbol and precede the symbol with it . At the receiver this so called guard interval is removed again. As long as the length of this interval is longer than the maximum channel delay. All reflections of previous symbols are removed and the orthogonality is preserved. Of course this is not for free, since by preceding the useful part of length by the guard interval we lose some parts of the signal that cannot be used for transmitting information. Taking all this into account the signal model for the OFDM transmission over a multipath channel becomes very simple: The transmitted symbols at time-slot l and subcarrier k are only disturbed by a factor which is the channel transfer function (the fourier transform of the cir) at the subcarrier frequency, an by additional white Gaussian noise n

As far as the analog components are concerned experience has shown that in the broadcasting applications under consideration here, they are not so critical. What remains is to establish 'perfect' synchronization. This requires a very sophisticated receiver. The general structure and the receiver of such a receiver which we have developed for the DVB-T application, will be outlined in the next section.

## Considering Subcarrier Frequency Offset of OFDM System:

Model of OFDM has a subcarrier frequency offset in AWGN (Additive White Gaussain Noise) channel. Modulation methods like 16 QAM and 64QAM are used. OFDM signal reduces system performance when orthogonality is corrupted between subcarriers in demodulating (Rajiv Kohosla, Robert J.Howlett and L. C. Jain, 2005). By the Doppler shift is influenced by the Frequency offset.

The receiver generates sine wave which is having a frequency gap from to by which the base band OFDM signal could be obtained. For simplifying the assumed transmission distortion is inexistent, in this the additional noises are erased. Frequency offset is referred by.

Shows the Model of OFDM system

The above figure shows the Model of OFDM system explains about the carrier frequency offset. In which the OFDM flow starts from the Modulation and ends by the demodulation. The signal is transmitted into the converter which is converted into multiple paths from the single path. A carrier is used in between. In this whole process the multiple paths are inter converted into the single paths in which the data is moved. IEEE 802.11 provides a wireless Ethernet capability at a rate of 1 or 2 Mbps in the 2.4 GHz ISM (Industrial Scientific Medical) band which is a first generation product. By making some changes the second generation systems where introduced with a 2.4GHz ISM band to 5.5 and 11 Mbps WLANs. This was achieved by supporting a new physical layer called as complementary code keying (CCK). For rectifying the errors the HIPERLAN/2 standard was developed in the ETSI (Error Reference source not found). The main intention of the HIPERLAN/2 standard is to provide up to 54 Mbps multimedia communications between different broadband core networks and portable terminals. From the above context it is observed that the wireless LAN is one of the important technologies which are beneficial for many areas. If the organization stress on the facilities and requirements of the residential areas they can benefit a lot.

OFDM MODULATION:

## Advantages of OFDM:

Orthogonal Frequency Division Multiplexing (OFDM) is commonly implemented in many emerging communication protocols because it provides many advantages when compared with the traditional FDM approach to communication channels. Mostly, OFDM systems allow for resilience to multi-path distortion and greater spectral efficiency reduced ISI (Inter Symbol Interference). OFDM is something called as discrete multi-tone modulation or multi-carrier. This is the modulation technique used for digital TV. For modulating a large number of sub-carriers OFDM is a method in such a way that each sub-carrier does not interfere with neighboring carriers and each sun-carrier is independent. Each carrier is classed as a channel or a data stream which is modulated with a conventional modulation scheme, and allows for several parallel data streams. The source information is divided into multi carrier frequency for transmission in OFDM. The following are the Advantages of OFDM

1. OFDM is spectrally efficient

2. IFFT/FFT operation ensures that sub-carriers do not interfere with each other.

3.OFDM has an inherent robustness against narrowband interference.

4. Narrowband interference will affect at most a couple of subchannels.

5. Information from the affected subchannels can be erased and recovered via the forward error

correction (FEC) codes.

6. Equalization is very simple compared to Single-Carrier systems

7. OFDM has excellent robustness in multi-path environments.

a. Cyclic prefix preserves orthogonality between sub- carriers.

b.Cyclic prefix allows the receiver to capture multi- path energy more efficiently.

10. Ability to comply with world-wide regulations:

It is clear from the above discussion that OFDM is a communications technique which divides a communications channel into a number of equally spaced frequency bands. The subcarrier carrying a portion of the user information and is transmitted in every band. Each subcarrier is orthogonal with every other subcarrier, differentiating OFDM from the commonly used frequency division multiplexing

a. Bands and tones can be dynamically turned on/off to comply with changing regulations.

11. Coexistence with current and future systems:

Bands and tones can be dynamically turned on/off for enhanced coexistence with the other devices.

## OFDM Applications:

OFDM (Orthogonal Frequency Division Multiplexing) provides good properties to build new wireless systems for broadcast system, cellular and non cellular and belongs to multi-carrier system

It finds its applications in the followings

solution to multipath

good digital signal processing.

Digital Broadcasting

OFDM for wireless LAN

3G Mobile Broadband Technology

Multiple-antenna OFDM

Digital Broadcasting - Digital broadcasting contains Digital Audio Broadcasting. This advances in fidelity (Hi-Fi) digital recording techniques. Digital Audio Broadcasting is a digital radio technology for Broadcasting Radio Station, used in many countries. In this Digital Audio Broadcasting analog audio signal is converted into digital signal and transmitted on assigned channel.

OFDM for Wireless LANs - Multi-carrier modulation offers several advantages and is a strong candidate for packet switched wireless applications than that of signals carrier approaches. An OFDM system is viable solution for Robustness against delay spread, Fall back mode, computational efficiency, Fast synchronization etc for higher data applications ranging from 10Mb/s up to 50Mb/s,.

3G Mobile Broadband Technology - Existing 3G mobile broadband technologies, including WCDMA/HSPA and CDMA2000 1EV-DO, use CDMA technology as the core radio access. Since it was first launch in 2000, 3G cellular technologies have enveloped to deliver high capabilities, throughputs, and efficiencies to support growing broadband-intensive data services.

Multiple-antenna OFDM - OFDM (Orthogonal Frequency-Division Multiplexing) is a form of modulation that offers a significant performance improvement over other modulation schemes on broadband frequency selective channels. These inherent advantages make OFDM the default choice of a variety of broadband applications.

## Chapter 3

## Channel

A channel can take many forms, including ones suitable for storage which can communicate a message over time as well as space. Examples of communications channels include

A connection between initiating and terminating nodes of a circuit.

A single path provided by a transmission medium via either

physical separation, such as by multi pair cable or

electrical separation, such as by frequency-division or time-division multiplexing.

A path for conveying electrical or electromagnetic signals, usually distinguished from other parallel paths.

The portion of a storage medium, such as a track or a band , that is accessible to a given reading or writing station or head.

In a communications system , the part that connects a data source to a data sink .

A specific radio frequency , pair or band of frequencies, usually named with a letter, number, or codeword, and often allocated by international agreement.

Examples:

Marine VHF radio uses some 88 channels in the VHF band for two-way FM voice communication. Channel 16, for example, is 156.800MHz. In the US, seven additional channels, WX1 - WX7, are allocated for weather broadcasts.

Tv channel such as North American TV Channel 2 = 55.25MHz, Channel 13 =211.25MHz. Each channel is 6MHz wide. Besides these "physical channels", television also has "virtual channels".

Wi-Fi consists of unlicensed channels 1-13 from 2412MHz to 2484MHz in 5MHz steps.

A room in the Internet Relay Chat (IRC) network, in which participants can communicate with each other.

All of these communications channels share the property that they transfer information. The information is carried through the channel by a signal.

## Channel models

A channel can be modeled physically by trying to calculate the physical processes which modify the transmitted signal. For example in wireless communications the channel can be modeled by calculating the reflection off every object in the environment. A sequence of random numbers might also be added in to simulate external interference and/or electronic noise in the receiver.

Statistically a communication channel is usually modeled as a triple consisting of an input alphabet, an output alphabet, and for each pair (i, o) of input and output elements a transition probability p(i, o). Semantically, the transition probability is the probability that the symbol o is received given that i was transmitted over the channel.

Statistical and physical modeling can be combined. For example in wireless communications the channel is often modeled by a random attenuation (known as fading ) of the transmitted signal, followed by additive noise. The attenuation term is a simplification of the underlying physical processes and captures the change in signal power over the course of the transmission. The noise in the model captures external interference and/or electronic noise in the receiver. If the attenuation term is complex it also describes the relative time a signal takes to get through the channel. The statistics of the random attenuation are decided by previous measurements or physical simulations.

Channel models may be continuous channel models in that there is no limit to how precisely their values may be defined.

Communication channels are also studied in a discrete-alphabet setting. This corresponds to abstracting a real world communication system in which the analog->digital and digital->analog blocks are out of the control of the designer. The mathematical model consists of a transition probability that specifies an output distribution for each possible sequence of channel inputs. In information theory , it is common to start with memory less channels in which the output probability distribution only depends on the current channel input.

## Channel Model for Mobile Communications

H(Î¾) S(t)

r(t)

Y(t)

W(t)

Complex baseband point-to-point communications channel

So far we studied the complex baseband model for point-to-point communications shown in above Figure Our goal now is to modify this channel model to incorporate the effects of the mobility. We will focus on terrestrial mobile communications channels satellite channels are more well behaved". The following are points worth noting in making the transition to the mobile communication channel model. The additive noise term w(t) is always present whether the channel is point-to-point or mobile, and usually w(t) is modeled as proper complex WGN. For point-to-point communications the channel response is generally well modeled by a linear time invariant (LTI) system. For mobile communications, the channel response is time-varying, and we will see that it is well modeled as a linear time-varying (LTV) system.

## Multi-path Fading Channel:

The communication channel is implemented as a multipath channel. It is represented by a Number of randomly distributed objects, and each with an amplitude and phase gain. When a

Multipath signal reflects on one of these objects along its propagation, the multipath signal Experiences amplitude and phase attenuations according the respective gains of the object, Due to the interaction between the multipath signal and the object. The objects are randomly generated and distributed in the channel. Both the amplitude and Phase gain of each object are manually assigned. In general, the amplitude gain a of an Object will vary from 0 to1, while the phase gain b will vary from 0 to2 p ,but b ò 0 or 2p .Figure below shows a possible configuration of the multipath fading channel with 3 multipath signals.

Figure A possible configuration of the multipath channel with 3 multipath signals.

Figure Insertion of AWGN

## AWGN channel

For the Additional White Gaussian Noise (AWGN) channel the received signal is equal to the transmitted signal with some portion of white Gaussian white noise added. This channel is particularly important for discrete models operating on a restricted number space, because this allows one to optimize the circuits in terms of their noise performance. The block diagram of the AWGN channel is given in the next figure.

s(t) = s(t) + n(t)

where n(t) is a sample function of a Gaussian random process. This represents white Gaussian noise.

## Noise in Channel

The channel noise is represented by the AWGN inserted in to the transmitting signal. AWGN is inserted in to the transmitted signal at the point when the signal just about to reach the Receiver as shown in above figure.

The AWGN represents the channel noise, and other signal interference in the channel AWGN is generated by using the "randn" function multiplied by a means , which will be

Manually assigned according to the test conditions in Chapter5.As each multipath signal Vector contains 12288 real and imaginary amplitude component pairs, AWGN is added each Amplitude components pair in the multi path signal vector by generating AWGN as

AWGN =s *(I*randn+Q*randn)

where is the mean of the AWGN, I is real amplitude component , I and Q is the imaginary amplitude component.

Black diagram for an OFDM system with phase noise and AWGN

## Phase Noise:

Phase noise is one of the key nonlinearity sine it results into inter carrier interference. There are many types of these like white phase noise, flicker noise, random walk frequency noise. The term phase noise emerges from the approaches of signal description as two independent noise sources that contribute either solely to amplitude perturbations or phase perturbations. But OFDM is very sensitive to these carrier phase noise due to its long symbol period .Phase noise can be carefully considered when dealing with OFDM systems while amplitude perturbations can be taken as negligible, since removing of ICI is the key concept of the system.

The concept of how this phase noise is introduce is key point to understand the effect, practically the modulators and demodulators in the oscillators usually work at baseband or at intermediate frequencies ,since we are supposed to transmit our signals at radio frequencies we must shift our modulated signal up to RF in the transmitter and down from RF to IF at the receiver. such frequency shifting oscillators are termed to be local oscillators whose frequencies are stabilized by means of phase locked loop(PLL) .

Phase noise estimation is very difficult in time domain, since phase noise is multiplied with transmitted signal than in frequency domain where the PSD of signal is being convolved with the PSD of noise.

Phase noise contributes to:

1. Common Phase Error (CPE), which causes the rotation of the desired signals;

2 Inter carriers Interference (ICI), which causes interference on the desired signals

## How is phase noise introduced - and why do we care:

A phase noise compensation scheme is proposed for OFDM-based wireless communications. The proposed scheme consists of two phases. One phase is the joint channel and phase noise estimation, and the other phase is the joint data symbol and phase noise estimation. The simulations show that the proposed scheme can effectively improve the system performance in terms of the effective SNR and the un coded BER. It is demonstrated that the proposed algorithm can reduce the sensitivity of OFDM receivers to phase noise by about 8 dB. Since oscillators with ultralow phase noise usually have the disadvantage of high implementation cost and high power consumption, the improvement will significantly reduce the cost and power consumption from the perspective of hardware designers.

There are mainly two types of oscillators used in practice, depending on whether or not they are used in a PLL. The so-called free-running oscillators operate without a PLL and the generated phase noise is modeled as the accumulation of random frequency deviations and hence has unbounded variance. On the other hand, in a PLL oscillator, the closed-loop control mechanism tracks the phase variations of the carrier signal, and consequently, the generated phase noise has finite variance. In receiver, the regularly scattered and continual pilots are disturbed by adjacent subcarriers due to convolution of R(k) and P(k). So it is not easy to solve P(k) from the plots inserted into received OFDM signal. In per-symbol method, we add five continual pilots dedicated to phase-noise estimation beyond both sides of the transmitted information band respectively. And five pilots are separated from information subcarriers by five empty subcarriers of which modulation information is zero. These empty subcarriers avoid pilots' convolving with information subcarriers and are of benefit to the phase-noise IC1 estimation. So per-symbol method uses only twenty subcarriers out of band to estimate reliably phase noise symbol by symbol. These twenty pilots dedicated to phase noise estimation are called phase-noise detection subcarriers. And the distribution of phase-noise detection s u b c a x h Practical oscillators suffer from phase noise - a random perturbation of the phase of the s teddy sinusoidal waveform. Practical modulators and demodulators usually work either at baseband or at a convenient intermediate frequency (IF). As we must transmit our signal at some allocated radio frequency (RF) it follows that in practice we must shift our modulated signal up to RF in the transmitter, and down from RF to IF or baseband in the receiver.

To do this we must use practical oscillators, whose phase noise will be imparted to the signal we convey Such frequency-shifting oscillators, usually described as local oscillators (LOs), commonly take the form of free-running oscillators whose frequency is then stabilized to the n ecessary accuracy by means of a phase-locked loop (PLL). The resulting phase-noise spectrum of such an LO is a function of the properties of the free-running oscillator, together with those of the components of the PLL The signal which is demodulated in the receiver will have superimposed on it the phase noise of all the Los in the chain between it and the modulator.

The design of those LOs cannot be specified unless we understand the effect that phase noise has on the demodulation process for the type of signal in use. If we get the specification wrong, then reception may be seriously impaired - or the LOs may be needlessly expensive. This article analyzes the effects of phase noise on the COFDM method of modulation used in DVB-T . It will (i) show that there are two different effects, one of which can be compensated for and

(ii) demonstrate how the concept of weighting functions can be applied to predict how much of each effect will.

## PHASE NOISE SPECTRUM:

Single sideband phase noise is a critical performance parameter of any frequency control system. Sideband noise can be converted into the frequency band of interest and reduce system sensitivity. A typical plot of a PLL noise characteristic is shown in Figure 1. When using a spectrum analyzer it can be safely assumed that both sides of the spectrum are identical. The integrated phase noise is not an "apples to apples" comparison for most systems, since this is highly dependent on the divider ratio, loop filter bandwidth, and damping or phase margin of the PLL. The spectrum peaking and loop bandwidth are functions of the loop bandwidth, while the noise "inside the loop" is generally proportional to the divider ratio. Noise outside the 3 dB loop bandwidth falls off rapidly, and does not contribute to the integrated noise significantly. The phase/frequency comparator's function is to adjust the voltage presented to the VCO until the feedback signal's frequency (and phase) match that of the reference signal. When this "phase-locked" condition exists, the VCO's frequency will be N times that of the comparison frequency. Where N is the programmable VCO divide ratio. It is assumed that any noise present at the input of the phase detector is multiplied up by a factor of N, and appears inside the loop of the PLL. This is generally synthesizer divider noise and phase detector noise. Obviously, this is an oversimplification of the noise properties of a PLL, but does serve as a way of normalizing phase noise measurements.

## TYPES:

## White FM Phase Noise

The case of white frequency modulated phase noise has been already addressed in the literature and detailed approaches exist both in the frequency and time domain .For the sake of completeness it is briefly repeated in the present section.

Let us assume phase noise Î¦2(t) that is generated by delta correlated frequency noise with PSD

S(w)=4âˆ2K2

The variance of the phase noise variation as

Then resultant PSD is S(w)=4âˆ2K2/w2

## Flicker FM phase noise

Let us assume noise Î¦3(t) that is generated by frequency fluctuations that exhibit a flicker noise PSD as S(w)=8âˆ3(2âˆ)-vK3/w1-v

## Random walk FM phase Noise

Let us assume random walk FM noise is Î¦4(t) generated by Brownian frequency noise and the PSD can be expressed as S(w)=16âˆ4K4/p2 +w2

Phase noise effects in OFDM systems have been analyzed many people, few of the most important are distinguished after FFT .They are

A constant rotation of the signal constellation

Loss of orthogonality among the subcarriers (tends to ICI)

## Mathematical Analysis

Let the received signal be x(t) is affected by the channel impulse response h(t) and by the phase Î¸(t) introduced by the local oscillators

## Methods to compensate these phase noises:

In this thesis we are using three compensation methods. They are

Minimum Mean Square Error (MMSE)

Least Square Method (LSM)

Weighted Functions

## Weighted rate compensation method:

The multicarrier technique OFDM is well established for broadband wireless communication. In upcoming standards, it will be combined with multiple input multiple output (MIMO) schemes using more than one transmit and receive antenna simultaneously. In the downlink of a multi-user scenario, resources must be allocated subject to a total power constraint. A suitable optimization criterion is the sum of weighted data rates. Many advanced scheduling algorithms can be cast into this framework, e.g. taking the inverse average throughputs as weighting factors leads to the proportional fair policy, while choosing the queue lengths as measure for the priorities reduces the risk of buffer overflows. A more sophisticated approach aims at the minimization of the average packet delay, and it is also possible to incorporate specific quality of service demands of different applications. It was shown in that all possible rate allocations for a given transmit power can be achieved by performing nonlinear dirty paper precoding at the base station. Interestingly, the same rate region results if the roles of transmitter and receivers are exchanged. This duality also holds for purely linear processing and its combination with nonlinear interference cancelation. Efficient optimization algorithms usually solve a certain problem for the uplink and transform the solution to the downlink afterwards.

A constant rotation of the signal constellation commonly referred to as common phase error (CPE).Pilots inserted in OFDM symbols can usually estimate CPE but cannot estimate ICI directly .This method is termed to be CPE correction method. The main limitation of this method is that error propagation results from a division feedback.

Later on the methods like Maximum likelihood (ML) and minimum mean square (MMSE) has come to emergence to compensate these phase noise components .There is a limitation with this too, this method offers a high payload in each OFDM symbol and the complexity is high.

The per symbol method proposed in estimates CPE and ICI based on the pilots added in the transmission spectrum and needs no feedback which is a over come first CPE correction method..The guard bands near the pilot avoid the convolution disturbances resulting from other data sub carriers and the this method applies the relation between the phase noise spectral components after CPE correction which lowers the computational complexity.

There is another method to compensate ICI is proposed in, which is an extension of the first method with addition of weighting function. The CPE and ICI effects can be quantified by simply applying weighting function phase noise spectrum. The weighting function are of great help in visualizing the impact of LO phase noise in OFDM systems. This method help the designers to choose the appropriate OFDM parameters and access whether a particular phase noise spectra are satisfactory to a particular application.

In a new algorithm is proposed to compensate this phase noise

Block type pilot symbol

Comb type symbol

Comb type symbol

Block type pilot symbol

This is a generalized block diagram of the method mentioned which In other words ,can reduce the sensitivity of OFDM receivers to phase noise by about 8 dB to that compared with CPE and ICI minimization algorithms mentioned above. The SNR can be increased more than 8dB by adding more pilot tones which increase Q. This method also bring diversity gain in MIMO systems by increasing its spectral efficiency.

## Compensation methods of the effect of phase noise on OFDM systems:

ORTHOGONAL frequency division multiplexing (OFDM) is a widely recognized modulation technique for high data rate communications over wireless links. Because of its capability to capture multipath energy and eliminate intersymbol interference, OFDM has been chosen as the transmission method for several standards, including the IEEE 802.11a wireless local area network (WLAN) standard in the 5-GHz band, the IEEE 802.11g WLAN standard in the 2.4-GHz band, and the European digital video broadcasting system (DVB-T).

Also, the OFDM-based physical layer is being considered by several standardization groups, such as the IEEE 802.15.3 wireless personal area network (WPAN) and the IEEE 802.20 mobile broad-band wireless access (MBWA) groups. The heightened interest in OFDM has resulted in tremendous research activities in this field to make the real systems more reliable and less costly in practice. One limitation of OFDM systems is that they are highly sensitive to the phase noise introduced by local oscillators. Phase noise is the phase difference between the phase of the carrier signal and the phase of the local oscillator, and its effect on OFDM receivers has been investigated in many previous works, such as. The distortion caused by phase noise is characterized by a common phase error (CPE) term and an intercarrier interference (ICI) term. The CPE term represents the common rotation of all constellation points in the complex plane, while the ICI term behaves like additive Gaussian noise. Compared to the single-carrier modulation methods that can track the fast variation in phase noise adaptively in a decision- directed manner, OFDM transmits data symbols over many low-rate subcarriers, which makes it more difficult to track and compensate for phase noise.

## Prior Work on Phase Noise Compensation:

The high sensitivity of OFDM receivers to phase noise imposes a stringent constraint on the design and fabrication of oscillators and the supplementary circuitry, such that the generated phase noise level will not cause the system to fail this requirement increases the implementation cost of OFDM receivers because impairments associated with fabrication variations are usually either unpredictable or uncontrollable. There have been works in the literature to mitigate the effects of phase noise in the digital domain. This approach provides an efficient, low-cost, and reliable solution to the phase noise problem. Some authors have proposed methods to compensate for the CPE term, in which the constellation rotation is estimated using pilot tones embedded in OFDM symbols and then corrected by the demodulator.

Since the ICI effect is either ignored or treated as additive noise in these schemes, they perform poorly if the phase noise varies fast in comparison to the OFDM symbol rate. To overcome this difficulty, some ICI compensation schemes have been proposed. The method in utilizes the pilot tones, which are sufficiently separated away from the data tones, to transmit pilot symbols for phase noise estimation. In the self-cancellation method presented , each data symbol is transmitted using two adjacent subcarriers and the received symbols are linearly combined to suppress ICI by exploiting the fact that the ICI coefficients change slowly over adjacent subcarriers.

Tx bits

OFDM modulator

channel

OFDM Demodulator

Rx bits

ejq(t)

W(t)

Model of OFDM system with phase noise

This technique has the advantage of low implementation complexity, but it reduces the spectral efficiency by one half. In, a finite-impulse response (FIR)-type equalizer is employ to compensate for phase noise and the filter coefficients are determined by the method of least squares. Since the filter length is limited by the number of pilot tones, it can only compensate for the ICI that is from adjacent subcarriers. A time-domain phase noise estimation and correction scheme is proposed in, where the phase noise process is parameterized by using sinusoidal waveforms as the bases and the parameters are estimated by the method of least squares.

However, using sinusoidal waveforms to approximate phase noise may not be optimal, and how to jointly estimate the model parameters and the transmitted symbols is not addressed in. Similarly, Liu and Zhu approximate phase noise by using a small number of sinusoidal components, and it is suggested to insert some pilot tones outside the spectrum occupied by data transmission and estimate the model parameters of phase noise using the received pilot signals. This scheme requires extra bandwidth and can only correct the ICI from adjacent subcarriers because of the approximation made in modeling.

Recently, a method that utilizes a prior information about phase noise spectrum to suppress phase noise is presented. All these ICI compensation schemes assume that the receiver has perfect channel state information; however, in wireless communications, the channel is time varying and the receiver has to estimate the channel in the presence of phase noise, which makes the scenario more complicated than what has been studied before. In, joint channel estimation and phase noise suppression are achieved by using the expectation-maximization (EM) algorithm; however, it simply models the ICI term as additive white noise. Also,Wu and Bar-Ness propose a channel estimation method with the aid of the cyclic prefix symbols, and Kim and Kim propose a joint channel estimation scheme using soft decision decoding. In, the maximum a posteriori (MAP) channel estimator is derived for the case when both frequency offset and phase noise are present.

## ALGORITHM FOR PHASE NOISE COMPENSATION:

If both A and H in were known, then the data vector could be recovered, e.g., by solving

However, in practice, neither the channel matrix H nor the phase noise matrixes A are known to the receiver. In this section, we propose a solution to deal with the situation when both A and H are unknown at the receiver. The proposed algorithm consists of two stages: One is the channel estimation stage and the other is the data transmission stage. In the channel estimation stage, we use block-type pilot symbols to jointly estimate H and A.

In the data transmission stage, comb-type symbols are transmitted such that can be jointly estimated with A by using the H estimated in the channel estimation stage. The motivation for this algorithm is based on the fact that wireless channels are usually slowly time varying compared to phase noise. Since the phase noise components may change significantly from one OFDM symbol to another, it is harmful to use the previous estimate of phase noise to help detect the data symbols in the subsequently received OFDM symbols. However, we can use the channel estimate for a few subsequent OFDM symbols due to the slowly time-varying nature of wireless channels. This motivates our approach to compensate for phase noise by using the joint channel estimation (with phase noise) first and then followed by the joint data symbol estimation (with phase noise). The algorithm is illustrated in Fig. 2.

Block type pilot symbol

Comb type symbol

Comb type symbol

Block type pilot symbol

Proposed algorithm

OFDM is an effective method to provide high bandwidth efficiency and to mitigate inter-symbol interference in handling time dispersion of multipath fading channels. It has been chosen as the transmission method of many standards, such as Digital Subscriber Line (DSL), European Digital Audio and Video Broadcasting terrestrial (DABBVB-T), European HIPERLA- N/2 and IEEE 802.1 ldg for wireless local area networks (WLAN) etc..

However, an OFDM signal is very sensitive to the carrier phase noise due to its long symbol period. Low cost tuners are associated with less good phase noise characteristics, i.e. their output spectrum cannot be modeled by a Dirac delta at the center frequency. Since receivers are usually manufactured at low cost, only phase noise is considered in receiver. Phase noise must he carefully considered when dealing with OFDM system design since an accurate prediction of the tolerable phase noise can allow the system and RF designers to relax with phase noise PSD. In this paper several continual pilots are added outside the information band transmitted and the distorted pilots in receiver is convolution of pilots signal and phase noise PSD.

And we can de-convolve the distorted pilots to estimate phase noise PSD. This method is called per-symbol phase noise, detection and compensation ('per-symbol method' to follow). Phase noise effects in OFDM have been analyzed by several authorsi2*'I. Two effects on the transmitted signal after FFT are distinguished: a constant rotation of the signal constellation (common phase error, i.e. CPE) and a loss of orthogonality among sub carriers (inter-carrier interference, i.e. ICI). Pilots inserted in OFDM symbols can usually estimate CPE, but cannot estimate IC1 directly. We call this method CPE correction (CPEC). Several authors have studied the phase noise compensation in OFDM ,including CPE and ICI. In , least square method is used to estimate the phase noise information that exists in scattered pilots and compensate it. Due to the convolution disturbance of subcarriers near pilots, the performance of the algorithm is not very ideal. Denis Petrovic et al argued that the phase noise waveform should be approximated using sinusoids and proposed a method for the phase noise suppression: correcting CPE using pilots and processing IC1 using a division feedback approaches'.

A key problem of the algorithm is the error propagation resulting from the division feedback. Florent Munier et al obtain the phase noise statistical properties based on several OFDM symbols and estimate phase noise using MMSE and ML methods. The algorithm in increases the payload in each OFDM symbol, and the complexity is high. The per-symbol method proposed in this paper estimates CPE and IC1 based on the pilots added in the transmission spectrum and needs no feedback loops. The guard bands near the pilots avoid the convolution disturbance resulting from other data subcarriers. The per-symbol method applying the relations between the phase noise spectral components after CPE correction lowers the computation complexity.

## Results:

## Conclusion:

We finally conclude that, by using the three methods like weighted unction, least squares and minimum mean square error technique we can minimize the phase error that arising due to the non linear characteristics of the awgn channel. From the results obtained we can conclude that the method MMSE observed to be more accurate in minimizing the error .Here we can see clearly that the error reduced is converged at a greater rate than compared with other two .

Computationally speaking both the least square and MMSE requires almost the same complexity where as the weighting function is a fore most and the simpler technique which also can be treated as a one of the good minimizing techniques.

## Future work:

This work may be further extended by opting for space time frequency orthogonal codes and can the error can be minimized more optimal than these.