Orthogonal Frequency Division Multiplexing (OFDM) is the best technology that is widely being used in many areas where there requires a high data rate like mobile wireless and cellular phone communications and also sophisticated ones like satellite communications and also the typical digital broadcasting of many audio sachems. To achieve all these, the main principle used here is the combat inter symbol interface and thus it plays a very important role in providing all the required capabilities for any typical OFDM.
During the periods of between 1960's and 1970's the actual invention of OFDM was done as part of the research, where the ISI, inter symbol interference was occurred due to the Multipath mechanism. Multi carrier modulation has several forms and now this particular OFDM can be considered as a sub form this and it has its own importance across like the sub carriers with much space and also the overlapping spectra and this particular feature allows the ability to multiple accesses. Now this MCM can be considered as the principle of transmitting the actual data with the principle of dividing the original stream into may bit level streams and also each and every bit stream is further divided with the help of sub streams and thus to modulate the several carriers. Multiple-access mechanism where the transmission scheme of same and fixed bandwidth can be further divided as below:
TDMA (Time Division Multiple Access)
FDMA (Frequency Division Multiple Access) and
CDMA (Code Division Multiple Access)
The main intention of this particular project is to implement the OFDM system with the help of Matlab programming. The complete process involves the transmission of data like text, speech and also few images and also and parallel de-multiplexing it at the receiver end without any disturbance and this particular simulation may explore both the advantages and disadvantages of this OFDM communication process.
I would like to make a special mention of the following people without whose help this project would have not been completed. First I render our thanks to Almighty God to give me the strength for completing this project. I would like to express our deep gratitude to our beloved principal Prof. Andy Pettit, for continuous encouragement and kind cooperation. He was a great source of confidence. I am greatly indebted and thankful to our Head of the Department, Prof. Karl.O.Jones, for his full support and his kind and able guidance.
I am very thankful Prof. E. Levi, my project guide for giving me an opportunity to do this project and also other staff members, friends and my parents who gave me support, encouragement and suggestion, which had helped to make the right choice at this juncture of my career.
Orthogonal Frequency Division Multiplexing (OFDM) proposal has been started in between 1960 and 1970 and it has taken 25 to 30 years to move from research side to industrial usage an introduced in to real world. The concept of OFDM is a very simple while studying but very complicated while implementing practically and it is completely a software implementation. The software implementation faces many problems in configuration and setup (Prasad, R. 1993). The basic principle of OFDM is Orthogonality; where it will allow the sub carriers to be orthogonal to each other and this mechanism allows a cross talk among the co channels to be eliminated and with this we can eliminate the need of inter carrier guard (Ministerie van Verkeer, 1993).
Orthogonal Frequency Division Multiplexing (OFDM) is considered as the digital carrier modulation mechanism. This mechanism will use a maximum number of closely spaced orthogonal sub-carriers to avoid the cross talking. Actually a single data stream can be further divided into many streams and again each stream is coded further and modulated with sub carrier and the basic and commonly used term is no other than the OFDM systems. Each and every sub carrier is perfectly modulated with the help of modulation scheme. Each modulated sub carrier is at very low symbol rate and also maintaining the rates of data transfer with in the range of same band width. By putting all these together, sub carries can reduce the higher bit rates to the lower bit rates (Chang, R.W. 1966). The generation and detection of OFDM performance can be done by the Fast Fourier Transform algorithm and in general the OFDM is developed with the help of a wideband digital communication a part of the copper wires. Before the proposal of OFDM has come in to the picture, people used to use the old one called FDM and all of them are independent of each other. In this system there will be some guard period between and also no overlaps in this system. The whole method woks perfectly in case of FDM, but when we consider with the typical cases like FM radio which also comes under FDM where there could be a loss in the bandwidth. FDM is not suitable for some of the wideband scheme and if this is used there could be chances where there is a loss in the bandwidth. But where as in the case of OFDM, there is a lot of chances of overlapping of subcarriers, this overlapping of subcarriers is because of the peak of sub carriers that occurs when all the other subcarriers will be at the zero level and this can be achieved by modifying the subcarriers all together using a particular method known as Inverse Fast Fourier Transform (IFFT) (Salzberg, B.R. 1967). IFFT takes the help of demodulator at the time of receiving end and also the parallel channels will use the FFT block, and all these can operate independently across the required channels. In OFDM systems, Orthogonality is very much important and also time and the synchronization across frequency should be excellent. When the Orthogonality is lost in OFDM system than Inter Carrier Interference (ICI) will arise. This particular interference will be from actual sub carrier to the other sub carrier. Beyond this, the cause of Fast Fourier Transform and Inverse Fast Fourier Transform is due to adding the guard interval without any transmission and this can also lead to the arrival of Inter Carrier Interference (Weinstein, S.B. 1971). Due to the delayed version of sub carriers there is a chance of rise in the cyclic prefix and this can interfere with some other sub carriers like the next symbol periods and this can be avoided with the help of delayed symbols and will have positive integer number of cycles across the Fast Fourier Transform integration intervals and this can remove the arrived Inter Carrier Interference as long as the delay spread is always is less than the actual guard period (Oppenheim, A.V. 1989).
The attitude with respect to the project is to identify and investigate the required OFDM system and to derive a separate and fully functional system as a part of software. Then analyze how inter symbol interference can be reduced by it, that was actually caused by the multipath fading channels and then estimating the channels of different kind and its effects and finally evaluating the ultimate performance of the OFDM scheme (Cimini, L.J. 1985).
Most first generated systems in general were evaluated in the middle of 1980's used to use along with the analog transmission methods and these can be used with the simple and multiple access techniques like a FDMA and the first generation telecommunications systems which are of type general Advanced Mobile Phone Services(AMPS) (Zou, W.Y. 1985). Here it also provides the overall voice communications in the channels and they can also suffer with a very lower user capacity and the related security levels. The introduction of second generation systems is in early 1990's. Digital technology is used by all these systems and this particular implementation can use the capacity a round three times and then the wave forms will be decrease the actual voice channels . General extension of the second generation is nothing but the third generation systems and they have introduced lot of advantages around the year 2000. The original system capacity and the first generation systems are to be seemed less than ten times than general system capacity. Regarding this, the complex multiple access techniques like the Code Division Multiple Access (CDMA) and the extension of TDMA. The flexibility of services available can be used to improve the system capacity. Now a day's telecommunication industry is facing many problems, like developing and providing the telephone services to continue their services to the very rural locations. There in the rural areas customers will face some problems like installation costs during the wired network are high comparatively. The only usable method of decreasing the very high infrastructure cost will be wired (Shelswell, P. 1995). This type of system can be handled lot of wireless radio network across the system. In general the common problem for the both rural and urban areas is to handle the large sized cells for sufficient coverage along the way of communication.
The figure given below explains the process of evaluation and the current services and the predefined networks for the general third generation networks that we are facing in the communication process. All services and all separate systems are like radio paging and the cordless telephony. They all truly combined with the required services that are provided with all required and general third generation telecommunications systems across the total communication systems (Telebit corporation, 1989). Now a day's GSM technology is also known as Global System for Mobile telecommunications. It can be applied through fixed wireless systems and phones across the rural areas. How ever the GSM can also use the typical time division multiple access (TDMA) can handle the high symbol rate leading with the multipath. This can cause the actual inter symbol interface as per the requirement and this can be achieved better results for the next generation of these digital phone systems. And it can be aimed in improving the overall efficiency of the system and it can also handle the multiple path variables that can be created with the help of inter symbol interference. There are numerous methods are there that can be considered with the help of digital phone systems (Alard, M. 1987). Here we can improve the capacity of cells and immunity of multi path and also the required flexibility. This scheme can be explained best with the help of CDMA and also with OFDM. Actually both of these techniques can be applied across the fixed wireless systems that can be suited for the rural divisions and areas. There are many new radio broadcasting systems were they are using OFDM and HDTV with the digital audio broadcasting techniques. Some research has done within the implementation of OFDM as per the transmission process and methods for the mobile telecommunication process. Actually the principal of the CDMA transmit the users and it sets the same frequency for the same broad and uses the special based codes on the channelization. These codes are aware by the base station and the required mobile station and the modulation can be used for the data which can be transformed with the help of OFDM/COFDM. This will also allows so many users for the transmission for a band which was measured by further dividing all the available bandwidth that can narrow all the required bandwidth. At the same time each and every user will be allocated which is again used to transmit their own data among the channels. This type of transmission process can be used to generate the orthogonal to each other's and should be packed along with the frequency division multiplexing(FDM) and it leads to the required OFDM/COFDM which can provide a high spectral efficiency across.
Multiple Access Techniques:
By using the multiple access schemes we can allow very high simultaneous for the typical users who are using the same fixed rate of bandwidth and radio spectrum across. In any radio system, the channels were allocated with the required bandwidth and it is always limited. For example mobile phone which can use up to 55 MHz, this can also be split in to half and this is used to forward and reverse all the available links for the required systems. We can increase the desired user capacity of any typical wireless is done by the general sharing of this system. Typical wireless are such as FDMA, CDMA and also the TDMA and these all can be used as the extensions for the hybrid techniques that are always clear (Thibault, L. 1997).
CHAPTER - 2
THEORY AND REASEARCH
2.1 Theory & Research Introduction:
The information is to be added additionally to the electronic or the optical signal carrier Modulation and it is applicable for the direct current and alternate current and for the optical signals. The smoke signal is like blanket waving when the transmission modulation is utilized. Actually a channel will act as a separate path in the telecommunications, it helps in the allowing the signals to flow. The channel will act as a separate wavelength of light with in a merged multiplexed light stream if the dense wavelength-division multiplexing is in the optical fiber transmission. The channels will be mainly pointed out by this telecommunication definition (Wahlqvist, M. 1996).
2.2 OFDM Principles:
OFDM is referred as another form of Multi Carrier Modulation (MCM). The closely spaced sub carrier with overlapping spectra is the feature of this and also multiple accesses will be possible. Multi Carrier Modulation (MCM) is known as the process of transmitting data by separating the stream in to various bit streams. Every bit stream contains a lower bit rate. These sub-streams are useful in order to adjust various carriers. This method is being observed by the coming generation, the transmission scheme for them wireless mobile communications networks (Lee, D. 1997).
2.3 Fourier Transform:
The OFDM applications were not ideal in 1960's; this is because at the point of time, to produce carrier frequencies the various banks of the oscillators are required and that are essential for the transmission of sub-channel. It is difficult to prove and overcome at that time of period. This system is not considered because it is not executed (Moose, P. 1994).
Whatever may be the case, the arrival of the Fourier Transform and the complexity of the OFDM system will be removed initially. Especially with the help of Fourier, frequencies will be produced. Inverse Fourier transforms are utilized to execute OFDM systems. Antenna studies, linear system analysis etc and it will make use of the Fourier transforms. To divide or decompose a waveform or function into sinusoids of various frequencies which will be aggregate with the original waveform the Fourier transform will be used. Various frequency sinusoids and their corresponding amplitudes will be pointed out or differentiated (Cooley, J.W. 1965).
In the geometric representation, orthogonal referred as "involving right angles". For the common use the term has been continued. It is of independent character. The other meaning is that it is non-overlapping, non-redundant or irrelevant. For original and difficult functions that are valued the orthogonality is described. jm(t) function and jn(t) function are considered as orthogonal that are corresponding to each other in between the interval of a < t < b if the condition is satisfied (Frigo, M. 1985).
2.5 OFDM Carriers:
As mentioned before, another form of Multi Carrier Modulation (MCM) is referred as OFDM. With this multiple-access will be possible. The waveforms of OFDM time domain are selected in such a way that mutual orthogonality will be existed even with the sub carriers with overlapping spectra. In relation with the OFDM, it is described that among all the carriers in the collection orthogonality is an identification of a definite and the fixed relationship. Each carrier is placed in such a way that it will appears at the point of zero energy frequency of all the remaining carriers. This function is used as an example in Fig. 2.1 contains this property and in the OFDM system it is utilized as a carrier (Johnson, S.G.).
2.6 Orthogonal Frequency Division Multiplexing:
OFDM is considered as a multicarrier transmission technique. The current spectrum will be divided into number of carriers by this method. It regulates each and every carrier with a low rate data stream. OFDM is nothing but same as FDMA. The bandwidth is subdivided into multiple channels with this system and again with this multiple channels user access took place. Also users are allocated by this multiple channels. In any case the OFDM utilizes the spectrum more effectively by making the channels spacing more closely together. This can be reached by arranging all the carriers orthogonal to one another, by arranging like this we can avoid interference intermediated in carriers which are closely spaced.
Coded Orthogonal Frequency Division Multiplexing (COFDM) is comparable to OFDM; the only difference is that the forward error correction is applied to the signal before the transmission (Bertoni, 2000).
Because of the carriers which do not exist from the channel noise, the remaining propagation effects and frequency selective fading errors occur during the transmission. In order to avoid these errors the forward error correction to the signal is applied before the transmission. For this discussion OFDM and COFDM are interchanged. First they mainly focused on the OFDM system, when we expect that the forward error correction is required then we utilize any other practical system, hence it may be considered has COFDM (Van Loan, C. 1992).
Each user of FDMA is allocated by a single channel; this will help in transmission of all the user information. The bandwidth will be from 10 kilo Hertz (kHz)-30 kilo Hertz (kHz) for the voice communications of each channel. Whatever the case may be, for speech at least we require a bandwidth of 3 kilo Hertz (kHz). If the allocated bandwidth is extended then the least amount needed to avoid the channel from interfering with one another. To accept signals from the neighboring channels, than that signals are to be filtered out by the bandwidth which is extra and also to accept and drift which exist in the centre frequency of the receiver or transmitter. Due to spacing which is extra that is intermediated in channels, which nearly 50% of total spectrum which is not in use in a typical system (Blaunstein, 2004).
Bandwidth of the channel is narrow then that situation will become worse and at the same time it increases the frequency band. Vocoders, it is the system by which it makes the digitized speech compress is utilized in most of the digital phone systems. When the bandwidth decreases, then the system capacity increases. This increased system capacity will accept which is required for each and every user. The Vocoders will be using the data rate between 4-13 kbps; it depends along with the sound quality and the type that is utilized. Each and every user requires the minimum bandwidth in between 2-7 kilo Hertz (kHz) by using the modulation of QPSK (Rappaport, 1996). Whatever the case may be this type of narrow band width will not be managed by simple FDMA in an effective manner. TDMA will avoid this type of situation by making use of wider band width channels, this is been used by various users. By data transmission in time slots, the multiple users will execute the same channel. So, number of low data rate users is merged together for a single channel transmission. The spectrum is used efficiently because of this sufficient bandwidth. There are two problems which are faced with TDMA. Because of the time slotting which is occurred in the channel, always an overhead will be associated with the change over that is intermediated in users. The change over time should be allocated for each user in order to accept the start time tolerance of each user. This will occur due to synchronization errors and propagation delay variations and it will also controls the number of users were they can perfectly manage each and every channel. However each channel symbol rate resulting very high in the problems including multipath delay spread (Saunders, 1999).
The problems which are going to occur due to FDMA and TDMA are been avoided by OFDM. The bandwidth existing is divided into number of narrow band channels (nearly 100-8000) by the OFDM. The channels in each carrier are arranged in orthogonally to one another, by avoiding the overhead of the carriers that will present in form of FDMA. Because of this, the users will not be in the use of time multiplex in the TDMA. So, by switching between users overhead will not be associated with the carriers (Davidson, 1997).
An integer number of cycles are contained by the each carrier over an each period of symbol in the carrier orthogonality. This is caused because each carrier of the spectrum will contains null and at the center frequency of the each carrier and every remaining carriers in the system. In between the carriers, interference will not be occurred and it allows the carriers to be closely spacing together. Spacing is needed in FDMA to avoid the problem of overhead carrier. The signal carrier in the OFDM consists of a narrow bandwidth of 1 kilohertz (KHz) so that it results in low symbol rate. This is due to high tolerance which took place in the signal to the multipath delay spread. The delay spread should be very far to cause significant ISI (Cox, 1983).
PROPAGATION OF CHANNEL CHARACTERISTICS
3.1 Propagation Characteristics of mobile radio channels:
In a practical radio channel, received signal will contain only a single direct path signal and for a transmission signal this will act as a perfect reconstruction. In any case, the signal will be changed in a real channel during the transmission in the channel takes place. We know that by the propagation medium, the performance of any wireless system will be affected and it is known as channel characteristics. In the telecommunications actually the channel will act as a separate path by which the signal will transfer. When we talk about practical situation, a direct line of sight will be desired between the transmitter and the receiver. And it is difficult to now what is happening in the channel, with a less number of errors the signal which is original will be reconstructed (Turkmani, 1993).
The combination of refracted, reflected, attenuated and diffracted replicas of the transmitted signal will be consisting in the received signal. By considering all the above, a noise is added to the signal by the channel and if transmitters or receivers are shifted or moved will be occurring in the carrier frequency. Making clear cut idea about the signal effects is essential; because the radio system performance is depend up on the characteristics of the radio channel
While transmitting the signal from one point to another if drops occur in the signal power then it is known as Attenuation. This will occur by the signal path obstructions, path length transmission, and effects of multipath. The Figure.3.1 explains the effects of the radio propagation which causes attenuation. Attenuation will occur only if any object is obstructed the line of the sight signal from the transmitter to receiver (Alexander, 1982).
If any objection is there between the transmitter and the receiver then the shadowing signal will be occurred. It occurs usually on the buildings and hills. It is a very essential environmental attenuation factor for receiving the signal. In high build up areas shadowing is very severe because of the shadowing from buildings. . In any case, it is a very big problem created by the hills due to production of large shadow (Hashemi, 1993).
The Radio signals will divide the object boundaries and this will avoid the shadowing of the signals across the hills and buildings. In any case, amount of the division will depend up on the radio frequency which has been utilized, with low frequencies which are dividing than that of the signals of high frequency. Ultra High Frequencies (UHF) and microwave signals are the high frequency signals. Mainly for capable signal strength a line of sight is required. Generally transmitters are elevated to a high extent as possible to reduce the number of objections and this will avoid the problem of shadowing (Lemieux, 1991). The amount of variations in attenuation which occurs due to shadowing is represented in Table 3.1. Shadowed areas should be large, so that the results in the signal power rate of change which is very slow. So it is named as lognormal shadowing or slow-fading.
3.1.2 Multipath Effects:
18.104.22.168. Rayleigh fading:
In the radio link, the RF signal will be reflected from the transmitter to the objects like hills, vehicles or buildings. By this existing multiple transmission paths, the receiver will be progressed (Rappaport, 1992). Constructive interference or destructive interference will be occurred at the Rx because of multiple reflected signals. This is occurred mainly in short distances, hence it is known as fast fading. Over a short distance the variations will change from 10-30dB (Rappaport, 1989).
22.214.171.124. Frequency Selective Fading:
In radio transmission, the channel spectral response is not smooth. The response in this contains dips and fades because of reflections involving cancellation at the receiver at the particular frequencies (Devasirvatham, 1990). The reflections of the particulars like ground, buildings and trees will cause the multiple path signals the same signal power as the direct signal. This will result in the formation of the deep nulls because of the destructive interference in the signal power which is received. If the response of the frequency is null in the narrow bandwidth transmission that occurs at the frequency transmission than the whole signal will be corrupted. This corruption can be avoided by two methods (Tarng, 1997).
In the spectrum the dips will be resulted in a small signal power loss because of the wide bandwidth signal or spread spectrum is transmitted as CDMA, rather than a complete loss. As same as in the COFDM/OFDM transmission the transmission is divided into number of bandwidth carriers and this will be considered as another method. The original signal will be spreaded over in the wide bandwidth. The nulls in the spectrum will occur unlikely at the carrier frequencies. Instead of entire signal we will lose some of the carriers. The information in the carriers which does not exist can be recovered and enough forward error corrections which are sent will be provided.
126.96.36.199. Delay Spread:
The radio signal which has been received from the transmitter is made up of a direct signal. And the reflections like mountains buildings and other objects etc are added. The reflected signals will be reached at a subsequent time. Because of the unnecessary path length the reflected signals will reach at time than that of direct signal, which progresses delicately at the different time of arrivals of the transmitted pulse. So the energy received is been spreader. The time of spreading in between the first arrival and the last arrivals of the multipath signal that is look after by the receiver is known as Delay spread.
The inter-symbol interference is caused by the delay spread in the digital system. This is due to the overlapping of the delayed multipath signal with the succeeding symbols. In the high bit rate systems, this will result in producing significant errors.
Especially, when the time division multiplexing (TDMA) are utilized, because of the delay spread on the received signal inter-symbol interference will be affected. This has been described in the Figure.3.4. When there is increase in the transmitted bit rate usually increases the amount of inter-symbol interference. If the spread of the delay is greater than ~50% of the bit time then this effect will starts to become more malleable.
The Inter-symbol interference can be minimized in the different ways. One of the methods is to bringing down the data rate of each and every channel will be reduced in order to bring down the symbol rate; this is of one type of method which has been used. The other method is for bearing inter-symbol interference like CDMA, the coding scheme is used.
3.1.3 Doppler Shift
The source will not be identical for the signal frequency which is received, if the wave source and the receiver are moving with respect to one another. The wave source will be less as the signal frequency which is receives is high, if the wave source and the receiver are moving towards each other. The frequency of the signal will be decreased when the wave source and the receiver approach each other. This will be known as Doppler Effect. It will approach and proceed if there is any alteration in the pitch in a horn of the cars. This effect is seemed to be more essential, when there is growth in the mobile radio systems. Because of the Doppler Effect the necessary amount of alteration in the frequency will depends on the intermediate relative motion in the source and receiver. And it is also depends up on the propagation speed of the wave. The frequency of the Doppler shift can be represented as:
From the above mentioned equation:
Df is referred as change in the source frequency viewed at the receiver.
fo is referred as source frequency.
'v' is referred as variation in the speed between the source and the transmitter.
And 'c' is the speed of the light.
Consider fo = 1GHz and v = 60km/hr (16.7m/s)
By using the above equation the Doppler shift will be calculated as follows:
This shift of 55Hz in the carrier will generally not affect the transmission. Usually, the transmission will not be changed with Doppler shift of 55 Hertz (Hz) that exists in the carrier. In any case, some important problems will be occurred because of this Doppler shift. This will took place if the technique of the transmission is delicate to carrier frequency offsets or due to the high relative speed (Gibson, 1999).
3.2 Inter Symbol Interference:
If the development takes place in the communication systems, then we need of high symbol rates and it becomes more visible. Whatever the case may be the present multiple accesses whose symbol rates are high will come up with various multi path problems in which ISI will cause. Echo is one of the duplicate copies of the real signal which is going to be occurring later in some time. When the echoes are on the different-length propagation paths then ISI will occurs, then overlapping occurs in the receiving symbols and then ISI will occurs. When the OFDM symbol lies with the next one then the problems will arise. In between the two consecutive OFDM symbols the correlation will not occur, therefore for the symbols, the interference from one symbol, the other will occur in the disturbed signal. Usually the channels band width the symbol rate of the communication system is ideally limited. The ISI effects will deal seriously with the higher symbol rates which are there. Equalization of various channel methods are used to put down the ISIs occurred due to the channel. To apply this in any case, the response of the CIR (channel impulse response) should be calculated approximately (Lafortune, 1990).
OFDM is used newly in order to transmit data over a multi-path channel, rather than attempting to remove the effects of the ISI channels. For the information symbols transmission in the direction of the sub-channels over the channel, a set of Sub-carriers are used in which the system's throughput will be the sum of the entire parallel channel's production.
This is the overall foundation of OFDM, how it works, by transmitting in the same direction through a set of sub-carriers, a conventional single carrier system data rate is nothing but the each sub-channel data rate which consist in fraction and which is of same output. So, in order to help in differentiating the high data rates with the requirements of the channel equalization systems will be constructed (Arnold, 1989).
Actually when the incoming signal is divided into the particular transmission sub-carriers for one time, then the guard interval will be added in between the each symbol. Each and every symbol contains a symbol duration referred as Ts and Guard interval referred as Dt, where the part of the time and signal of Ts will be repeated cyclically. This is represented in the Figure.3.5. Considering the delay of the multi path propagation will not cross the interval duration, inter-symbol interference will not be occurred so the channel equalization will not be required.
Types of the transmission signal of the electromagnetic wave will travels from the transmitter to the receiver. While it travels a wide range of different types of environments are encountered by the wave. Channel models will focus the attempt to model these various environments. The main aim is to produce well defined disturbances to the transmission signal. In this collection of discussion about the various channel models will took place. For the DAB transmission it is very difficult or typical. The noise, signal reflection and movement effects are to be considered. Before introducing the usual project is the mathematical model, we should also provide the pictorial representation of the channel environment (Whitman, 1995).
The figure represents the communication system block diagram. This system contains 'Sender', 'Channel' and 'Receiver'. In this class we mainly discuss about the point of the channel aspect of the communication system. From the block diagram, we can clearly say that s (t) will be referred as transmission signal and s (t) will be referred as received transmission signal.
For the Added White Gaussian Noise (AWGN) channel the received signal is similar with the transmitted signal with some portion of white Gaussian white noise added additionally. For the different models that are executed on a number space which is restricted this channel is important (Seidel, 1994). So, this will accepts one to optimize the circuits with in the period of their noise execution.
The multipath channel will be considered as last in the static channels. It tells the fact that the electromagnetic waves can travel from to receiver antenna from transmission antenna through the different types of paths. The receiver antenna which contains electromagnetic waves will adds all the various types of signals. So, the development in the received transmission signal will takes place with the help of the mathematical model of the multipath environment and in turn they will be adding all scaled and delayed versions of the real transmission signal. Because of the superposition of signals the ISI will takes place. Fading channels:
Mathematical model is represented by the Fading channels for the wireless data exchange in a physical environment which changes with the time. These changes will take place because of two types: data exchange in the wireless system in a physical environment the representation is done by the mathematical model is designed by the fading channels, these change will occurs because of two reasons:
There is a variation in the environment even though the transmitter and receiver are stable. The following are the examples:
Alterations in the ionosphere,
Alterations in the movement of foliage
Alterations in the movement of reflectors and
Alterations in the scatterers.
To the beneath of the physical phenomenon, DSP model and the mathematical description are very similar. If this will cause for the practical channel models it is not suitable. Statistical methods are provided to abstract in order to generate practical channel models and also to give an idea about the fading channel models. The discussion will be going on the below two mentioned subsections, fading channels, they are of Rayleigh and Rician. Rayleigh and Rician are going to represent the statistical channel modes. But the only difference is that a direct or prominent path will not be assumed in the Rayleigh model but in the Rician model the direct path is assumed. At last the channel model will increases the thoughts of Rayleigh and Rician fading channels with mobility aspects. The remaining mobile fading channels model will reduce the effects in the frequency domain of wireless multipath channels.
This type of model is occurred due to multipath reception. A large number of that is we can say infinity number of scattered and reflected waves will be received by the mobile antenna. The spontaneous received power that is caused by moving antenna and it becomes to be a random variable, depending up on the antenna location this is due to the occurrence of the wave cancellation effects.
Rician fading channel:
Rician fading model and Rayleigh models are all most all identical but the only difference is that, in a Rician fading model a strong dominant component will be present. This governing component now it acts as line-of-sight wave.
The dominant wave which will act as like a phasor, this is sum of two or more dominant signals, for examples the line-of- sight, and a ground reflection. The signal which is synthesized is then mostly referred as a deterministic (fully predictable) process.
The dominant wave is also referred to shadow attenuation. This is the famous assumption in the designing of satellite channels. A large number of infinite reflected and scattered waves will be received by the mobile antenna which has been existing beside the dominant component.
The electromagnetic wave can travel through a prominent or direct path is shown in the Rician fading channel. When this is compared with the Rayleigh channel model on oreder to reflect the prominent path an additional Acos(2pifct) component is contained in the Rician fading channel model.
CHAPTER - 4
THE KALMAN FILTER
In the year 1960, R.E. Kalman has introduced a popular paper in order to describe the recursive solution to the separate data linear filtering problem. From the year 1960, R.E.Kalman filter is referred as extensive research and application. Specifically in the autonomous area or assisted navigation area, he referred as a mathematical power tool. This plays an important role in the computer graphics in which the sensing of the genuine world systems are included (J. Dailing, 1992).
4.2 What is meant by Kalman Filter?
Kalman filter had theoretically estimated for what is called the "linear quadratic problem", which has been focus on estimating the instantaneous "state" of a linear dynamic system perturbed by white noise. It is statistical that the estimator is optimal with respect to any of the quadratic function of estimation errors. In the history of statistical estimation theory, kalman filter has practiced and one of the greater researcher who discovered the possibly the greatest discovery in the twentieth century. It has been proved that mankind has to do many things that could not have been done without it, and it becomes like silicon which is indispensible in the preparation of many electric systems (Dersch, 1994).
For the linear quadratic problem Kalman Filter is an idea, where as it is mainly concentrates on expecting state of a linear dynamic system, which occurs instantly and that has been disturbed by the white noise particularly with reference to the quadratic function of the estimation errors, and this estimator will act as optimal.
In the estimation statistical theory generally Kalman Filter as remained as a greatest discoverer. Great discovery in the twentieth is done by the Kalman Filter. It makes easy to the mankind to implement many of things which are not possible without Kalman Filter. It becomes to be very difficult to omit as silicon in the designing of electric systems or goods (Honcharenko, 1983).
In the dynamic way, complex systems are dynamically controlling the spacecrafts or ships, aircraft and the other systems like which are continuously in manufacturing processes are very closed to the applications of the Kalman Filter. We should aware of all the process which we had done before to manage a dynamic system. The variable which we want to control will not be able calculate always the each and every variable with this application. The Kalman Filter had effort to collect the information and want to express his conclusion which is missing from the indirect measurements. Kalman Filter has investigated some of the wonderful things by identifying similar future courses of the dynamic systems, and this is not able manage by the people, like the defects of celestial bodies or traded commodities prices, flow of rivers during the floods. The views of this section from the ideal point of view are expressed as follows:
Kalman Filter is only a tool
It is tool because that will support the mankind in each and every problem solving. In any case, by its own it cannot solve any problem. So, in any case we cannot call this has a physical tool. But can be referred as mathematical tool. This tool is designed by mathematical models. By giving brief explanation, we can say that particularly these tools are for the mind. With the help of this, they will support the mental work become to be operated more perfectly and effectively. It is just like mechanical tools in which they make slowness physical work to be less. One can use this tool effectively if and only if the usage and functionality should be known. It is very important to known functionality before one can use this tool.
Kalman Filter is a computer program
An exact representation of the estimated problem will be utilized by this computer program. This is said to be a definite number of variables. Hence, because of this it is called as "ideally suited to digital computer implementation". In any case, suppose if we assume that these variables are genuine numbers with infinite precision, some or the other problem will be occurred. This is due because of the differentiation between the finite dimension and finite information. When in an ideal side the Kalman filtering is used, along with the theory the problems which are mentioned above should be included in the theory.
Kalman Filter is a complete statistical characterization of an estimation problem
This complete statistical characterization of an estimation will represents the entire characterization of the present state of knowledge of the dynamic system. In which we can also include all these effects of the previous measurements. There is a main reason behind on why it is much more than the estimator than that is propagation of the complete probability distribution of the variable is lead to be estimated. Statistical analysis will makes use of these probability distributions and also to identify the sensor systems design.
In a limited context, Kalman Filter is a learning method
The designing the estimation problem is possible only in one way of differentiating between phenomena and noumena. The state of knowledge about the noumena is reached from the phenomena from the above. Taking the help of the probability distribution, the state of knowledge will be represented and also the knowledge of the original world is also represented along this probability distribution. So we can say that the increased process of knowledge is considered as learning process. In many of the application it will work quiet effectively.
4.3 For what purpose it will be used?
The numbers of fields are enclosed by the applications of the Kalman fiter. It is used as a tool. And the usage of this tool is because of two reasons:
- Estimating analysis of the estimators.
- Performance analysis of the estimators.
Kalman filter uses the whole description of the probability of the estimation errors such that to decide the optimal filtering profits. To regulate its execution as a function of the design parameter of the estimation system which are mentioned as follows:
- Utilizing the sensors of different types for the estimation;
- Locations and orientations of the different types of sensors are to be estimated according to the type of systems;
- Noise characteristics of the sensors are accepted;
- The methods of Pre-filtering are introduced for smoothing sensor noise;
- Data sampling rates are provided for different types of sensors to estimate;
The level of model simplification is utilized in order to avoiding implementation requirements.
For an estimation system a system designer has an ability to allocate an "error budget" to the sub systems. This is possible if and only if by using analytical capability of the Kalman filter act. In addition to this, if when we are going to reach a required level of estimation accuracy than it exchanges off budget allocations to measure the executions of others or to optimize the cost (Qian, J. 1992).
4.4 Relative Advantages of Kalman Filter
The relative advantages of the kalman filter are mention below. Previously a filter named Wiener Filter was used it was very popular at that time. The information is gathered based on this when it is compared with this popular filter which is introduced before the kalman filter. This is explained in detail as following:
The algorithm of the kalman filter is applicable on the digital computer. This was put back by the analog circuitry for the estimation and for controlling the analog circuitry when the Kalman filter was first presented. The Kalman Filter was compared with the Wiener analog filters but this execution very slow and however it is applicable due to greater accuracy (W., H. L. Bertoni, 1986).
The properties of the Kalman filter which are fixed are not needed for the random processes or deterministic dynamics. Many of the applications on demand contain the non-stationary stochastic processes. A competition will take place for dynamic systems in between the Kalman filter and s state-space formulation of optimal controllers. It is now proved that it is used for 2 properties of the estimation for these systems and to control these systems.
When kalman filter is compared with wiener filter, in concern to learn for the modern control engineering student a Kalman filter needed a less additional mathematical preparation.
The important and essential information for mathematically sound, for detecting and rejecting anomalous calculations, statistically-based decision methods are used and to provide with the help of kalman filter.
4.5 Process to be estimated:
After invoking some of the introduction and some of the advantages that will obtain with the use of kalman filter, now we can have a sight at the magnificent filter process. The process starts with the addresses of a common problem. This is going to attempt to estimate the state of discrete-time controlled process that is to be controlled by a linear stochastic difference equation:
4.6 Algorithm of Discrete Kalman Filter
This Algorithm of Discrete Kalman Filter section starts with a extensive overview, as well as the "high-level" operation of one type of the Discrete Kalman filter. Next the high-level representation is viewed; the focus to the specific equations is limited. They will be used in this discrete version of the filter. Actually in what way the Kalman filter works? Initially, by utilizing a type of feedback control loop a process will be estimated. By which the process state has been estimated by the filter later. Then in the form of measurements the feedback will be provided. The equations of the Kalman filter are divided into two groups. They are named as "Time Update equations" and "Measurement Update equations".
For analyzing, the time updates for the equations of the current state and error covariance estimates. And also it should have some responsibilities to get the estimates for the next time step. For the feed back the updated equations measurements are responsible that is to bond a recent measurement in to deductive estimate in order to get a progressive derived estimate (Clarke, 1986).
he "predictor" equations are also be considered by the equations which are updated with time. This can also be done when the equations which are updated with measurement and that can be considered as "corrector" equations. In general, the loop process of the algorithm of final estimation to be as such as algorithm of predictor-corrector. This will help to solve the problems numerically. It is represented in the following figure:
4.7 Filter Parameters and the Tuning
Generally the measurement noise covariance R is calculated before the execution takes place in the filter. It is also applicable in the real implementation of Kalman filter. In general the calculation of the measurement noise covariance R is ideally applicable because of the precision that the requirement wanted to be calculate the process noise covariance Q. it is capable to gather some of the samples of the off line measurements in order to declare the variation of the measurement noise.
Actually to determine the process noise covariance Q it is very difficult. This is caused because of the main reason that it is not able to notice it directly what the process is to be estimated (Devasirvatham, 1986).
Usually it is more difficult to determine the process noise covariance Q. This will be caused due to the main reason that it is not able to notice directly the process to be estimated. From time to time a simple (poor) process model can be generated and accepted results , if one "injects" sufficiently which is seemed to being uncertain into the process by means of the selection of the Q (usually , one can expect that the process measurements are suitable).
In the other case, for the parameter, a rational basis is selected or a rational basis is not selected for the parameters. Filter parameters Q and R are tuned in order to get the higher filter performance.
Finally we can conclude that, if the conditions of the Q and R are stable, both the estimation error covariance Pk and the Kalman gain kk will quickly stabled and also remain constant (Have a look at filter update equations in Fig 3.2). If this is the situation, there is need to pre-compute these parameters either by executing the filter off-line, or for sample by declaring the steady-state value of Pk as discussed in.
CHAPTER - 5
IMPLEMENTATION OF THE OFDM SYSTEM
5.1 OFDM System Implementation:
By making use of Matlab an OFDM system is designed in order to accept different type of parameters of the system to be altered and tested. The main aim is to executing the simulations in order to improve the measurements of OFDM under various channel conditions and also it is to be accepted for various OFDM configurations to be checked (Katedra, 1998).
5.2 OFDM Model which is being used:
5.2.1 Serial to Parallel Conversion:
The input serial data stream is converted into the word sized for transmission. Sample 2bit/word for QPSK, and converted into the parallel format. Then in the same direction information is transmitted by allocating each data word to one carrier during the transmission (Keenan, 1990).
5.2.2 Modulation of Data:
The data which has been transmitted on each carrier then it will be encoded with previous symbols, and then mapped into a phase shift-keying format. Since initial phase reference requires a differential encoding for an extra symbol is added at the start for this purpose. Phase angle based on the modulation method on which data on each symbol is then mapped. For example QPSK the phase angles used are 0, 90, 180, and 270 degrees. The utilization of phase shift keying produces a constant amplitude signal and was chosen to reduce problems and for its simplicity with amplitude fluctuations due to fading (Blaunstein, 1998).
5.2.3 Inverse Fourier Transform:
An inverse Fourier transform is used to find the corresponding time waveform (IFFT -Convert frequency domain signal to time domain signal) after the required spectrum is worked out. At the start of each symbol the guard period is then added.
5.2.4 Guard Period:
Based up on the two sections, the guard period has being designed. First half of the portion of the guard is referred as zero amplitude transmission. The second part of the i.e., second half of the portion of the guard period is referred as cyclic extension of the symbol to be transmitted. To accept this symbol timing it is to be freely regained by envelope detection (Kanatas, 1997).
What ever the case may be, it is represented that in any of the simulations this guard period is not needed. For the position of the samples the timing should be exactly declared. COFDM will act as a modulation method with the help of a CDMA for the wireless telecommunications. If additionally the guard is added later, then the symbols are formatted back to a serial time waveform. Then this will act as the base band signal for the OFDM transmission.
5.2.5 The Channel:
The implementation of the transmitted signal is done by the channel model. This channel model accepts the signal to multipath, noise ratio, and peak power clipping which is to be controlled. By combining a known amount of white noise to the transmitted signal the signal to noise ratio is fixed. Simultaneously the delay spread is making use of an FIR filter then the Multipath delay spread will be added. The maximum delay spread is indicated by the FIR filter length. The coefficient amplitude shows the reflected signal magnitude.
Actually, receiver has done the opposite operation to the transmitter. The guard period which is there will be moved away. Then to identify the original transmitted spectrum the FFT of each symbol is utilized. Each and every transmission carrier phase angle is evaluated and converted in to data word by the received phase demodulation. Then these data words are combined back to become the identical word size as such as the original data (Rappaport, 1991).
From the above diagram we can clearly say that the bit error goes on decreasing with the increase in the signal to noise ratio. We can also see that it converges to zero very fast if there are more pilots signals. This figure is attained with N=256 and SNR is being varied from 0 to 10 db and for the different pilot signals. The below figure is also with the same variation but with N=128. Here we can also see that BER reduces to zero with more number of pilot signals at a very fast rate.
The main aim of this document is to provide a deep view of the power of the OFDM transmission scheme. It not only provided the clear description of the transmission scheme itself, but also provided the issues that occur in mobile communications and also the methods to solve them.
Digital communications is a quickly progressed industry. In this technology, Orthogonal Frequency Division Multiplexing is leading a great position. OFDM will prove to bring about a radical change in mobile communications by accepting it to be more suitable and powerfully built while holding a high date rate which is demanded by the digital communications.
* Prasad, R. Oct. 27-28. 1993. "An overview of millimeter waves for future personal Wireless Communication Systems", Proc. IEEE First symposium on communications and vehicular technology in the Benelux, K3, Delft, Netherlands.
* Van Verkeer en Waterstaat. 1993. Hoofddirectie Telecommunicatie en Post, Frequency allocations in the Netherlands, 2nd edition, Groningen.
* Chang, R.W. December 1966"Synthesis of Band-Limited Orthogonal Signals for Multichannel Data Transmission", Bell Syst. Tech. J., vol.45, pp. 1775-1796.
* Salzberg, B.R. Dec. 1967. "Performance of an efficient parallel data transmission system", IEEE Trans.Commun. Technol., vol. COM-15, pp. 805-813.
* Weinstein, S.B. and Ebert, P.M. Oct. 1971. "Data transmission by frequency-division multiplexing using the discrete Fourier transform", IEEE Trans. Commun. Technol., vol. COM-19, pp. 628-634.
* Van den Enden, A.W.M and N.A.M. Verhoeckx, N.A.M. 1989. Discrete-time signal processing: an introduction. London: Prentice Hall Int. ISBN 0-13-216763-8.
* Oppenheim, A.V. and Schaffer, R.W. 1989. Discrete -time signal processing, Prentice-Hall International. ISBN 0-13-216771-9.
* Cimini, L.J. July 1985. "Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing", IEEE Trans. Commun., vol. COM-33, pp. 665-675.
* Zou, W.Y. and Wu, Y. March 1995. "COFDM: An overview", IEEE Trans. Broadc., vol. 41, no. 1, pp. 1-8.
* Shelswell, P. June 1995. "The COFDM modulation system: The heart of digital audio broadcasting", Electronics & communication engineering journal, pp. 127-136.
* Telebit Corporation. Sept. 1989. "Comparative performance results for asymmetrical duplex, V.32 (extended), and multicarrier modems", CCITT SG XVII, contribution D56. Introduction to OFDM, II edition 18 10/30/98/TUD-TVS.
* Alard, M. and Lassalle, R. Aug. 1987. "Principles of modulation and channel coding for digital broadcasting for mobile receivers", EBU Review, no. 224, pp. 3-25.
* Thibault, L. and Le, M.T. March 1997. "Performance Evaluation of COFDM for Digital Audio Broadcasting, Part I: Parametric Study", IEEE Transactions on Broadcasting, Vol. 43, No. 1, pages 64-75.
* Wahlqvist, M., stberg, C., Beek, J., Edfors, O and Brjesson, P. May 1996. "A Conceptual Study of OFDM-based Multiple Access Schemes", Technical Report Tdoc 117/96, ETSI STC SMG2 meeting no 18, Helsinki, Finland.
* Lee, D and Cheun, K. August 1997. "A new symbol timing recovery algorithm for OFDM systems", IEEE Transactions on Consumer Electronics, Vol. 43, No. 3, pages 766-775.
* Moose, P. October 1994. "A Technique for Orthogonal Frequency Division Multiplexing Frequency Offset Correction", IEEE Transactions on Communications, Vol. 42, No. 10, pages 2908-2914.
* Cooley, J.W and Tukey, J.W. 1965. An algorithm for the machine calculation of complex Fourier series, Mathematics of Computation, pp. 297-301.
* Frigo, M. 1998. FFTW: adaptive software architecture for the FFT, in Proceedings of the 1998 IEEE International Conference on Acoustics Speech and Signal Processing, http://www.fftw.org.
* Johnson, S.G. Links to FFT-related resources. http://www.fftw.org/links.html
* Solar Influences Data Center, Sunspot archive and graphics. http://sidc.oma.be
* Van Loan, C. 1992. Computational Frameworks for the Fast Fourier Transform, SIAM, Philadelphia.
* Bertoni, H.L. 2000. Radio Propagation for Modern Wireless Systems, Prentice Hall PTR, New Jersey.
* Blaunstein, N. 2004. Wireless Communication Systems, Handbook of Engineering Electromagnetics, Ch. 12, 417-489, Marcel Dekker, NY.
* Rappaport, T.S. 1999. Wireless Communications, Prentice Hall PTR, NewYork, 1996.
* Saunders, S.R. 1989. Antennas and Propagation for Wireless Communication Systems, J. Wiley & Sons, New York.
* Cox, D.C., Murray, R.R and Norris, A.W. 1983. "Measurements of 800MHz radio transmission into buildings with metallic walls," AT&T Bell Lab. Tech. J., Vol. 62, 2695-2717.
* Davidson, A. and Hill, C. 1997. "Measurement of building penetration into medium building at 900 and 1500 MHz," IEEE Trans. Veh. Technol., Vol. 46, 161-167.
* Turkmani, A.M.D. and de Toledo,A.F. 1993. "Modeling of radio transmission into and within multistory buildings at 900, 1800, and 2300 MHz," IEE Proc.-1, Vol. 40, 462-470.
* Alexander, S.E.M. 1982. "Radio propagation within buildings at 900 MHz," Electronics Letters, Vol. 18, No. 21, 913-914.
* Hashemi, H. 1993 "The indoor radio propagation channel," Proc. IEEE, Vol. 81, No. 7, 943-968.
* Lemieux, J.F., Tanany, M. and Hafez, H.M. 1991. "Experimental evaluation of space/frequency/polarization diversity in the indoor wireless channel," IEEE Trans. Veh. Technol., Vol. 40, No. 3, 569- 574.
* Rappaport, T. S. 1989. "Characterization of UHF multipath radio channels in factory buildings," IEEE Trans. Antennas Propagat., Vol. 37, No. 8, 1058-1069.
* Devasirvatham, D.M., Krain, M.J. and Rappaport, T.S. 1990. "Radio propagation measurements at 850 MHz, 1.7 GHz, and 4.0 GHz inside two dissimilar office buildings," Electronics Letters, Vol. 26, No. 7, 445-447.
* Rappaport, T. S. and Hawbaker, D.A. 1992. "Wide-band microwave propagation parameters using cellular and linear polarized antennas for indoor wireless channels," IEEE Trans. On Communications, Vol. 40, No. 2, 231-242.
* Tarng, J. H., Chang, W.R. and Hsu, B.J. 1997. "Three-dimensional modeling of 900MHz and 2.44 GHz radio propagation in corridors," IEEE Trans. Veh. Technol., Vol. 46, 519-526.
* Gibson, T. B. and Jenn, D.C. 1999. "Prediction and measurements of wall intersection loss," IEEE Trans. Antennas Propagat., Vol. 47, 55-57.
* Lafortune, J.F. and Lecours, M. 1990. "Measurement and modeling of propagation losses in a building at 900 MHz," IEEE Trans. Veh. Technol., Vol. 39, 101-108.
* Arnold, H. W., Murray, R.R. and D. C. Cox, D.C. 1989. "815MHz radio attenuation measured within two commercial buildings," IEEE Trans. Antennas Propagat., Vol. 37, 1335-1339.
* Whitman, G.M., Kim, K.S. and Niver, E. 1995. "A theoretical model progress in Electromagnetics Research, PIER 59, 2006 173 for radio signal attenuation inside buildings," IEEE Trans. Veh. Technol., Vol. 44, 621-629.
* Seidel, S.Y. 1994. "Site-specific propagation prediction for wireless in-building personal communication system design," IEEE Trans. Veh. Technol., Vol. 43, 879-891.
* Rappaport, T.S. 1992. "914MHz path loss prediction models for indoor wireless communication in multifloored buildings," IEEE Trans. Antennas Propagat., Vol. 40, No. 2, 207- 217.
* Honcharenko, W., Bertoni, H.L., Qian, J. and Lee, H.D. 1992-1993. "Mechanisms governing UHF propagation on single floors in modern office buildings," IEEE Trans. Veh. Technol., Vol. 41, No. 4, 496-504.
* Dersch, U. and Zollinger, E. 1994. "Propagation mechanisms in microcell and indoor environments," IEEE Trans. Veh. Technol., Vol. 43, 1058-1066.
* Clarke, R.H. 1968. "A statistical theory of mobile-radio reception," Bell Systems Technical Journal, Vol. 47, 957-1000.
* et al, T.L. 1991. "Statistical channel impulse response models for factory and open plan building communication system design," IEEE Trans. on Communications, Vol. 39, No. 5, 794-805.
* Devasirvatham, D.M.J. 1986. "Time delay spread and signal level measurements of 850 MHz radio waves in building environments," IEEE Trans. Antennas Propagat., Vol. 34, No. 2, 1300-1305.
* Rappaport, T.S. and Fung, V. 1991. "Simulation of bit error performance of FSK, BPSK, and p/4-DQPSK in flat fading indoor radio channels using measurement-based channel model," IEEE Trans. Veh. Technol., Vol. 40, No. 4, 731-739.
* Kanatas, A.G., Kountouris,.I.D., Kostraras, G.B. and Constantinou, P. 1997. "A UTD propagation model in urban microcellular environments," IEEE Trans. Veh. Technol., Vol. 46, No. 2, 185-193.
* Katedra, M.F., Perez, J., de Adana, F.S. and Gutierrez, O. 1998. "Efficient ray-tracing techniques for three-dimensional analysis of propagation in mobile communications: application to picocell and microcell scenarios," IEEE Antennas Propagat. Magazine, Vol. 40, No. 2, 15-28.
* Kim, S.C., Guarino, B.J., Willis, T.M., et al, T.L. 1999. "Radio propagation measurements and prediction using three dimensional ray tracing in urban environments at 908MHz and 1.9 GHz," IEEE Trans. Veh. Technol., Vol. 48, 931-946.
* Keenan, J. M. and Motley, A.J. 1990. "Radio coverage in buildings," BT Tech. J., Vol. 8, No. 1, 19-24.
* Blaunstein, N. 1998. "Average field attenuation in the non-regular impedance street waveguide," IEEE Trans. on Antennas Propagation, Vol. 46, No. 12, 1782-1789.