The Power of Fate vs. Free

The Power of Fate vs. Free Will Essay 1001 Nights has many stories, with the same theme fate vs. free will. In these stories several characters have to deal with the choices they make and their outcome. What is fate verse free will? Fate could be more destined to happen, as free will could be the ability to do what you want, and pursue your interests. In the story, aâ‚ ¬? The Enchanted Horse,aâ‚ ¬? it was either fate or free will of man that decided the outcome of the story. In ancient times fate was considered to be part of life. Almost every aspect of life was based upon fate. An example of fate in aâ‚ ¬? The Enchanted Horse,aâ‚ ¬? would be when the king did not allow the Indianaâ‚ ¬Ã¢â€ž ¢s reward to marry the princess, so the Indian tricked the Prince into riding the horse. The Indian was locked away in prison by the King for allowing the prince to leave on the magic horse, Well, your head shall answer for it, returned the monarch, and if in three months he is not safe back with me, or at any rate does not send me news of his safety, your life shall pay the penalty. So saying, he ordered his guards to seize the Indian and throw him into prison. (Lane Pg 1). This quote from the story shows how this story could be choosing fate for not only the prince but also the Indian. This quote once said by someone can relate to this topic and story in several ways: It is my fate to control my destiny, and it is my destiny to control my fate, People have free will and can decide how their life turns out. Regarding kings, magic, and genies, mankind has the ability to control their lives. In the story the prince had the choice to fly around or go back home after discovering the switch on the horses neck but chose to find a princess instead. He then remembered that he had never waited to ask how he was to get back to again, and understood the danger in which he stood. Luckily, he did not lose his head, and set about examining the horses neck with great care, till at last, to his intense joy, he discovered a tiny little peg, much smaller than the other, close to the right ear. This he turned, and found him-self dropping to the earth, though more slowly than he had left it. (Lane pg 2) Towards the end of the story he won over the princess by beating the kings large army. By the prince choosing free will he chose a cause and effect to take place. He chose to find a princess instead of willing able to return home. After reading the story it was hard to distinguish which is best, fate or free will. It is the enchanting story that keeps you wondering which will it be. Fate and free will both decide the turn out of the prince in this story. With the help of the magic, trickery, and kings in the story, that helped show the themes of fate and free will.

High Performance Wireless Telecommunications Modulation

High Performance Wireless Telecommunications Modulation Introduction The primary goal of the project is to analyze of OFDM system and to assess the suitability of OFDM as a modulation technique for wireless communications. In the part of project is covered two leading successfully implementation of OFDM based technologies are Digital Video Broadcasting (DVB-T and DVB-H) and Long Term Evolution (LTE advanced for 4G). Wireless communications is an emerging field, which has seen enormous growth in the last several years. The huge uptake rate of mobile phone technology, Wireless Local Area Networks (WLAN) and the exponential growth of the Internet have resulted in an increased demand for new methods of obtaining high capacity wireless networks. For cellular mobile applications, we will see in the near future a complete convergence of mobile phone technology, computing, Internet access, and potentially many multimedia applications such as video and high quality audio. In fact, some may argue that this convergence has already largely occurred, with the advent of being able to send and receive data using a notebook computer and a mobile phone. The goal of third and fourth generation mobile networks is to provide users with a high data rate, and to provide a wider range of services, such as voice communications, videophones, and high speed Internet access. The higher data rate of future mobile networks will be achieved by increasing the amount of spectrum allocated to the service and by improvements in the spectral efficiency. OFDM is a potential candidate for the physical layer of fourth generation mobile systems. Basic Principles of OFDM OFDM overview The Orthogonal Frequency Division Multiplexing (OFDM) is a modulation technique where multiple low data rate carriers are combined by a transmitter to form a composite high data rate transmission. The first commercial use of OFDM in the communication field was in the 1980s, and it was later widely used in the broadcast audio and video field in the 1990s in such areas as, ADSL, VHDSL, ETSI standard digital audio broadcast (DAB), digital video broadcast (DVB), and high-definition digital TV (HDTV). Digital signal processing makes OFDM possible. To implement the multiple carrier scheme using a bank of parallel modulators would not be very efficient in analog hardware. However, in the digital domain, multi-carrier modulation can be done efficiently with currently available DSP hardware and software. Not only can it be done, but it can also be made very flexible and programmable. This allows OFDM to make maximum use of available bandwidth and to be able to adapt to changing system requirements. Figure 1 is illustrated, Instead of separate modulators; the outgoing waveform is created by executing a high-speed inverse DFT on a set of time-samples of the transmitted data (post modulation). The output of the DFT can be directly modulated onto the outgoing carrier, without requiring any other components. Each carrier in an OFDM system is a sinusoid with a frequency that is an integer multiple of a base or fundamental sinusoid frequency. Therefore, each carrier is like a Fourier series component of the composite signal. In fact, it will be shown later that an OFDM signal is created in the frequency domain, and then transformed into the time domain via the Discrete Fourier Transform (DFT). Two periodic signals are orthogonal when the integral of their product, over one period, is equal to zero. This is true of certain sinusoids as illustrated in Equation 1. Definition of Orthogonal The carriers of an OFDM system are sinusoids that meet this requirement because each one is a multiple of a fundamental frequency. Each one has an integer number of cycles in the fundamental period. [2, 145-153; 6] The importantance of being orthogonal The main concept in OFDM is orthogonality of the sub-carriers.Since the carriers are all sine/cosine wave, we know that area under one period of a sine or a cosine wave is zero. Lets take a sine wave of frequency m and multiply it by a sinusoid (sine or a cosine) of a frequency n, where both m and n are integers. The integral or the area under this product is given by These two components are each a sinusoid, so the integral is equal to zero over one period. When we multiply a sinusoid of frequency n by a sinusoid of frequency m/n the area under the product is zero. In general for all integers n and m , sin(mx), cos(mx), cos(nx) , sin(nx) are all orthogonal to each other. These frequencies are called harmonics. Making the subcarriers mathematically orthogonal was a breakthrough for OFDM because it enables OFDM receivers to separate the subcarriers via an FFT and eliminate the guard bands. As figure 3 shows, OFDM subcarriers can overlap to make full use of the spectrum, but at the peak of each subcarrier spectrum, the power in all the other subcarriers is zero. OFDM therefore offers higher data capacity in a given spectrum while allowing a simpler system design. Creating orthogonal subcarriers in the transmitter is easy using an inverse FFT. To ensure that this orthogonality is maintained at the receiver (so that the subcarriers are not misaligned), the system must keep the transmitter and receiver clocks closely synchronizedwithin 2 parts per million in 802.11a systems. The 802.11a standard therefore dedicates four of its 52 subcarriers as pilots that enable phase-lock loops in the receiver to track the phase and frequency of the incoming signal. The 802.11a standard therefore dedicates four of its 52 subcarriers as pilots that enable phase-lock loops in the receiver to track the phase and frequency of the incoming signal. This method also eliminates low-frequency phase noise.Separating the subcarriers via an FFT require about an order of magnitude fewer multiply-accumulate operations than individually filtering each carrier. In general, an FFT implementation is much simpler than the RAKE receivers used for CDMA and the decision-feedback equalizers for TDMA.This idea are key to understanding OFDM. The orthogonality allows simultaneously transmission on a lot of sub- carriers in a tight frequency space without interference form each other. In essence this is similar to CDMA, where codes are used to make data sequences independent (also orthogonal) which allows many independent users to transmitin same space successfully.[2, 153-154; 6 ; 7] OFDM Operation Preliminary Concepts When the DFT (Discrete Fourier Transform) of a time signal is taken, the frequency domain results are a function of the time sampling period and the number of samples as shown in Figure 4. The fundamental frequency of the DFT is equal to 1/NT (1/total sample time). Each frequency represented in the DFT is an integer multiple of the fundamental frequency. Parameter Mapping from Time to Frequency for the DFT The maximum frequency that can be represented by a time signal sampled at rate 1/T is fmax = 1/2T as given by the Nyquist sampling theorem. This frequency is located in the center of the DFT points. All frequencies beyond that point are images of the representative frequencies. The maximum frequency bin of the DFT is equal to the sampling frequency (1/T) minus one fundamental (1/NT).The IDFT (Inverse Discrete Fourier Transform) performs the opposite operation to the DFT. It takes a signal defined by frequency components and converts them to a time signal. The parameter mapping is the same as for the DFT. The time duration of the IDFT time signal is equal to the number of DFT bins (N) times the sampling period (T).It is perfectly valid to generate a signal in the frequency domain, and convert it to a time domain equivalent for practical use (The frequency domain is a mathematical tool used for analysis. Anything usable by the real world must be converted into a real, time domain signal). This is how modulation is applied in OFDM. In practice the Fast Fourier Transform (FFT) and IFFT are used in place of the DFT and IDFT, so all further references will be to FFT and IFFT.[1 ,118 ; 4] Definition of Carriers The maximum number of carriers used by OFDM is limited by the size of the IFFT. This is determined as follows in Equation 2. OFDM Carrier Count In order to generate a real-valued time signal, OFDM (frequency) carriers must be defined in complex conjugate pairs, which are symmetric about the Nyquist frequency (fmax). This puts the number of potential carriers equal to the IFFT size/2. The Nyquist frequency is the symmetry point, so it cannot be part of a complex conjugate pair. The DC component also has no complex conjugate. These two points cannot be used as carriers so they are subtracted from the total available. If the carriers are not defined in conjugate pairs, then the IFFT will result in a time domain signal that has imaginary components. This must be a viable option as there are OFDM systems defined with carrier counts that exceed the limit for real-valued time signals given in Equation 2.In general, a system with IFFT size 256 and carrier count 216. This design must result in a complex time waveform. Further processing would require some sort of quadrature technique (use of parallel sine and cosine processing paths). In this report, only real-value time signals will be treated, but in order to obtain maximum bandwidth efficiency from OFDM, the complex time signal may be preferred (possibly an analogous situation to QPSK vs. BPSK). Equation 2, for the complex time waveform, has all IFFT bins available as carriers except the DC bin. Both IFFT size and assignment (selection) of carriers can be dynamic. The transmitter and receiver just have to use the same parameters. This is one of the advantages of OFDM. Its bandwidth usage (and bit rate) can be varied according to varying user requirements. A simple control message from a base station can change a mobile units IFFT size and carrier selection.[2,199-206; 4] Modulation Binary data from a memory device or from a digital processing stream is used as the modulating (baseband) signal. The following steps may be carried out in order to apply modulation to the carriers in OFDM: combine the binary data into symbols according to the number of bits/symbol selected convert the serial symbol stream into parallel segments according to the number of carriers, and form carrier symbol sequences apply differential coding to each carrier symbol sequence convert each symbol into a complex phase representation assign each carrier sequence to the appropriate IFFT bin, including the complex conjugates take the IFFT of the result OFDM modulation is applied in the frequency domain. Figure 5 and Figure 6 give an example of modulated OFDM carriers for one symbol period, prior to IFFT. OFDM Carrier Magnitude prior to IFFT For this example, there are 4 carriers, the IFFT bin size is 64, and there is only 1 bit per symbol. The magnitude of each carrier is 1, but it could be scaled to any value. The phase for each carrier is either 0 or 180 degrees, according to the symbol being sent. The phase determines the value of the symbol (binary in this case, either a 1 or a 0). In the example, the first 3 bits (the first 3 carriers) are 0, and the 4th bit (4th carrier) is a 1. OFDM Carrier Phase prior to IFFT Note that the modulated OFDM signal is nothing more than a group of delta (impulse) functions, each with a phase determined by the modulating symbol. In addition, note that the frequency separation between each delta is proportional to 1/N where N is the number of IFFT bins. The frequency domain representation of the OFDM is described in Equation 3. OFDM Frequency Domain Representation (one symbol period) After the modulation is applied, an IFFT is performed to generate one symbol period in the time domain. The IFFT result is shown in 7. It is clear that the OFDM signal has varying amplitude. It is very important that the amplitude variations be kept intact as they define the content of the signal. If the amplitude is clipped or modified, then an FFT of the signal would no longer result in the original frequency characteristics, and the modulation may be lost. This is one of the drawbacks of OFDM, the fact that it requires linear amplification. In addition, very large amplitude peaks may occur depending on how the sinusoids line up, so the peak-to-average power ratio is high. This means that the linear amplifier has to have a large dynamic range to avoid distorting the peaks. The result is a linear amplifier with a constant, high bias current resulting in very poor power efficiency. OFDM Signal, 1 Symbol Period Figure 8 is provided to illustrate the time components of the OFDM signal. The IFFT transforms each complex conjugate pair of delta functions (each carrier) into a real-valued, pure sinusoid. Figure 8 shows the separate sinusoids that make up the composite OFDM waveform given in Figure 7. The one sinusoid with 180 phase shift is clearly visible as is the frequency difference between each of the 4 sinusoids. Transmission The key to the uniqueness and desirability of OFDM is the relationship between the carrier frequencies and the symbol rate. Each carrier frequency is separated by a multiple of 1/NT (Hz). The symbol rate (R) for each carrier is 1/NT (symbols/sec). The effect of the symbol rate on each OFDM carrier is to add a sin(x)/x shape to each carriers spectrum. The nulls of the sin(x)/x (for each carrier) are at integer multiples of 1/NT. The peak (for each carrier) is at the carrier frequency k/NT. Therefore, each carrier frequency is located at the nulls for all the other carriers. This means that none of the carriers will interfere with each other during transmission, although their spectrums overlap. The ability to space carriers so closely together is very bandwidth efficient. OFDM Time Waveform Figure 9 shows the OFDM time waveform for the same signal. There are 100 symbol periods in the signal. Each symbol period is 64 samples long (100 x 64 = 6400 total samples). Each symbol period contains 4 carriers each of which carries 1 symbol. Each symbol carries 1 bit. Note that Figure 9 again illustrates the large dynamic range of the OFDM waveform envelope. OFDM Spectrum Figure 10 shows the spectrum for of an OFDM signal with the following characteristics: 1 bit / symbol 100 symbols / carrier (i.e. a sequence of 100 symbol periods) 4 carriers 64 IFFT bins spectrum averaged for every 20 symbols (100/20 = 5 averages) Red diamonds mark all of the available carrier frequencies. Note that the nulls of the spectrums line up with the unused frequencies. The four active carriers each have peaks at carrier frequencies. It is clear that the active carriers have nulls in their spectrums at each of the unused frequencies (otherwise, the nulls would not exist). Although it cannot be seen in the figure, the active frequencies also have spectral nulls at the adjacent active frequencies. It is not currently practical to generate the OFDM signal directly at RF rates, so it must be up converted for transmission. To remain in the discrete domain, the OFDM could be upsampled and added to a discrete carrier frequency. This carrier could be an intermediate frequency whose sample rate is handled by current technology. It could then be converted to analog and increased to the final transmit frequency using analog frequency conversion methods. Alternatively, the OFDM modulation could be immediately converted to analog and directly increased to the desired RF transmits frequency. Either way, the selected technique would have to involve some form of linear AM (possibly implemented with a mixer). [1, 122-125; 6] Reception and Demodulation The received OFDM signal is down converted (in frequency) and taken from analog to digital. Demodulation is done in the frequency domain (just as modulation was). The following steps may be taken to demodulate the OFDM: partition the input stream into vectors representing each symbol period take the FFT of each symbol period vector extract the carrier FFT bins and calculate the phase of each calculate the phase difference, from one symbol period to the next, for each carrier decode each phase into binary data sort the data into the appropriate order OFDM Carrier Magnitude following FFT Figure 11 and Figure 12 show the magnitude and spectrum of the FFT for one received OFDM symbol period. For this example, there are 4 carriers, the IFFT bin size is 64, there is 1 bit per symbol, and the signal was sent through a channel with AWGN having an SNR of 8 dB. The figures show that, under these conditions, the modulated symbols are very easy to recover. OFDM Carrier Phase following FFT In Figure 12 that the unused frequency bins contain widely varying phase values. These bins are not decoded, so it does not matter, but the result is of interest. Even if the noise is removed from the channel, these phase variations still occur. It must be a result of the IFFT/FFT operations generating very small complex values (very close to 0) for the unused carriers. The phases are a result of these values. [1, 125 -128; 3] OFDM transceiver OFDM signals are typically generated digitally due to the difficulty in creating large banks of phase lock oscillators and receivers in the analog domain. Figure 13 shows the block diagram of a typical OFDM transceiver. The transmitter section converts digital data to be transmitted, into a mapping of subcarrier amplitude and phase. It then transforms this spectral representation of the data into the time domain using an Inverse Discrete Fourier Transform (IDFT). The Inverse Fast Fourier Transform (IFFT) performs the same operations as an IDFT, except that it is much more computationally efficiency, and so is used in all practical systems. In order to transmit the OFDM signal the calculated time domain signal is then mixed up to the required frequency. Block diagram showing a basic OFDM transceiver [3] The receiver performs the reverse operation of the transmitter, mixing the RF signal to base band for processing, then using a Fast Fourier Transform (FFT) to analyze the signal in the frequency domain. The amplitude and phase of the subcarriers is then picked out and converted back to digital data. The IFFT and the FFT are complementary function and the most appropriate term depends on whether the signal is being received or generated. In cases where the Signal is independent of this distinction then the term FFT and IFFT is used interchangeably. [1, 125 -128, 3] Analysis of OFDM characteristics Guard Period OFDM demodulation must be synchronized with the start and end of the transmitted symbol period. If it is not, then ISI will occur (since information will be decoded and combined for 2 adjacent symbol periods). ICI will also occur because orthogonality will be lost (integrals of the carrier products will no longer be zero over the integration period), To help solve this problem, a guard interval is added to each OFDM symbol period. The first thought of how to do this might be to simply make the symbol period longer, so that the demodulator does not have to be so precise in picking the period beginning and end, and decoding is always done inside a single period. This would fix the ISI problem, but not the ICI problem. If a complete period is not integrated (via FFT), orthogonality will be lost. The effect of ISI on an OFDM signal can be further improved by the addition of a guard period to the start of each symbol. This guard period is a cyclic copy that extends the length of the symbol waveform. Each subcarrier, in the data section of the symbol, (i.e. the OFDM symbol with no guard period added, which is equal to the length of the IFFT size used to generate the signal) has an integer number of cycles. Because of this, placing copies of the symbol end-to-end results in a continuous signal, with no discontinuities at the joins. Thus by copying the end of a symbol and appending this to the start results in a longer symbol time. Addition of a guard period to an OFDM signal [3] In Figure 14, The total length of the symbol is Ts=TG + TFFT, where Ts is the total length of the symbol in samples, TG is the length of the guard period in samples, and TFFT is the size of the IFFT used to generate the OFDM signal. In addition to protecting the OFDM from ISI, the guard period also provides protection against time-offset errors in the receiver. For an OFDM system that has the same sample rate for both the transmitter and receiver, it must use the same FFT size at both the receiver and transmitted signal in order to maintain subcarrier orthogonality. Each received symbol has TG + TFFT samples due to the added guard period. The receiver only needs TFFT samples of the received symbol to decode the signal. The remaining TG samples are redundant and are not needed. For an ideal channel with no delay spread the receiver can pick any time offset, up to the length of the guard period, and still get the correct number of samples, without crossing a symbol boundary. Function of the guard period for protecting against ISI [3] Figure 15 shows this effect. Adding a guard period allows time for the transient part of the signal to decay, so that the FFT is taken from a steady state portion of the symbol. This eliminates the effect of ISI provided that the guard period is longer than the delay spread of the radio channel. The remaining effects caused by the multipath, such as amplitude scaling and phase rotation are corrected for by channel equalization. In order to avoid ISI and ICI, the guard period must be formed by a cyclic extension of the symbol period. This is done by taking symbol period samples from the end of the period and appending them to the front of the period. The concept of being able to do this, and what it means, comes from the nature of the IFFT/FFT process. When the IFFT is taken for a symbol period (during OFDM modulation), the resulting time sample sequence is technically periodic. This is because the IFFT/FFT is an extension of the Fourier Transform which is an extension of the Fourier Series for periodic waveforms. All of these transforms operate on signals with either real or manufactured periodicity. For the IFFT/FFT, the period is the number of samples used. Guard Period via Cyclic Extension With the cyclic extension, the symbol period is longer, but it represents the exact same frequency spectrum. As long as the correct number of samples are taken for the decode, they may be taken anywhere within the extended symbol. Since a complete period is integrated, orthogonality is maintained. Therefore, both ISI and ICI are eliminated. Note that some bandwidth efficiency is lost with the addition of the guard period (symbol period is increased and symbol rate is decreased) [2,154-160, 3] Windowing The OFDM signal is made up of a series of IFFTs that are concatenated to each other. At each symbol period boundary, there is a signal discontinuity due to the differences between the end of one period and the start of the next. These discontinuities can cause high frequency spectral noise to be generated (because they look like very fast transitions of the time waveform). To avoid this, a window function (Hamming, Hanning, Blackman, ) may be applied to each symbol period. The window function would attenuate the time waveform at the start and the end of each period, so that the discontinuities are smaller, and the high frequency noise is reduced. However, this attenuation distorts the signal and some of the desired frequency content is lost.[1, 121;2 154] Multipath Characteristics OFDM avoids frequency selective fading and ISI by providing relatively long symbol periods for a given data rate. This is illustrated in Figure 17. For a given transmission channel and a given source data rate, OFDM can provide better multipath characteristics than a single carrier. OFDM vs. Single Carrier, Multipath Characteristic Comparison However, since the OFDM carriers are spread over a frequency range, there still may be some frequency selective attenuation on a time-varying basis. A deep fade on a particular frequency may cause the loss of data on that frequency for a given time, but the use of Forward Error Coding can fix it. If a single carrier experienced a deep fade, too many consecutive symbols may be lost and correction coding may be ineffective. [8] Bandwidth A comparison of RF transmits bandwidth between OFDM and a single carrier is shown in Figure 18 (using the same example parameters as in Figure 17). OFDM Bandwidth Efficiency In Figure 18, the calculations show that OFDM is more bandwidth efficient than a single carrier. Note that another efficient aspect of OFDM is that a single transmitters bandwidth can be increased incrementally by addition of more adjacent carriers. In addition, no bandwidth buffers are needed between transmit bandwidths of separate transmitters as long as orthogonality can be maintained between all the carriers.[2, 161-163; 8; 9] Physical Implementation Since OFDM is carried out in the digital domain, there are many ways it can be implemented. Some options are provided in the following list. Each of these options should be viable given current technology: ASIC (Application Specific Integrated Circuit) ASICs are the fastest, smallest, and lowest power way to implement OFDM Cannot change the ASIC after it is built without designing a new chip General-purpose Microprocessor or MicroController PowerPC 7400 or other processor capable of fast vector operations Highly programmable Needs memory and other peripheral chips Uses the most power and space, and would be the slowest Field-Programmable Gate Array (FPGA) An FPGA combines the speed, power, and density attributes of an ASIC with the programmability of a general purpose processor. An FPGA could be reprogrammed for new functions by a base station to meet future (currently unknown requirements).This should be the best choice.[9] OFDM uses in DVB (Digital Video Broadcasting) DVB (Digital Video Broadcast) is a set of standards for the digital transmission of video and audio streams, and also data transmission. The DVB standards are maintained by the DVB Project, which is an industry-led consortium of over 260 broadcasters, manufacturers, network operators, software developers, regulatory bodies and others in over 35 countries. DVB has been implemented over satellite (DVB-S, DVB-S2), cable (DVB-C), terrestrial broadcasting (DVB-T), and handheld terminals (DVB-H). the DVB standard following the logical progression of signal processing steps, as well as source and channel coding, COFDM modulation, MPEG compression and multiplexing methods, conditional access and set-top box Technology. In this project is presented an investigation of two OFDM based DVB standards, DVB-T and DVB-H. DVB-T (Digital Video Broadcasting Terrestrial) The first Terrestrial Digital Video Broadcasting pilot transmissions were started in the late 90s, and the first commercial system was established in Great Britain. In the next few years the digital broadcasting system has been set up in many countries, and the boom of the digital terrestrial transmission is estimated in the next few years, while the analogue transmission will be cancelled within about 15 years. The greatest advantage of the digital system is the effective use of the frequency spectrum and its lower radiated power in comparison with the analogue transmission, while the covered area remains the same. Another key feature is the possibility of designing a so-called Single Frequency Network (SFN), which means that the neighboring broadcast stations use the same frequency and the adjacent signals dont get interfered. The digital system transmits a data stream, which means that not only television signals but data communication (e.g. Internet service) may be used according to the demands. The data stream consists of an MPEG-2 bit stream, which means a compression is used, enabling the transfer of even 4 or 5 television via the standard 8 MHz wide TV channel. For the viewer, the main advantages are the perfect, noise-free picture, CD quality sound, and easier handling, as well as services like Super Teletext, Electronic Programme Guide, interactivity and mobility.[11, 251-253] Modulation technique in DVB-T The DVB-T Orthogonal Frequency Division Multiplexing (OFDM) modulation system uses multi-carrier transmission. There are 2 modes, the so-called 2k and 8k modes, using 1705 and 6817 carriers respectively, with each carrier modulated separately and transmitted in the 8 MHz TV channel. The common modulation for the carriers is typically QPSK, 16-QAM or 64-QAM. Each signal can be divided into two, so-called „In Phase (I) and „Quadrature Phase components, being a 90Â ° phase shift between them. The constellation diagram and the bit allocation is shown in bellow 16-QAM constellation diagram and bit allocation [6] This modulation can be demonstrated in the constellation diagram, where the 2 axes represent the 2 components (I and Q). In case of using 16-QAM modulation, the number of states is 16, so 1 symbol represents 4 bits. [11, 255; 6; 14] Bir errors If we simulate all the carriers in the constellation diagram we get not just 1 discrete point, but many points, forming a „cloud and representing each state. In case of additive noise the „cloud gets bigger and the receiver may decide incorrectly, resulting in bit errors. Figure 2 shows the measured constellation diagram without and with additive noise. Measured 16-QAM constellation diagram a) without additive noise b) with additive noise [6] To ensure perfect picture quality, the DVB-T system uses a 2 level error correction (Reed-Solomon and Viterbi). This corrects the bad bits at an even 10-4 Bit Error Rate (BER) and enables error-free data transmission. [13, 32-36] The multi-carrier structure The structure of carriers can be illustrated also in the function of time (Figure 20). The horizontal axis is the frequency and the vertical axis is the time. The 8 MHz channel consists of many carriers, placed 4462 Hz or 1116 Hz far from each other according to the modulation mode (2k or 8k). Structure of OFDM carriers [13] There are some reserved, so-called Transmission Parameter Signalling (TPS) carriers that do not transfer payload, just provide transmission mode information for the receiver, so the total number of useful carriers is 1512 and 6048 respectively in the two transmission modes, and the resultant bit rate is between 4,97 and 31,66 Mbit/s, depending on the modulation (QPSK, 16-QAM or 64-QAM), the transmission mode (2k or 8k), the Code Rate (CR) used for error correction and the selected Guard Interval (GI). This guard interval means that there is a small time gap between each symbol, so the transmission is not continuous. This guarding time enables perfect reception by eliminating the errors caused by multipath propagation.[4, 79-90; 13] Frequency spectrum In 2k mode, 1705 carriers are modulated in the 8 MHz TV channel, so each carrier is 4462 Hz far from its neighbor, while in 8k mode this distance is 1116 Hz. In digital broadcasting, there are no vision and sound carriers, so the power for each carrier is the same. This mean High Performance Wireless Telecommunications Modulation High Performance Wireless Telecommunications Modulation Introduction The primary goal of the project is to analyze of OFDM system and to assess the suitability of OFDM as a modulation technique for wireless communications. In the part of project is covered two leading successfully implementation of OFDM based technologies are Digital Video Broadcasting (DVB-T and DVB-H) and Long Term Evolution (LTE advanced for 4G). Wireless communications is an emerging field, which has seen enormous growth in the last several years. The huge uptake rate of mobile phone technology, Wireless Local Area Networks (WLAN) and the exponential growth of the Internet have resulted in an increased demand for new methods of obtaining high capacity wireless networks. For cellular mobile applications, we will see in the near future a complete convergence of mobile phone technology, computing, Internet access, and potentially many multimedia applications such as video and high quality audio. In fact, some may argue that this convergence has already largely occurred, with the advent of being able to send and receive data using a notebook computer and a mobile phone. The goal of third and fourth generation mobile networks is to provide users with a high data rate, and to provide a wider range of services, such as voice communications, videophones, and high speed Internet access. The higher data rate of future mobile networks will be achieved by increasing the amount of spectrum allocated to the service and by improvements in the spectral efficiency. OFDM is a potential candidate for the physical layer of fourth generation mobile systems. Basic Principles of OFDM OFDM overview The Orthogonal Frequency Division Multiplexing (OFDM) is a modulation technique where multiple low data rate carriers are combined by a transmitter to form a composite high data rate transmission. The first commercial use of OFDM in the communication field was in the 1980s, and it was later widely used in the broadcast audio and video field in the 1990s in such areas as, ADSL, VHDSL, ETSI standard digital audio broadcast (DAB), digital video broadcast (DVB), and high-definition digital TV (HDTV). Digital signal processing makes OFDM possible. To implement the multiple carrier scheme using a bank of parallel modulators would not be very efficient in analog hardware. However, in the digital domain, multi-carrier modulation can be done efficiently with currently available DSP hardware and software. Not only can it be done, but it can also be made very flexible and programmable. This allows OFDM to make maximum use of available bandwidth and to be able to adapt to changing system requirements. Figure 1 is illustrated, Instead of separate modulators; the outgoing waveform is created by executing a high-speed inverse DFT on a set of time-samples of the transmitted data (post modulation). The output of the DFT can be directly modulated onto the outgoing carrier, without requiring any other components. Each carrier in an OFDM system is a sinusoid with a frequency that is an integer multiple of a base or fundamental sinusoid frequency. Therefore, each carrier is like a Fourier series component of the composite signal. In fact, it will be shown later that an OFDM signal is created in the frequency domain, and then transformed into the time domain via the Discrete Fourier Transform (DFT). Two periodic signals are orthogonal when the integral of their product, over one period, is equal to zero. This is true of certain sinusoids as illustrated in Equation 1. Definition of Orthogonal The carriers of an OFDM system are sinusoids that meet this requirement because each one is a multiple of a fundamental frequency. Each one has an integer number of cycles in the fundamental period. [2, 145-153; 6] The importantance of being orthogonal The main concept in OFDM is orthogonality of the sub-carriers.Since the carriers are all sine/cosine wave, we know that area under one period of a sine or a cosine wave is zero. Lets take a sine wave of frequency m and multiply it by a sinusoid (sine or a cosine) of a frequency n, where both m and n are integers. The integral or the area under this product is given by These two components are each a sinusoid, so the integral is equal to zero over one period. When we multiply a sinusoid of frequency n by a sinusoid of frequency m/n the area under the product is zero. In general for all integers n and m , sin(mx), cos(mx), cos(nx) , sin(nx) are all orthogonal to each other. These frequencies are called harmonics. Making the subcarriers mathematically orthogonal was a breakthrough for OFDM because it enables OFDM receivers to separate the subcarriers via an FFT and eliminate the guard bands. As figure 3 shows, OFDM subcarriers can overlap to make full use of the spectrum, but at the peak of each subcarrier spectrum, the power in all the other subcarriers is zero. OFDM therefore offers higher data capacity in a given spectrum while allowing a simpler system design. Creating orthogonal subcarriers in the transmitter is easy using an inverse FFT. To ensure that this orthogonality is maintained at the receiver (so that the subcarriers are not misaligned), the system must keep the transmitter and receiver clocks closely synchronizedwithin 2 parts per million in 802.11a systems. The 802.11a standard therefore dedicates four of its 52 subcarriers as pilots that enable phase-lock loops in the receiver to track the phase and frequency of the incoming signal. The 802.11a standard therefore dedicates four of its 52 subcarriers as pilots that enable phase-lock loops in the receiver to track the phase and frequency of the incoming signal. This method also eliminates low-frequency phase noise.Separating the subcarriers via an FFT require about an order of magnitude fewer multiply-accumulate operations than individually filtering each carrier. In general, an FFT implementation is much simpler than the RAKE receivers used for CDMA and the decision-feedback equalizers for TDMA.This idea are key to understanding OFDM. The orthogonality allows simultaneously transmission on a lot of sub- carriers in a tight frequency space without interference form each other. In essence this is similar to CDMA, where codes are used to make data sequences independent (also orthogonal) which allows many independent users to transmitin same space successfully.[2, 153-154; 6 ; 7] OFDM Operation Preliminary Concepts When the DFT (Discrete Fourier Transform) of a time signal is taken, the frequency domain results are a function of the time sampling period and the number of samples as shown in Figure 4. The fundamental frequency of the DFT is equal to 1/NT (1/total sample time). Each frequency represented in the DFT is an integer multiple of the fundamental frequency. Parameter Mapping from Time to Frequency for the DFT The maximum frequency that can be represented by a time signal sampled at rate 1/T is fmax = 1/2T as given by the Nyquist sampling theorem. This frequency is located in the center of the DFT points. All frequencies beyond that point are images of the representative frequencies. The maximum frequency bin of the DFT is equal to the sampling frequency (1/T) minus one fundamental (1/NT).The IDFT (Inverse Discrete Fourier Transform) performs the opposite operation to the DFT. It takes a signal defined by frequency components and converts them to a time signal. The parameter mapping is the same as for the DFT. The time duration of the IDFT time signal is equal to the number of DFT bins (N) times the sampling period (T).It is perfectly valid to generate a signal in the frequency domain, and convert it to a time domain equivalent for practical use (The frequency domain is a mathematical tool used for analysis. Anything usable by the real world must be converted into a real, time domain signal). This is how modulation is applied in OFDM. In practice the Fast Fourier Transform (FFT) and IFFT are used in place of the DFT and IDFT, so all further references will be to FFT and IFFT.[1 ,118 ; 4] Definition of Carriers The maximum number of carriers used by OFDM is limited by the size of the IFFT. This is determined as follows in Equation 2. OFDM Carrier Count In order to generate a real-valued time signal, OFDM (frequency) carriers must be defined in complex conjugate pairs, which are symmetric about the Nyquist frequency (fmax). This puts the number of potential carriers equal to the IFFT size/2. The Nyquist frequency is the symmetry point, so it cannot be part of a complex conjugate pair. The DC component also has no complex conjugate. These two points cannot be used as carriers so they are subtracted from the total available. If the carriers are not defined in conjugate pairs, then the IFFT will result in a time domain signal that has imaginary components. This must be a viable option as there are OFDM systems defined with carrier counts that exceed the limit for real-valued time signals given in Equation 2.In general, a system with IFFT size 256 and carrier count 216. This design must result in a complex time waveform. Further processing would require some sort of quadrature technique (use of parallel sine and cosine processing paths). In this report, only real-value time signals will be treated, but in order to obtain maximum bandwidth efficiency from OFDM, the complex time signal may be preferred (possibly an analogous situation to QPSK vs. BPSK). Equation 2, for the complex time waveform, has all IFFT bins available as carriers except the DC bin. Both IFFT size and assignment (selection) of carriers can be dynamic. The transmitter and receiver just have to use the same parameters. This is one of the advantages of OFDM. Its bandwidth usage (and bit rate) can be varied according to varying user requirements. A simple control message from a base station can change a mobile units IFFT size and carrier selection.[2,199-206; 4] Modulation Binary data from a memory device or from a digital processing stream is used as the modulating (baseband) signal. The following steps may be carried out in order to apply modulation to the carriers in OFDM: combine the binary data into symbols according to the number of bits/symbol selected convert the serial symbol stream into parallel segments according to the number of carriers, and form carrier symbol sequences apply differential coding to each carrier symbol sequence convert each symbol into a complex phase representation assign each carrier sequence to the appropriate IFFT bin, including the complex conjugates take the IFFT of the result OFDM modulation is applied in the frequency domain. Figure 5 and Figure 6 give an example of modulated OFDM carriers for one symbol period, prior to IFFT. OFDM Carrier Magnitude prior to IFFT For this example, there are 4 carriers, the IFFT bin size is 64, and there is only 1 bit per symbol. The magnitude of each carrier is 1, but it could be scaled to any value. The phase for each carrier is either 0 or 180 degrees, according to the symbol being sent. The phase determines the value of the symbol (binary in this case, either a 1 or a 0). In the example, the first 3 bits (the first 3 carriers) are 0, and the 4th bit (4th carrier) is a 1. OFDM Carrier Phase prior to IFFT Note that the modulated OFDM signal is nothing more than a group of delta (impulse) functions, each with a phase determined by the modulating symbol. In addition, note that the frequency separation between each delta is proportional to 1/N where N is the number of IFFT bins. The frequency domain representation of the OFDM is described in Equation 3. OFDM Frequency Domain Representation (one symbol period) After the modulation is applied, an IFFT is performed to generate one symbol period in the time domain. The IFFT result is shown in 7. It is clear that the OFDM signal has varying amplitude. It is very important that the amplitude variations be kept intact as they define the content of the signal. If the amplitude is clipped or modified, then an FFT of the signal would no longer result in the original frequency characteristics, and the modulation may be lost. This is one of the drawbacks of OFDM, the fact that it requires linear amplification. In addition, very large amplitude peaks may occur depending on how the sinusoids line up, so the peak-to-average power ratio is high. This means that the linear amplifier has to have a large dynamic range to avoid distorting the peaks. The result is a linear amplifier with a constant, high bias current resulting in very poor power efficiency. OFDM Signal, 1 Symbol Period Figure 8 is provided to illustrate the time components of the OFDM signal. The IFFT transforms each complex conjugate pair of delta functions (each carrier) into a real-valued, pure sinusoid. Figure 8 shows the separate sinusoids that make up the composite OFDM waveform given in Figure 7. The one sinusoid with 180 phase shift is clearly visible as is the frequency difference between each of the 4 sinusoids. Transmission The key to the uniqueness and desirability of OFDM is the relationship between the carrier frequencies and the symbol rate. Each carrier frequency is separated by a multiple of 1/NT (Hz). The symbol rate (R) for each carrier is 1/NT (symbols/sec). The effect of the symbol rate on each OFDM carrier is to add a sin(x)/x shape to each carriers spectrum. The nulls of the sin(x)/x (for each carrier) are at integer multiples of 1/NT. The peak (for each carrier) is at the carrier frequency k/NT. Therefore, each carrier frequency is located at the nulls for all the other carriers. This means that none of the carriers will interfere with each other during transmission, although their spectrums overlap. The ability to space carriers so closely together is very bandwidth efficient. OFDM Time Waveform Figure 9 shows the OFDM time waveform for the same signal. There are 100 symbol periods in the signal. Each symbol period is 64 samples long (100 x 64 = 6400 total samples). Each symbol period contains 4 carriers each of which carries 1 symbol. Each symbol carries 1 bit. Note that Figure 9 again illustrates the large dynamic range of the OFDM waveform envelope. OFDM Spectrum Figure 10 shows the spectrum for of an OFDM signal with the following characteristics: 1 bit / symbol 100 symbols / carrier (i.e. a sequence of 100 symbol periods) 4 carriers 64 IFFT bins spectrum averaged for every 20 symbols (100/20 = 5 averages) Red diamonds mark all of the available carrier frequencies. Note that the nulls of the spectrums line up with the unused frequencies. The four active carriers each have peaks at carrier frequencies. It is clear that the active carriers have nulls in their spectrums at each of the unused frequencies (otherwise, the nulls would not exist). Although it cannot be seen in the figure, the active frequencies also have spectral nulls at the adjacent active frequencies. It is not currently practical to generate the OFDM signal directly at RF rates, so it must be up converted for transmission. To remain in the discrete domain, the OFDM could be upsampled and added to a discrete carrier frequency. This carrier could be an intermediate frequency whose sample rate is handled by current technology. It could then be converted to analog and increased to the final transmit frequency using analog frequency conversion methods. Alternatively, the OFDM modulation could be immediately converted to analog and directly increased to the desired RF transmits frequency. Either way, the selected technique would have to involve some form of linear AM (possibly implemented with a mixer). [1, 122-125; 6] Reception and Demodulation The received OFDM signal is down converted (in frequency) and taken from analog to digital. Demodulation is done in the frequency domain (just as modulation was). The following steps may be taken to demodulate the OFDM: partition the input stream into vectors representing each symbol period take the FFT of each symbol period vector extract the carrier FFT bins and calculate the phase of each calculate the phase difference, from one symbol period to the next, for each carrier decode each phase into binary data sort the data into the appropriate order OFDM Carrier Magnitude following FFT Figure 11 and Figure 12 show the magnitude and spectrum of the FFT for one received OFDM symbol period. For this example, there are 4 carriers, the IFFT bin size is 64, there is 1 bit per symbol, and the signal was sent through a channel with AWGN having an SNR of 8 dB. The figures show that, under these conditions, the modulated symbols are very easy to recover. OFDM Carrier Phase following FFT In Figure 12 that the unused frequency bins contain widely varying phase values. These bins are not decoded, so it does not matter, but the result is of interest. Even if the noise is removed from the channel, these phase variations still occur. It must be a result of the IFFT/FFT operations generating very small complex values (very close to 0) for the unused carriers. The phases are a result of these values. [1, 125 -128; 3] OFDM transceiver OFDM signals are typically generated digitally due to the difficulty in creating large banks of phase lock oscillators and receivers in the analog domain. Figure 13 shows the block diagram of a typical OFDM transceiver. The transmitter section converts digital data to be transmitted, into a mapping of subcarrier amplitude and phase. It then transforms this spectral representation of the data into the time domain using an Inverse Discrete Fourier Transform (IDFT). The Inverse Fast Fourier Transform (IFFT) performs the same operations as an IDFT, except that it is much more computationally efficiency, and so is used in all practical systems. In order to transmit the OFDM signal the calculated time domain signal is then mixed up to the required frequency. Block diagram showing a basic OFDM transceiver [3] The receiver performs the reverse operation of the transmitter, mixing the RF signal to base band for processing, then using a Fast Fourier Transform (FFT) to analyze the signal in the frequency domain. The amplitude and phase of the subcarriers is then picked out and converted back to digital data. The IFFT and the FFT are complementary function and the most appropriate term depends on whether the signal is being received or generated. In cases where the Signal is independent of this distinction then the term FFT and IFFT is used interchangeably. [1, 125 -128, 3] Analysis of OFDM characteristics Guard Period OFDM demodulation must be synchronized with the start and end of the transmitted symbol period. If it is not, then ISI will occur (since information will be decoded and combined for 2 adjacent symbol periods). ICI will also occur because orthogonality will be lost (integrals of the carrier products will no longer be zero over the integration period), To help solve this problem, a guard interval is added to each OFDM symbol period. The first thought of how to do this might be to simply make the symbol period longer, so that the demodulator does not have to be so precise in picking the period beginning and end, and decoding is always done inside a single period. This would fix the ISI problem, but not the ICI problem. If a complete period is not integrated (via FFT), orthogonality will be lost. The effect of ISI on an OFDM signal can be further improved by the addition of a guard period to the start of each symbol. This guard period is a cyclic copy that extends the length of the symbol waveform. Each subcarrier, in the data section of the symbol, (i.e. the OFDM symbol with no guard period added, which is equal to the length of the IFFT size used to generate the signal) has an integer number of cycles. Because of this, placing copies of the symbol end-to-end results in a continuous signal, with no discontinuities at the joins. Thus by copying the end of a symbol and appending this to the start results in a longer symbol time. Addition of a guard period to an OFDM signal [3] In Figure 14, The total length of the symbol is Ts=TG + TFFT, where Ts is the total length of the symbol in samples, TG is the length of the guard period in samples, and TFFT is the size of the IFFT used to generate the OFDM signal. In addition to protecting the OFDM from ISI, the guard period also provides protection against time-offset errors in the receiver. For an OFDM system that has the same sample rate for both the transmitter and receiver, it must use the same FFT size at both the receiver and transmitted signal in order to maintain subcarrier orthogonality. Each received symbol has TG + TFFT samples due to the added guard period. The receiver only needs TFFT samples of the received symbol to decode the signal. The remaining TG samples are redundant and are not needed. For an ideal channel with no delay spread the receiver can pick any time offset, up to the length of the guard period, and still get the correct number of samples, without crossing a symbol boundary. Function of the guard period for protecting against ISI [3] Figure 15 shows this effect. Adding a guard period allows time for the transient part of the signal to decay, so that the FFT is taken from a steady state portion of the symbol. This eliminates the effect of ISI provided that the guard period is longer than the delay spread of the radio channel. The remaining effects caused by the multipath, such as amplitude scaling and phase rotation are corrected for by channel equalization. In order to avoid ISI and ICI, the guard period must be formed by a cyclic extension of the symbol period. This is done by taking symbol period samples from the end of the period and appending them to the front of the period. The concept of being able to do this, and what it means, comes from the nature of the IFFT/FFT process. When the IFFT is taken for a symbol period (during OFDM modulation), the resulting time sample sequence is technically periodic. This is because the IFFT/FFT is an extension of the Fourier Transform which is an extension of the Fourier Series for periodic waveforms. All of these transforms operate on signals with either real or manufactured periodicity. For the IFFT/FFT, the period is the number of samples used. Guard Period via Cyclic Extension With the cyclic extension, the symbol period is longer, but it represents the exact same frequency spectrum. As long as the correct number of samples are taken for the decode, they may be taken anywhere within the extended symbol. Since a complete period is integrated, orthogonality is maintained. Therefore, both ISI and ICI are eliminated. Note that some bandwidth efficiency is lost with the addition of the guard period (symbol period is increased and symbol rate is decreased) [2,154-160, 3] Windowing The OFDM signal is made up of a series of IFFTs that are concatenated to each other. At each symbol period boundary, there is a signal discontinuity due to the differences between the end of one period and the start of the next. These discontinuities can cause high frequency spectral noise to be generated (because they look like very fast transitions of the time waveform). To avoid this, a window function (Hamming, Hanning, Blackman, ) may be applied to each symbol period. The window function would attenuate the time waveform at the start and the end of each period, so that the discontinuities are smaller, and the high frequency noise is reduced. However, this attenuation distorts the signal and some of the desired frequency content is lost.[1, 121;2 154] Multipath Characteristics OFDM avoids frequency selective fading and ISI by providing relatively long symbol periods for a given data rate. This is illustrated in Figure 17. For a given transmission channel and a given source data rate, OFDM can provide better multipath characteristics than a single carrier. OFDM vs. Single Carrier, Multipath Characteristic Comparison However, since the OFDM carriers are spread over a frequency range, there still may be some frequency selective attenuation on a time-varying basis. A deep fade on a particular frequency may cause the loss of data on that frequency for a given time, but the use of Forward Error Coding can fix it. If a single carrier experienced a deep fade, too many consecutive symbols may be lost and correction coding may be ineffective. [8] Bandwidth A comparison of RF transmits bandwidth between OFDM and a single carrier is shown in Figure 18 (using the same example parameters as in Figure 17). OFDM Bandwidth Efficiency In Figure 18, the calculations show that OFDM is more bandwidth efficient than a single carrier. Note that another efficient aspect of OFDM is that a single transmitters bandwidth can be increased incrementally by addition of more adjacent carriers. In addition, no bandwidth buffers are needed between transmit bandwidths of separate transmitters as long as orthogonality can be maintained between all the carriers.[2, 161-163; 8; 9] Physical Implementation Since OFDM is carried out in the digital domain, there are many ways it can be implemented. Some options are provided in the following list. Each of these options should be viable given current technology: ASIC (Application Specific Integrated Circuit) ASICs are the fastest, smallest, and lowest power way to implement OFDM Cannot change the ASIC after it is built without designing a new chip General-purpose Microprocessor or MicroController PowerPC 7400 or other processor capable of fast vector operations Highly programmable Needs memory and other peripheral chips Uses the most power and space, and would be the slowest Field-Programmable Gate Array (FPGA) An FPGA combines the speed, power, and density attributes of an ASIC with the programmability of a general purpose processor. An FPGA could be reprogrammed for new functions by a base station to meet future (currently unknown requirements).This should be the best choice.[9] OFDM uses in DVB (Digital Video Broadcasting) DVB (Digital Video Broadcast) is a set of standards for the digital transmission of video and audio streams, and also data transmission. The DVB standards are maintained by the DVB Project, which is an industry-led consortium of over 260 broadcasters, manufacturers, network operators, software developers, regulatory bodies and others in over 35 countries. DVB has been implemented over satellite (DVB-S, DVB-S2), cable (DVB-C), terrestrial broadcasting (DVB-T), and handheld terminals (DVB-H). the DVB standard following the logical progression of signal processing steps, as well as source and channel coding, COFDM modulation, MPEG compression and multiplexing methods, conditional access and set-top box Technology. In this project is presented an investigation of two OFDM based DVB standards, DVB-T and DVB-H. DVB-T (Digital Video Broadcasting Terrestrial) The first Terrestrial Digital Video Broadcasting pilot transmissions were started in the late 90s, and the first commercial system was established in Great Britain. In the next few years the digital broadcasting system has been set up in many countries, and the boom of the digital terrestrial transmission is estimated in the next few years, while the analogue transmission will be cancelled within about 15 years. The greatest advantage of the digital system is the effective use of the frequency spectrum and its lower radiated power in comparison with the analogue transmission, while the covered area remains the same. Another key feature is the possibility of designing a so-called Single Frequency Network (SFN), which means that the neighboring broadcast stations use the same frequency and the adjacent signals dont get interfered. The digital system transmits a data stream, which means that not only television signals but data communication (e.g. Internet service) may be used according to the demands. The data stream consists of an MPEG-2 bit stream, which means a compression is used, enabling the transfer of even 4 or 5 television via the standard 8 MHz wide TV channel. For the viewer, the main advantages are the perfect, noise-free picture, CD quality sound, and easier handling, as well as services like Super Teletext, Electronic Programme Guide, interactivity and mobility.[11, 251-253] Modulation technique in DVB-T The DVB-T Orthogonal Frequency Division Multiplexing (OFDM) modulation system uses multi-carrier transmission. There are 2 modes, the so-called 2k and 8k modes, using 1705 and 6817 carriers respectively, with each carrier modulated separately and transmitted in the 8 MHz TV channel. The common modulation for the carriers is typically QPSK, 16-QAM or 64-QAM. Each signal can be divided into two, so-called „In Phase (I) and „Quadrature Phase components, being a 90Â ° phase shift between them. The constellation diagram and the bit allocation is shown in bellow 16-QAM constellation diagram and bit allocation [6] This modulation can be demonstrated in the constellation diagram, where the 2 axes represent the 2 components (I and Q). In case of using 16-QAM modulation, the number of states is 16, so 1 symbol represents 4 bits. [11, 255; 6; 14] Bir errors If we simulate all the carriers in the constellation diagram we get not just 1 discrete point, but many points, forming a „cloud and representing each state. In case of additive noise the „cloud gets bigger and the receiver may decide incorrectly, resulting in bit errors. Figure 2 shows the measured constellation diagram without and with additive noise. Measured 16-QAM constellation diagram a) without additive noise b) with additive noise [6] To ensure perfect picture quality, the DVB-T system uses a 2 level error correction (Reed-Solomon and Viterbi). This corrects the bad bits at an even 10-4 Bit Error Rate (BER) and enables error-free data transmission. [13, 32-36] The multi-carrier structure The structure of carriers can be illustrated also in the function of time (Figure 20). The horizontal axis is the frequency and the vertical axis is the time. The 8 MHz channel consists of many carriers, placed 4462 Hz or 1116 Hz far from each other according to the modulation mode (2k or 8k). Structure of OFDM carriers [13] There are some reserved, so-called Transmission Parameter Signalling (TPS) carriers that do not transfer payload, just provide transmission mode information for the receiver, so the total number of useful carriers is 1512 and 6048 respectively in the two transmission modes, and the resultant bit rate is between 4,97 and 31,66 Mbit/s, depending on the modulation (QPSK, 16-QAM or 64-QAM), the transmission mode (2k or 8k), the Code Rate (CR) used for error correction and the selected Guard Interval (GI). This guard interval means that there is a small time gap between each symbol, so the transmission is not continuous. This guarding time enables perfect reception by eliminating the errors caused by multipath propagation.[4, 79-90; 13] Frequency spectrum In 2k mode, 1705 carriers are modulated in the 8 MHz TV channel, so each carrier is 4462 Hz far from its neighbor, while in 8k mode this distance is 1116 Hz. In digital broadcasting, there are no vision and sound carriers, so the power for each carrier is the same. This mean

Cognitive Explanations of Depression

Cognitive Explanations of Depression The cognitive explanation of depression basically rests the idea that disorders happen because of faulty thinking. There are other explanations for depression, and other treatments. The cognitive approach assumes that behaviours are controlled by thoughts and beliefs. Therefore irrational thoughts and beliefs cause abnormal behaviours. There are many different models that help to explain how irrational thoughts can lead to depression. Examples are: Elliss ABC model This ABC three stage model was proposed by Ellis in 1962. This model claims that disorders start off with an activating event (A) for example failing an exam, which then leads to a belief (B) about why this happened. The belief can either be rational or irrational. A rational belief would be like for example I didnt prepare well enough whereas an irrational belief would be Im too stupid to pass exams. These beliefs then lead to consequences (C). According to Ellis, rational beliefs lead to healthy emotional outcomes and produce adaptive consequences like for example more revision needs to be done, whereas on the other hand irrational beliefs lead to unhealthy emotional outcomes and produce maladaptive consequences, including depression. Here is the flow chart of Elliss ABC model: Becks negative triad Beck (1963) developed a cognitive explanation for mental disorders, but focussed it on depression. He believed that individuals who are depressed feel as they do due to their thinking being biased towards negative interpretations of the world and lacking a perceived sense of control. Beck then identified a negative triad which was a cognitive approach of understanding depression, focusing on how negative expectations (schema) about themselves (e.g. I cant succeed at anything), the world (e.g. I must be successful to be a good person) and the future (e.g. nothing will ever change) lead to depression. Beck then claimed that negative schemas may be acquired in an individuals childhood due to a traumatic event. Experiences that might contribute to negative schemas include parental rejection, bullying at school, and the death of a sibling. People with negative schemas become prone to making logical errors in their thinking and they usually focus selectively on certai n points within a situation going on while ignoring the relevant information. Cognitive behaviour therapy (CBT) is an effective treatment for all mental health problems including depression. CBT is based on the idea that how we think (cognition), how we feel (emotion) and how we act (behavior) all interact together. Basically, our thoughts determine our feelings and our behavior. It is the idea that patients learn how to notice negative thoughts when they have them, and then test how accurate they are. During CBT, what generally happens is: The therapist and patient identify the patients faulty cognitions. The therapist then tries to help the patient see that these faulty cognitions are not true, for example that the patient does not always fail on anything they do. Both the therapist and patient then set goals to think in a more positive perspective or adaptive ways, for example focusing on things the patient has succeeded in and trying to build on them. Even though the patient may sometimes need to glance back to past experiences, the CBT mainly focuses on the current situation. Therapists sometimes encourage their patient to keep track of a diary so that they are able to accurately record their feelings, actions and patterns. CBT differs from other depressions treatments because it focuses on specific problems for a patient and is goal orientated. Along with this cognitive behaviour treatment is educational too because therapists use structured learning experiences that teach the patient to monitor and write down their mental images and negative thoughts. Furthermore, cognitive therapy helps individuals develop alternative ways of behaving and thinking, which tries to reduce their psychological stress.

The Reforms of Michel Fokine Essay -- essays research papers

The Reforms of Michel Fokine   Ã‚  Ã‚  Ã‚  Ã‚     Ã‚  Ã‚  Ã‚  Ã‚  Photography, painting, videography, and literature have all progressed over time. New technology, and new ways of thinking have brought these arts to new levels. There seems to be a broad misconception, though, that ballet is an art form that does not progress; does not change. Many people assume that ballet’s set vocabulary of movement places limitations on how far the art can expand. Little do many people realize that this vocabulary is a mere foundation for the myriad of interpretations that the art went and will continue to go in. Michel Fokine is one revolutionary ballet choreographers, whose reforms have taken this previously monotonous art to a new level.   Ã‚  Ã‚  Ã‚  Ã‚  Fokine’s ideas were revolutionary for his time, but ironically made perfect sense. He believed that all of the elements in a ballet should be parallel. In other words, he thought that the music, costuming, makeup, movements, and sets should all reflect the same culture and time period of the ballet. During this time in ballet there were often incongruencies. For example, there would be Russian music, and pointe shoes in a ballet that supposedly was based on a foreign medieval culture. Fokine was extremely and consciously consistent in his works. Fokine explains, â€Å"The ballet should be staged in conformity with the epoch represented.†   Ã‚  Ã‚  Ã‚  Ã‚  Fokine sets his 1911 ballet, Petrouchka, in Russia. The first scene is a street fair, which Fokine sets appropriately. He is sure to make the costumes realistic of that time and place. Rather than dressing the dancers in tutus and leotards, they wear dresses that are brightly colored and long. They are bundled up appropriately in many colorful layers, considering the chilling temperatures of Russian winters. They also do not wear pointe Atkins 2 shoes with long laces, but instead high heel character shoes that were typical of the time period. Fokine also successfully creates personalities for the three dolls, partly by their costumes. Petrouchka, who is a forlorn rag doll, wears a thin suit that is as lifeless and limp as his personality. The costume and makeup is effective in showing his lack of motivation and sadness. The Moor doll on the other hand, who is a very bold and vain character is seen in dress that corres... ...ure to not let the music dictate the dance, as many artists before him had done. In his Memoirs of a Ballet Master, he wrote â€Å"The choreography for [a pas de deux I performed with Anna Pavlova] we mostly staged ourselves . . . We did whatever we felt we could do best,† (Fokine quoted in Cass). This superficial movement was completely against what Fokine believed in. Movement that did not contribute to the purpose and plot af the piece was useless. Due to his intense focus on his intent, he successfully gave the music, choreography, costumes, and sets equal importance and relevance to the entire creation.   Ã‚  Ã‚  Ã‚  Ã‚  Fokine’s exceptional dedication to his art is quite obvious. It is simply seen thorough his opinion of applause, that his focus is his art, more than any recognition he may get for it. While most artists would bask in the glory of each set of applause, Fokine despised it, except at completely appropriate times. He believed that to move on from tradition, one must be thoroughly trained in that technique, which he was. His many daring reforms truly opened the world of ballet up to new possibilities, while not straying too far from traditional technique.

How Nelson Mandela used Rugby to unify South Africa Essay -- Politics,

After spending twenty-seven years in prison, Nelson Mandela was released from prison on February 11, 1990. In 1991, Nelson Mandela was chosen to become president of the African National Congress. In 1993, Mandela and South African President F.W. de Klerk announced an agreement that the African National Congress and the National Party form a transitional government, effectively ending apartheid and opening the political process to all South Africans (Williamson). Mandela was elected President of South Africa in 1994, and de Klerk became his first deputy. However, even with apartheid abolished, South Africa was still a divided country. Mandela’s legal adviser, Nicholas Haysom, said, â€Å"South Africa in 1994 was a country that was split, historically, culturally, racially, and so many other ways.† Within South Africa, there was a vast division between blacks and whites, and Mandela’s job was to bring them together. One way that Nelson Mandela brought South Africa together was through rugby. While this would seem to be an unlikely way to ease the racial tension, rugby was a crucial piece in the unification of South Africa. While Mandela was serving his time in prison, the international community began to put more pressure on South Africa to release him and end apartheid. To make sure their pressure was felt, opposing nations, especially New Zealand, began violently protesting when the Springboks visited to play (30for30). The Springboks, South Africa’s national rugby team, were banned from rugby in 1981. The ban was intended to affect the white South Africans and give the black South Africans leverage to use in negotiations to end apartheid. In 1992, after Mandela was freed, the African National Congress revoked the ban on rugby... ...any, 1994. Print. Mandela, Nelson. Mandela An Illustrated Autobiography. Boston: Little, Brown and Company, 1994. Print. Sampson, Anthony. Mandela The Authorized Biography. New York, NY: Alfred A. Knoff, 1999. Print. "Nelson Mandela: inauguration speech (1994)." World History: The Modern Era. ABC-CLIO, 2011. Web. 30 Aug. 2011. "Nelson Mandela: speech on his release from prison (1990)." World History: The Modern Era. ABC-CLIO, 2011. Web. 30 Aug. 2011. Taylor, Paul. "Father of His Country." Washington Post (Washington, DC). Feb. 13 1994: Mag. Sec. 10+. SIRS Researcher. Web. 30 Aug 2011. Williams, Michael W. "Nelson Mandela." Great Lives from History: The Twentieth Century. Ed. Robert F. Gorman. 10 vols. Pasadena, California: Salem Press, 2008. Salem History Web. 30 Aug. 2011. Carlin, John. Playing the Enemy. New York: The Penguin Press, 2008. Print.

Advantages of Standardization

Standardization is the process by which a company makes it methods, especially its production processes, uniform throughout its organization. Standardization helps cut costs by eliminating duplicated effort and allows a company to take advantage of economies of scale when purchasing supplies. However, some advantages may be lost when a company decided to standardize its operations. Disadvantages Loss of Uniqueness If a company builds up a customer base that values its unique niche products, or if the company serves a specialized market, standardizing its processes may mean it loses some of its former customers. For example, if a restaurant builds its reputation on a varied and exotic menu, then changes to a standardized menu to provide a more predictable customer experience, its former customers may defect to competitors who provide more variety. Loss of Responsiveness. When a company expands into new markets, especially in foreign markets, standardization may work against the firm. While it may be cheaper for a restaurant to buy its trademark hamburgers in bulk, if it expands into a new market where people buy chicken much more often, its standardization measures may make it slower to respond to market conditions and end up costing money. Unsuited to Some Aspects of Business Standardization may be advantageous in some areas of business, such as production, but some aspects of a business should be tailored to the customers' needs. Customer service, advertising, distribution and product pricing must be driven by local market conditions to be successful. Stifles Creativity and Response Time Standardization has the potential to get a business into a rut. Standards, once implemented, soon become the status quo and may become entrenched in the corporate culture, making them hard to change when change is needed. However, market conditions often change, and companies that change quickly are best positioned to take advantage of them. Standardization may also stifle creativity, particularly in product design.

Random Variable and Highest Expected Profit

I. Introduction Arrowmark Vending has the contract to supply pizza at football games for a university. The operations manager, Tom Kealey, faces the challenge of determining how many pizzas to make available at the games. We have been provided with demand distributions for pizza based on past experience and know that Tom will only supply plain cheese and pepperoni and cheese combo pizzas. We also know that there is a fixed cost of $1,000 allocated equally between the two types of pizzas, and that the costs to make plain cheese pizza and pepperoni and cheese pizza are $4. 50 and $5. 0 respectively. Both pizzas sell for $9. 00 and unsold pizzas have no value. The purpose of this report is to provide Tom with some information regarding how many of each type of pizza he should produce if he wants to achieve the highest expected profit from pizza sales at the game. II. Analysis In order to determine at which production level Tom will achieve the highest expected profit, it is first necess ary to determine the potential profit or loss associated with producing at each demand level. To do this, a discrete probability distribution is composed for each potential level of production.For example, if 200 plain cheese pizzas are produced and 200 are demanded, the potential profit is $400. This profit consists of $1800 in sales revenue minus $1400 in costs ($900+$500 fixed). This profit will result regardless of whether more than 200 are demanded. Accordingly, if 400 cheese pizzas are produced and only 200 demanded, there is a potential loss of $500. Using these distributions, we are then able calculate the distribution’s mean, which is the expected value of the profits at each level of production.The expected profits in this case are the weighted average of the potential profit values, in which the weights are the probabilities. The expected profits associated with each type of pizza are provided in the tables below: | | Expected Profits at each Production Level| | | 200| 300| 400| 500| 600| 700| 800| 900| Plain Cheese Demand| 200| $40| -$5| -$50| -$95| -$140| -$185| -230| -275| | 300| $60| $128| $60| -$8| -$75| -$143| -210| -277. 5| | 400| $60| $128| $195| $128| $60| -$8| -75| -142. | | 500| $80| $170| $260| $350| $260| $170| 80| -10| | 600| $80| $170| $260| $350| $440| $350| 260| 170| | 700| $40| $85| $130| $175| $220| $265| 220| 175| | 800| $20| $43| $65| $88| $110| $133| 155| 132. 5| | 900| $20| $43| $65| $88| $110| $133| 155| 177. 5| | Total| $400 | $760 | $985 | $1,075 | $985 | $715 | $355 | $(50)| | | 300| 400| 500| 600| 700| 800| Pepperoni and Cheese Demand| 300| $70| $20| -$30| -$80| -$130| -$180| | 400| $140| $220| $120| $20| -$80| -$180| | 500| $175| $275| $375| $250| $125| $0| | 600| $175| $275| $375| $475| $350| $225| | 700| $105| $165| $225| $285| $345| $270| 800| $35| $55| $75| $95| $115| $135| | Total| $700 | $1,010 | $1,140 | $1,045 | $725 | $270 | III. Recommendation If Kealey wants to achieve the highest expected profit from p izza sales at the game, he should produce 500 cheese pizzas and 500 pepperoni and cheese pizzas. Looking at the tables, we know this is the best option because we see the highest expected profit of $1,075 associated with this production level for cheese pizza and $1,140 in profit for pepperoni and cheese pizza. This number takes into account the probabilities at each demand level, so we can be reasonably assured that this is an accurate recommendation.