Mathematical description of OFDM

Mathematical description of OFDM When we talk about the Mathematical description of OFDM then we cannot neglect the following mathematical treatments: The Fourier transform The use of the Fast Fourier Transform in OFDM The guard interval and its implementation As we have discussed above that a large number of narrowband carriers which are spaced close to each other in frequency domain are transmitted by OFDM. The modern digital technique that is used in the OFDM is FFT i-e Fast Fourier transform (FFT) and due to the use of FFT it reduces the number of modulators and demodulators both at the receiver and transmitter side. Fig. 4 Examples of OFDM spectrum (a) a single subchannel, (b) 5 carriers At the central frequency of each subchannel, there is no crosstalk from other subchannels. Mathematically, each carrier can be described as a complex wave: (1) sc(t) = the real part of original signal. Ac(t) = the Amplitude f c(t) = Phase of carrier (t)= symbol duration period Ac(t) and f c(t) use to fluctuate on symbol by symbol basis. Parameter values are constant over (t). As we know that OFDM posses many carriers. So the complex signals ss(t) is represented as: (2) where This is of course a continuous signal. If we consider the waveforms of each component of the signal over one symbol period, then the variables Ac(t) and f c(t) take on fixed values, which depend on the frequency of that particular carrier, and so can be rewritten: If the signal is sampled using a sampling frequency of 1/T, then the resulting signal is represented by: (3) At this point, we have restricted the time over which we analyse the signal to N samples. It is convenient to sample over the period of one data symbol. Thus we have a relationship: t =NT If we now simplify eqn. 3, without a loss of generality by letting w 0=0, then the signal becomes: (4) Now Eq. 4 can be compared with the general form of the inverse Fourier transform: (5) In eq. 4, the function is no more than a definition of the signal in the sampled frequency domain, and s(kT) is the time domain representation. Eqns. 4 and 5 are equivalent if: (6) This is the same condition that was required for orthogonality (see Importance of orthogonality). Thus, one consequence of maintaining orthogonality is that the OFDM signal can be defined by using Fourier transform procedures. The Fourier transform Fourier transform actually relate events in time domain to events in frequency domain. There are different version of FFT which are used according to requirement of different sort of work The conventional transform provide the relation of continuous signals. Note that Continuous signals are not limited in both time and frequency domain. Though, it is better to sample the signal so that the signal processing becomes simpler. But it lead to an aliasing when we sample the signals with infinite spectrum and the processing of signals which are not time limited can lead to another problem that is referred to as space storage. DFT (discrete Fourier transforms) is use to overcome the above problem of signal processing. The original definition of DFT reveals that the time waves have to repeat frequently and similarly frequency spectrum repeat frequently in frequency domain. Basically in DFT the signals can be sampled in time domain as well as in frequency domain. The Fourier transform is the process in which the signal represented in the time domain transformed in frequency domain, while the reverse process uses IFT which is the inverse Fourier transform. The use of the Fast Fourier Transform in OFDM The main reason that the OFDM technique has taken a long time to become a prominence has been practical. It has been difficult to generate such a signal, and even harder to receive and demodulate the signal. The hardware solution, which makes use of multiple modulators and demodulators, was somewhat impractical for use in the civil systems. The ability to define the signal in the frequency domain, in software on VLSI processors, and to generate the signal using the inverse Fourier transform is the key to its current popularity. The use of the reverse process in the receiver is essential if cheap and reliable receivers are to be readily available. Although the original proposals were made a long time ago [Weinstein and Ebert], it has taken some time for technology to catch up. At the transmitter, the signal is defined in the frequency domain. It is a sampled digital signal, and it is defined such that the discrete Fourier spectrum exists only at discrete frequencies. Each OFDM carrier corresponds to one element of this discrete Fourier spectrum. The amplitudes and phases of the carriers depend on the data to be transmitted. The data transitions are synchronised at the carriers, and can be processed together, symbol by symbol (Fig. 5). Fig. 5 Block diagram of an OFDM system using FFT, pilot PN sequence and a guard bit insertion [Zou and Wu] The definition of the (N-point) discrete Fourier transform (DFT) is: (DFT) (7) and the (N-point) inverse discrete Fourier transform (IDFT): (IDFT) (8) A natural consequence of this method is that it allows us to generate carriers that are orthogonal. The members of an orthogonal set are linearly independent. Consider a data sequence (d0, d1, d2, †¦, dN-1), where each dn is a complex number dn=an+jbn. (an, bn= ± 1 for QPSK, an, bn= ± 1,  ± 3 for 16QAM, †¦ ) k=0,1,2, †¦, N-1 (9) where fn=n/(ND T), tk=kD t and D t is an arbitrarily chosen symbol duration of the serial data sequence dn. The real part of the vector D has components k=0,1,..,N-1 (10) If these components are applied to a low-pass filter at time intervals D t, a signal is obtained that closely approximates the frequency division multiplexed signal (11) Fig. 5 illustrates the process of a typical FFT-based OFDM system. The incoming serial data is first converted form serial to parallel and grouped into x bits each to form a complex number. The number x determines the signal constellation of the corresponding subcarrier, such as 16 QAM or 32QAM. The complex numbers are modulated in a baseband fashion by the inverse FFT (IFFT) and converted back to serial data for transmission. A guard interval is inserted between symbols to avoid intersymbol interference (ISI) caused by multipath distortion. The discrete symbols are converted to analog and low-pass filtered for RF upconversion. The receiver performs the inverse process of the transmitter. One-tap equalizer is used to correct channel distortion. The tap-coefficients of the filter are calculated based on the channel information. Fig. 6 Example of the power spectral density of the OFDM signal with a guard interval D = TS/4 (number of carriers N=32) [Alard and Lassalle] Fig 4a shows the spectrum of an OFDM subchannel and Fig. 4b and Fig. 6 present composite OFDM spectrum. By carefully selecting the carrier spacing, the OFDM signal spectrum can be made flat and the orthogonality among the subchannels can be guaranteed. The guard interval and its implementation The orthogonality of subchannels in OFDM can be maintained and individual subchannels can be completely separated by the FFT at the receiver when there are no intersymbol interference (ISI) and intercarrier interference (ICI) introduced by transmission channel distortion. In practice these conditions can not be obtained. Since the spectra of an OFDM signal is not strictly band limited (sinc(f) function), linear distortion such as multipath cause each subchannel to spread energy into the adjacent channels and consequently cause ISI. A simple solution is to increase symbol duration or the number of carriers so that distortion becomes insignificant. However, this method may be difficult to implement in terms of carrier stability, Doppler shift, FFT size and latency. Fig. 7 The effect on the timing tolerance of adding a guard interval. With a guard interval included in the signal, the tolerance on timing the samples is considerably more relaxed. Fig. 8 Example of the guard interval. Each symbol is made up of two parts. The whole signal is contained in the active symbol (shown highlighted for the symbol M) The last part of which (shown in bold) is also repeated at the start of the symbol and is called the guard interval One way to prevent ISI is to create a cyclically extended guard interval (Fig. 7, 8), where each OFDM symbol is preceded by a periodic extension of the signal itself. The total symbol duration is Ttotal=Tg+T, where Tg is the guard interval and T is the useful symbol duration. When the guard interval is longer than the channel impulse response (Fig. 3), or the multipath delay, the ISI can be eliminated. However, the ICI, or in-band fading, still exists. The ratio of the guard interval to useful symbol duration is application-dependent. Since the insertion of guard interval will reduce data throughput, Tg is usually less than T/4. The reasons to use a cyclic prefix for the guard interval are: to maintain the receiver carrier synchronization ; some signals instead of a long silence must always be transmitted; cyclic convolution can still be applied between the OFDM signal and the channel response to model the transmission system. http://www.wirelesscommunication.nl/reference/chaptr05/ofdm/ofdmqual.htm Multipath Challenges In an OFDM-based WLAN architecture, as well as many other wireless systems, multipath distortion is a key challenge. This distortion occurs at a receiver when objects in the environment reflect a part of the transmitted signal energy. Figure 2 illustrates one such multipath scenario from a WLAN environment. Figure 2: Multipath reflections, such as those shown here, create ISI problems in OFDM receiver designs. Click here for larger version of Figure 1b Multipath reflected signals arrive at the receiver with different amplitudes, different phases, and different time delays. Depending on the relative phase change between reflected paths, individual frequency components will add constructively and destructively. Consequently, a filter representing the multipath channel shapes the frequency domain of the received signal. In other words, the receiver may see some frequencies in the transmitted signal that are attenuated and others that have a relative gain. In the time domain, the receiver sees multiple copies of the signal with different time delays. The time difference between two paths often means that different symbols will overlap or smear into each other and create inter-symbol interference (ISI). Thus, designers building WLAN architectures must deal with distortion in the demodulator. Recall that OFDM relies on multiple narrowband subcarriers. In multipath environments, the subcarriers located at frequencies attenuated by multipath will be received with lower signal strength. The lower signal strength leads to an increased error rate for the bits transmitted on these weakened subcarriers. Fortunately for most multipath environments, this only affects a small number of subcarriers and therefore only increases the error rate on a portion of the transmitted data stream. Furthermore, the robustness of OFDM in multipath can be dramatically improved with interleaving and error correction coding. Lets look at error correction and interleaving in more detail. Error Correction and Interleaving Error correcting coding builds redundancy into the transmitted data stream. This redundancy allows bits that are in error or even missing to be corrected. The simplest example would be to simply repeat the information bits. This is known as a repetition code and, while the repetition code is simple in structure, more sophisticated forms of redundancy are typically used since they can achieve a higher level of error correction. For OFDM, error correction coding means that a portion of each information bit is carried on a number of subcarriers; thus, if any of these subcarriers has been weakened, the information bit can still arrive intact. Interleaving is the other mechanism used in OFDM system to combat the increased error rate on the weakened subcarriers. Interleaving is a deterministic process that changes the order of transmitted bits. For OFDM systems, this means that bits that were adjacent in time are transmitted on subcarriers that are spaced out in frequency. Thus errors generated on weakened subcarriers are spread out in time, i.e. a few long bursts of errors are converted into many short bursts. Error correcting codes then correct the resulting short bursts of errors. OR for guard interval Handling ISI The time-domain counter part of the multipath is the ISI or smearing of one symbol into the next. OFDM gracefully handles this type of multipath distortion by adding a guard interval to each symbol. This guard interval is typically a cyclic or periodic extension of the basic OFDM symbol. In other words, it looks like the rest of the symbol, but conveys no new information. Since no new information is conveyed, the receiver can ignore the guard interval and still be able to separate and decode the subcarriers. When the guard interval is designed to be longer than any smearing due to the multipath channel, the receiver is able to eliminate ISI distortion by discarding the unneeded guard interval. Hence, ISI is removed with virtually no added receiver complexity. It is important to note that discarding the guard interval does have an impact on the noise performance since it reduces the amount of energy available at the receiver for channel symbol decoding. In addition, it reduces the data rate since no new information is contained in the added guard interval. Thus a good system design will make the guard interval as short as possible while maintaining sufficient multipath protection. Why dont single carrier systems also use a guard interval? Single carrier systems could remove ISI by adding a guard interval between each symbol. However, this has a much more severe impact on the data rate for single carrier systems than it does for OFDM. Since OFDM uses a bundle of narrowband subcarriers, it obtains high data rates with a relatively long symbol period because the frequency width of the subcarrier is inversely proportional to the symbol duration. Consequently, adding a short guard interval has little impact on the data rate. Single carrier systems with bandwidths equivalent to OFDM must use much shorter duration symbols. Hence adding a guard interval equal to the channel smearing has a much greater impact on data rate. http://www.commsdesign.com/design_corner/showArticle.jhtml?articleID=16504605 As we know that cyclic prefix is used to restore the orthogonality and preserve ISI, but the question that arises is that how the orthogonality destroyed between the subcarriers and how cyclic prefix restore the orthogonality. [1] [2] The orthogonality between subcarriers is destroyed due to the channel dispersion whenever the signal is transmitted over a channel and this cause ICI and due to the longer delay ISI occur among the OFDM symbols which are in sequence. [1] Further more there is no any interference in uncorrupted OFDM signal when they are demodulated but when we talk about the time dispersive channel the OFDM subcarriers lost there orthogonality. The main cause behind this is that the demodulator correlation interval for one path will overlap with the symbol boundary of a different path as show in the figure [ ] [ 2] Fig. 4.11 16QAM constellation We will see that this makes equalization in the receiver very simple. If multipath exceeds the CP, then constellation points in the modulation is distorted. As can be seen from Fig. 4.11, when multipath delay exceeds the CP, the subcarriers are not guaranteed to be orthogonal anymore, since modulation points may fall into anywhere in the respective contour. As delay spread gets more severe, the radius of the contour enlarges and crosses the other contours. Hence, this causes error. The CP is utilized in the guard period between successive blocks and constructed by the cyclic extension of the OFDM symbol over a period Ï„ : (4.3) The required criteria is that Ï„ is chosen bigger than channel length Ï„h so as not to experience an ISI. The CP requires more transmit energy and reduces the bit rate to (Nb/NT +Ï„ ), where b is the bits that a subcarrier can transmit. The CP converts a discrete time linear convolution into a discrete time circular convolution. Thus, transmitted data can be modeled as a circular convolution between the channel impulse response and the transmitted data block, which in the frequency domain is a pointwise multiplication of DFT samples. Then received signal becomes Where (4.5) Hence, kth subcarrier now has a channel component Hk, which is the fourier transform of h(t) at the frequency fk. The OFDM symbol is sampled (t = nT and fk = k/NT) in the receiver and demodulated with an FFT. Consequently, the received data has the following form yk = Hk xk, k = 0, . . . ,N −1. (4.6) The received actual data can be retrieved with N parallel one-tap equalizers. One-tap equalizer simply uses the estimated channel ( ˆHk) components and use it to retrieve estimated ˆ xk as follows (4.7) Also note that the spectrum of OFDM decays slowly. This causes spectrum leakage to neighboring bands. Pulse shaping is used to change the spectral shape by either commonly used raised cosine time window or passing through a filter. An OFDM system design considers setting the guard interval (Ï„ ) as well as the symbol time (T) and FFT size with respect to desired bit rate B and given tolerable delay spread. The guard interval is selected according to delay spread, and typically it is 2–4 times the root-mean-squared delay spread with respect to chosen coding and modulation. Symbol time is set with respect to guard time and it is desirable to select much larger than the guard time since the loss in SNR in the guard time is compensated. Symbol time as we know determines the subcarrier spacing ( fb = 1/T). Number of subcarriers N is found with respect to desired bit rate, since total number of bits (bT ) to carry in one symbol is found with B/(T +Ï„ ) and selected coding and modulation determines the number of bits (b) in one subcarrier. Hence, the number of subcarriers is N = bT /b. For instance, b is two for 16QAM with rate 1/2. The required bandwidth (W) is then N âˆâ€" fb. Alternatively, this method is reversed to find out the symbol time starting from the given bandwidth. OR Cyclic-prefix insertion As I m talking about the time dispersive channel I want to include that in time dispersive channel the subcarrier not only have inter symbol interference within them but they also posses interference between them. As we know that in case of time dispersive channel the frequency-selective channel frequency response is equivalent to time dispersion on the radio channel. There are two reasons of orthogonality between OFDM subcarriers. Due to frequency-domain separation. The specific frequency-domain structure of each subcarrier. Even if the frequency-domain channel is constant over a bandwidth corresponding to the main lobe of an OFDM subcarrier and only the subcarrier side lobes are corrupted due to the radio-channel frequency selectivity, the orthogonality between subcarriers will be lost with inter-subcarrier interference as a consequence. Due to the relatively large side lobes of each OFDM subcarrier, already a relatively limited amount of time dispersion or, equivalently, a relatively modest radio-channel frequency selectivity may cause non-negligible interference between subcarriers. Time dispersion and corresponding received-signal timing Figure 9 Time dispersion and corresponding received-signal timing. To deal with this problem and to make an OFDM signal truly insensitive to time dispersion on the radio channel, so-called cyclic-prefix insertion is typically used in case of OFDM transmission. As illustrated in Figure 10, cyclic-prefix insertion implies that the last part of the OFDM symbol is copied and inserted at the beginning of the OFDM symbol. Cyclic-prefix insertion thus increases the length of the OFDM symbol from Tu to Tu +TCP, where TCP is the length of the cyclic prefix, with a corresponding reduction in the OFDM symbol rate as a consequence. As illustrated in the lower part of Figure 10, if the correlation at the receiver side is still only carried out over a time interval Tu =1/∆f , subcarrier orthogonality will then be preserved also in case of a time-dispersive channel, as long as the span of the time dispersion is shorter than the cyclic-prefix length. Cyclic-prefix insertion Figure 10. Cyclic-prefix insertion Cyclic-prefix insertion is beneficial in the sense that it makes an OFDM signal insensitive to time dispersion as long as the span of the time dispersion does not exceed the length of the cyclic prefix. The drawback of cyclic-prefix insertion is that only a fraction Tu /( Tu +TCP) of the received signal power is actually utilized by the OFDM demodulator, implying a corresponding power loss in the demodulation. In addition to this power loss, cyclic-prefix insertion also implies a corresponding loss in terms of bandwidth as the OFDM symbol rate is reduced without a corresponding reduction in the overall signal bandwidth. One way to reduce the relative overhead due to cyclic-prefix insertion is to reduce the subcarrier spacing ∆f , with a corresponding increase in the symbol time Tu as a consequence. http://wirelesscafe.wordpress.com/2009/04/20/ofdm-as-downlink-transmission-scheme-for-lte/

Ancient Discoveries: Troy Essay

This report covers a brief historic background on the discovery of the Hisarlik site of Troy; Heinrich Schliemann (refer to figure 1.), its discoverer and his methodologies whilst excavating the site. It focuses primarily on his second campaign, the most famous of the five- and his lack of scientific archaeological structure whilst excavating, rather using philological and relative dating methods; mistakes as a result of careless excavations, and the legacy it has left on history and archaeology of Troy till this day. As a child, Heinrich Schliemann had an obsession with Homer’s epic cycles/poems the Iliad and the Odyssey. After cornering the market at the age of 41, he became a millionaire and retired from merchantry to pursue his love of archaeology, committing to proving the actual historicity of the â€Å"Trojan War† and the Homeric city of Troy. (Refer to figure 2.) Schliemann had a good idea of where to begin looking. In 1868, Schliemann journeyed to Greece and Asia Minor in search of the lost city, travelling north-west Turkey to examine both mounds Bunarbashi and Hisarlik. Because, according to Greek myth, the general Agamemnon collected his force in Aulis, a site on the eastern shores of Greece, Troy must have lain to the east of Greece. The Iliad mentioned that Mount Ida was visible from the walls of Troy, but from Bunarbashi the mountain could not be seen. There were also a number of topographical discrepancies such as, the distance from the sea being eight miles where Schliemann approximated from the text that it should not be more than four. Using geographic clues from his copy of the Iliad, Schliemann discovered another hill near the village of Hisarlik that seemed to fit Homer’s description. Schliemann’s decision to excavate at Hisarlik was confirmed after incurring a preceded theory by British archaeologist, Frank Calvert that Hisarlik was indeed the ancient city of Troy. Calvert had been working on the mound for over 20 years and had acquired half of the hill but lacked in finances to pursue further investigations on the site, so he decided to confide his archaeological findings with Schliemann, gaining collaboration with the rich benefactor in uncovering Troy. (Refer to figure 13.) The exact location of Troy (or Ilium) was lost after 400 B.C., and over the centuries the site was buried under many layers of earth, however fortunately preserving the site for its future excavations. Schliemann was to excavate Hisarlik during five separate campaigns: Mycenae (1876-78), Ithaca (1878), Orchomenus, Boeotia (1881-82), and Tiryns (1884-85); but it was the second one of 1871-1873 which proved to be famous. Ruins were uncovered soon after the excavation began at Hisarlik. Nevertheless, Schliemann was perplexed by the complexity of the mound, whose stratification resulted in the discovery of four superimposed towns (later excavations revealing nine cities). (Refer to figure 3.) To get to the supposed level of Homer’s Troy, Troy II, he dug vast trenches through the entire mound, unceasingly demolishing later structures and crucial historical evidence- his reason being that he thought it was built later than Homer, and was therefore in the way. Schliemann mentions employing large numbers of local labourers on the site, which varied from 80-125 men at a time using crude pickaxes, spades, and wheelbarrows to dispose of â€Å"intervening rubble†. On his way through the mound he destroyed the foundations of a large building. Completely ignoring all the layers which clearly revealed a variety of different settlements, he continued to dig- removing an estimated 325,000 cubic yards of earth. (Refer to figure 4.) Priam’s Treasure (refer to figure 5.) consisted of 8700 pieces of golden pendants, earrings, bracelets, rings, diadems, cups, salvers, cauldrons, vases; however Schliemann’s account of finding the treasure unfortunately is believed untrue. His fixation to reach what he considered to be â€Å"the real troy† was so intense as to render him cataloguing some of the more interesting finds even if his dating was totally wrong. Subsequent checks of dates/events do not support Schliemann’s claims. For example, Priam’s alleged Treasure was assigned to Troy II, whereas, we now know from Wilhelm Dà ¯Ã‚ ¿Ã‚ ½rpfeld’s later excavations that King Priam would have reined Troy VI or VIIa, which occupied hundreds of years later. (Refer to figure 6.) Unlike many of his scholarly contemporaries, Heinrich Schliemann regarded the stories of the ancient Greek poet Homer as being literally true. He used this as the basis of dating all artefacts obtained from the dig, essentially using philology as a method of relative dating. In an analogy to philological methods, he used the term â€Å"comparative archaeology† to his system as early as 1880, pointing out in a letter: â€Å"In its way comparative pottery is as important as comparative philology.† His diaries, such as Troja, (refer to figure 7.) reveal detailed records containing sketches and accounts of all the finds- geological, botanical, and meteorological observations. However, Schliemann worked in an era when archaeology was mostly treasure-hunting. Only some of the most advanced archaeologists were beginning to understand that excavation is a destructive process- It must be done slowly and carefully, while recording detailed information, to learn as much as possible. When Schliemann began excavating, there was no accepted practice existed for archaeological fieldwork. Stratigraphy had been observed and understood in the Danish peat bogs, the Jutland barrows, and the prehistoric Swiss Lake dwellings, but Hisarlik was the first large dry-land man-made mound to be dug. Schliemann was no pioneer of the rudimentary scientific archaeology and did not adhere to a scientific method when carelessly excavating Troy. Later on as his career progressed, he eventually enlisted the help of specialists such as Rudolph Virchow (pathologist, anthropologist, pre-historian, biologist), Archibald Sayce (linguist), Max Mà ¯Ã‚ ¿Ã‚ ½ller (German philologist and orientalist), and Wilhelm Dà ¯Ã‚ ¿Ã‚ ½rpfeld. Wilhelm Dà ¯Ã‚ ¿Ã‚ ½rpfeld, a famous architect can be accredited for teaching Schliemann archaeological method, specifically how to dig stratigraphically at Troy, majorly assisting with Troy’s stratigraphical dating methodology (and after Schliemann’s death was able to determine that Troy VI, not Troy II was most probably Homer’s Troy). Ironically, Dà ¯Ã‚ ¿Ã‚ ½rpfeld joined the team around 1882, once Schliemann had already mass-destructively excavated Troy layer-by-layer from top through to bottom. It was then that Schliemann realized that he had gone too far because the settlement at the Hisarlik site predated Troy II by 1,700 years, however all in vain as irreversible damage done to the stratigraphy meant the loss of its multiple cities. A popular tourist attraction, this can still be seen today in Turkey at the ruins of Troy where walls from different historical periods have been excavated. (Refer to Figures 8 and 9.) Many other archaeologists followed Schliemann, conducting more methodical and scientific excavations of lands surrounding the Aegean. Recent archaeology of the classic civilizations of Europe has concentrated on the lives of common citizens. American archaeologist David Soren, for example, led a research team in the 1980s in southwestern Cyprus. Soren and his team reconstructed the events of a powerful earthquake that struck the Roman port of Kourion in AD 365. Soren’s team uncovered collapsed buildings in which entire families had been buried in their sleep. Despite Schliemann’s controversial reputation as a fraudulently cunning and amateur archaeologist among historians, his discovery and excavations of Troy has left a legacy on historians and archaeologists today. More importantly, Schliemann revived the lost interest in Ancient Greek societies and was one of the first popularisers of archaeology. With his books and dispatches to The Times, the Daily Telegraph and other papers he kept the world informed and excited by his archaeological discoveries as no one had done before. (Refer to figure 14.) Most scholars considered Homer’s stories of the Trojan War to be just Myths. (Refer to figure 12.) By excavating Hisarlik, Schliemann successfully disproved them; although his work raised more controversy over the existence of troy and the authenticity and historicity of Homer’s Epic poems/cycles among historians [i.e. Michael Woods] (refer to Figure 11.). This has lead on to a legacy of excavations to be held at Troy till this day (Refer to Figure 10.) including those of Dà ¯Ã‚ ¿Ã‚ ½rpfeld, Carl Blegen, and Manfred Korfmann who all proved evidence of occupation/activity on the site from findings of skeletons, helmets, bronze weaponry as described in the Iliad; with the help of University knowledge and more advanced technology which helped draw conclusions of more accurate stratigraphy dating of the cities and artefacts. If the Trojan War is accepted as an authentic event in history, there are many opinions divided over the subject of the wooden horse leading to Troy’s downfall. Cline, a Bronze Age scholar, has suggested that the Trojan Horse could have been a reference to an earthquake, since Poseidon- the sea god also known as â€Å"Earth-shaker†- had the horse as his particular animal. (Refer to figure 16.) As mentioned earlier, Schliemann worked in an era when archaeology was mostly treasure-hunting, but he had successfully demonstrated the value of archaeology for historical purposes, being the first person to test an ancient myth by excavating an archaeological site. He discovered Homeric Troy as well as a citadel that existed long before homer- a prehistoric Bronze Age civilisation in Turkey. Prior to that, historians only recognised 4 empires: Greece, Rome, Egypt, and Babylon-Assyria. Schliemann discovered two new civilisations which lengthened the perspective of history; nearly discovering a third, situated in prehistoric Crete. Because of his errors and mistakes, archaeologists are more wary of archaeological methods of excavation and have improved in preserving/conserving sites whilst excavating. Another contribution to archaeologists was his very careful observation of pottery. In the 1800s, objects such as pottery were only important for display in museum show cases. But Schliemann insisted that pottery, even fragments of unpainted coarse ware, constitute as a historical document/clue. He realized value of pottery for chronological and stratigraphical questions. In an 1873 newspaper, Schliemann wrote â€Å"At any place, where there have been human settlements, we find lots of potsherds, which are far more durable than city-walls or fortification-walls†¦They give us two termini for the date of the enclosing walls: they can neither be older than the oldest potsherds, nor later than the latest.† For example, most historians and archaeologists of the time believed the city of Troy never existed and among the few that did, most deemed Bunarbashi-located a few miles inland from the Aegean sea as the location. Schliemann, not only argued this using philological comparison to the Iliad, but also proved that Bunarbashi could not be the site of troy, because of potsherds-he found no potsherd older than the fifth or 6th century BC. Ancient Greek historians placed the Trojan War variously in our 12th, 13th, or 14th century BC: Eratosthenes to 1184 BC, Herodotus to 1250 BC, and Duris of Samos to 1334 BC. The legacy of Troy has since prompted Hollywood’s â€Å"long love affair† with the ancient world- inspiring the genre of the â€Å"sword and sandal epics†; and continues to be a popular subject that many Hollywood directors attempt to interpret and reconstruct- despite the highly inaccurate facts regarding characters and the series of events plot development. However, they remain imbedded in our mass media and popular culture; varying from 1950s-1960s classics like that of Ben Hur, Cleopatra, Spartacus, The Ten Commandments or the more contemporary editions such as 2004 make Troy starring the likes of Brad Pitt, Eric Bana, Rose Byrne, and Orlando Bloom. (Refer to Figure 15.) In conclusion, Heinrich Schliemann’s discovery of Troy served as a stepping stone in what we know as modern archaeology. He uncovered Troy of Homeric legend and found a new world of recovered history. But the question of if he really did find Homer’s city of Troy, no one can know for sure. Whether or not it is, Schliemann definitely won himself a place in history as the â€Å"father of archaeology’- and his excavations at Troy are still widely studied by many students; who learn from his mistakes in crude methodology as well as adopt his romance for the lost city (or cities) of troy.

Bilingual Education Essay

The presence of bilingual students in U. S. schools is significant and the result of internal and external historical factors. Educators and policymakers must consider their needs and potential contribution to our education system. The multiplicity of languages and the complex nature of bilinguals renders a complicated but exciting educational field for research, practice, and educational innovation. Unfortunately, languages become entangled in political battles, dragging the education and the future of innocent children into such conflicts. Indigenous inhabitants, colonizers, and immigrants to the United States have and continue to represent a variety of language backgrounds. Like it or not, the United States is highly multilingual. Fashions in using language in education and attitudes toward bilingualism have undergone many changes since the United States became independent. During the initial colonization of the United States, European settlers used the languages of their countries of origin. The Continental Congress considered French and German important for political purposes. It recognized the need to disseminate information among disparate populations to broaden the cause of independence (Heath, 1976). The settlers established schools that educated their children in their own languages, especially French, German, Spanish, and Swedish, while teaching English as a second language. Schools that used English as the medium of instruction taught one of the other European languages as a second language ( Keller & Van Hooft, 1982). The presence of many languages in U. S. schools was an accepted reality until the 1870s. â€Å"Newspapers, schools, and societies provided instructional support for diverse languages† (Heath, 1981, p. 7). There was, however, concern for seeking a common language, especially to conduct government affairs (Heath, 1981). The original colonies and territories incorporated later into the Union comprised local governments that used different languages, such as German in Pennsylvania, French in Louisiana, and Spanish in New Mexico and California. English, nevertheless, always played an important role in the public life of the colonies because from the beginning England colonized the United States. The form of government embraced after the American Revolution reflected English values (Conklin & Lourie, 1983). Economic and historic factors helped solidify the position of English as the language of government. During the first half of the 20th century, English was imposed as the language of instruction in most states. As many as 34 states enacted laws mandating English as the language of instruction. Other languages were forbidden and teachers could be fined or jailed if found using them: â€Å"No polyglot empire of the old world has dared be as ruthless in imposing a single language upon its whole population as was the liberal republic ‘dedicated to the proposition that all men are created equal'† ( Johnson, 1949, pp. 118-119). Political, social, and economic rationales for denigrating all languages other than English advanced linguistic and cognitive theories that attacked bilingualism. Public schools quickly adopted a â€Å"sink or swim† attitude during the first half of the 20th century. Special programs such as English as a Second Language (ESL) served only adults. The assumption was that children learn languages easily and nothing special needed to be done. Nevertheless, despite the lack of public support for bilingual education, there were bilingual programs–mostly dual language programs–in private and parochial schools. These schools extended the required curriculum to include instruction in the cultural, linguistic, and religious heritages of the particular ethnic group. A great number of them were bilingual (Fishman & Markman, 1979). National interest in bilingual education spread when Title VII, the Bilingual Education Act (an amendment to the Elementary and Secondary Education Act) was enacted in 1968. This federal legislation provided funds to create bilingual programs in poor school districts (Lyons, 1990). The impact of the federal law, both good and bad, was widely felt. A number of states reversed the laws that permitted English as the only language of instruction by passing bilingual education legislation. Massachusetts was the first state to enact such a law with its Transitional Bilingual Education Act (1971). More than 20 other states followed Massachusetts’ example by creating transitional bilingual education programs (August & Garcia, 1988). Evidently, during the past two centuries, use of languages in education has been increasingly politicized. History has repeated itself but in modified ways. The acceptance of languages in education observed in the early part of the 19th century was apparent again in the 1970s but languages other than English appeared in schools with a much lower status with respect to English than they had a century earlier. The imposition of English only at the turn of the century reappeared in the 1980s, although this time some minority students were served by special English language programs rather than leaving all to sink or swim. Efforts to make English speakers fluent in other languages have also seen ups and downs. Suspicion toward foreigners in the early part of the century discouraged second language learning. Interest in foreign language learning following World War II wavered in the 1970s. The pendulum is swinging again in favor of bilingualism for English speakers. Foreign language programs are starting earlier in elementary schools and bilingual education programs that promote bilingualism are becoming increasingly popular (Met & Galloway, 1992). However, most successful bilingual programs have been created not by legislative mandates but by concerned educators and communities working together. Good education for bilingual students should not be the outcome of compliance with legislation. Schools must be willing to create good programs suitable for all students, including bilinguals. To overcome resistance to implementing bilingual education, many communities resort to politics or lawsuits to force school districts to provide bilingual education. However, political solutions create their own problems, paradoxically compromise and rigidity. For example, laws and regulations that impose a 3-year maximum for students attending bilingual education programs arose as a compromise between the forces for and against bilingual education. Research shows time and again that students profit from long-term bilingual instruction, even though some students who stay shorter periods eventually succeed in mainstream education (Kleinfeld, 1979). Consequently, it is clear that historically Americans have not showed great tolerance to linguistic diversity. There have been repeated efforts to make English an official language in the country by restricting bilingualism, as well as attempts to enhance more ESL programs on the other side. There is an ongoing disagreement regarding whether or not ESL program meets its initial objective, the ways it affects American society, and its necessity. The opponents of bilingual teaching argue it is expensive for the country, keeps immigrants socially isolated, slows down the assimilation process, creates a retreat of an official language and dissolves the unity of America. Generally, a lot of people form negative assumptions about bilingual programs based on their ideological beliefs, political views, personal observations, negative experience or simply generalizations and stereotyping based on limited knowledge about ESL classes (Rojas, 2003). These judgments usually lack evidence and logical reasoning, and thus cannot objectively analyze the program’s weaknesses or disadvantages. As Maria Brisk observes, â€Å"Much of the debate on bilingual education is politically motivated, more suitable for talk shows than for improving schools† (Rojas, 2003). And indeed, ESL programs are viewed more as a tool to solve multiple social problems (which, certainly, are also important)–minority groups’ rights, language diversity, melting pot, the unity of the country, a threat to the existence of dominant culture, and so on–instead of focusing on the quality of education our school-age population is receiving and the environment they are placed in. Policymakers should definitely pay more attention to the program’s educational effectiveness and dramatic improvement in students’ academic progress when deciding whether public schools need ESL classes. Because public schools have quite a significant influence on children’s learning and personal development, we are responsible of making it a positive schooling experience for all students despite their ethnic background or native language. Bilingual education helps students to learn English faster, provides a friendly learning environment, improves academic progress, encourages kids to become proficient in two languages, teaches cultural awareness, and preserves minorities’ linguistic human rights. It has been proven that students who are enrolled in bilingual classes have better scores on standardized tests, such as the ACT’s and SAT’s, than those who are not enrolled in bilingual classes. Bilingual education is beneficial for our country and enables students to learn English as well as keeping their native tongue for future success in our global economy. Bilingual education works in our society and should stay intact within the schools and should be funded to enable students who wish to take these classes should be able to. However, it is not the question of whether bilingual programs work (obviously they do), but more the question of how our society addresses cultural and linguistic diversity. Recent studies have proven that bilingual teaching dramatically increases students’ educational progress both in English communicational skills and other content in curriculum. Students who attend a regular English class right away usually fall behind in subjects taught in English and experience negative consequences in psychological development. ESL system doesn’t disregard the need for acquisition of English; indeed, it one of the most important outcomes of effective bilingual education programs (Zehr, 2004). Looking at the money spent on bilingual education program (when funds are being cut off from other public services across the country) may lead to consideration of abolishing bilingual system and focusing on the projects that affect all students in education system instead. The United States spends approximately $12 billion on bilingual education each year (Wood, 1997) and over $100 million was spent to study the effectiveness of ESL programs (Mujica, 2003). Because American taxpayers don’t benefit from bilingual instruction directly, many communities and states are unwilling to pay that expense and are quick to cut back regardless its potential positive results. Nevertheless, even though we give up other things that could be otherwise purchased, bilingual programs in public schools is a critical factor in foreign students’ learning process. Besides the fact that bilingual teaching dramatically increases academic performance, it also encourages more parents to send their children to school and that, in turn, motivates more students to become educated. In other words, the money spent on ESL programs should not be associated with an opportunity cost of ignoring other important problems. Instead, it is a valuable investment in students’ success at school as well as assimilation into American society. The issue of bilingual education in relationship to our global economy enables students enrolled in these classes to have a better future than those students who only speak English. Jeff MacSwan, supporter of bilingual education and assistant professor of curriculum and instruction at Arizona State University, is quoted about bilingual education in our global economy when he says, â€Å"Multilingualism is an asset, and Arizona must embrace it† (MacSwan, 1998). Arizona Senator John McCain also believes that bilingual education is an asset to children. He states that, â€Å"Arizona should strengthen them (bilingual classes) and make similar resources available to all children† (MacSwan). In fact, McCain has introduced a program that enables students to be in programs like these. McCain’s program is called â€Å"English-Plus† (MaSwan) which acknowledges the great importance of bilingualism in our modern global economy. McCain is quoted concerning bilingual education when he says, â€Å"People should not have to abandon the language of their birth to learn the language of their future†¦The ability to speak languages in addition to English is a tremendous resource to our community† (MacSwan). In addition, the benefits of bilingual education in our global economy can be seen when US Secretary Richard Riley said, â€Å"When they enter the work force in several years we will regret the inability of our children to speak two languages. Our global economy demands it; our children deserve it† (Pratt, 2000). Undoubtedly, in addition to educational advantage, adult bilinguals with a complete grasp of two or more languages, can be more successful economically and benefit more to their communities than their single-language peers. Our public services employ staff as translators in order to keep abreast of the constantly growing immigrant population. Increased marketable skills are an advantage of bilingual fluency. Because of the aforementioned educational advantages, bilinguals can offer a flexibility and level of problem-solving ability that surpasses the average monolingual. According to Graciela Kenig, author of The Best Careers for Bilingual Latinos: Market Your Fluency in Spanish to get Ahead on the Job, employers are looking for people â€Å"with a broader scope of experience and strong problem-solving ability. † (1998, p. 5). The marketplace is also focusing on the global economy. Bilinguals are uniquely qualified to give the U. S. a competitive edge. The utilization of well-educated American bilinguals can give our country a significant advantage in the global marketplace. In aspect of Rudolph Giuliani’s view that bilingual education doesn’t work and that it is too expensive should be better thought out and he should look at the benefits that come from it. Giuliani was quoted regarding bilingual education by saying, â€Å"It’s cruel to them and gives them less of a chance to succeed† (Willen, 1998). Giuliani has some reason to argue that it is too expensive considering that â€Å"New York City alone spends $300 million annually on its program serving 126,000 students† (Chavez, 1995). In addition, Giuliani has a reason to argue that bilingual education it too time consuming considering the outrageous number of students who are eligible for bilingual classes. Although these are good reasons Giuliani should realize that, â€Å"half the Hispanic children in bilingual classes (New York City) are American-born. And many- if not most- speak English better than they do Spanish† (Chavez, 1995). The number one reason why these students are enrolled in these particular classes is because that New York automatically places these students in these classes by whether or not they score above the 40th percentile on a standard eyes test. These tests should not be done because it is evident that the students are learning English just maybe not as fast at other students. Giuliani’s claims are somewhat relevant but he should consider all of the benefits that come from bilingual education. Although Giuliani believes it is too expensive this should not be an issue considering that our country can benefit as a whole with multilingualism. During the Restrictive Period (1880s-1960s) the need of being able to effectively communicate in English was motivating immigrants to learn the language and assimilate into society (Ovando, 2003). Single language was meant to unify the members of a society (Schaefer, 2003, p. 66). However, today conformity to a single language would probably be regarded as â€Å"racist† (Mujica, 2003). Currently, most people would rather agree with Eliana D. Rojas, an assistant professor of bilingual education, that the right to maintain one’s native language and culture is a part of a person’s human rights (Mujica). The main reason so many people protest attempts to implement bilingual programs in public schools is a belief that such step will lead to dissolving the unity of the country. The government provides funds for translators in most government organizations which allow immigrants to function in their own language, doesn’t encourage foreigners to learn English and thus isolates them from the rest of the community. In response, they are more likely to form a small group or even a subculture within the dominant society with different norms, values and language. â€Å"We cannot assimilate and we won’t! † one day proclaimed the executive director of the League of United Latin American Citizens, an organization originally supporting pro assimilation (Mujica, 2003, p. 2). According to the Census statistics in 2000, 18 percent of American population over the age of 5 speaks a language other than English as their primary language (Schaefer, 2003, p. 65), while 8 percent of them are classified as â€Å"limited English proficient† (Mujica, 2003, p. 2). Hispanic population is the fastest growing minority in the U. S. and large parts of the country are becoming increasingly â€Å"Latinized†. Americans â€Å"feel strangers in their own neighborhoods and aliens in their own country† (Schaefer, 2003, p. 66). It may look like sooner or later we will have to say â€Å"Hasta la Vista to the ‘United’ States and Adelante to Canadian-style discord over the issues of language and ethnicity† (Mujica, 2003, p. 4). Therefore, blaming such programs as bilingual instructing in schools is based primarily on nationalistic concerns. The recent studies have proven, though, that only a small percent of children attending bilingual classrooms will still be able to communicate in their native language in a few years (Worthy, 2003). In some ESL classes students are actually encouraged to maintain their first language and are introduced to elements from both American and their native cultures. It seems apparent that a child will more likely associate himself or herself with other immigrants rather than Americans and it may seem hard for that student to assimilate into American society. It may be difficult for him or her to learn English later because any language cannot be taught successfully in isolation – proficient communicational skills can only develop through everyday practice and a practical need to apply new knowledge. In reality it takes about the same time for a person to learn English in the all-English class than gradually switching from the native language to the regular English instructing. Despite the fact they differ in the length of the transition to English and how long they allow students to remain in bilingual classrooms, all ESL students receive enough practice and even become monolingual English speakers pretty soon, as a yearlong study of fifth-grade children attending bilingual class has proven (Worthy, 2003). As the teacher encouraged students to read, write and speak Spanish, most of them were losing their ability to communicate in Spanish and had English as their dominant language both in school and informal situations. The study concludes that at a certain time social and peer pressure are more important for children than family influence, the reason why many of them started feeling uncomfortable speaking their native language with their friends (Worthy, 2003). Evidently, bilingual education is an asset to our country and the benefits can be seen throughout our global economy. People such as Giuliani should embrace the idea of this type of education and should help fund programs as it will undoubtedly further enrich our economy. In addition, why should students loose their native language simply for the reason that the majority of people speak English? The ability to speak multiple languages enables them for future aspirations, success, and priority over those who can only speak only English fluently. Our society extremely benefits from bilingual education and there no significant reason for eliminating it. All in all, bilingual education in public schools is definitely not a threat to an official language or unity of the country. Nor it is a waste of funds since it is so essential in children’s first years of education. ESL classes do not slow down assimilation, and even if in some cases American culture is so diverse that even abolishing all programs helping immigrants to maintain their language will not have a great impact on American melting pot. Instead, English-only initiatives have only negative consequences for limited-English proficient groups and their interaction with the dominant society (Barker, 2001). Abolishing bilingual education in schools will not create an intense for immigrants to learn English, but most likely will result in protests, racial conflicts, even prejudice against minority groups, and that is a certain way to dissolve a country. References August, D. , & Garcia E. E. (1988). Language minority education in the United States. Springfield, IL: Thomas. Barker, Valerie, Howard Giles, Kimberly Noels, Julie Duck, Michael Hecht, and Richarde Clement. (Mar 2001). The English-only movement: A Communication analysis of changing perceptions of language vitality. Journal of Communication,51 (1), 3. Proquest. DeVry University, Federal Way, WA. Retrieved February 3, 2006 from http:\www. il. proquest. compdauto>. Chavez, Linda. (1995, April 2). Bilingual education was to teach English, not trap students. Minneapolis Star Tribune, 23. Conklin, N. F. , & Lourie, M. A. (1983). A host of tongues: Language communities in the United States. New York: The Free Press. Fishman, J. A. , & Markman, B. R. (1979). The ethnic mother-tongue school in America: Assumptions, findings, directory. New York: Ferkauf Graduate School, Yeshiva University. Heath, S. B. (1976). A national language academy: Debate in the new nation. International Journal of the Sociology of Language, 47(11), 9-43. Heath, S. B. (1981). English in our language heritage. In C. A. Ferguson & S. B. Heath (Eds. ), Language in the U. S. A. (pp. 6-20). Cambridge, UK: Cambridge University Press. Johnson, G. W. (1949). Our English heritage. Philadelphia: Lippincott. Keller, G. D. , & Van K. S. Hooft. (1982). A chronology of bilingualism and bilingual education in the United States. In J. A. Fishman & G. D. Keller (Eds. ), Bilingual education for Hispanic students in the United States (pp. 3-19). New York: Teachers College, Columbia University. Kenig, Graciela. (1998). The best careers for bilingual latinos: Market your fluency in Spanish to get ahead on the job. McGraw-Hill. Kleinfeld, J. S. (1979). Eskimo school on the Andreafsky: A study of effective bicultural education. New York: Praeger. Lyons, J. J. (1990). The past and future directions of federal bilingual education policy. In C. B. Cazden & C. E. Snow (Eds. ), English plus: Issues in bilingual education (pp. 66-80). Newbury Park, CA: Sage. Macswan, Jeff. (1998, August 6). Bilingual education an asset that can offer global rewards. Arizona Republic. Retrieved February 4, 2006 from www. onenation. org/0898/080698. html Met, M. , & Galloway, V. (1992). Research in foreign language curriculum. In P. Jackson (Ed. ) Handbook of research on curriculum (pp. 852-890). New York: Macmillan. Mujica, Maero E. (2003, Dec). Why the US needs an official language. The World and I, 18(12), 36. Proquest. Devry University, Federal Way, WA. Retrieved February 4, 2006 from http://www. il. proquest. com/pdauto Ovando, Carlos J. (Spring 2003). Bilingual education in the United States: Historical development and current issues. Bilingual Research Journal 27(1), 1, 25. Proquest. DeVry University, Federal Way, WA. Retrieved February 4, 2006 from http:\www. il. proquest. compdauto>. Pratt, Chasity. (2000, April 4). One class, two languages: Both English, foreign benefit bilingual schools. Newsday, 6. Rojas, E. D. & Reagan, T. (Winter 2003). Linguistic human rights: A new perspective on bilingual education. Educational Foundations 17(1), 5. Proquest. DeVry University, Federal Way, WA. Retrieved February 4, 2006 from http:\www. il. proquest. compdauto Schaefer, Richard T. (2003). Sociology: A Brief introduction. McGraw Hill: New York Willen, Liz. (1998, January, 16). Bilingual debate: Rudy’s push to limit education programs draws flak. Newsday, 8. Wood, Daniel B. (1997, July 30). Next big push from California: No bilingual education. The Christian Science Monitor United States. Retrieved February 4, 2006 from http://csmweb2. emcweb. com/durable/1997/07/03/us/us. 1. html Worthy, J. , Alejandra Rodriguez-Galindo, Lori Czop Assaf, Leticia Martinez and Kimberly Cuero. (Summer 2003). Fifth-grade bilingual students and precursors to ‘subtractive

The American Revolution - 877 Words

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