DSP-OFDM Modulator Project

DSP-OFDM Modulator Project Chapter One Introduction to the DSP-OFDM Modulator Project 1.1 Introduction The Orthogonal Frequency Division Multiplexing (OFDM) digital communication technique has been attracting a great concern of researchers all over the world, due to its unique characteristics. The designers and engineers of mobile wireless communication systems and wireless multimedia broadband are looking forward to exploit the OFDM to be the air interface of these devices and systems. This exploitation has already been done with several systems and standards such as Wireless Local Area Networks 802.11a and Digital Video Broadcast-Terrestrial (DVB-T). The DSP-OFDM Modulator project studies the essential parts of the OFDM modulator and demodulator and implements the OFDM modulator and demodulator on two separate DSP boards. For the OFDM modulator, the project studies the hardware DSP implementation of the OFDM modulators different parts such as the QAM mapper and the IFFT. This applies on the OFDM demodulator too. Additionally, for the OFDM demodulator, the project studies the carrier recovery issue to recover the OFDM information signal from the carrier signal and the OFDM symbol timing recovery issue to correctly pinpoint each OFDM symbols boundaries. The Projects involves several aspects of the digital communications and the theoretical and practical DSP and uses the MATLAB and the Code Composer Studio (CCS) to analyze and simulate the designs to be practically implemented. 1.2 The Aim and the Objectives The aim of the DSP OFDM Modulator project is to implement OFDM modulator and demodulator on two separate DSP boards. The implementation is not tied to any existing OFDM standard such that used in the DVB-T or other standards. The DSP hardware implantation comprises many DSP and digital communication operations to be implemented through writing the C codes that perform these operations i.e. the QAM mapping and de-mapping, the IFFT and FFT, the digital IIR filters and the synchronization. Therefore, the implementation will be first simulated by MATLAB and the Code Composer Studio (CCS) part by part before and with the hardware implementation on the DSP boards. The CCS will be used to simulate not only the modulator and demodulator but also the subparts of the hardware implementation such as the FFT and IFFT C codes. For example, the C code that will be used to perform N-Point IFFT to a complex array containing N complex elements to produce N outputs. These N outputs or discrete values will be compared with those N outputs or discrete values obtained from performing N-Point IFFT to the same N element-complex array in MATLAB in order to check that this C code will work properly in the DSP real time implementation of the OFDM modulator. 1.3 The Research Background and Motivations The good presentation of the theoretical and practical DSP during the taught part of the course encouraged me to tackle this project, as I had not done any practical DSP before I enrolled in the MSc Wireless Communication Systems course. The good understanding of the discrete Fourier transform (DFT) allows presenting the Conjugate Symmetric approach. The use of the Conjugate Symmetric distribution of the subcarrier vectors on the IFFT input points makes the IFFT produce a multicarrier signal with a real part (In-phase) (I) only in the time domain, as the imaginary part (Quadrature) (Q) is always set to zero. It is easier to modulate and demodulate the OFDM information signal with a real part only, as the quadrature modulation is no longer required. The Conjugate Symmetric proposal allows applying the FM modulation to transmit and receive the multicarrier OFDM information signal. 1.4 The Thesiss Organization The thesis consists of five chapters. Chapter two is considered as a literature survey. Chapter two explains the OFDM spectrum and the principles of the OFDM modulator and demodulator. It illustrates how the OFDM information signal carries or represents the digital data bits and how the IFFT N outputs (discrete values) are actually the samples of the OFDM multicarrier information signal for the current OFDM symbol being generated. It will be shown how the OFDM symbol has longer duration than those of other digital communication modulation techniques without affecting the data rate to be more resilient with dispersive channels and many other aspects of the OFDM modulation technique. This project is not tied to any existing OFDM standard. However, it resembles these standards in terms of the general block diagrams of the OFDM systems and the use of the pilot carriers, hence the employment of the OFDM in the DVB-T and the WLAN 802.11a are described briefly in chapter two. Chapter three shows and simulates by using MATLAB the approaches and ideas that will be used for the hardware DSP implementation. It discusses the (Conjugate Symmetric) proposal that has come out of this project to facilitate the modulation and demodulation of the OFDM information signal and the use of the squared cosine method to recover the OFDM information signal from the modulated carrier signal. The use of the cyclic prefix (CP) to recover the OFDM symbol timing is also discussed in chapter three. Chapter four presents the hardware implementation of the DSP OFDM modulator and demodulator on two separate DSP boards and shows the different results of the hardware implantation on the oscilloscopes screen as well as it shows the results of the CCS simulation of the OFDM modulator and demodulator and compares the OFDM spectrum of the generated OFDM information signal generated by the Conjugate Symmetric approach with that generated from the traditional method. Chapter five is for the conclusion points that have come out of this project and the further work to be implemented in the future. The attached CD contains the real time DSP implantation CCS projects of the OFDM modulator (OFDM-TX project) and OFDM demodulator (OFDM-RX project) and the CCS simulation of the OFDM modulator and demodulator (Simulation project) as well as the MATLAB codes and an electronic copy of the thesis. Chapter Two OFDM Basics 2.1 Introduction In the digital communications, the transmitted signal over a wireless channel is more preferred, when the symbol duration is significantly greater than the delay spread (s) of this channel to avoid the intersymbol interference (ISI) due to the time dispersion of transmitted symbols. But unfortunately, the symbol duration is reversely proportional to the bit rate which means a great constraint when high data rate transmission is required over a wireless channel with a relatively high delay spread due to the multipath environment of that channel [1]. The OFDM technique produces the solution to this problem, as it divides the high rate bit stream into (N) very low rate bit streams that are transmitted simultaneously using (N) orthogonal subcarriers for every OFDM symbol. Each of these low rate bit streams modulates an individual subcarrier. Therefore, the symbol duration is increased as many as (N) times without reducing the actual bit rate. 2.2 The Spectrum of the OFDM Subcarriers Figure (2-1) y(t) (the dotted curve) is the algebraic summation of the 5 sinusoidal waves Figure (2-2) the spectrum of y(t) in the frequency domain (five stems or tones) Figure (2-3) the rectangular function with (?t) duration in the time domain Figure (2-4) the spectrom of the rectangular function in the frequency domain Figure (2-5) the spectrum of the OFDM symbol with five subcarriers Suppose y(t) is a signal consisting of the algebraic summation of five sinusoidal waves (subcarriers) in the time domain with five different frequencies (f1, f2, f3, f4 and f5) respectively figure (2-1). Suppose these subcarriers have the same frequency spacing (?f) between each adjacent subcarriers in the frequency domain. The spectrum of y (t) in the frequency domain in terms of the magnitude has five stems at f1 to f5 respectively. Each stem (single tone) represents one of these five sinusoidal waves or subcarriers figure (2-2). Now, suppose an OFDM symbol (with symbol duration = (?t)) consists of the same five sinusoidal subcarriers mentioned earlier. The spectrum of this OFDM symbol in the frequency domain does not now consist of five stems; instead the spectrum is like that one in figure (2-5). The spectrum in figure (2-5) consists of five overlapped sinc functions each of which represents an individual subcarrier. Actually, our OFDM symbol is not identical to y(t). More precisely, it is a (truncated y(t)) with truncation duration equal to the OFDM symbol duration (?t). When a signal is truncated in the time domain with equal gain over all the truncated points within the period (?t), that means mathematically multiplying this signal with a rectangular function in the time domain with a time duration equal to (?t) figure (2-3). The shape of the spectrum of rectangular function in terms of the magnitude is single sinc wave in the frequency domain cutting the horizontal axis at points equal to the integer multiples of the reciprocal of the time duration (1/?t) figure (2-4). Basically, when any two signals are multiplied in the time domain, the resultant signal of this multiplication has a spectrum in the frequency domain equal to the convolution of the spectrums of the two original signals. Therefore the spectrum in figure (2-5) represents the resultant of the convolution operation between the fiv e stems of y(t) figure (2-2) and the sinc of the rectangular function figure (2-4) in the frequency domain. Looking at figure (2-5) again, it is easy to notice that the peak of each subcarrier sinc occurs at a point where all other four sincs have magnitudes equal to zero at which. This situation is the condition of the orthogonality between the subcarriers as it ensures the least interference between the subcarriers in the frequency domain. The orthogonality between subcarriers is not achieved, unless the frequency spacing between the subcarriers (?f) is equal to the reciprocal of the OFDM symbol duration (1/(?t)) [2]. 2.3 The OFDM Modulator The OFDM Modulator uses the Quadrature Amplitude Modulation (QAM) Mapper and the Inverse Fast Fourier Transformer (IFFT) to simultaneously generate and modulate the subcarriers of each OFDM symbol. Figure (2-6) shows a general block diagram of the OFDM modulator. The OFDM modulator builds and transmits each OFDM symbol consisting of a number of subcarriers equal to N as follows. The QAM mapper maps the data bits to (N) QAM vectors. Each of these vectors has real and imaginary components and represents a single subcarrier. The number of data bits that are mapped to each QAM vector (subcarrier) depends on the QAM order (M) as shown in table (2-1). Using QAM mapper with higher order produces higher data rate. However, this will be at the cost of the reception quality as the constellation of higher order QAM allows higher Bit Error Rate (BER) for a given The QAM Mapper stage maps data bits to QAM vectors in accordance with the QAM constellation. The Serial to Parallel (S/P) buffers the QAM vectors of each OFDM symbol to prepare them for the IFFT operation. The IFFT stage converts the buffered QAM vectors (the subcarriers) from the frequency domain to produce an OFDM symbol sequence equivalent to the algebraic summation of these sinusoidal subcarriers in the time domain to be buffered in the next stage. Guard Interval Insertion and Parallel to Serial stages add the guard interval to each buffered OFDM symbol sequence and produces it serially to the next stage. The DSP Low Pass Filter (LPF) and The Digital to Analogue Convertor (DAC) stages are to smooth the signal and convert the digital sequence into analogue signal. The Up Conversion and The Power Amplification stages. Figure (2-6) general block diagram of the OFDM modulator. The 4-QAM constellation, which is identical to Quadrature Phase Shift Keying (QPSK) constellation, gives the receiver more tolerance to the changes of the amplitude and phase of any received QAM vector and allows the receiver to de-map it to the correct 2-bit-combination, as long as it still lies in the same quadrant from which it was originated at the transmitter, whereas 16 and 64 QAM constellations give less tolerance to the change in the phase and amplitude of the received QAM vector due to the noise and interference. Not all subcarriers of an OFDM symbol are used to carry the data bits, some of which are used as pilot carriers for the synchronization and channel estimation purposes and for providing the receiver with specific information such as the order of QAM being used by the transmitter. The Serial to Parallel (S/P) stage buffers the N vectors from the QAM stage for each OFDM symbol to produce them in parallel way to IFFT stage. The number of IFFT points is always greater than the number of the subcarriers (N), so the (S/P) pads the remaining IFFT points, which have not been assigned QAM vectors, with zeroes. The IFFT stage is the heart of the OFDM modulator. It gives the QAM vectors the mathematical ability to be considered as the OFDM subcarriers in the frequency domain and converts them to the time domain to form the multi-subcarrier information signal. In other words, as all the (N) QAM vectors of each OFDM symbol are the parallel inputs of the IFFT operation, the IFFT stage considers these QAM vectors as tones or stems in the frequency domain and converts them into correspondent subcarriers in the time domain for the given OFDM symbol duration. Each QAM vector has a specific phase and amplitude which corresponds to the bit combination this vector represents in accordance with the QAM constellation. The IFFT coverts each QAM vector into a correspondent sinusoidal subcarrier in the time domain with amplitude and phase directly related to those of that vector and a frequency that is directly proportional with the sequence of IFFT point, to which the vector has been assigned. That means if a QAM vector with sequence (n) (assigned to an IFFT point with sequence n) generates a subcarrier with frequency equal to (f), the vector with sequence (n-1) generates a subcarrier with a frequency equal to (f ?f) and the vector with sequence (n+1) generates a subcarrier with a frequency equal to (f + ?f). The IFFT stage can simultaneously produce all the N-subcarriers for each OFDM symbol as it performs the conversion from the frequency domain to the time domain for N (QAM vectors) in one parallel operation for each OFDM symbol. The OFDM symbol signal in the time domain represents the algebraic summation of all subcarriers of that symbol. Now, it is obvious how the OFDM modulator divides the high rate bit stream into (N) lower rate bit streams which are simultaneously transmitted over (N times higher OFDM symbol duration) without reducing the actual bit rate. The Guard Interval Insertion stage appends a guard period at the beginning of each OFDM. The Guard Interval (GI) (also called the Cyclic Prefix (CP)) makes a separation between the consecutive OFDM symbols to contribute in the ISI reduction and to eliminate the Intercarrier Interference (ICI) between the subcarriers. The guard interval must be greater than the highest path difference duration. As a result, multipath signals with delay smaller than the GI cannot cause ICI [3]. The guard interval is generally equal to or less than the quarter symbol duration [4]. Practically, the guard interval is generated by taking an exact copy of the end part of the OFDM symbol and adding it to the beginning of the symbol. The guard interval (GI) can be used by the receiver to determine the beginning and end of each received OFDM symbol through the cross correlation operation. Now, the sequence of the OFDM symbol is converted into serial sequence. The Guard Interval Insertion and the Parallel to Serial (P/S) stages are shown as one stage in figure (2-6). The DSP LPF smoothes the information signal. The Digital to Analogue Convertor (DAC) converts the incoming digital sequence into analogue signal. Finally, the Up Conversion and Power Amplification stage mixes the information signal with a locally generated carrier and boosts the resulted signal to be transmitted. The input data bits to the OFDM modulator in figure (2-6) may be first scrambled for the security purposes, encoded for the Forward Error Correction (FEC) purposes and interleaved (to randomize the bursts of error [5]). Therefore, scrambler, encoder and interleaver blocks may precede the other stages to provide the OFDM modulator with scrambled, encoded and interleaved coded bits [6]. It is also possible to up convert the signal whilst it is still in the digital signal processing domain before converting it to the analogue form. The Carrier Recovery and the Down Converting stage recovers the information signal from the carrier signal. The Sample and Hold circuit and the Analogue to Digital Convertor (ADC) stage converts the information signal from the analogue form to produce the digital sequence for the DSP processing. The Guard Interval Removal and the Serial to Parallel (S/P) stage removes the cyclic prefix (CP) and produces all the useful samples of the current OFDM symbol being processed to the FFT stage simultaneously. The FFT stage converts the subcarriers of the OFDM symbol from the time domain to the frequency domain and produces them to the QAM De-mapper as vectors through the (P/S) buffer. One tap Equalizer can be used to equalize the vector constellation after the FFT stage. The Parallel to Serial (P/S) stage buffers the vectors of each OFDM symbol to produce them serially to the QAM De-mapper. The QAM De-mapper assigns each vector to the correspondent bit combination to produce the data bits. Figure (2-7) general block diagram of the OFDM demodulator. 2.4 The OFDM Demodulator The OFDM modulation operation is completely reversed in the demodulator. At first, the information signal must be recovered from the carrier. This is done by the carrier recovery and down converting stage. Figure (2-7) shows a general block diagram of the OFDM demodulator. The analogue to digital convertor (ADC) converts the information signal into a digital sequence. The guard interval removal stage removes the inserted guard interval or cyclic prefix from the beginning of each OFDM symbol. The OFDM demodulator could use the cyclic prefix at the beginning of each OFDM symbol to pinpoint the beginning and end of each symbol, as the cyclic prefix at the beginning of each OFDM symbol is identical to the end part of that symbol within a duration equal to the cyclic prefix duration. Now, the digital sequence of each OFDM symbol, which represents the algebraic summation of the subcarriers signals in the time domain, is simultaneously presented to the FFT stage to convert these subcarriers into their correspondent vectors in the frequency domain. The parallel presentation of the symbols digital sequence to the FFT stage involves the idea of serial to parallel conversion of this sequence. The subcarriers may also be equalized before being presented to the QAM de-mapper using a one tap equalizer. The QAM de-mapper assigns each vector in the frequency domain to the correspondent binary bit combination in accordance with the QAM constellation being used in the transmitter and receiver. The serial sequence of the received coded bits must be de-interleaved and then decoded and descrambled, if the scrambling, encoding and the interleaving are applied in the transmission side. The number of data bits per each OFDM symbol can be easily calculated by multiplying the number of subcarriers that are used to carry the data bits (Payload subcarriers) by the number of bits represented by the QAM vector in accordance with the QAM constellation table (2-1). The carrier recovery operation can also be done after the sample and hold stage within the digital signal processing unit. 2.5 Digital Video Broadcasting-Terrestrial (DVB-T) The DVB-T employs the OFDM due to its excellent performance in the multipath environments which are common in the terrestrial broadcasting, as the OFDM distributes a high bit stream over a high number of orthogonal subcarriers, each of which carries a low bit rate stream simultaneously, which makes the symbol duration much higher than the delay of the indirect paths [7]. The DVB-T has two modes 2K and 8K. As 2K and 8K modes have the same data rata, selecting which mode should be used depends on the requirements. The 2K mode has about 250 Â µ S symbol duration and 4 KHz spacing between its subcarriers, whereas the 8K mode has about 1 m S symbol duration and 1 KHz spacing between its subcarriers. These characteristics make the 8K mode with its higher symbol duration more resilient with multipath situations and channels with a high delay spread but the 2K mode resists better the shift in the frequency caused by Doppler effects due to the relative mobility between the transmitter and receiver, as it has higher frequency spacing between its subcarriers. The DVB-T has (FEC) similar to that of the DVB-S (Satellite) [8]. It has the following code rates (1/2, 2/3, 3/4, 5/6 and 7/8). Not all subcarriers are used as payload carriers to carry the coded bits (data bits + redundant bits); some subcarriers are used for channel estimation and correction. These subc arriers are the pilot carriers which have vectors lying on the I (In-phase) axis of the QAM constellation with angles equal to either 0 degrees or 180 degrees, hence they have only real components unlike the payload vectors which have real and imaginary components in order to recognize between them. The mapping of the pilot carriers to be delivered as vectors to the IFFT stage in the OFDM modulator is achieved through the BPSK modulation which uses the I (in-phase) axis of the constellation. Figure (2-8) shows the locations of DVB-T subcarriers on the 4-QAM constellation. The locations of the payload carriers The locations of the continual and scatter pilot carriers The locations of the TPS pilot carriers Figure (2-7) general block diagram of the OFDM demodulator. The DVB-T uses 4, 16 or 64 QAM to modulate the coded bits to be represented as payload subcarrier vectors, therefore each payload subcarrier can carry 2, 4 or 6 coded bits every OFDM symbol respectively. The DVB-T uses a guard interval length equal to (1/4, 1/8, 1/16 or 1/32) of the OFDM symbol duration [8]. 2.5.1 The DVB-T OFDM Subcarriers The DVB-T 2K mode has 2048 subcarriers, but it only uses 1705 subcarriers and sets the rest to zero. The 1705 carriers are numbered from 0 to 1704. It uses 1512 subcarriers as payload carriers and the remaining 193 subcarriers as pilot carriers. There are three types of the pilot carriers the continual pilots, scatter pilots and the (Transmission Parameter Signaling) (TPS) pilots. The continual pilots have fixed positions in the OFDM symbol spectrum. For example the sequences 0, 48, 969, 1683 and 1704 in the range (0 1704) are reserved as positions for the continual pilots. The continual pilots are used by the receiver to estimate the amount of phase rotation of the received QAM vectors. Every group of 12 subcarrier vectors has only one scatter pilot. The scatter pilots do not have fixed positions. Among each 12 carriers positions there is one variable position for one scatter pilot. The position of each scatter pilot regularly varies from symbol to symbol by jumping 3 positions for ward with respect to its position in the previous symbol. The scatter pilots are used to estimate the channel too. The TPS pilot carriers have fixed positions and are used by the transmitter to inform the receiver about the transmission parameters such as. The DVB-T mode (2K or 8K) Modulation type of the payload subcarrier vectors (4, 16, or 64) QAM FEC code rate (1/2, 2/3, 3/4, 5/6 or 7/8) Length of the guard interval (1/4, 1/8, 1/16 or 1/32) Like the continual and scatter pilots, the TPS pilot carriers lie on the I (in-phase) axis. Each OFDM symbol in the 2K mode has 17 TPS pilot carriers with fixed positions. Within the same symbol all the 17 TPS pilots are either at 0 degrees or 180 degrees. The receiver determines the state of TPS pilots whether the TPS pilots of the received symbol are at 0 degrees or 180 degree based on the majority voting rule. Through the TPS pilots, the transmitter sends the receiver 67 information bits every OFDM frame. The OFDM frame consists of 68 OFDM symbols. The TPS pilots are Differential Bi-Phase Shift Keying (DBPSK) modulated. That means the receiver considers receiving an information bit = (0), if the state of the TPS pilots change from the previous symbol to the current symbol and considers receiving an information bit = (1), if the phase or state of the TPS pilots does not change from the previous symbol to the current symbol. 68 OFDM symbols are required to transmit the 67 informatio n bits, as the first symbol is used to determine the initializing state of the TPS pilots. The 67 bits inform the receiver about the transmission parameters, for example: Bits 26 and 27 represent the QAM order (00=4, 01=16, 10=64) Bits 31, 32 and 33 represent the code rate (000=1/2, 001=2/3, 010=3/4, 011=5/6, 100=7/8) The DVB-T 8K mode has 6817 subcarrier per each OFDM symbol. The subcarriers of the 8K have the same principles and use of those of 2K with difference in their numbers only. Table (2 2) shows the different subcarriers of both 2K and 8K modes. The scatter pilot carriers have two different numbers of the subcarriers, as the scatter pilot carriers coincide with fixed locations of the continual pilot carriers due to their jumping [8]. 2.6 WLAN 802.11a Wireless Local Area Networks (WLANs) 802.11a employ OFDM as a digital communication technique for reliable and high data rate transmission. Each OFDM symbol is expressed by 64 subcarriers, but the actual used subcarriers are (52) (64 52 =12 subcarriers are set to zero). There are 48 payload carriers to carry the coded bits (data and redundancy bits) and 4 pilot carriers. The frequency spacing between the subcarriers is (?f = 312.5 KHz). The required channel bandwidth can be calculated by multiplying the total number of subcarriers by the frequency spacing = 312.5 K * 64 = 20 MHz. To achieve the orthogonality between the subcarriers the OFDM symbol duration (?t) must be equal to the reciprocal of (?f) (?t = 1/ ?f), hence ?t = 1/312.5 KHz = 3.2 Â µs. 802.11a appends a guard interval (GI) equal of (1/4) the OFDM symbol duration at the beginning of each OFDM symbol (GI = 0.25 * 3.2 Â µs = 0.8 Â µs), therefore each OFDM symbol occupies (3.2 Â µs + 0.8 Â µs = 4 Â µs) time interval. That means a wireless device transmits 250,000 OFDM symbol per second. 802.11a allows wireless devices to have (8) transmission data rates or modes (6, 9, 12, 18, 24, 36, 48 and 54) M bits/sec. 802.11a uses (BPSK, QPSK, 16-QAM or 64-QAM) to modulate the payload carriers and uses (1/2, 2/3 or 3/4) code rate for the FEC in accordance with transmission data rate being used. The different (8) modes use different modulation types and different code rates as shown in table (2-3) [6]. 802.11a uses BPSK modulation to modulate the payload carries in modes 1 and 2 unlike the DVB-T which only uses QAM modulation to modulate the payload carriers. For each mode, the OFDM symbol has the same total duration (4 Â µs) (250,000 OFDM symbol/Sec) and the same channel bandwidth (20 MHz), as it has the same number of subcarriers (48 payload carriers and 4 pilot carriers). Looking back at table (2-3) (Mode (8) 54 Mbps), as the 64-QAM modulation is used to modulate the payload carriers, each payload carrier in the OFDM symbol carries (log2 (64) = 6 coded bits). Each OFDM symbol carries (48 payload carriers/OFDM symbol * 6 coded bits/payload carrier = 288 coded bits / OFDM symbol). The number of data bits per each OFDM symbol = 288 * (code rate = 3/4) = 216 data bits / OFDM symbol. There are 250,000 OFDM symbols / Sec, hence the data bit rate = 216 * 250,000 = 54 Mbps. Chapter Three The MATLAB Analyses for the Hardware Implementation Approaches 3.1 Introduction Throughout this chapter the ideas and approaches that will be used for the DSP hardware implementation of the OFDM modulator and demodulator on two separate DSP boards will be discussed and simulated by using the MATLAB. There are mainly three approaches. The use of the (Conjugate Symmetric) with the carrier vectors which are the inputs of the IFFT stage in the OFDM modulator to produce an OFDM information signal in the time domain with a real part only for easier modulation and demodulation, which is the proposal that has come out from this project. The use of the squared cosine to recover the OFDM information signal from the carrier signal in the receiver (the synchronization of the carrier frequency signal). The make use of the guard interval (GI) or the cyclic prefix (CP) for the synchronization of the OFDM symbol (i.e. The Symbol Clock Recovery) to allow the receiver to know the correct boundaries of each received OFDM symbol to set the FFT window at the correct positions of the received OFDM signal. 3.2 The Mathematical Analysis of a Multicarrier Signal To understand the idea of the (Conjugate Symmetric) and the role of the IFFT and FFT in the OFDM system, lets consider y(t) as a continuous multicarrier signal with a real part only in the time domain consisting of the algebraic summation of five sinusoidal waves or subcarriers which have the following frequencies (1, 2, 3, 4 and 5) KHz and phase shifts (p4,,3p4, 5p4, 7p2, 9p4) respectively with equal amplitude = (28) for each. For our y(t), each two adjacent subcarriers (in the frequency domain) have 90 degrees phase shift. y(t) can be expressed in the time domain as in Eq. (3-1) It is not necessary for the five subcarriers forming y(t) to have the same magnitude. It is just to simplify this discussion. Now, if y(t) is sampled with sampling frequency (Fs). Fs must be greater than (2 * 5 KHz = 10 KHz), where 5 KHz is the highest frequency of y(t) according to the Nyquist-Shannon theorem. Nyquist-Shannon theorem stipulates that the sampling rate or frequency must be at least two times greater than the highest frequency of the sampled signal to avoid the aliasing which prevents providing the DSP system with a right copy of the sampled signal [9]. When a continuous signal in the time domain is sampled, a sample is taken at every (t = n * Ts). Ts is the sampling interval (Ts = 1 / Fs) and n is zero or positive integer number representing the sequence of the sample. y(t) is no longer continuous. Now, y(t) represents a sequence of discrete values. In Eq. (3-1), y(t) is replaced by y(n) in the left hand side and (t) is replaced by (n * Ts) or (n / Fs) in the right hand side as in Eq. (3-2). If Fs is set to 16 KHz (16 KHz > 10 KHz) and 16-point FFT operation is performed to y(n) to produce y(n)s spectrum in the frequency domain in order to study it. The 16 point FFT operation needs 16 discrete values or samples of y(n) for n = 0, 1, 2,13, 14, 15. The results of 16 point FFT operation are 16 complex vectors in the frequency domain. The 16 discrete values (samples) of y(n) are the inputs of the FFT in the time domain and the outputs are 16 complex vectors of Y(m) which represents y(n)s spectrum in the frequency domain. Table (3-1) lists the 16 discrete values of y(n) in the time domain and table (3-2) lists the 16 vectors

Power To change An Event In History Essay

Cold War precipitated fifty years of propaganda by two super powers, on-field battles while balancing barrels on others’ shoulders and huge amount of capital investment to manufacture weapons. An even in history that could have easily averted the Cold War was Stalin’s opportunistic rise to power on death of Lenin in 1924. Undoubtedly, a single event that I could change would be the ability to delay the death of Lenin.   Noted historians and Russian policy experts admit that Stalin was not Lenin’s choice. Lenin was aware that rude negotiation and ruthless intention were the qualities of Stalin’s personality. He would have definitely blocked Stalin’s rise to power. However, Stalin went on take advantage of the situation that arose from Lenin’s death. He easily sidelined Trotsky and other senior members of the communist party. In first few years of his rule, Stalin systematically got his adversaries assassinated. Through the policy of â€Å"collectivization† of farms, Stalin inflicted deep scars of famine on the Russian people. Medium and large farms were forcibly acquired by the state in order form huge collective farms this led to steep drop in agricultural output. Since, the ideals of Soviet Union prevented from any import or export, millions of people died because of starvation. Within few years of coming to power, Stalin acquired the status of a totalitarian. In 1945, George Orwell crafted a wonderful satire that depicted the greed and corruption as the driving motives behind a dictatorial regime. (Orwell, George, 1945) USA and other allies of World War 2 soon realized that Stalin has built a fear of his personality to control and intimidate other members of the Soviet Union. Perhaps the most gruesome of his policies were to imprison millions of Russians and use them in labor camps for construction of roads and dams. Because of his policies, USSR and USA got embroiled into issues like Korea War and Vietnam War. Even though Stalin died in 1956, his policies continued to haunt the world for decades. Had Lenin survived a few hours and passed the command to a more humane leader, the world would have been considerably more prosperous and secure for the next fifty years. Bibliography Orwell, George. â€Å"Animal Farm† London. 1945

Robert Rauschenbergs Combines

The Beliefs Of The Amish s Worldview - 1335 Words

The main focus of the Amish’s worldview is to bring themselves and their community closer to God. Geertz’s theory of religion explains that religious people find their meaning of the world through their â€Å"system of symbols† (Geertz, page 349). This meaning is then applied to situations in which the religious man has trouble comprehending. Considering, the Amish’s worldview is based on the need to be closer to God, they pray to become closer to him in times of suffering and sickness. Though prayer is their main way of finding meaning when they or their family is sick, the Amish will also use additional practices to help get better. One of the essential beliefs of the Amish is to allow God’s Will to be done. The Amish’s worldview has lead them to live a lifestyle free of many modern conveniences. They rid themselves of these modern commodities because they believe their lifestyle allows them to be closer to God. Since there is such a large emphasis on letting the Will of God happen, the Amish view death and sickness in a different way than most. The Amish do not see death as a negative thing because they consider themselves simply â€Å"pilgrims passing through this world† (The Amish) and once they die they move on Heaven with their God. Throughout the readings I have done for this class, there is in fact little exact mention of the way in which Amish pray. One of the times Amish prayer is mention is in the video called The Amish where they talked about how the Amish usually areShow MoreRelatedThe Debate Regarding Parents Control Of Their Children s Education1739 Words   |  7 PagesWiscon sin v. Yoder (1972) talked about the Free Exercise Clause by putting together a three-part explanation to balance out people s education and religious freedom. â€Å"The balancing test marked the move from belief-action doctrine in the nineteenth century.†(Politics, 2014) Through the case its decisions impacted the debate regarding parents control of their children s education. Free Exercise Clause of the First Amendment posed some challenges to court, which was faced with the conflicts betweenRead More The Impact on Culture of Islam and Christianity Essay3721 Words   |  15 Pagesreligion has two parts in the Webster’s dictionary, the first being a simple belief or reverence in a supernatural being, the second being a personal or institutionalized system grounded in such belief. The common man often sees the large religions in the simplest forms, creating obvious differences between the basic beliefs of major religions. These differences, seen in the comparison o f Judeo-Christian and Islam worldviews, have had an immense impact upon each separate culture and interpretationRead MoreA Brief Note On Ultra Orthodox Jewish Culture Essay2335 Words   |  10 Pagesin focus is current Hasidism, an Ultra-Orthodox sect of Judaism which preserves its religious conservatism and social isolation from mainstream society. (Levine, 2016) Ultra-Orthodox Jewish culture maintains historical customs and likens to the Amish culture from outside observation, their community and family lives have seemingly stopped in time. They are recognizable by their differential style with characteristics reminiscent of the eighteenth and nineteenth century. The males adorn black

Nonvaccinated Children in Public Schools - 1793 Words

Non-vaccinated Children Allowed to Attend Public Schools – This Is Not Acceptable Assignment 4 – Persuasive Paper Part 1: Revision of a Problem Exists English 215 February 24, 2013 This is a question that every parent must consider when they allow their school-aged child to attend public or even private school. How do you feel about allowing your child to attend school with children who have not been vaccinated? Would it bother you? I’m sure there are several different answers to these questions. This paper will focus on the reasons why unvaccinated children should not be allowed to attend public schools as well as the benefits of vaccination. Every parent wants to raise a healthy child. Every parent wants to make sure†¦show more content†¦The US Court of Federal Claims Office of Special Masters, between 1988 and 2009, has awarded compensation to 1,322 families whose children suffered brain damage from vaccines. Even though these cases were brought to the public, we have to keep in mind that every child is different. We all react differently to medications and vaccinations. On August 25th, 2011 the Institute of Medicine issued an 800-page r eport, â€Å"Adverse Effects of Vaccines: Evidence and Causality†. This report provided the outcome of many studies done regarding the link between vaccinations and possible side effects. According to the conclusion, the evidence was negative to an effect of possible brain damage. There is no better solution to keeping our children safe except for vaccinating them. As mentioned previously, it does not only help our children but others around them. Vaccinations can save lives especially within the beginning years of life. I think that every state should have mandatory laws for vaccinating children. This is considered a benefit and not a hindrance. References Phyllis Freeman, The Biology of Vaccines and Community Decisions to Vaccinate, Public Health Reports, Jan.-Feb. 1997 Childrens’ Hospital of Philadelphia Vaccine Education Center, A Look at Each Vaccine: MMR (Measles, Mumps and RubellaShow MoreRelatedNonvaccinated Children in Public Schools1785 Words   |  8 PagesNon-vaccinated Children Allowed to Attend Public Schools – This Is Not Acceptable Assignment 4 – Persuasive Paper Part 1: Revision of a Problem Exists English 215 February 24, 2013 This is a question that every parent must consider when they allow their school-aged child to attend public or even private school. How do you feel about allowing your child to attend school with children who have not been vaccinated? Would it bother you? I’m sure there are several different answers to theseRead MoreUsing Kingdon s Policy Streams Model1199 Words   |  5 Pagesstates in the country that is considered to be more lenient on vaccination requirements for school aged children. The Nevada school system will take medical and religious exemptions when it comes to vaccinations. All fifty states and the District of Columbia grant medical exemptions to immunization requirements (Blank, Caplan, Constable, 2013). While medical exemptions are a rational reason as to why children cannot receive certain vaccines the question that is being asked is: whether or not religious

Compare the Ways Free Essays

To highlight this attention has to be given to the story and roots of youth work in England. One of the first types of youth work provision was the early network of Sunday Schools founded by Robert Raises and Hannah Moore in 1780. Their idea was to morally educate the children and young people of the working classes because at this time less than a third of children of school age actually attended school; hence the young population, especially females, were uneducated (Smith, Bibb). We will write a custom essay sample on Compare the Ways or any similar topic only for you Order Now However the working class attempted to create bottom-up forms of education themselves with the formation of the Young Man’s Christian Association in 1844 by George Williams. Within the association were the early characteristics of a youth work approach and an emphasis on healthy spiritual well-being especially for city dwelling young males (Smith, AAA; Smith, Bibb). This reflects the morally upright and patriarchal Victorian views of the time along with the recognition of youth as a discipline in its own right (Staunton Rogers, 2004). By the mid nineteenth century the struggles of the working class had been all but lost with the influx of top-down institutions which were mainly church led. Toward the end of the century young sections of the population were identified as needing activities to engage in to improve their leisure time and to maintain social control. It was widely accepted that this leadership would be undertaken by a range of philanthropic institutions and state run establishments. One of the most significant youth organizations of this period was the Scouting movement started by Robert Baden-Powell. To accentuate the importance of state social control and the Liberalism’s political agenda school attendance became compulsory up to the age of ten with the introduction of the 1880 and 1902 Education Acts (Smith, AAA). It was also around this time and Britain’s early globalization and the changing social and economic conditions that prompted the Politician’s and educated members of society to develop country wide youth practice as observers believed that the youth of English nation were experience new and harsh encounters and a lot of this was to do with the newly constructed phase of adolescence, this new breed of child needed discipline , protection and some nurturing(Davies,1967). As Russell and Rugby commented â€Å"some of the challenges were domestic. As the demand for unskilled especially child) labor reduced more and more young people were neither in school nor work† they felt that the young adolescence leisure time was not being fulfilled and the young â€Å"indulge in ‘one main amusement gambling (Russell Rugby, 1908: 10-11). D The youth of the country were seen as being tested, too, within a new international context who should, who could, take on these emerging responsibilities? Pragmatic and often major compromises with the laissez-fairer principles which had so shaped Victorian Britain had already been made – in order for example to errant public health and spread elementary education to the whole population. Nonetheless, in this later nineteenth century period and even into the early decades of the twentieth century the state remained, at best, an unwelcome intruder into the personal and social spheres of people’s lives. For responding to the newly identified leisure-time needs of young people, a state role was therefore never apparently considered. Self-evidently, these were suitable fields for voluntarily supported clubs’ (Berry, 1919: 96) – a task for thinking people who felt something must be done†¦ (Russell and Rugby, 1908: 12); for those who were conscious of what their ‘happier fortune has bestowed on us from our circumstances’ (Button, 1985: 14); who were fortunately placed’ and therefore felt very strongly that in some way (action) was incumbent on us’ (Chill, 1935: 5). By the early decades of the twentieth century the result was a network of local independent boys and girls clubs across the I-J. From the sass, under the influence of William Smith, military-style brigades for boys and girls also took hold and by the sass were being supplemented and indeed often underpinned by Baden Bowel’s Boy Scouts and later the Girl Guides. In due course these sought mutually supportive links by setting up a range of local, regional and national associations and federations. The Boer War highlighted the need for a fitter, healthier generation of young men and this was supported by social research (Staunton Rogers, 2004). In response to these findings the Children Act 1908 was introduced to establish a Juvenile Justice system, specific medical treatment and free school meals specifically for minors. However, despite young people during this period beginning to be recognized in heir own right there was an ulterior political and philanthropic agenda to enforce social control and Christian morals for both girls and boys (Staunton Rogers, 2004). Nevertheless society began to change during World War One as young men were conscripted into the horrors of war and returned transformed. Whereas women were no longer perceived as, â€Å"delicate maidens of Victorian sensibilities† but instead began to be recognized as capable individuals with their own identities (Staunton Rogers, 2004: 4). Subsequently it was recognized that state intervention was needed ND powers and funding were given to local authorities to invest in Juvenile Organizing Committees (Smith, AAA). Up until this point it was still normal to talk about work with or among boys and girls (or young men and women or youth). In the late sass we see the growing use of the term ‘youth work’. The first booklet in the UK appeared with it in its title: Methods in Youth Work (Walked et al 1931). Bibliography Davies, B. And Gibson, A. (1967). The social education of the adolescent, London: University of London Press. IPPP. Laudable, J. (1989) ‘Children in history: concepts of nature and society In: Scarce, G. Deed) Children, Parents and Politics. Cambridge: Cambridge University Press. IPPP-20. Russell, C. E. B. And Rugby, L. M. 1908, Working Lads Clubs, London, MacMillan and Co Ltd. Smith, M. K. (AAA) Youth Work an Introduction. Http://www. Infer. Org/youth’s/b-WY. HTML [accessed 08. 11. 12]. Smith, M. K. (Bibb) ‘Hannah More: Sunday schools, education and youth work’ The Encyclopedia of Informal Education. Http://www. Infer. Org/thinkers/more. HTML [accessed 9. 11. 12]. Poverty was abundant and with the start of the industrial revolution it was inevitable that children wer e used as cheap labor (Laudable,1989. Smith, 2002). How to cite Compare the Ways, Papers

Sustainable Business Education

Question: Discuss about the Sustainable Business Education. Answer: Introduction Every industry is influenced by the variables of external environment including education sector. The business education and corresponding consumers are identifiable as graduates: industries, business, and agencies of government, not for profits as well as universities. Over the foregoing decades, this business education has witnessed persistent growth along with deepening diversification. This has led it to being the single most rapid growing economic sector globally. It has converted to an essential driver for socio-economic advancement. Especially, over the previous 2 decades political, social, technological and ethical and legal environmental developments have culminated in alterations in the manner business education runs. This paper presents a critical work anchored on this revelation through a critical analysis of major international development or changes of business education environment and showcase how business education is operated over the foregoing two decades. Education-an Economic Social Phenomenon Major International Development Pestle analysis remains a significant technique in educational sector by making it feasible to enhance the decision making process. This is particularly true when one considers chnaging global demands and the need to make sure education aligns to such altering needs. It further assists emphasize on bigger image of future of education. In education industry, this examination makes it feasible to determine environment alterations which could influence the planning, management as well forthcoming financing of this industry. The following is the outline of economic, technological, social, political, and environment variables affecting and influencing education sector (Hicks 2017). Political Factors The schools are presently being privatized while skills required for a person to become a tutor or a teacher are also changing towards efficiency. The expectations to becoming self-financing is also being witnessed while the government have adopted initiatives that establish risk of sector failing. The curriculum is changing which come with lessened lead times (Yousef 2017). Economic Factors The cost of resource like books and paper, teaching and support staff along with technology solutions like laptops are being availed. There is shortages of material on both national and international markets. Further, there is a further risk of high valued staff members shifting from low performing schools or institutions into high performing ones. Parents ability to raise the corresponding funds required for the optional activities is being questioned. The local industry closure affects the fund raising plans of the industry (Sinha 2017). The central and local government funding decisions affect the overal performance of the sector. Social Factors The birth rate is declining that manifest in national trends and there is also local population changes. There is also inability to attract to qualified staff with the preferences of parents increasing the tendency of parents to select which school their kids are attending. Demographic alterations affect student rolls or nature of the students needs. The inability of the staff to obtain as well as access training required to make sure this industry continues to flourish. Technological Factors There is a shift from paper to electronic book readers. Some obsolete computers have also been identified. The new computer viruses have also affected the industry operations besides the risk of selecting irrelevant technology. Alterations in equipment along with the required standards and illegal images on internet have affected security measures. Legislative/Legal Factors New legislation have created non-compliance with law as well as creating administrative barricades. The changes in child protection and raise in age of people leaving school have as well as been noted. Environmental Factors There is a decrease in green space available for activities and utilization of enormous amount of photocopier toner as well as paper for delivering printed information. Newfangled development which pose a threat to leaners in this industry. Disposal of waste as well as alterations in local routes have also affected the business education. Changes of Business Education Environment The business schools have gone through prominent changes in their education environment. Ethics has been substantially integrated into the corresponding programs effectively at both graduate and undergraduate level via a diversity of improvements. This incorporation of ethics at all levels has worked. The business education has broadened their perspective alongside positively impact their behavior of students in the long term. This has been achieved via highly integrated, creative as well as agile approach. The business education presently provide students with holistic understanding of ethics, CSR and sustainability, within the setting of international business along with society. Unlike a great proportion of American business curricula that were built on educational model which grew in 1950s, the current models have changed from the initial one. Presently, the models do not divide learning into disparate functional regions and, merges them with overarching soft skills such as communication as well as teamwork. The present educational experience. There has been a greater willingness along with capability to be increasingly open-minded, flexible as well as diverse approach to timing decisions. Business education management has further adopted increased speedy and agility thereby uprooting the old stability-oriented managerial approaches which are less appropriate. Currently, there has been curriculum changes alongside faculty responsiveness to new topics, new studies as well as new competencies. The business schools are currently proactive and have abandoned ancient approaches. Greater emphasis is presently put towards projects by adopting a more eclectic curriculum. The curriculum currently has a close and rapid co-operations crossways discipline which integrates marketing, RD, sales, finance and manufacturing to ensure students know how to effectively develop new products. Also, there has been collaboration between communication, logistics, manufacturing, legal expertise and marketing and sales that ensure that students understand how to enter new markets effectively (Faridi, Arif and Kumar 2017). The traditional functional and discipline-oriented curriculum designs have been dropped and disciplinary-oriented academic departments along with discipline-oriented (A-Journal) research have diminished. Business education has adopted a swift response to the changing needs. There has been a multidimensional, multidisciplinary teaching as well as research approaches are being implemented by uprooting the present consensually-oriented academic governance mechanisms (Schworm et al. 2017). There has been radical changes based on reinventing, reframing as well as rebuilding of education of the future business leaders. There has been reinvention of undergraduate education curriculum as witnessed by Villanova School of Business whereby Business Dynamics is being taught by new teams to first-year learners about overarching purpose of business in society. Student currently have an understanding of the big picture of business alongside its impact on welfare of individuals globally (Yousef 2017). Learners are currently being realistic regarding the need for self-preparation and possible for challenging job market. Indeed, merely holding generalist MBA degree is no longer sufficient. There has been a shift towards increasingly job-specific Master of Science degrees appears precise as outlined in European Bologna Agreement. M.Sc. professionals currently entails banking, high-end marketing, finance, business analytics, human capital management, sports management and shipping management (Landrum and Ohsowski 2017). The academic institution are designing relevant and meaningful connections between general management degrees and specialists as well uphold strong quality, academic standards along with norms in corresponding programme offerings. Conclusion Queries are raised about more traditional business models of various schools provided their corresponding severe financial challenges due to extremely high fixed costs alongside lower demand. Business education are adopting mire cost-effective business models that integrate the utilization of educational technology whereas time maintaining academic quality simultaneously. Increasingly, faculty is being used more effectively, classroom exposure being increased and interaction of students being enhanced by uprooting many traditional academic settings (Pascal, Mersland and Mori 2017). A closer attention has been put towards cash flow received from public funding particularly in income side. The business education increasingly looks at how to affect income side, by ushering new programmes alongside being additionally attentive to breakeven point of schools. References Pascal, D., Mersland, R. and Mori, N., 2017. The influence of the CEOs business education on the performance of hybrid organizations: the case of the global microfinance industry. Small Business Economics, pp.1-16. Landrum, N.E. and Ohsowski, B., 2017. Content Trends in Sustainable Business Education: An Analysis of Introductory Courses in the US. International Journal of Sustainability in Higher Education, 18(3). Schworm, S.K., Cadin, L., Carbone, V., Festing, M., Leon, E. and Muratbekova-Touron, M., 2017. The impact of international business education on career successEvidence from Europe. European Management Journal. Faridi, M.R., Arif, S.M. and Kumar, H., 2017. Mapping the Terrain of Business Education. International Review of Management and Marketing, 7(1). Hicks, P., 2017, March. Moving From Business Education to Computer Science Concepts in the Middle Grades. In Proceedings of the 2017 ACM SIGCSE Technical Symposium on Computer Science Education (pp. 700-700). ACM. Yousef, D.A., 2017. Factors Influencing Academic Performance in Quantitative Courses among Undergraduate Business Students of a Public Higher Education Institution. Journal of International Education in Business, 10(1). Kim, J.B. and Watson, E., 2017, January. Exploring Practical Potentials of Business Simulation Games. In Proceedings of the 50th Hawaii International Conference on System Sciences. Sinha, A., 2017. From Management Institutes to Business Schools: An Indian Journey. In Management Education in India (pp. 43-53). Springer Singapore.