1. Transmit 5 5.2 Transmission
2. Transmit 5 5.25

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SOL # 5.2 Blueprint Categories % The student will investigate and understand how sound is created and transmitted, and how it is used. Key concepts include a)compression waves; b)vibration, compression, wavelength, frequency, amplitude; c)the ability of different media (solids, liquids, and gases) to transmit sound; and d)uses and applications of sound waves. Scientific Investigations 25% Force, Motion, Energy, and Matter **(includes 4.2 a-d 4.3 a-f )** 25% Life Processes and Living Systems 25% Earth/Space Systems and Cycles 25%

Prior Knowledge Previous/Related SOL Vocabulary Words and Definitions Assessment(s) the list below shows what is expected of a student to know, however, review is necessary Students should already know: Objects vibrate to produce sound Exposure to the word 'energy sound frequency waves wavelength peak crest compression trough vibration transmit media/medium solid liquid gas pitch amplify amplitude molecules musical instruments string woodwind percussion brass animal sounds bats dogs whales energy produce matter longitudinal rarefaction vacuum volume force

Resources Books Technology Lessons Trade Books The Science of Sound; by Steve Parker Sound; by Christopher Cooper Sound; by Sally Walker Sound; Fiona Bayrock Sound; by Kay Manolis Breaking the Sound Barrier; by Alan Pierce Text Books Textbook Reference (McGraw-Hill) F56 – F59 F68 – F69 F74 – F75 Websites SOL Pass (password required) BrainPop SMARTboard (See files below) Sound Vibrations Instrument Sounds Sound Waves Study Guides VA DOE Resources Enhanced Scope and Sequence Investigating Sounds Other

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Curriculum Framework 2012 UNDERSTANDING THE STANDARD (Teacher Notes) ESSENTIAL KNOWLEDGE, SKILLS, AND PROCESSES ·Sound is a form of energy produced and transmitted by vibrating matter. ·Sound waves are compression (longitudinal) waves. ·When compression (longitudinal) waves move through matter (solid, liquid, or a gas), the molecules of the matter move backward and forward in the direction in which the wave is traveling. As sound waves travel, molecules are pressed together in some parts (compression) and in some parts are spread out (rarefaction). A child’s toy in the form of a coil is a good tool to demonstrate a compression (longitudinal) wave. ·The frequency of sound is the number of wavelengths in a given unit of time. ·The wavelength of sound is the distance between two compressions or between two rarefactions. The wavelength can be measured from any point on a wave as long as it is measured to the same point on the next wave. ·When we talk, sound waves travel in air. Sound also travels in liquids and solids. Sound waves must have a medium through which to travel.In a vacuum sound cannot travel because there is no matter for it to move through. ·Pitch is determined by the frequency of a vibrating object. Objects vibrating faster have a higher pitch than objects vibrating slower. A change in frequency of sound waves causes an audible sensation—a difference in pitch. ·Amplitude is the amount of energy in a compression (longitudinal) wave and is related to intensity and volume. For example, when a loud sound is heard, it is because many molecules have been vibrated with much force. A soft sound is made with fewer molecules being vibrated with less force. ·Sound travels more quickly through solids than through liquids and gases because the molecules of a solid are closer together. Sound travels the slowest through gases because the molecules of a gas are farthest apart. ·Some animals make and hear ranges of sound vibrations different from those that humans can make and hear. ·Musical instruments vibrate to produce sound. There are many different types of musical instruments and each instrument causes the vibrations in different ways. The most widely accepted way to classify musical instruments is to classify them by the way in which the sound is produced by the instrument. The four basic classifications are percussion instruments (e.g., drums, cymbals), stringed instruments (e.g., violin, piano, guitar), wind instruments (e.g., flute, clarinet, trumpet, trombone), and electronic instruments (e.g., electronic organ, electric guitar). In order to meet this standard, it is expected that students will ·use the basic terminology of sound to describe what sound is, how it is formed, how it affects matter, and how it travels. ·create and interpret a model or diagram of a compression wave. ·explain why sound waves travel only where there is matter to transmit them. ·explain the relationship between frequency and pitch. ·design an investigation to determine what factors affect the pitch of a vibrating object. This includes vibrating strings, rubber bands, beakers/bottles of air and water, tubes (as in wind chimes), and other common materials. ·compare and contrast sound traveling through a solid with sound traveling through the air. Explain how different media (solid, liquid, and gas) will affect the transmission of sound. ·compare and contrast the sound (voice) that humans make and hear to those of other animals. This includes bats, dogs, and whales. ·compare and contrast how different kinds of musical instruments make sound. This includes string instruments, woodwinds, percussion instruments, and brass instruments.

5.2 OFDM Transmission

In 1966, Bell Labs proposed the Orthogonal Frequency Division Multiplexing (OFDM) patent. Later, in 1985, Cimini suggested its use in mobile communications. In 1997, ETSI included OFDM in the DVB-T system. In 1999, the WiFi WLAN variant IEEE 802.11g considered OFDM for its PHYsical Layer. The purpose of this chapter is not to provide a complete reference for the OFDM theory and the associated mathematical proofs. Rather, the aim is to introduce the basic results needed for a minimum understanding of WiMAX.

OFDM is a very powerful transmission technique. It is based on the principle of transmitting simultaneously many narrow-band orthogonal frequencies, often also called OFDM subcarriers or subcarriers. The number of subcarriers is often noted N. These frequencies are orthogonal to each other which (in theory) eliminates the interference between channels. Each frequency channel is modulated with a possibly different digital modulation (usually the same in the first simple versions). The frequency bandwidth associated with each of these channels is then much smaller than if the total bandwidth was occupied by a single modulation. This is known as the Single Carrier (SC) (see Figure 5.6). A data symbol time is N times longer, with OFDM providing a much better multipath resistance.

Having a smaller frequency bandwidth for each channel is equivalent to greater time periods and then better resistance to multipath propagation (with regard to the SC). Better resistance to multipath and the fact that the carriers are orthogonal allows a high spectral efficiency. OFDM is often presented as the best performing transmission technique used for wireless systems.

5.2.1 Basic Principle: Use the IFFT Operator

The FFT is the Fast Fourier Transform operator. This is a matrix computation that allows the discrete Fourier transform to be computed (while respecting certain conditions). The FFT works for any number of points. The operation is simpler when applied for a number N which is a power of 2 (e.g. N = 256). The IFFT is the Inverse Fast Fourier Transform operator and realises the reverse operation. OFDM theory (see, for example, Reference ^[12]) shows that the IFFT of magnitude N, applied on N symbols, realises an OFDM signal, where each symbol is transmitted on one of the N orthogonal frequencies. The symbols are the data symbols of the type BPSK, QPSK, QAM-16 and QAM-64 introduced in the previous section. Figure 5.7 shows an illustration of the simplified principle of the generation of an OFDM signal. In fact, generation of this signal includes more details that are not shown here for the sake of simplicity.

If the duration of one transmitted modulation data symbol is T_d, then T_d = 1 Δf, where Δf is the frequency bandwidth of the orthogonal frequencies. As the modulation symbols are transmitted simultaneously,

This duration, Δf, the frequency distance between the maximums of two adjacent OFDM subcarriers, can be seen in Figure 5.8. This figure shows how the neighbouring OFDM subcarriers have values equal to zero at a given OFDM subcarrier maximum, which is why they are considered to be orthogonal. In fact, duration of the real OFDM symbol is a little greater due to the addition of the Cyclic Prefix (CP).

5.2.2 Time Domain OFDM Considerations

After application of the IFFT, the OFDM theory requires that a Cyclic Prefix (CP) must be added at the beginning of the OFDM symbol (see Figure 5.9). Without getting into mathematical details of OFDM, it can be said that the CP allows the receiver to absorb much more efficiently the delay spread due to the multipath and to maintain frequency orthogonality. The CP that occupies a duration called the Guard Time (GT), often denoted T_G, is a temporal redundancy that must be taken into account in data rate computations. The ratio T_G/T_d is very often denoted G in WiMAX/802.16 documents. The choice of G is made according to the following considerations: if the multipath effect is important (a bad radio channel), a high value of G is needed, which increases the redundancy and then decreases the useful data rate; if the multipath effect is lighter (a good radio channel), a relatively smaller value of G can be used. For OFDM and OFDMA PHY layers, 802.16 defined the following values for G: 1/4, 1/8, 1/16 and 1/32. For the mobile (OFDMA) WiMAX profiles presently defined, only the value 1/8 is mandatory. The standard indicates that, for OFDM and OFDMA PHY layers, an SS searches, on initialization, for all possible values of the CP until it finds the CP being used by the BS. The SS then uses the same CP on the uplink. Once a specific CP duration has been selected by the BS for operation on the downlink, it cannot be changed. Changing the CP would force all the SSs to resynchronize to the BS ^[1].

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5.2.3 Frequency Domain OFDM Considerations

All the subcarriers of an OFDM symbol do not carry useful data. There are four subcarrier types (see Figure 5.10):

• Data subcarriers: useful data transmission.

• Pilot subcarriers: mainly for channel estimation and synchronisation. For OFDM PHY, there are eight pilot subcarriers.

• Null subcarriers: no transmission. These are frequency guard bands.

• Another null subcarrier is the DC (Direct Current) subcarrier. In OFDM and OFDMA PHY layers, the DC subcarrier is the subcarrier whose frequency is equal to the RF centre frequency of the transmitting station. It corresponds to frequency zero (Direct Current) if the FFT signal is not modulated. In order to simplify Digital-to-Analogue-and Analogue-to-Digital Converter operations, the DC subcarrier is null.

In addition, subcarriers used for PAPR reduction (see below), if present, are not used for data transmission.

5.2.4 OFDM Symbol Parameters and Some Simple Computations

The main WiMAX OFDM symbol parameters are the following:

• The total number of subcarriers or, equivalently, the IFFT magnitude. For OFDM PHY, N_FFT = 256, the number of lower-frequency guard subcarriers is 28 and the number of higher-frequency guard subcarriers is 27. Considering also the DC subcarrier, there remains N_used, the number of used subcarriers, excluding the null subcarriers. Hence, N_used, = 200 for OFDM PHY, of which 192 are used for useful data transmission, after deducing the pilot subcarriers.

• BW, the nominal channel bandwidth

• n, the sampling factor.

The sampling frequency, denoted f_s, is related to the occupied channel bandwidth by the following (simplified) formula:

This is a simplified formula because, according to the standard, f_s is truncated to an 8kHz multiple. According to the 802.16 standard, the numerical value of n depends of the channel bandwidths. Possible values are 8/7, 86/75, 144/125, 316/275 and 57/50 for OFDM PHY and 8/7 and 28/25 for OFDMA PHY.

5.2.4.1 Duration of an OFDM Symbol

Based on the above-defined parameters, the time duration of an OFDM symbol can be computed:

The OFDM symbol duration is a basic parameter for data rate computations (see below).

5.2.4.2 Data Rate Values

In OFDM PHY, one OFDM symbol represents 192 subcarriers, each transmitting a modulation data symbol (see above). One can then compute the number of data transmitted for the duration of an OFDM symbol (which value is already known). Knowing the coding rate, the number of uncoded bits can be computed. Table 5.2 shows the data rates for different Modulation and Coding Schemes (MCSs) and G values. The occupied bandwidth considered is 7 MHz and the sampling factor is 8/7 (the value corresponding to 7 MHz according to the standard).

Table 5.2: OFDM PHY data rates in Mb/s. (From IEEE Std 802.16-2004 ^[1]. Copyright IEEE 2004, IEEE. All rights reserved.)
Open table as spreadsheet

G ratio	BPSK 1/2	QPSK 1/2	QPSK 3/4	16-QAM 1/2	16-QAM 3/4	64-QAM 2/3	64-QAM 3/4
1/32	2.92	5.82	8.73	11.64	17.45	23.27	26.18
1/16	2.82	5.65	8.47	11.29	16.94	22.59	25.41
1/8	2.67	5.33	8.00	10.67	16.00	21.33	24.00
1/4	2.40	4.80	7.20	9.60	14.40	19.20	21.60

It should be noted here that these data rate values do not take into account some overheads such as preambles (of the order of one or two OFDM symbols per frame) and signalling messages present in every frame (see Chapter 9 and others in this book). Hence these data rates. known as raw data rates, known as raw data rates, are optimistic values.

5.2.5 Physical Slot (PS)

The Physical Slot (PS) is a basic unit of time in the 802.16 standard. The PS corresponds to four (modulation) symbols used on the transmission channel. For OFDM and OFDMA PHY Layers, a PS (duration) is defined as ^[1]

PS = 4/f_s.

Therefore the PS duration is related to the system symbol rate.

This unit of time defined in the standard allows integers to be used while referring to an amount of time, e.g. the definition of transition gaps (RTG and TTG) between uplink and downlink frames in the TDD mode.

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5.2.6 Peak-to-Average Power Ratio (PAPR)

A disadvantage of an OFDM transmission is that it can have a high Peak-to-Average Power Ratio (PAPR), relative to a single carrier transmission. The PAPR is the peak value of transmitted sub carriers to the average transmitted signal. A high PAPR represents a hard constraint for some devices (such as amplifiers). Several solutions are proposed for OFDM PAPR reduction, often including the use of some subcarriers for that purpose. These subcarriers are then no longer used for data transmission. The 802.16 MAC provides the means to reduce the PAPR. PAPR reduction sequences are proposed in Reference ^[2].