# 11选5任8 8注必中: 通信原理(英文版)5.ppt

1,Chaper 5 Representation and Transmission of Baseband Digital Signal,5.1 Introduction The purpose of representing digital signal by using different methods during transmission: To remove D.C. and very low frequency components; To obtain information of the beginning and the ending instants of each symbol in the receiver; To enable the frequency spectrum of the signal match with the transmission characteristic of the channel.,2,5.2 Coding method of character What are characters: --- Chinese characters, digits, and English letters, … Coding method of Chinese characters: To use 4 decimal digits denotes one Chinese character.For example, in telegraph, “中” ? “0022”，“国” ? “0948”in “zone and location code”, “中” ? “5448”，“国” ? “2590” Coding method of English letters and symbols:ASCII code ---- 7 binary digits denoting a character.,3,5.3 Waveform of baseband digital signal Unipolar waveform Bipolar waveform Unipolar return-to-zero waveform Bipopar return-to-zerowaveform Differential waveform Multi-level waveform,4,5.4 Symbol code types of baseband digital signals for transmission Requirements on the symbol code types for transmission: No D.C. component and very small low frequency components; Containing timing information of symbols; High transmission efficiency; Certain error-detecting ability; Suitable for various information sources, i.e., the above performance is independent of the statistic characteristic of the information source.,5,AMI code --- Alternative Mark Inverse code Coding rule: “1” converts into “＋1” and “－1” alternatively, “0” keeps “0”，For example: message symbol: 0 1 0 1 1 0 0 0 1AMI code: 0 +1 0 -1 +1 0 0 0 -1 Advantages: no D.C. component, simple decoder, easy to find errors Disadvantages: When a long string of 0 appears there will be no way to get timing information in the receiver. It is also called “1B/1T” code.,6,HDB3 code Coding rule: Firstly, the message symbol is convert into AMI code. Then, the continuous 0s in AMI code are checked: When there are no more than 4 (including 4) continuous 0s, no change will be made, and the AMI code is just HDB3 code. When 4 or more than 4 continuous 0s appear, the fourth 0 will be converted into a symbol which has the same polarity of the previous non-0 (“＋1” or “－1”) symbol. This symbol is called “violation symbol”, and is denoted by a V, i.e., +V represents +1, and –V represents -1.,7,To guarantee the polarity alternatively inverse of the adjacent Vs:* When there are odd non-0 symbols between the adjacent Vs, it can be guaranteed. * When there are even non-0 symbols between the adjacent Vs, the requirement cannot be satisfied. To solve this problem, it is necessary to convert the first 0 of the continuous 0 string into a +B or a –B. The sign of B is the inverse of the sign of the previous non-0 symbol; and the sign of the following non-0 symbol begins to alternatively change from symbol V.,8,Example: Message: 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 AMI code: -1 0 0 0 0 +1 0 0 0 0 -1 +1 0 0 0 0 -1 +1 HDB3 code: -1 0 0 0 -V +1 0 0 0 +V -1 +1 -B 0 0 -V +1 -1-1 0 0 0 -1 +1 0 0 0 +1 -1 +1 -1 0 0 -1 +1 -1Decoding： -1 0 0 0 0 +1 0 0 0 0 -1 +1 0 0 0 0 +1 -11 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 Decoding: When two continuous “1” with the same sign appear, then the latter “1” and its preceding three symbols will be decoded as “0”. Finally, all -1s are converted into +1s, then the original message symbols are obtained. Advantages: In addition to the advantages of AMI, HDB3 code can also let the number of continuous 0s be no more than 3, and be independent of the statistic characteristic of the information source.,,9,Biphase code － Manchester code Coding rule: message symbol “0” ? transmission code “01”message symble “1” ? transmission code “10”For example:Message symbol: 1 1 0 0 1 0 1Biphase code: 10 10 01 01 10 01 10 Decoding rule: There are continuouse two 0s or 1s at the alternative point of the message, it can be used as the boundary of different message symbols. Advantages: no D.C. component, a lot of timing information, and simple coding method.Disadvantage: occupied frequency bandwidth is doubled.,10,Miller code Coding rule:Message symbol “1” ? is expressed by the voltage jump at the middle point of the symbol duration. In other words, it is expressed by “01” or “10”.Message symbol “0” ? 1. the voltage doesn’t change for single “0”; 2. the voltage jumps at the boundary of adjacent 0s for continuous 0s. In other words, it is expressed by “11” or “00”.,11,Property: When there is one “0” between two “1s” in the message symbols, the longest duration of the waveform width will appear. It equals twice the duration of the message symbol. This property can be used for error detection. Generation: The descending edge of the biphase code is just corresponding to the jump edge of Miller code. Hence, Miller code may be obtained by triggering a bistable trigger/flip-flop using the descending edge of the biphase code.,12,CMI code － Coded Mark Inversion code Coding rule: message symbol “1” ? alternatively use “11” and “00” to express it;message symbol “0” ? use “01” to express it.,13,nBmB code This is a kind of block codes. In this code, n binary symbols in the message stream are combined into a group, and converted into a binary code of m bits, where m n. The latter has 2m kinds of combination. There are (2m – 2n) combinations more in the latter than those in the former, since m n. In 2m combinations, a specific part may be selected as allowable codes and the others are forbidden codes for obtaining good coding characteristic. Bipolar code, Miller code, and CMI code may be regarded as 1B2B codes. In optical fiber communication system, m = n + 1 is often used, e.g., 5B6B code, and others. In addition to nBmB code, there are also such codes as nBmT code and others. nBmT code expresses that n binary symbols are converted into m ternary symbols.,14,5.5 Frequency characteristic of baseband digital signal Power spectral density of binary random signal sequence Let waveforms of message symbols 0 and 1 in a binary random signal sequence be g1 (t) and g2 (t)，the bandwidth of the symbol equal T.,15,Assume the random signal sequence is a stationary random process where the occurring probabilities of 0 and 1 are P and (1-P) respectively, and their occurrences are statistically independent from each other, thenwhere,,,,,16,Its power spectral density:where, Tc is the duration of a segment of the truncated signal. Let it bewhere N is a large enough integer. Thus, andIf frequency spectral density Sc(f) of truncatedd signal sc(t) has been found, then power spectral density Ps(f) of the signal can be calculated by the above equation,,,,,17,Calculation result:Double-side power spectral density expression:Single-side power spectral density expression:,,,,,18,Examples of power spectral density calculation Unipolar binary signal Assume the signal g1(t) = 0, g2(t) = g(t), then the double-side power spectral density of the random sequence composed of it is:where, G( f ) is the frequency spectrum function of g(t). When P = 1 / 2 and g(t) is the rectangular pulse:the frequency spectrum function of g(t) is Thereforewhere,,,,,,,19,Bipolar binary signalAssume the signal g1(t) = -g2(t) = g(t), then the double-side power spectral density of the random sequence composed of it is:When P = ?, the above equation can be rewritten asIf g(t) is a rectangular pulse, then substituting its frequency spectrum G( f ) into the above equation, we obtain,,,,,,20,As can be seen from the above two equations:1. Generally speaking, power spectral density of a random pulse signal sequence contains a continuous spectrum and a discrete spectrum. However, for bipolar signal g(t) = -g(t) and when the probability P = ?, there is no discrete spectral component.2. If g1(t) = g2(t), then there is only discrete spectrum without any continuous component in the power spectral density. That is to say, the signal sequence is a periodic sequence and it doesn’t contain any information.,21,5.6 Transmission and intersymbol interference of baseband digital signal 5.6.1 Model of baseband digital signal transmission systemLet: GT(f) － transfer function of transmitting filter,GR(f) － transfer function of receiving filter,C(f) － transfer function of channel, H(f) = GT(f)?C(f)?GR(f)。,22,5.6.2 Intersymbol interference and Nyquist criterion Intersymbol interference － overlap of adjacent symbols Causation of producing intersymbol interference － limitation of system overall transfer characteristic H(f). Characteristic of intersymbol interference － it appears when the signal appears, and disappears when the signal disappears. (multiplicative interference) Principles of overcoming intersymbol interferenceLet the system overall transfer function be H(f) which has ideal rectangular characteristic, i.e., letwhere T is the duration of the symbol.When the system input is a unit impulse function ?(t), the received signal waveform h(t) before sampling should be the inverse Fourier transform of H(f):,,,23,As can be seen from fig. (b), the space between zeros of h(t) equals T, with only the space between the first zeros around the origin equaling 2T. Theoretically we might use the symbols with duration T for transmission without intersymbol interference as shown in fig. (c).Now, transmission bandwidth W = 1/(2T) Hz transmission rate RB = (1/T) Baud rate to bandwidth ratio: RB/W ＝ 2 Baud/Hz － Nyquist rate Problems of ideal transfer characteristic It can’t be physically realized. The “tail” of the waveform haslarge fluctuation and lasts a verylong time. Hence the sampling instant should be very accurate.,24,Practically used no intersymbol interference transfer characteristic requires:Transfer function is a realfunction, and is odd symmetricat the point f = w.－called Nyquist criterion,25,Example: transfer function with raised-cosine “roll-off” characteristicIts impulse response is:W1/W － roll-off coefficient When W1/W = 1, it is called raised-cosine characteristic; now the sidelobe of s0(t) is less than 31.5 dB, and there are more zeros.Roll-off characteristic still keeps the transmission rate of 2W Baud, but the occupied bandwidth is increased.,,,26,5.6.3 Partial response system Problem solved by partial response system: Ideal rectangular transfer characteristic: bandwidth is min. but can’t be realized. Roll-off characteristic: can be realized but bandwidth is increased. Partial response characteristic: can solve the above contradiction.,,27,Principles of partial response characteristic:Example: Assume the transfer function H(f) is an ideal rectangular. When two unit impulses with space of one symbol time T are added to the input, output waveform of the system should be the superposition of these two sinx/x waveforms:where, W = 1/2T,,28,The frequency spectrum of the above waveform is － cosinusoidal, bandwidth =1/2Tg(t) can be reduced as: － g(t) decreases along with increase of t 2From the above equation, we obtainIf g(t) is used, and transmitted at the space of one symbol T, then there is mutual interference at the sampling instant only between the two adjacent symbols, and no mutual interference with other symbols at the sampling instant. By superficial observation, it seems impossible to transmit symbols with space T since there is interference between the adjacent symbols. However, correct transmission with rate 1/T Baud is still possible, because this kind of interference is deterministic.,,,,,,Sampling instants,a -1 a0 a1 a2,29,Assume the input binary symbol sequence of the system is {ak}, where ak = ?1. When symbol ak is transmitted, sample Ck of the received waveform at the corresponding sampling instant is decided byhence, we haveThe possible values of Ck are only ＋2, 0, and －2.As can be seen from the above equation:∴ If the previous symbol ak-1 has already been received and decided, i.e., its value is known, then the value of ak can be found after Ck is obtained.The above example illuminates that it is possible, in principle, to use the waveform with intersymbol interference to reach the ideal frequency band utilization and to let the “tail” of the symbol waveform attenuating rapidly. However, there is error propagation problem, it can’t be used in practice.,,,,,30,Practical partial response characteristicLet input symbol ak at the transmitter be expressed by binary digits 0 and 1.Firstly, ak is converted into bk according to the following equation:where ? is the modulo 2 addition; bk is a binary digit 0 or 1.Then, {bk} is used for transmission. According to the above principle, we can obtain － precoding (correlative coding)If the operation of the addition mod 2 is applied on the above equation, then we haveThe above equation shows that if the operation of addition mod 2 is directly applied on Ck , then ak can be obtained and there is no need of foreknown ak-1 , and no error propagation problem either.,,,,31,Example: let {ak} be 1 1 1 0 1 0 0 1，then the decoding process is:Initial status bk-1＝0 Initian status bk-1＝1Binary sequence {ak} 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 1Binary sequence {bk-1} 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 1Binary sequence {bk} 1 0 1 1 0 0 0 1 0 1 0 0 1 1 1 0Sequence {Ck} 1 1 1 2 1 0 0 1 1 1 1 0 1 2 2 1Binary sequence {[Ck]mod} 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 1Bipolar input {ak} ＋＋＋－＋－－＋ ＋＋＋－＋――＋Bipolar signal {bk} ＋－＋＋―――＋ －＋――＋＋＋－Bipolar signal {bk-1} －＋－＋＋――― ＋－＋――＋＋＋Sequence {Ck} 0 0 0 2 0 –2 –2 0 0 0 0 –2 0 2 2 0Decision criterion: If Ck = 0, then the decision is ak = +1; if Ck = ? 2, then the decision is ak = -1.,32,Block diagramThe above system is called the first kind of partial response system, and also called duobinary signal transmission system.,,33,General partial response characteristic: letwhere, kn( n = 1, 2, …, N) － weighting coefficient, it may take positive value, negative value, or zero.The Fourier transform of g(t) in the above equation is its frequency spectrum G(f):As can be seen from the above equation, spectrum G(f) still exists within the interval (-1/2T, 1/2T).,,,,,,34,Assume the input sequence is {ak}, and the corresponding coded sequence is {Ck}, then we havewhere ak may be L-ary digits.The precoding rule is:where ? is the addition mod L. The correlative encoding rule for bk is:At last, the operation of mod L on Ck is:As can be seen from the above equation, here no error propagation exists. According to the above principle, the partial response waveforms currently presented can be classified into 5 classes.,,,,,,,35,5.7 Eye pattern Eye patter － a method of practical observation of the received signal by using a oscilloscope. For bipolar binary signal: Under ideal situation, the display will be like an opened eye. If interference exists, then different degrees of the opening of the “eye” represent the strength of the interference.,36,Model of eye pattern The location of thecentral perpendicularline is the optimum sampling instant. The middle horizontalline represents the optimum decision threshold level. The perpendicular height of the shadow region represents the distortion range of the received signal. The slope of the bevel edge of the “eye” represents sensitivity of the sampling instant to the timing error. Under no noise situation, the degree of the opening of the “eye is the noise tolerance; if noise at the sampling instant exceeds this tolerance, then error decision may happen.,