Exercise 4 Data Scrambling and Descrambling EXERCISE OBJECTIVE When you have completed this exercise, you will be familiar with data scrambling and descrambling using a linear feedback shift register. DISCUSSION OUTLINE The Discussion of this exercise covers the following points: The purpose of data scrambling and descrambling Scrambling and descrambling circuits The choice of polynomial Descrambler impulse response Scrambling and descrambling in the QAM/DQAM application DISCUSSION The purpose of data scrambling and descrambling The purpose of scrambling and descrambling is not necessarily for security or secrecy. In most communication systems, the input data is scrambled only to ensure frequent transitions and to avoid situations where periodic data or a repetitive input produces very little change in the signal. Frequent transitions are required for timing recovery and for proper operation of automatic gain control circuits. Ideally, a modulated signal should have many transitions and all the points in the constellation should be visited at regular intervals. Scrambling ensures this condition for any input data. Scrambling also makes the power spectrum independent of the transmitted data, spreading the power smoothly over the available bandwidth. This reduces radio frequency interference and channel crosstalk, because the power is not concentrated in a narrow frequency band. When scrambling is used, the input data is passed through the scrambler before modulation. Then the modulated signal is passed through the communications channel and is demodulated. Finally, the demodulated data is passed through the descrambler to recover the original data. Scrambling and descrambling circuits The basic circuit for a scrambler is a linear feedback shift register. This consists of a group of registers with the output of one register connected to the input of the next so that data is shifted one position down the line at each clock cycle (see Figure 56). The feedback is produced by connections (taps) from specific registers. The outputs of these taps are combined using the exclusive-or (XOR) operation ( ) and the resulting feedback sequence is XORed with the input data stream. The descrambler uses a similar circuit (see Figure 57). Festo Didactic 39866-00 73
Exercise 4 Data Scrambling and Descrambling Discussion Locations: INPUT Taps: OUTPUT Figure 56. Scrambling circuit with polynomial 1 + 0 x + 1 x 2 + 1 x 3 (or x 3 + x 2 +1). Locations: INPUT Taps: OUTPUT Figure 57. Descrambling circuit with polynomial 1 + 0 x + 1 x 2 + 1 x 3 (or x 3 + x 2 +1). The specific configurations of the scrambler and descrambler circuits must match each other for the scrambling/descrambling operation to succeed. To this end, the internal connections of each are defined as a polynomial, referred to as the characteristic polynomial of the circuit, of the form: This type of polynomial is called a polynomial mod 2 because it is manipulated using modulus 2 arithmetic. Each coefficient A m is 0 or 1. The XOR operation is equivalent to modulus 2 addition or subtraction. A scrambler circuit performs modulus 2 division of the input data by the polynomial. The descrambler recovers the original data by performing modulus 2 multiplication using the same polynomial. The details of modulus 2 arithmetic are outside the scope of the manual. where n is the number of registers. P(x) = An x n +... + A2 x 2 + A1 x 1 + A0 x 0 With n registers, there are n +1 locations where a connection (tap) can be made. The value of each coefficient Am of the polynomial (where m ranges from 0 to n) is either 0 or 1, depending on whether the tap is absent or present at location m. In Figure 56 and Figure 57, taps are present at locations 0, 2, and 3. There is no tap at location 1. Therefore the polynomial P(x) = 1 x 0 + 0 x 1 + 1 x 2 + 1 x 3 or x 3 + x 2 +1. a In this manual, the locations of a scrambler or descrambler circuit are numbered from input to output. This is a matter of convention. An equally valid convention is to number the locations from output to input. In this case, the polynomial representing the circuits in Figure 56 and Figure 57 would be 1x 3 + 0 x 2 + 1 x 1 +1x 0, or x 3 + x+1. When writing out a polynomial using x s, the order of the terms does not matter: x 3 + x 2 +1 is the same as 1 + x 2 + x 3. Terms with a zero coefficient do not need to be included: x 3 + x 2 +1 is the same as x 3 + x 2 + 0x +1. When expressing a polynomial as a binary number or as an N-tuple, the leftmost digit always corresponds to the highest-order term of the polynomial. For example, the binary number 1101 and the 4-tuple (1,1,0,1) both represent to the polynomial x 3 + x 2 +1. Since there is always a tap at the input and at the output of the shift register, the first and last coefficients of the polynomial are always 1. As long as the polynomials for the scrambler and descrambler match (using the same convention), the scrambling and descrambling operations will succeed. If not, the output remains scrambled and is meaningless. In a system designed for secrecy, it might be useful to keep this polynomial a secret, known only to the intended recipient of a message (although this simple approach would offer little real data security). In a system designed for efficiency, the polynomial to be used is defined and published in the modem standard, and is permanently built-in to both the modulator and demodulator circuits. 74 Festo Didactic 39866-00
Exercise 4 Data Scrambling and Descrambling Discussion The scrambler ensures frequent transitions in the transmitted data even if the input data is highly structured. However mixed up the scrambled data appears to be on the channel, it is easily descrambled in the corresponding descrambler circuit in the receiver. The choice of polynomial Since the purpose of scrambling is to randomize the data, it is important to note how the scrambler behaves under the worst case, that is, when the input data consists of a long string of 1s or 0s. If all registers of the scrambler initially contain 0 and the input data is all 0s, then the output of the scrambler is all zeros and no scrambling occurs. However, if one of the registers initially contains a 1 and the input data is all zeros or all ones, then the output is a continuous sequence that appears to be random but that is actually periodic and totally predictable for a given polynomial and initial state. The longer the period of this sequence, the closer it approximates truly random data. In this case, the scrambler acts as a pseudo-random binary sequence (PRBS) generator using the corresponding polynomial. The length L (in bits) of the pseudo-random sequence produced under these conditions corresponds to the ability of the scrambler to effectively randomize data. For a given polynomial, the length may be as great as 2 n -1 bits where n is the order of the polynomial (that is, the highest non-zero term in the polynomial). The order n equals the number of registers used in the scrambler. If n = 3, for example, the maximum possible length L = 2 3 1 = 7 bits. For n = 16, L could be as great as 2 16 1 = 65 535 bits. However, not all polynomials of order n will produce a periodic sequence of length 2 n -1. The details of polynomial factoring are outside the scope of the manual. In order for a polynomial P(x) to produce the maximum length possible for the number of registers used, the polynomial must be a primitive prime: The polynomial P(x) of order n is a prime polynomial if it is not divisible (using modulus 2 arithmetic) by any lower-order polynomials. P(x) is called primitive if it is a factor of the polynomial x L +1 (where L = 2 n -1), and of no other lower-order polynomial of the same form. Descrambler impulse response The operation of a descrambler can be tested by sending a single 1 bit into the descrambler input, followed by many zeros. Under these conditions, the descrambler output is effectively a measure of the impulse response of the descrambler. The impulse response can be used to determine the polynomial of an unknown descrambler circuit. This is illustrated in Figure 58. When the impulse appears at the input of the descrambler, the first bit to appear at the output (according to the convention used in this manual) is A0 (the coefficient of the lowest-order term of the polynomial), followed by A1 (the coefficient of the second-lowest order term), then A2, etc. After the bit corresponding to the coefficient of the highest-order term, the output is all zeros. Festo Didactic 39866-00 75
Outline With the descrambling circuit shown in Figure 57, where P(x) = x 3 + x 2 + 1, the output would be a 1 (1x 0 ), followed by a 0 (0x 1 ), followed by a 1 (1x 2 ), and then another 1 (1x 3 ), and then all zeros. This test directly indicates the characteristic polynomial. Impulse in Response out 1 0 1 1 Polynomial 1x 0 + 0x 1 + 1x 2 + 1x 3 Figure 58. Descrambler impulse response for polynomial 1 x 0 + 0 x 1 + 1 x 2 + 1 x 3 (or x 3 + x 2 +1). Scrambling and descrambling in the QAM/DQAM application In the LVCT QAM/DQAM application, the Scrambler in the modulator and the Descrambler in the demodulator use a fixed polynomial that conforms to the ITU-T V.22 bis recommendation. The Scrambler and the Descrambler can be turned on or off individually. PROCEDURE OUTLINE This Procedure is divided into the following sections: Set-up and connections Scrambling a repetitive data stream Descrambling The effect of scrambling on power distribution Determining the descrambler polynomial from its impulse response PROCEDURE Set-up and connections 1. Turn on the RTM Power Supply and the RTM and make sure the RTM power LED is lit. File Restore Default Settings returns all settings to their default values, but does not deactivate activated faults. Double-click to select SWapp 2. Start the LVCT software. In the Application Selection box, choose QAM/DQAM and click OK. This begins a new session with all settings set to their default values and with all faults deactivated. b If the software is already running, choose Exit in the File menu and restart LVCT to begin a new session with all faults deactivated. 3. Make the Default external connections shown on the System Diagram tab of the software. For details of connections to the Reconfigurable Training Module, refer to the RTM Connections tab of the software. b Click the Default button to show the required external connections. 76 Festo Didactic 39866-00
Scrambling a repetitive data stream 4. Make the following settings: Generator Settings Generation Mode... User Entry Binary Sequence... 0101 QAM Settings Differential Encoding... On (DQAM) Scrambler... On Low-Pass Filters... On Descrambler... Off Oscilloscope Channel X and Y... 1 V/div X-Y... On Display Mode... Dots Sampling Window... 200 ms 5. Connect the probes to the QAM Modulator as follows: Oscilloscope Probe Connect to Signal 1 TP14 I-channel D/A Converter output 2 TP15 Q-channel D/A Converter output Logic Analyzer Probe Connect to Signal C TP2 CLOCK INPUT 1 TP1 DATA INPUT 2 TP4 Scrambler output Use the Logic Analyzer to observe the signals at the input and output of the Scrambler in the modulator (see example in Figure 59). Festo Didactic 39866-00 77
Logic Analyzer Settings: Display Width... 10 ms Clock Grid... Rising Edge Source... Clock Source Edge... Rising Clock Edge... Rising S1 Data... [ch1] S2 Data... [ch2] Figure 59. Scrambler input and output. Describe the effect of the Scrambler on the input data. 6. Use the Oscilloscope in the X-Y mode to observe the constellation. Make these observations with the Scrambler both Off and On (see Figure 60 and Figure 61). Click the Drop 1 Bit button on the Serial to Parallel Converter and repeat your observations (do this several times). Figure 60. Example of constellation with Scrambler Off. 78 Festo Didactic 39866-00
Figure 61. Example of constellation with Scrambler On. What effect does scrambling have on the constellation? Descrambling 7. Connect the Logic Analyzer probes to the QAM Demodulator as follows: Logic Analyzer Probe Connect to Signal C TP22 CLOCK OUTPUT E TP23 BSG SYNC. OUTPUT 1 TP20 Descrambler input 2 TP21 DATA OUTPUT Make sure that both the Scrambler and Descrambler are On. Observe the data using the Logic Analyzer (see Figure 62). Festo Didactic 39866-00 79
Figure 62. Descrambler input and output data (Descrambler On). What is the effect of the Descrambler? What allows the Descrambler to operate successfully? 8. Set the Binary Sequence to 0000 or to 1111 and repeat your observations with the Scrambler Off and On. The effect of scrambling on power distribution 9. Make the following settings: Generator Settings Generation Mode... User Entry Binary Sequence 0111 QAM Settings Differential Encoding... On (DQAM) Scrambler... Off Low-Pass Filters On 80 Festo Didactic 39866-00
10. Connect probes to the QAM Modulator as follows: Oscilloscope Probe Connect to Signal 1 TP14 I-channel D/A Converter output 2 TP15 Q-channel D/A Converter output Other Probes Connect to Signal Spectrum Analyzer TP22 QAM Modulator OUTPUT Spectrum Analyzer Settings: Maximum Input... 10 dbv Scale Type... Logarithmic Scale... 10 dbv/div Averaging... 16 Frequency Span... 2 khz/div Reference Frequency... 0 khz 11. With the Scrambler Off, observe the constellation using the Oscilloscope and the power spectrum of the modulated signal using Spectrum Analyzer. Use the Drop 1 bit button to change the grouping of data bits into quadbits. Experiment with different Binary Sequences, using the Drop 1 bit button, to obtain constellations with various numbers of points. Observe the effect on the spectrum (see Figure 63 to Figure 65). Figure 63. QAM signal spectrum - 2 constellation points. Festo Didactic 39866-00 81
Figure 64. QAM signal spectrum - 4 constellation points. Figure 65. QAM signal spectrum - 16 constellation points. Describe the relationship between the number of points present in the constellation and the power distribution of the QAM spectrum. 82 Festo Didactic 39866-00
12. Observe the constellation and the spectrum of the QAM signal with the Scrambler On and Off. Describe the effect of scrambling on this signal. Determining the descrambler polynomial from its impulse response 13. Make the following settings: Generator Settings Generation Mode... User Entry Binary Sequence... 10000000000000000000000000000000 Bit Rate... 2000 bit/s b QAM Settings This Binary Sequence consists of 1 followed by 31 zeros. In the Binary Sequence setting, type 1 and then hold down the 0 key until more than 31 0s have been entered. When you press Enter, the sequence will automatically be truncated to 32 characters. Differential Encoding... On (DQAM) Scrambler... Off Low-Pass Filters... On Descrambler... Off Logic Analyzer Settings: Display Width... 10 ms Clock Grid... Rising Edge Source... Ch 1 Source Edge... Rising Clock Edge... Rising S1 Data... [ch1] S2 Data... [ch2] 14. Observe the Descrambler input and output using the Logic Analyzer. Figure 66 shows what you should observe with the Descrambler Off. Figure 66. Descrambler input (Ch 1) and output (Ch 2) Descrambler Off. Turn the Descrambler On and repeat your observations. Figure 67 shows what you should observe. Festo Didactic 39866-00 83
Exercise 4 Data Scrambling and Descrambling Conclusion Figure 67. Descrambler input (Ch 1) and output (Ch 2) Descrambler On. The polynomial used in the Scrambler and Descrambler conforms to the ITU-T recommendation V.22 bis. Use the Descrambler impulse response to determine this polynomial. 15. When you have finished using the system, exit the LVCT software and turn off the equipment. CONCLUSION In this exercise, you observed how data is scrambled using a linear feedback shift register. You observed that, with constant or repetitive input data, the scrambler produces a pseudo-random bit pattern. You also observed that a descrambler using the same polynomial as the scrambler correctly recovers the original data, and saw how the descrambler impulse response reveals the polynomial that is used. You also saw that scrambling causes all constellation points to be visited regularly and causes the power in the transmitted signal to be spread over the spectrum. REVIEW QUESTIONS 1. What effects does scrambling have on the time-domain characteristics of the modulated signal? 84 Festo Didactic 39866-00
Exercise 4 Data Scrambling and Descrambling Review Questions 2. What effects does scrambling have on the frequency-domain (power spectrum) characteristics of the modulated signal? 3. Describe how scrambling and descrambling are usually implemented. 4. What factors influence the choice of polynomial in a scrambler/descrambler? 5. How can you determine the polynomial of a descrambler circuit? Festo Didactic 39866-00 85