Signal Encoding Techniques Lecture 3 G Noubir noubirccs
Signal Encoding Techniques Lecture 3 G. Noubir noubir@ccs. neu. edu
Reasons for Choosing Encoding Techniques n Digital data, digital signal n n Equipment less complex and expensive than digital-to-analog modulation equipment Analog data, digital signal n Permits use of modern digital transmission and switching equipment COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 2
Reasons for Choosing Encoding Techniques n Digital data, analog signal n n n Some transmission media will only propagate analog signals E. g. , optical fiber and unguided media Analog data, analog signal n n Analog data in electrical form can be transmitted easily and cheaply Done with voice transmission over voice-grade lines COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 3
Signal Encoding Criteria n What determines how successful a receiver will be in interpreting an incoming signal? n n n Signal-to-noise ratio Data rate Bandwidth An increase in data rate increases bit error rate An increase in SNR decreases bit error rate An increase in bandwidth allows an increase in data rate COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 4
Factors Used to Compare Encoding Schemes n Signal spectrum n n With lack of high-frequency components, less bandwidth required With no dc component, ac coupling via transformer possible Transfer function of a channel is worse near band edges Clocking n Ease of determining beginning and end of each bit position COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 5
Factors Used to Compare Encoding Schemes n Signal interference and noise immunity n n Performance in the presence of noise Cost and complexity n The higher the signal rate to achieve a given data rate, the greater the cost COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 6
Basic Encoding Techniques n Digital data to analog signal n Amplitude-shift keying (ASK) n n Frequency-shift keying (FSK) n n Amplitude difference of carrier frequency Frequency difference near carrier frequency Phase-shift keying (PSK) n Phase of carrier signal shifted COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 7
Basic Encoding Techniques
Amplitude-Shift Keying n n One binary digit represented by presence of carrier, at constant amplitude Other binary digit represented by absence of carrier n where the carrier signal is Acos(2πfct) COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 9
Amplitude-Shift Keying n n Susceptible to sudden gain changes Inefficient modulation technique On voice-grade lines, used up to 1200 bps Used to transmit digital data over optical fiber COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 10
Binary Frequency-Shift Keying (BFSK) n Two binary digits represented by two different frequencies near the carrier frequency n where f 1 and f 2 are offset from carrier frequency fc by equal but opposite amounts COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 11
Binary Frequency-Shift Keying (BFSK) n n Less susceptible to error than ASK On voice-grade lines, used up to 1200 bps Used for high-frequency (3 to 30 MHz) radio transmission Can be used at higher frequencies on LANs that use coaxial cable COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 12
Multiple Frequency-Shift Keying (MFSK) n n More than two frequencies are used More bandwidth efficient but more susceptible to error n n n f i = f c + (2 i – 1 – M)f d f c = the carrier frequency f d = the difference frequency M = number of different signal elements = 2 L L = number of bits per signal element COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 13
Multiple Frequency-Shift Keying (MFSK) n To match data rate of input bit stream, each output signal element is held for: Ts=LT seconds n n where T is the bit period (data rate = 1/T) So, one signal element encodes L bits COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 14
Multiple Frequency-Shift Keying (MFSK) n Total bandwidth required 2 Mfd Minimum frequency separation required 2 fd=1/Ts Therefore, modulator requires a bandwidth of n n Wd=2 L/LT=M/Ts COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 15
Multiple Frequency-Shift Keying (MFSK) COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 16
Phase-Shift Keying (PSK) n Two-level PSK (BPSK) n Uses two phases to represent binary digits COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 17
Phase-Shift Keying (PSK) n Differential PSK (DPSK) n Phase shift with reference to previous bit n n Binary 0 – signal burst of same phase as previous signal burst Binary 1 – signal burst of opposite phase to previous signal burst COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 18
Phase-Shift Keying (PSK) n Four-level PSK (QPSK) n Each element represents more than one bit COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 19
Phase-Shift Keying (PSK) n Multilevel PSK n Using multiple phase angles with each angle having more than one amplitude, multiple signals elements can be achieved n n D = modulation rate, baud R = data rate, bps M = number of different signal elements = 2 L L = number of bits per signal element COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 20
Performance n Bandwidth of modulated signal (BT) n n ASK, PSK FSK n n n BT=(1+r)R BT=2 DF+(1+r)R R = bit rate 0 < r < 1; related to how signal is filtered DF = f 2 -fc=fc-f 1 COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 21
Performance n Bandwidth of modulated signal (BT) n MPSK n MFSK n n L = number of bits encoded per signal element M = number of different signal elements COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 22
Quadrature Amplitude Modulation n QAM is a combination of ASK and PSK n Two different signals sent simultaneously on the same carrier frequency COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 23
Quadrature Amplitude Modulation
Additive White Gaussian Noise: n n n As previously seen, noise has several sources Thermal noise source is the motion of electrons in amplifiers and circuits Its statistics were determined using quantum mechanics It is flat for all frequencies up to 1012 Hz. We generally call it: Additive White Gaussian Noise (AWGN) Its probability density function (pdf) (zero mean noise voltage): COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 25
Bit Error Rate [Sklar 1988] n BER for coherently detected BPSK: n BER for coherently detected BFSK: COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 26
Reasons for Analog Modulation n Modulation of digital signals n n When only analog transmission facilities are available, digital to analog conversion required Modulation of analog signals n n A higher frequency may be needed for effective transmission Modulation permits frequency division multiplexing COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 27
Basic Encoding Techniques n Analog data to analog signal n n Amplitude modulation (AM) Angle modulation n n Frequency modulation (FM) Phase modulation (PM) COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 28
Amplitude Modulation n n n cos 2 fct = carrier x(t) = input signal na = modulation index n n Ratio of amplitude of input signal to carrier a. k. a double sideband transmitted carrier (DSBTC) COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 29
Spectrum of AM signal
Amplitude Modulation n Transmitted power n n Pt = total transmitted power in s(t) Pc = transmitted power in carrier COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 31
Single Sideband (SSB) n Variant of AM is single sideband (SSB) n n n Advantages n n n Sends only one sideband Eliminates other sideband carrier Only half the bandwidth is required Less power is required Disadvantages n Suppressed carrier can’t be used for synchronization purposes COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 32
Angle Modulation n Angle modulation n Phase is proportional to modulating signal n np = phase modulation index COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 33
Angle Modulation n Frequency modulation n Derivative of the phase is proportional to modulating signal n nf = frequency modulation index COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 34
Angle Modulation n Compared to AM, FM and PM result in a signal whose bandwidth: n n is also centered at fc but has a magnitude that is much different n n Angle modulation includes cos( (t)) which produces a wide range of frequencies Thus, FM and PM require greater bandwidth than AM COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 35
Angle Modulation n Carson’s rule where n The formula for FM becomes COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 36
Basic Encoding Techniques n Analog data to digital signal n n Pulse code modulation (PCM) Delta modulation (DM) COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 37
Analog Data to Digital Signal n Once analog data have been converted to digital signals, the digital data: n n n can be transmitted using NRZ-L can be encoded as a digital signal using a code other than NRZ-L can be converted to an analog signal, using previously discussed techniques COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 38
Pulse Code Modulation n n Based on the sampling theorem Each analog sample is assigned a binary code n n Analog samples are referred to as pulse amplitude modulation (PAM) samples The digital signal consists of block of n bits, where each n-bit number is the amplitude of a PCM pulse COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 39
Pulse Code Modulation
Pulse Code Modulation n n By quantizing the PAM pulse, original signal is only approximated Leads to quantizing noise Signal-to-noise ratio for quantizing noise Thus, each additional bit increases SNR by 6 d. B, or a factor of 4 COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 41
Delta Modulation n Analog input is approximated by staircase function n n Moves up or down by one quantization level ( ) at each sampling interval The bit stream approximates derivative of analog signal (rather than amplitude) n n 1 is generated if function goes up 0 otherwise COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 42
Delta Modulation
Delta Modulation n Two important parameters n n n Accuracy improved by increasing sampling rate n n Size of step assigned to each binary digit ( ) Sampling rate However, this increases the data rate Advantage of DM over PCM is the simplicity of its implementation COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 44
Reasons for Growth of Digital Techniques n Growth in popularity of digital techniques for sending analog data n Repeaters are used instead of amplifiers n n TDM is used instead of FDM n n No additive noise No intermodulation noise Conversion to digital signaling allows use of more efficient digital switching techniques COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 45
Spread Spectrum
Spread Spectrum n Input is fed into a channel encoder n n Signal is further modulated using sequence of digits n n n Produces analog signal with narrow bandwidth Spreading code or spreading sequence Generated by pseudonoise, or pseudo-random number generator Effect of modulation is to increase bandwidth of signal to be transmitted COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 47
Spread Spectrum n n On receiving end, digit sequence is used to demodulate the spread spectrum signal Signal is fed into a channel decoder to recover data COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 48
Spread Spectrum COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 49
Spread Spectrum n What can be gained from apparent waste of spectrum? n n n Immunity from various kinds of noise and multipath distortion Can be used for hiding and encrypting signals Several users can independently use the same higher bandwidth with very little interference COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 50
Frequency Hoping Spread Spectrum (FHSS) n Signal is broadcast over seemingly random series of radio frequencies n n n A number of channels allocated for the FH signal Width of each channel corresponds to bandwidth of input signal Signal hops from frequency to frequency at fixed intervals n n n Transmitter operates in one channel at a time Bits are transmitted using some encoding scheme At each successive interval, a new carrier frequency is selected COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 51
Frequency Hoping Spread Spectrum n n n Channel sequence dictated by spreading code Receiver, hopping between frequencies in synchronization with transmitter, picks up message Advantages n n Eavesdroppers hear only unintelligible blips Attempts to jam signal on one frequency succeed only at knocking out a few bits COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 52
Frequency Hoping Spread Spectrum COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 53
FHSS Using MFSK n n MFSK signal is translated to a new frequency every Tc seconds by modulating the MFSK signal with the FHSS carrier signal For data rate of R: n n duration of a bit: T = 1/R seconds duration of signal element: Ts = LT seconds Tc Ts - slow-frequency-hop spread spectrum Tc < Ts - fast-frequency-hop spread spectrum COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 54
FHSS Performance Considerations n n Large number of frequencies used Results in a system that is quite resistant to jamming n n Jammer must jam all frequencies With fixed power, this reduces the jamming power in any one frequency band COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 55
Direct Sequence Spread Spectrum (DSSS) n n Each bit in original signal is represented by multiple bits in the transmitted signal Spreading code spreads signal across a wider frequency band n n Spread is in direct proportion to number of bits used One technique combines digital information stream with the spreading code bit stream using exclusive-OR (Figure 7. 6) COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 56
Direct Sequence Spread Spectrum (DSSS)
DSSS Using BPSK n Multiply BPSK signal, sd(t) = A d(t) cos(2 fct) by c(t) [takes values +1, -1] to get s(t) = A d(t)c(t) cos(2 fct) n n A = amplitude of signal fc = carrier frequency d(t) = discrete function [+1, -1] At receiver, incoming signal multiplied by c(t) n Since, c(t) x c(t) = 1, incoming signal is recovered COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 58
DSSS Using BPSK
Code-Division Multiple Access (CDMA) n Basic Principles of CDMA n n D = rate of data signal Break each bit into k chips n n Chips are a user-specific fixed pattern Chip data rate of new channel = k. D COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 60
CDMA Example n If k=6 and code is a sequence of 1 s and -1 s n For a ‘ 1’ bit, A sends code as chip pattern n n For a ‘ 0’ bit, A sends complement of code n n <c 1, c 2, c 3, c 4, c 5, c 6> <-c 1, -c 2, -c 3, -c 4, -c 5, -c 6> Receiver knows sender’s code and performs electronic decode function n n <d 1, d 2, d 3, d 4, d 5, d 6> = received chip pattern <c 1, c 2, c 3, c 4, c 5, c 6> = sender’s code COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 61
CDMA Example n User A code = <1, – 1, 1> n n n User B code = <1, 1, – 1, 1, 1> n n To send a 1 bit = <1, – 1, 1> To send a 0 bit = <– 1, 1, 1, – 1> To send a 1 bit = <1, 1, – 1, 1, 1> Receiver receiving with A’s code n (A’s code) x (received chip pattern) n n n User A ‘ 1’ bit: 6 -> 1 User A ‘ 0’ bit: -6 -> 0 User B ‘ 1’ bit: 0 -> unwanted signal ignored COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 62
CDMA for Direct Sequence Spread Spectrum
Categories of Spreading Sequences n Spreading Sequence Categories n n n For FHSS systems n n PN sequences most common For DSSS systems not employing CDMA n n PN sequences Orthogonal codes PN sequences most common For DSSS CDMA systems n n PN sequences Orthogonal codes COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 64
PN Sequences n n PN generator produces periodic sequence that appears to be random PN Sequences n n Generated by an algorithm using initial seed Sequence isn’t statistically random but will pass many test of randomness Sequences referred to as pseudorandom numbers or pseudonoise sequences Unless algorithm and seed are known, the sequence is impractical to predict COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 65
Important PN Properties n Randomness n Uniform distribution n n Balance property Run property Independence Correlation property Unpredictability COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 66
Linear Feedback Shift Register Implementation COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 67
Properties of M-Sequences n Property 1: n n Property 2: n n Has 2 n-1 ones and 2 n-1 -1 zeros For a window of length n slid along output for N (=2 n-1) shifts, each n-tuple appears once, except for the all zeros sequence Property 3: n n n Sequence contains one run of ones, length n One run of zeros, length n-1 One run of ones and one run of zeros, length n-2 Two runs of ones and two runs of zeros, length n-3 2 n-3 runs of ones and 2 n-3 runs of zeros, length 1 COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 68
Properties of M-Sequences n Property 4: n The periodic autocorrelation of a ± 1 sequence is COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum m- 69
Definitions n Correlation n n The concept of determining how much similarity one set of data has with another Range between – 1 and 1 n n 1 The second sequence matches the first sequence 0 There is no relation at all between the two sequences -1 The two sequences are mirror images Cross correlation n The comparison between two sequences from different sources rather than a shifted copy of a sequence with itself COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 70
Advantages of Cross Correlation n The cross correlation between an m-sequence and noise is low n n This property is useful to the receiver in filtering out noise The cross correlation between two different msequences is low n n This property is useful for CDMA applications Enables a receiver to discriminate among spread spectrum signals generated by different m-sequences COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 71
Gold Sequences n n Gold sequences constructed by the XOR of two m-sequences with the same clocking Codes have well-defined cross correlation properties Only simple circuitry needed to generate large number of unique codes In following example (Figure 7. 16 a) two shift registers generate the two m-sequences and these are then bitwise XORed COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 72
Gold Sequences COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 73
Orthogonal Codes n Orthogonal codes n n n All pairwise cross correlations are zero Fixed- and variable-length codes used in CDMA systems For CDMA application, each mobile user uses one sequence in the set as a spreading code n n Provides zero cross correlation among all users Types n n Walsh codes Variable-Length Orthogonal codes COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 74
Walsh Codes n Set of Walsh codes of length n consists of the n rows of an n ´ n Walsh matrix: n W 1 = (0) n n = dimension of the matrix Every row is orthogonal to every other row and to the logical not of every other row Requires tight synchronization n Cross correlation between different shifts of Walsh sequences is not zero COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 75
Typical Multiple Spreading Approach n Spread data rate by an orthogonal code (channelization code) n n Provides mutual orthogonality among all users in the same cell Further spread result by a PN sequence (scrambling code) n Provides mutual randomness (low cross correlation) between users in different cells COM 3525 Wireless Networks: Signal Encoding – Spread Spectrum 76
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