Spread Spectrum Chapter 7 Spread Spectrum n Input
![Spread Spectrum Chapter 7 Spread Spectrum Chapter 7](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-1.jpg)
![Spread Spectrum n Input is fed into a channel encoder n n Signal is Spread Spectrum n Input is fed into a channel encoder n n Signal is](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-2.jpg)
![Spread Spectrum n n On receiving end, digit sequence is used to demodulate the Spread Spectrum n n On receiving end, digit sequence is used to demodulate the](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-3.jpg)
![Spread Spectrum Spread Spectrum](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-4.jpg)
![Spread Spectrum n What can be gained from apparent waste of spectrum? n n Spread Spectrum n What can be gained from apparent waste of spectrum? n n](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-5.jpg)
![Frequency Hoping Spread Spectrum (FHSS) n Signal is broadcast over seemingly random series of Frequency Hoping Spread Spectrum (FHSS) n Signal is broadcast over seemingly random series of](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-6.jpg)
![Frequency Hoping Spread Spectrum n n n Channel sequence dictated by spreading code Receiver, Frequency Hoping Spread Spectrum n n n Channel sequence dictated by spreading code Receiver,](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-7.jpg)
![Frequency Hoping Spread Spectrum Frequency Hoping Spread Spectrum](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-8.jpg)
![Frequency Hoping Spread Spectrum Frequency Hoping Spread Spectrum](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-9.jpg)
![Frequency Hoping Spread Spectrum Frequency Hoping Spread Spectrum](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-10.jpg)
![Multiple Frequency-Shift Keying (MFSK) n n More than two frequencies are used More bandwidth Multiple Frequency-Shift Keying (MFSK) n n More than two frequencies are used More bandwidth](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-11.jpg)
![FHSS Using MFSK n n MFSK signal is translated to a new frequency every FHSS Using MFSK n n MFSK signal is translated to a new frequency every](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-12.jpg)
![FHSS Using MFSK FHSS Using MFSK](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-13.jpg)
![FHSS Using MFSK FHSS Using MFSK](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-14.jpg)
![FHSS Performance Considerations n n Large number of frequencies used Results in a system FHSS Performance Considerations n n Large number of frequencies used Results in a system](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-15.jpg)
![Direct Sequence Spread Spectrum (DSSS) n n Each bit in original signal is represented Direct Sequence Spread Spectrum (DSSS) n n Each bit in original signal is represented](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-16.jpg)
![](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-17.jpg)
![DSSS Using BPSK n Multiply BPSK signal, sd(t) = A d(t) cos(2 fct) by DSSS Using BPSK n Multiply BPSK signal, sd(t) = A d(t) cos(2 fct) by](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-18.jpg)
![DSSS Using BPSK DSSS Using BPSK](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-19.jpg)
![DSSS Performance Considerations DSSS Performance Considerations](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-20.jpg)
![Code-Division Multiple Access (CDMA) n Basic Principles of CDMA n n D = rate Code-Division Multiple Access (CDMA) n Basic Principles of CDMA n n D = rate](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-21.jpg)
![CDMA Example n If k=6 and code is a sequence of 1 s and CDMA Example n If k=6 and code is a sequence of 1 s and](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-22.jpg)
![CDMA Example n User A code = <1, – 1, 1> n n n CDMA Example n User A code = <1, – 1, 1> n n n](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-23.jpg)
![CDMA for Direct Sequence Spread Spectrum CDMA for Direct Sequence Spread Spectrum](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-24.jpg)
![Categories of Spreading Sequences n Spreading Sequence Categories n n n For FHSS systems Categories of Spreading Sequences n Spreading Sequence Categories n n n For FHSS systems](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-25.jpg)
![PN Sequences n n PN generator produces periodic sequence that appears to be random PN Sequences n n PN generator produces periodic sequence that appears to be random](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-26.jpg)
![Important PN Properties n Randomness n Uniform distribution n n Balance property Run property Important PN Properties n Randomness n Uniform distribution n n Balance property Run property](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-27.jpg)
![Linear Feedback Shift Register Implementation Linear Feedback Shift Register Implementation](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-28.jpg)
![Linear Feedback Shift Register Implementation Linear Feedback Shift Register Implementation](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-29.jpg)
![LFSR n n n For any given size of LSFR, a number of different LFSR n n n For any given size of LSFR, a number of different](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-30.jpg)
![Properties of M-Sequences n Property 1: n n Property 2: n n Has 2 Properties of M-Sequences n Property 1: n n Property 2: n n Has 2](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-31.jpg)
![Properties of M-Sequences n Property 4: n The periodic autocorrelation of a ± 1 Properties of M-Sequences n Property 4: n The periodic autocorrelation of a ± 1](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-32.jpg)
![Autocorrelation Autocorrelation](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-33.jpg)
![Definitions n Correlation n n The concept of determining how much similarity one set Definitions n Correlation n n The concept of determining how much similarity one set](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-34.jpg)
![Advantages of Cross Correlation n The cross correlation between an m-sequence and noise is Advantages of Cross Correlation n The cross correlation between an m-sequence and noise is](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-35.jpg)
![Gold Sequences n n Gold sequences constructed by the XOR of two msequences with Gold Sequences n n Gold sequences constructed by the XOR of two msequences with](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-36.jpg)
![Gold Sequences Gold Sequences](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-37.jpg)
![Orthogonal Codes n Orthogonal codes n n n All pairwise cross correlations are zero Orthogonal Codes n Orthogonal codes n n n All pairwise cross correlations are zero](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-38.jpg)
![Walsh Codes n Set of Walsh codes of length n consists of the n Walsh Codes n Set of Walsh codes of length n consists of the n](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-39.jpg)
![Typical Multiple Spreading Approach n Spread data rate by an orthogonal code (channelization code) Typical Multiple Spreading Approach n Spread data rate by an orthogonal code (channelization code)](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-40.jpg)
- Slides: 40
![Spread Spectrum Chapter 7 Spread Spectrum Chapter 7](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-1.jpg)
Spread Spectrum Chapter 7
![Spread Spectrum n Input is fed into a channel encoder n n Signal is Spread Spectrum n Input is fed into a channel encoder n n Signal is](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-2.jpg)
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
![Spread Spectrum n n On receiving end digit sequence is used to demodulate the Spread Spectrum n n On receiving end, digit sequence is used to demodulate the](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-3.jpg)
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
![Spread Spectrum Spread Spectrum](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-4.jpg)
Spread Spectrum
![Spread Spectrum n What can be gained from apparent waste of spectrum n n Spread Spectrum n What can be gained from apparent waste of spectrum? n n](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-5.jpg)
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
![Frequency Hoping Spread Spectrum FHSS n Signal is broadcast over seemingly random series of Frequency Hoping Spread Spectrum (FHSS) n Signal is broadcast over seemingly random series of](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-6.jpg)
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
![Frequency Hoping Spread Spectrum n n n Channel sequence dictated by spreading code Receiver Frequency Hoping Spread Spectrum n n n Channel sequence dictated by spreading code Receiver,](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-7.jpg)
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
![Frequency Hoping Spread Spectrum Frequency Hoping Spread Spectrum](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-8.jpg)
Frequency Hoping Spread Spectrum
![Frequency Hoping Spread Spectrum Frequency Hoping Spread Spectrum](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-9.jpg)
Frequency Hoping Spread Spectrum
![Frequency Hoping Spread Spectrum Frequency Hoping Spread Spectrum](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-10.jpg)
Frequency Hoping Spread Spectrum
![Multiple FrequencyShift Keying MFSK n n More than two frequencies are used More bandwidth Multiple Frequency-Shift Keying (MFSK) n n More than two frequencies are used More bandwidth](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-11.jpg)
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
![FHSS Using MFSK n n MFSK signal is translated to a new frequency every FHSS Using MFSK n n MFSK signal is translated to a new frequency every](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-12.jpg)
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
![FHSS Using MFSK FHSS Using MFSK](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-13.jpg)
FHSS Using MFSK
![FHSS Using MFSK FHSS Using MFSK](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-14.jpg)
FHSS Using MFSK
![FHSS Performance Considerations n n Large number of frequencies used Results in a system FHSS Performance Considerations n n Large number of frequencies used Results in a system](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-15.jpg)
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
![Direct Sequence Spread Spectrum DSSS n n Each bit in original signal is represented Direct Sequence Spread Spectrum (DSSS) n n Each bit in original signal is represented](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-16.jpg)
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)
![](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-17.jpg)
![DSSS Using BPSK n Multiply BPSK signal sdt A dt cos2 fct by DSSS Using BPSK n Multiply BPSK signal, sd(t) = A d(t) cos(2 fct) by](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-18.jpg)
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
![DSSS Using BPSK DSSS Using BPSK](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-19.jpg)
DSSS Using BPSK
![DSSS Performance Considerations DSSS Performance Considerations](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-20.jpg)
DSSS Performance Considerations
![CodeDivision Multiple Access CDMA n Basic Principles of CDMA n n D rate Code-Division Multiple Access (CDMA) n Basic Principles of CDMA n n D = rate](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-21.jpg)
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
![CDMA Example n If k6 and code is a sequence of 1 s and CDMA Example n If k=6 and code is a sequence of 1 s and](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-22.jpg)
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
![CDMA Example n User A code 1 1 1 n n n CDMA Example n User A code = <1, – 1, 1> n n n](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-23.jpg)
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
![CDMA for Direct Sequence Spread Spectrum CDMA for Direct Sequence Spread Spectrum](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-24.jpg)
CDMA for Direct Sequence Spread Spectrum
![Categories of Spreading Sequences n Spreading Sequence Categories n n n For FHSS systems Categories of Spreading Sequences n Spreading Sequence Categories n n n For FHSS systems](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-25.jpg)
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
![PN Sequences n n PN generator produces periodic sequence that appears to be random PN Sequences n n PN generator produces periodic sequence that appears to be random](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-26.jpg)
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
![Important PN Properties n Randomness n Uniform distribution n n Balance property Run property Important PN Properties n Randomness n Uniform distribution n n Balance property Run property](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-27.jpg)
Important PN Properties n Randomness n Uniform distribution n n Balance property Run property Independence Correlation property Unpredictability
![Linear Feedback Shift Register Implementation Linear Feedback Shift Register Implementation](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-28.jpg)
Linear Feedback Shift Register Implementation
![Linear Feedback Shift Register Implementation Linear Feedback Shift Register Implementation](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-29.jpg)
Linear Feedback Shift Register Implementation
![LFSR n n n For any given size of LSFR a number of different LFSR n n n For any given size of LSFR, a number of different](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-30.jpg)
LFSR n n n For any given size of LSFR, a number of different unique m-sequences can be generated by using different values for coefficients. Generator polynomial. Find the sequence generated by the corresponding LSFR, by taking reciprocal of the polynomial.
![Properties of MSequences n Property 1 n n Property 2 n n Has 2 Properties of M-Sequences n Property 1: n n Property 2: n n Has 2](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-31.jpg)
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
![Properties of MSequences n Property 4 n The periodic autocorrelation of a 1 Properties of M-Sequences n Property 4: n The periodic autocorrelation of a ± 1](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-32.jpg)
Properties of M-Sequences n Property 4: n The periodic autocorrelation of a ± 1 sequence is m-
![Autocorrelation Autocorrelation](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-33.jpg)
Autocorrelation
![Definitions n Correlation n n The concept of determining how much similarity one set Definitions n Correlation n n The concept of determining how much similarity one set](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-34.jpg)
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
![Advantages of Cross Correlation n The cross correlation between an msequence and noise is Advantages of Cross Correlation n The cross correlation between an m-sequence and noise is](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-35.jpg)
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
![Gold Sequences n n Gold sequences constructed by the XOR of two msequences with Gold Sequences n n Gold sequences constructed by the XOR of two msequences with](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-36.jpg)
Gold Sequences n n Gold sequences constructed by the XOR of two msequences 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
![Gold Sequences Gold Sequences](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-37.jpg)
Gold Sequences
![Orthogonal Codes n Orthogonal codes n n n All pairwise cross correlations are zero Orthogonal Codes n Orthogonal codes n n n All pairwise cross correlations are zero](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-38.jpg)
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
![Walsh Codes n Set of Walsh codes of length n consists of the n Walsh Codes n Set of Walsh codes of length n consists of the n](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-39.jpg)
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
![Typical Multiple Spreading Approach n Spread data rate by an orthogonal code channelization code Typical Multiple Spreading Approach n Spread data rate by an orthogonal code (channelization code)](https://slidetodoc.com/presentation_image_h/ddeff873e802c02662bd26bdf48d2667/image-40.jpg)
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
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