1 / 33

DIGITAL SPREAD SPECTRUM SYSTEMS

DIGITAL SPREAD SPECTRUM SYSTEMS. ENG-737 Lecture 5. Wright State University James P. Stephens. GOLD CODE IMPLEMENTATION. Gold Codes are used by GPS and are constructed by the linear combination of two m-sequences of length n=10 There are 1023 possible codes possible for n=10

gervaise-odin
Download Presentation

DIGITAL SPREAD SPECTRUM SYSTEMS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. DIGITAL SPREAD SPECTRUM SYSTEMS ENG-737 Lecture 5 Wright State University James P. Stephens

  2. GOLD CODE IMPLEMENTATION • Gold Codes are used by GPS and are constructed by the linear combination of two m-sequences of length n=10 • There are 1023 possible codes possible for n=10 • Each different code is generated by inputting a different initial fill into the G2 Coder • Each GPS satellite is assigned a different Gold code

  3. GPS C/A CODER

  4. KASAMI CODES • Kasami sequences are one of the most important types of binary sequence sets because of their very low cross-correlation and their large number of available sets • There are two different sets of Kasami sequences, Kasami sequences of the ‘small set’ and sequences of the ‘large set’ • A procedure similar to that used for generating Gold sequences will generate the ‘small set’ of Kasami sequences with M = 2n/2 binary sequences of period N = 2n/2 + 1 • In this procedure, we begin with an m-sequence ‘a’ and we form the sequence a’ by decimating ‘a’ by 2n/2 + 1 • It can be verified that the resulting sequence a’ is an m-sequence with period 2n/2 - 1

  5. b = 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 Repeats 1 2 3 4 5 KASAMI CODE IMPLEMENTATION X4 + X + 1 q = 2n/2 + 1 = 5 m = 2n/2 - 1 = 3 Where, q = decimation value m = period of a’ a a = 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0 a’ = 1 1 0 • a xor b = 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 • Kasami codes are generated by cyclically shifting ‘a’ 2n/2 -2 = 2 times • Including a and b there are 2n/2 = 4 sequences

  6. KASAMI CODE IMPLEMENTATION Example: • Let n=10, therefore, N=2n - 1 = 1023 (length of ‘a’) • The decimation value is 2n/2 + 1 = 33 which is used to create a’ • 1023/33 = 31 which will be the length of a’ • If we observe 1023 bits of sequence a’, we will see 33 repetitions of the 31-bit sequence which we will call sequence ‘b’ • Now taking 1023 bits of sequence ‘a’ and ‘b’ we form a new set of sequences by adding (modulo-2 addition) the bits from ‘a’ and the bits from ‘b’ and all 2n/2 – 2 cyclic shifts of the bits from ‘b’ • By including ‘a’ in the set, we obtain a set of 2n/2 = 32 binary sequences of length 1023 • All the elements of a ‘small set’ of Kasami sequences can be generated in this manner

  7. KASAMI CODE IMPLEMENTATION • The autocorrelation and cross-correlation functions provide excellent properties, as good or better, than Gold Codes • The ‘large set’ of Kasami sequences is generated in a similar manner with the addition of another register • The two registers are a preferred pair as in Gold Code and therefore when combined with the decimated sequence, produce all the associated Gold Codes and the Kasami sequences for an even larger let of sequences

  8. FACTORS FOR DETERMINING SIGNALING FORMAT • Signal spectrum • Synchronization • Interference and noise immunity • Error detection capability • Cost and complexity Before we begin a more in-depth discussion of direct sequence spread spectrum, it will be helpful to compare various encoding and / or signaling techniques used in digital communications

  9. DIGITAL SIGNAL ENCODING FORMATS • Biphase-Space Always a transition at beginning of interval • 1 = no transition in middle of interval • 0 = transition in middle of interval • Differential Manchester Always a transition at middle of interval • 1 = no transition at beginning of interval • 0 = transition at beginning of interval • Delay Modulation (Miller) • 1 = transition in middle of interval • 0 = no transition if followed by 1, transition at end of interval if followed by 1 • Bipolar • 1 = pulse in first half of bit interval, alternating polarity from pulse to pulse • 0 = no pulse • Nonreturn to zero-level (NRZ-L) • 1 = high level • 0 = low level • Nonreturn to zero-mark (NRZ-M) • 1 = transition at beginning of interval • 0 = no transition • Nonreturn to zero-space (NRZ-S) • 1 = no transition • 0 = transition at beginning of interval • Return to zero (RZ) • 1 = pulse in first half of bit interval • 0 = no pulse • Biphase-Level (Manchester) • 1 = transition from hi to lo in middle of interval • 0 = transition from lo to hi in middle of interval • Biphase-Mark Always a transition at beginning of interval • 1 = transition in middle of interval • 0 = no transition in middle of interval

  10. DIGITAL SIGNAL ENCODING FORMATS

  11. NRZ-M NRZ-S Input Input + + + + + + + + + + + + + + + + + + + + DIFFERENTIAL ENCODING Inversion 1 0 1 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0

  12. DIGITAL SIGNAL ENCODING FORMATS • Phase-encoding schemes are used in magnetic recording systems, optical communication, and in some satellite telemetry links • Schemes with transitions during each interval are self-clocking • Schemes that transition in the middle are naturally shorter pulses and require greater bandwidth • Differential encodes provides non-coherent detection

  13. DIRECT SEQUENCE SYSTEMS • DSSS is the most common commercially • Sometimes called PN spread spectrum • Used in CDMA Cellular systems, GPS, some earlier cordless telephones, and 802.11(b) • DSSS directly modulates a carrier with a high rate code that is combined with data • DSSS usually employs PSK and the code is often combined with data by mod-2 addition, i.e. code inversion keying • Predominantly, in practice, a DSSS transmitted signal is either: • BPSK (Binary Phase Shift Keyed) • QPSK (Quadrature Phase Shifted Keyed) • MSK (Minimum Shifted Keyed)

  14. X Data + Code Output Carrier BINARY SHIFT KEYING • This technique is implemented with a ‘Balanced Modulator’ • Two basic types of modulators are: • Single balanced • Double balanced • Three port devices in which  1’s on the code + data input cause 180 degree phase shifts of the carrier

  15. BINARY PHASE SHIFT KEYING (BPSK) Data + Code Typically more than one cycle per chip 1800 Phase Shifts BPSK Carrier

  16. BPSK Power Spectral Density Suppressed Carrier Discrete spectral lines

  17. SUPPRESSED CARRIER Reasons that make suppressed carrier desirable are: • More difficult for adversary to detect signal • Power not wasted on carrier • Signal has constant envelop level so that power efficiency is maximized for the bandwidth used • Bi-phase modulators are simple, stable, low cost devices

  18. BPSK CIRCUIT IMPLEMENTATION

  19. 00 1800 PHASOR REPRESENTATION • BPSK is called antipodal • Antipodal means that two symbols that meet the following criteria: s1 = -s2 • BPSK other than 1800 is not antipodal

  20. 900 00 1800 2700 QUADRATURE PSK OR QPSK • QPSK does not degrade as seriously as BPSK when passed through non-linearity simultaneous with interference • Bandwidth is one-half required by BPSK at same data rate (or twice the data rate in the same bandwidth)

  21. x Σ x x x ~ 900 QPSK BLOCK DIAGRAM m1(t)cos(2πft) Code 1 cos(2πft) Data 1 Carrier SQPSK sin(2πft) Code 2 m2(t)sin(2πft) m2(t) Data 2 SQPSK(t) = m1cos(2πft) + m2sin(2πft) m1(t) Twice the data same BW

  22. x Σ x x ~ 900 ALTERNATIVE IMPLEMENTATION OF QPSK 2-bit serial to parallel Code Data QPSK Half the BW same data rate

  23. NEAR FAR PROBLEM FOR DSSS • Major requirement for DSSS implementation is that one must maintain power control • If one user has more power than others, at the receiver, the capacity of the system is degraded • For maximum capacity, transmitters must maintain equal distance and equal power, i.e. mobile cellular must therefore maintain power control

  24. NEAR FAR PROBLEM ANALYSIS • There are many ways in which the received powers can be unequal for a DSSS CDMA system • For this analysis assume that all users transmit with equal power, but are different distances from the jth receiver • Then the received power from the ith transmitter may be represented as: Pi = Po / diα Where, Po = received power at unit distance di = distance from the ith transmitter to the jth receiver α = propagation law • The parameter α is the propagation law and depends upon the medium in which the transmission takes place

  25. NEAR FAR PROBLEM ANALYSIS (Cont.) • In free space, α is the propagation law and depends upon the medium in which the transmission takes place • In free space, α = 2 • At UHF over an ideal earth, α tends to change to between 3 and 4 (determined experimentally) • The above make it possible to represent the ratio of the power received from the ith transmitter to that received from the jth transmitter, which is the desired signal

  26. U No Beff + Σ[dj / di]α Pj i=1 i ≠ j NEAR FAR PROBLEM ANALYSIS (Cont.) • This is shown by: Pi = [dj / di]α Pj Pi / Pj = (Po / djα) / (Po / djα) = (dj / di)α • The SNR at the output of the jth receiver may now be written as: 2 tm Beff Pj 2Eb / No = (SNR)j = = (SNR)o

  27. U Σ[dj / di]α ≤ 2 tm Beff [(1/(SNR)o) – (1/(SNR)j)] i=1 i ≠ j NEAR FAR PROBLEM ANALYSIS (Cont.) • Solving for the term that is related to the distances gives: • The term (1/(SNR)j) subtracts off for the intended signal

  28. U Σ[dj / di]α = (2.5)α + U - 2 i=1 i ≠ j NEAR FAR PROBLEM ANALYSIS (Cont.) • To find the capacity of a CDMA system where all powers are equal and the distances are the same, let Beff = 20 x 106 Tm = 1/ 30,000 SNRo = 14 SNRj = 25 • Therefore, for all users U, U = [2(20x106) / 30000][(1/14) – (1/25)] = 42 • Now if one user is 2.5 times closer than all other users but still with equal power, Subtracts off closer user and intended user

  29. NEAR FAR PROBLEM ANALYSIS (Cont.) • For α = 3.68 U = 1 + [1 - (2.5)3.68 + 2 tm Beff [(1/(SNR)o) – (1/(SNR)j)] U = 1 + [1 - (2.5)3.68 + 2 x 20 x 106 / 30000)(1/14 – 1/25) U ≈ 14 • The number of users has been reduced by a factor of 3 simply by one transmitter being 2.5 times closer than all of the others • The system would completely fail as a multiple access system if dj / di > 2.78, since only one user could be supported and none of the others would be received with the desired SNRo • This is the Near Far Problem !

  30. PROCESSING GAIN = PG Processing gain is the improvement seen by a spread spectrum system in SNR, within the system’s information bandwidth, over the SNR in the transmission channel. Typically Bi = baud rate PG = BS / Bi = BS / Ri PG(dB) = 10 log (Bs / Ri) Typical PG = 20 to 60 dB Bs Typically Bs = null-to-null 0 -4/T -3/T -2/T -1/T 1/T 2/T 3/T 4/T

  31. JAMMING MARGIN • In a general system with both noise and interference present, the receiver output SNR can be expressed as: (SNR)o = PG (SNR)i Where, PG = processing gain (SNR)o = Output SNR (SNR)I = Input SNR • The ability of a communication system to reduce the effects of jamming is called Jamming Margin

  32. JAMMING MARGIN = MG Jamming margin takes into account the requirement for a useful system output SNR and allow for internal losses. MG = GP – [Lsys + (S/N)out ] , dB Where, Lsys = system implementation losses (S/N)out = SNR at information, despread, output

  33. JAMMING MARGIN EXAMPLE Given, Chip rate = 107 chips / sec Message bit rate = 100 bits / sec Desired SNRo = 25 = 14 dB System losses = 2 dB Find MJ(dB) PG = Bs / Ri = 2 rc / Ri = 2 x 107 / 100 = 2 x 105 PG (dB) = 10 log (2 x 105) = 53 dB MJ(dB) = 53 dB – 2 dB – 14 dB = 37 dB The required output SNR will be obtained if the jamming signal is less than 37 dB greater than the desired signal

More Related