Basics of Spread Spectrum Systems

IMPERIAL COLLEGE LONDON, DEPARTMENT of ELECTRICAL and ELECTRONIC ENGINEERING. COMPACT LECTURE NOTES on COMMUNICATION SYSTEMS. Prof. Athanassios Manikas, Autumn 2007 Basics of Spread Spectrum Systems

1. Introduction General Block Diagram of a Digital Comm. System (DCS) H( f) Spread Spectrum Systems 2 ˆ Most of the current cellular systems, such as GSM, use frequency division multiplex - time division multiplex (FDM-TDM) techniques to improve the system capacity. Message signal bandwidth F g =4kHz Uniform quantizer Q=2 13 i.e. 456 bits 20 msec r b =22.8kbits/s Gaussian MSK M=4 operating on 148 bits per TDMA frame BUE=0.3 0.577ms 148bits plus 8.25 guard bits Sampling Frequency F s =8kHz 160 levels 20 msec = 2080 bits 20 msec i.e. r b =104kbits/s i.e. 260 bits 20 msec r b =13kbits/s SPECTRUM 0 200kHz TDMA FRAME=4.615ms 890MHz 915MHz 935MHz 960MHz Downlink 25MHz Uplink=25MHz f Spread Spectrum Systems 3

HSCDS: High Speed Circuit Switched Data GPRS: General Packet Radio Systems (2+) EDGE: Enhanced Data Rate GSM Evolution (2+ UMTS:Universal Mobile Telecommunication Systems (3G) Spread Spectrum Systems 4 Spread Spectrum Systems 5

Industry Transformation and Convergence [from Ericsson 2006, LZT 123 6208 R5B] Note: CDMA belong to the class of SSS Spread Spectrum Systems 6 When a DCS becomes a Spread Spectrum Systems ÐSSS Ñ: Spread Spectrum Systems 7

Ú Ý LEMMA 1: CS SSS iff Û Ý Ü ì Bss message Bandwidth Ði.e. BUE=largeÑ ì B =/ f{ message} ss where B ss =transmitted SS signal bandwidth our AIM: ways of accomplishing LEMMA-1. Spread Spectrum Systems 8 N.B.: B transmitted-signal B message Ê SSS distributes the transmitted energy over a wide bandwidth Ê SNIR at the receiver input is LOW. Nevertheless, the receiver is capable of operating succesfully because the transmitted signal has distinct characteristics relative to the noise Spread Spectrum Systems 9

BLOCK DIAGRAM of a SSS b(t) j(t) jammer of power P j Dig. Demod b(t) Spread Spectrum Systems 10 Classification of SSS interference is averaged over a large time interval transmitted signal is made to avoid the interference a large fraction of time Ê interf œ Æ e.g. DS/BPSK e.g. FH/FSK DS/QPSK bt ÐÑ=!![8Ó.-Ðt nt Ñ where Ö! Ò8Ó is a sequence of 1's; -Ð Ñ is an energy signal of duration n c t X- Spread Spectrum Systems 11

The PN signal,ð>ñ is a function of a PN sequence of 1's {![ 8]} ìthe sequences Ö! Ò8Ó must agreed upon in advance by Tx and Rx and they have status of password. ìthis implies that : ˆknowledge of {!Ò8Ó} Ê demodulation=possible ˆwithout knowledge of Ö! Ò8Ó Ê demod.= very difficult ìif Ö! Ò8Ó Ði.e. "password" Ñ is purely random, with no mathematical structure, then ˆ without knowledge of Ö!Ò8Ó Ê demodulation=impossible Spread Spectrum Systems 12 ìhowever all practical random sequences have some periodic structure. This means:! Ò8Ó œ! Ò8 R Ó where Rœperiod of sequence i.e. pseudo-random sequence (PN-sequence) Spread Spectrum Systems 13

1.1.Applications of Spread Spectrum Techniques A. Interference Rejection: to achieve interference rejection due to: a Ñ Jamming Ðhostile interferenceñ N.B.: protection against cochannel interference is usually called anti-jamming ÐAJÑ bñ other users ÐMultiple Access Ñ: Spectrum shared by coordinated " users. cñmultipath: self-jamming by delayed signal Spread Spectrum Systems 14 B. Energy Density Reduction Ðor Low Probability of Intercept LPI Ñ: LPI' main objectives: añto meet international allocations regulations bñto reduce Ðminimize Ñthe detectability of a transmitted signal by someone who uses SPECTRAL ANALYSIS cñprivacy in the presence of other listeners C. Range or Time Delay Estimation N.B.: application-a =most important Spread Spectrum Systems 15

Jamming source, or, simply Jammer Jammer = intentional (hostile) interference ì the jammer has full knowledge of SSS design except the jammer does not have the key to the PN-sequence generator, i.e. the jammer may have full knowledge of the SSSystem but it does know the PN sequence used. Spread Spectrum Systems 16 1.2. PROCESSING GAIN ÐPGÑ PG: is a measure of the interference rejection capabilities definition: PG F where "ÎX- X F = "ÎX œ X == -= -= - F= bandwidth of the conventional system Spread Spectrum Systems 17

2Þ Principles of PN-sequences ì PN-codes (or PN-sequences, or spreading codes) are sequences of +1s and -1s (or 1s and 0s) having special correlation properties which are used to distinguish a number of signals occupying the same bandwidth. ì Five Properties of Good PN-sequences: Property-1. easy to generate Property-2. randomness Property-3. long periods Property-4. impulse-like auto-correlation functions Property-5. low cross-correlation Spread Spectrum Systems 18 ì Comments on Properties 1, 2 & 3 Property-1 is easily achieved with the generation of PN sequences by means of shift registers, while Property-2 & Property-3 are achieved by appropriately selecting the feedback connections of the shift registers. Spread Spectrum Systems 19

ì Comments on Property-4 to combat multipath, consecutive bits of the code sequences should be uncorrelatedþ i.e. code sequences should have impulse-like autocorrelation functions. Therefore it is desired that the made as small as possible. auto-correlation of a PN-sequence is Spread Spectrum Systems 20 The success of any spread spectrum system relies on certain requirements for PN-codes. Two of these requiremnets are: a. the autocorrelation peak must be sharp and large (maximal) upon synchronisation (i.e. for time shift equal to zero) b. the autocorrelation must be minimal (very close to zero) for any time shift different than zero. Autocorrelation function 1 0-1/31-5 0 5 10 15 20 25 30 Time Delay in units oft c A code that meets the requirements (a) and (b) above is the maximum period shift register sequence (m-sequence) which is ideal for handling multipath channels. Spread Spectrum Systems 21

The figure below shows a shift register of 5 stages together with a modulo-2 adder. By connecting the stages according to the coefficients of the polynomial D5+D²+1 an m- sequence of length 31 is generated (output from Q5). The autocorrelation function of this m-sequence signal is shown in the previous page Modulo-2 adder + Modulo-2 adder + o/p Q 1 Q 2 Q 3 Q 4 Q 5 Q 3 Q 5 i/p 1 2 3 4 5 i/p 1 2 3 4 5 clock Shift register clock 1/T c Shift register (a) (b) Spread Spectrum Systems 22 ì Comments on Property-5 If there are a number of PN-sequences Ö! Ò5Ó ß Ö! Ò5Ó,..., Ö! Ò5Ó 1 # K then if these code sequences are not totally uncorrelated, there is always an interference component at the output of the receiver which is proportional to the cross-correlation between different code sequencesþ Therefore it is desired that this possible. cross-correlation is made as small as Spread Spectrum Systems 23

ì Properties-4 and 5: Trade-off In a CDMA communication environment there are a number of PN-sequences Ö! Ò5Ó ß Ö! Ò5Ó,..., Ö! Ò5Ó of period R 1 # K which are used to distinguish a number of signals occupying the same bandwdith. Therefore, based on these sequences, we should be able to ˆ combat multipath (which implies that the auto-correlation of a PN-sequence Ö! 3 Ò5Ó should be made as small as possible) ˆ remove interference from other users/signals, ( which implies that the cross-correlation should be made as small as possible). Spread Spectrum Systems 24 However # # V auto V -ross a constant which is a function of period R i.e. there is a trade-off between the peak autocorrelation and crosscorrelation parameters. Thus, the autocorrelation and cross-correlation functions cannot be both made small simultaneously. The design of the code sequences should be therefore very careful. N.B.: A code that provides a trade-off between auto and cross correlation is the goldsequence. Spread Spectrum Systems 25

2.1. m-sequences m-seq. : widely used in SSS because of their very good autocorrelation properties. PN code generator: is periodic Å i.e the sequence that is produced repeats itself after some period of time 2.1.1. Definition of m-sequ. A sequence generated by a linear 7-stages FB shift register is called a maximal length or a maximal sequence if its period is m Rœ# " Ðwhich is the maximum period for the above shift register generator) The initial contents of the shift register are called initial conditions. Spread Spectrum Systems 26 The period R depends on the feedback connections (i.e. coefficients -Ñ and 7 Rœ7+B, i.e. Rœ# ", when the characteristic polynomial 3 7 7 " -ÐHÑ œ - H - H... - H - with - = " 7 7 " "!! is a primitive polynomial of degree m. rule: if 0 Ê no connection - 3 =œ " Ê there is connection definition of PRIMITIVE polynomial = very important (see Appendix 4C) Spread Spectrum Systems 27

ì Some Examples of Primitive Polynomials degree-7 polynomial $ $ D+D+ " % % D+D+ " & # & D+D+ " ' ' D+D+ " ( ( D+D+ " ( Appendix 4.E provides some tables of irreducible & primitive polynomial over GF(2)) 2.1.2. Implementation ì use a maximal length shift register i.e. in order to construct a shift register generator for sequences of any permissible length, it is only necessary to know the coefficients of the primitive polynomial for the corresponding value of m " f œ œ chip rate œ clock rate - X - Spread Spectrum Systems 28 7 7 " 0 Ê no connection -ÐD Ñœ-7H -7 " H... -H - "! with -! œ" rule: if -3= œ " Ê there is connection Note that the sequence of 0's and 1's is transformed to a sequence of by using the following function (o/p œ 1 2 i/p) i.e.![ 8] œ " #. 8 1s Spread Spectrum Systems 29

$ ì Example: -ÐHÑ= H H " = primitive Êcoefficient = Ð"ß!ß "ß " Ñ power=m=3 o/p " st # nd $ rd initial condition " " " clock pulse No. " clock pulse No. # clock pulse No. $ clock pulse No. % clock pulse No. & clock pulse No. ' clock pulse No. (! " "!! " "!!! "! "! " " "! " " " 7 - - R œ 7 œ # " i.e. period œ 7. X Spread Spectrum Systems 30 2.1.3. Autocorrelation of 'm-sequences' e![ 8 ] f ha = a two valued auto-correlation function: R V!![ 5] œ "![ 8]![ 8 5] œ œ R 5 œ!79. R (1) 8œ" " 5Á!79.R 7 Note: that a sequence e![ 8] fof period Rœ2 ", generated by a linear FB shift register, is called a maximal length sequence. Spread Spectrum Systems 31

2.2 Þ Gold Sequences ì Although 7-sequences possess excellent randomness Ðand especially autocorrelation Ñ properties, they are not generally used for CDMA purposes as it is difficult to find a set of 7-sequences with low crosscorrelation for all possible pairs of sequences within the set. ì However, by slightly relaxing the conditions on the autocorrelation function, we can obtain a family of code sequences with lower crosscorrelation. ì Such an encoding family can be achieved by Gold sequences or Gold codes which are generated by the modulo-2 sum of two 7-sequences of equal period. Spread Spectrum Systems 32 The Gold sequence is actually obtained by the modulo-2 sum of two 7-sequences with different phase shifts for 7 the first 7-sequence relative to the second. Since there are R œ # " different relative phase shifts, and since we can also have the two 7-sequences alone, the actual number of different Gold-sequences that can be 7 generated by this procedure is # ". These sequences, however, are not maximal length sequences. Therefore, their auto-correlation function is not the two valued one given by Equ. (1). The auto-correlation still has the periodic peaks, but between the peaks the auto-correlation is no longer flat. Spread Spectrum Systems 33

127 150 100 50 0 m-seq. 127 auto-co -50-150 -100-50 0 50 100 150 lag k 150 100 50 0-50 -150-100 -50 0 50 100 150 lag k Spread Spectrum Systems 34 Spread Spectrum Systems 35

ì Example for a DS-QPSK SSS [with 9 =45./1 - Gray code]. point-b: 0 0 1 0 0 1 point-t: mt () bt () point-t1: st () th n interval T cs th (n+1) interval T cs Aexp( j45) (=m 1 ) Aexp( j315) (= ) Aexp( j135) (= ) +m +m +m a[1] a[6] a[1] +1 +1 +1 +1 +1 +1 +1 +1 +1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1 a[3] a[3] +m 4 +m 4 +m 4 +m 2 +m 2 +m 2 1 1 1 m 4 th (n+2) interval T cs a[n] a[n+1] a[n+2] m 2 t t T c T c Spread Spectrum Systems 36 point-a: 0 0 1 0 0 1 th n interval T cs th (n+1) interval T cs th (n+2) interval T cs point-t1: +m 1 +m 1 +m 1 +m 4 +m 4 +m 4 +m 2 +m 2 +m 2 s1() t t AT THE RECEIVER: point-t1: rt () xk xk +m 1 +m 1 +m 1 +m 4 +m 4 +m 4 +m 2 +m 2 +m 2 t τ k T c T c T cs T cs T cs point-t: m 1 k m 4 k m 2 k t m 1 k 2 m 4 k 2 m 2 k 2 t Spread Spectrum Systems 37