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Radioelektronika 20051 Spread Spectrum Signals in Modern Communications Jan Šimša Institute of Radio Engineering and Electronics AS CR simsa@ure.cas.cz

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Radioelektronika 20052 spread spectrum What signal has spread spectrum? §Any digitally modulated signal whose ratio of bandwidth to its whose ratio of bandwidth to its data (modulation) symbol rate data (modulation) symbol rate is substantially greater than is substantially greater than one. one. Spreading of spectrum – generation of signal using shaping or modulation

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Radioelektronika 20053 Contents Motivation Classification of signals and methods of spreading spectrum Features of SS signals Optimum reception (detection) Synchronization Code division multiplex (multiple access) Conclusions

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Radioelektronika 20054 Motivation Why is spreading utilized? l Transmission of an additional information? l Decrease of error rate in AWGN channel? ????? l ????? l Decrease of error rate in any more disturbing channel? l Preserving of unauthorized reception? l Advantageous multiple utilization of a channel? What is the price we pay for these advantageous features? Complexity of a system realization No (user) No Yes

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Radioelektronika 20055 Heavily distorting communication channels §Time variant channels §Multipath channels §Frequency selective channels §Channels with interferences

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Radioelektronika 20056 Frequency diversity §Frequency selective / nonselective channels §Channel coherence bandwidth is given by parameters of the channel §Narrowband signals can fade completely §Frequency nonselective selective

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Radioelektronika 20057 Frequency diversity §Distortion by frequency selective channel §One deep fade model – rectangular fade

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Radioelektronika 20058 Frequency diversity §Impulse response of the rectangular fade Response to one chip of the rectangular shape

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Radioelektronika 20059 Frequency diversity Response y 1i (t) to positive chip for B.T c = 0.01 (solid line ) B.T c = 0.05 (dotted line)

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Radioelektronika 200510 Classification of signals and methods of spreading spectrum § Any spread spectrum signal belongs to one of the three categories: §signals without a carrier §signals with a single carrier §signals with multiple carriers

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Radioelektronika 200511 Signals without carrier are created by a sequence of very narrow pulses (< 1ns) of a proper shape ( Gaussian, wavelets) §their spectrum bandwidth is by some orders of magnitude wider than the modulation rate. Such signals are often referred to as Ultra Wide-Band (UWB) signals (and related UWB systems). Their bandwidth B≥500 MHz, B/f 0 ≥ 0.2 §it can reach bandwidth > 5 GHz

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Radioelektronika 200512 Single carrier signals §Harmonic carrier spread spectrum (SS) signals §three basic subgroups l Direct Sequence (DS) – spreading by BPSK, QPSK keying l Frequency Hopping (FH) l Time Hopping (TH) - slow (SFH) - fast (FFH)

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Radioelektronika 200513 Direct Sequence (DS) Spreading

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Radioelektronika 200514 Direct Sequence (DS) Spreading

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Radioelektronika 200515 Direct Sequence (DS) Spreading

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Radioelektronika 200516 Direct Sequence Spreading

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Radioelektronika 200517 Direct Sequence Spreading

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Radioelektronika 200518 Direct Sequence Spreading

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Radioelektronika 200519 Direct Sequence Spreading §BPSK data modulation b(t) and BPSK spreading modulation c(t) Spreading modulation c(t) Data modulation b(t) where T- symbol interval, T c - chip interval The period of spreading modulation is T=L.T c

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Radioelektronika 200520 Optimization of linear receiver §Matched filter (MF) – correlator Its response MF impulse response is defined by the signal to which MF is matched - MF[s(t)] MF response at t=t 0 =T to finite signal s(t) whose interval of nonzero values is (0,T),is

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Radioelektronika 200521 Optimization of linear receiver §MF §correlator

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Radioelektronika 200522 Interferences §Response of MF[s(t)] to interfering signal s 1 Correlation coef. §Orthogonal signals do not cause any interference §Correlation in time domain – frequency domain §Parseval’s formula Orthogonal signals have orthogonal spectra

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Radioelektronika 200523 Code synchronization §Code synchronization is an alignment of the spreading modulation of received signal and the replica at the multiplier producing despreaded signal §It consists of two steps l Acquisition – coarse alignment of the modulation and the replica l Tracking – accurate alignment and time- variations tracking

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Radioelektronika 200524 DS Code acquisition with the aid of a system of correlators - Matched filters Uncertainty region – the interval of prospective alignments. The position is nonsensitive to shifts by an integer multiple of the spreading signal period (modulo L.T c ) The goal (penalty) function of code acquisition process optimization Mean acquisition time – minimization Probability of acquisition within given time interval – max Code acquisition process is defined by acquisition detector rule by search strategy - a sequence of points defining the replica positions within an uncertainty region Classification according to changes of replica position l Stepping correlator l Sliding correlator

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Radioelektronika 200525 Classification of DS code acquisition detectors as to the number of channels l Single channel detector – for serial search on uncertainty region l Multiple channel detector – for parallel / serio- parallel search as to the realization of each channel of the detector l Passive correlator - multiplier/integrator l Active correlator - Matched Filter (DSP, SAW) as to the rule of the final decision making l Single dwell detector l Multiple dwell detector

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Radioelektronika 200526 Spreading signal - optimization §Sharp and narrow main lobe of autocorrelation §DC component-free §Low- level side lobes of autocorrelation §Long linear span §Low croscorrelation between signal and interferences §Generating constant- envelope signal §Noise-like signals – pseudonoise (PN) signals §M-sequences, Gold codes, Kasami codes, Walsh Hadamard sequences, bent sequences,

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Radioelektronika 200527 Slow Frequency Hopping

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Radioelektronika 200528 Slow Frequency Hopping

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Radioelektronika 200529 Fast Frequency Hopping

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Radioelektronika 200530 Time hopping §Packet transmission §Fixed length of packets §Pseudorandom position of packets within frame §Position control by code sequence

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Radioelektronika 200531 Two-path channel

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Radioelektronika 200532 Multipath channel – Rake receiver

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Radioelektronika 200533 Interferences §Orthogonal signals do not cause interferences (orthogonality is not generally invariant to mutual shift of signals) §Nonorthogonal (correlated) signals cause interference §Interference is proportional to amplitude of interfering signal §This amplitude can be greater than the amplitude of useful (target) signal = near-far effect Efekt nestejných vzdáleností (efekt nestejných amplitud)

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Radioelektronika 200534 Multicarrier CDMA T N = T, = f i+1 – f i =( i+1 - i )/2 = T -1 Components are orthogonal on the interval T

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Radioelektronika 200535 Multicarrier DS CDMA T N = T/N, = f i+1 – f i =( i+1 - i )/2 =T c -1 Components are orthogonal on the interval T c

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Radioelektronika 200536 Multitone CDMA T N = N.T, = fi+1 – fi =( i+1- i)/2 =(N T) -1 Components are orthogonal on the interval T N

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Radioelektronika 200537 Comparison in frequency domain

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Radioelektronika 200538 Shared communication channel §Multiplex (Multiple Access) Frequency division Time division Code division Timing of symbols – identical = synchronous CDMA - nonidentical = symbol asynchronous CDMA > identical chip timing = chip synchronous CDMA > nonidentical chip timing = chip asynchronous

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Radioelektronika 200539 Code Division Multiple Access Signal space - dimensionality 2BT = number of mutually orthogonal signals

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Radioelektronika 200540 Synchronous and Asynchronous CDMA

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Radioelektronika 200541 CDMA signal §Signal at detector input signature where b i (t) is data signal of the i-th user, is its delay and s i (t) is its spreading modulation, which in CDMA is labeled to as a signature. Usually, signature has unit energy ( a system of orthogonal signatures is in the same time orthonormal). As c i 2 (t)=1, the unit energy signature s i (t) is preserved if

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Radioelektronika 200542 Synchronous CDMA §CDMA is synchronous, iff Then Without loss of generality let it be This signal causes response y m of MF matched to the signature of m-th user MUI

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Radioelektronika 200543 The second component of the right side of the equation represents Multiuser Interference (MUI / MAI) This component is zero if the signatures at the detector input are ortogonal. If system designer is not able ensure validity of this condition (it is the usual case as parameters of channel are unknown and time variable) Detector minimizing MUI is not MF any more; it is more complex, usually nonlinear. To keep the complexity of receiver acceptably low, suboptimum linear detectors are used. Multiuser interference (MUI)

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Radioelektronika 200544 Multiuser detection §Vector notation §Matrix of amplitudes and correlation matrix Detector estimates vector of data Optimum detector is described by the equation Vector y can now be expressed as

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Radioelektronika 200545 It can be expressed using likelihood where and Averaging over random variable b k is not performed. For a priori equiprobable symbols the above average is Optimum receiver is nonlinear.

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Radioelektronika 200546 Using vector notation it is where Approximation of the optimum detector - linear detectors Linear detector consists of the bank of filters matched to the signatures of individual users and weighted sum of their outputs is created. Weights in summation are chosen in a way minimizing MUI or noise plus MUI, respectively. Linear detectors

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Radioelektronika 200547 Block diagram of linear multiuser detector

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Radioelektronika 200548 Conventional detector This detector is optimum in the case of uncorrelated signatures, i.e. if If signatures are correlated, MAI is nonzero. Conventional detector – bank of MFs

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Radioelektronika 200549 Decorrelating detector §Matrix M is the inverse to correlation matrix R Then and k-th component of the detector output is MUI component is totally compensated but noise component has increased. but noise component has increased.

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Radioelektronika 200550 MMSE detector It minimizes men square error of the vector b estimate. We search for the matrix M minimizing this error where the norm of vector is defined as After some manipulation

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Radioelektronika 200551 We expand After substitution y it can be rearranged to the shape where Minimum MSE is reached for Decision rule of MMSE detector is MMSE detector

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Radioelektronika 200552 Asymptotic cases AAdaptive methods MF detector Decorrelating detector - Trained methods - Blind methods To avoid periodical repetition of measurements of values of matrices A and R in the case of time variant channel adaptive MMSE methods can be used.

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Radioelektronika 200553 Spread Spectrum Signals §Advantages »Interference resistant »Multipath resistant »Selective fades resistant »Sharing communication channel by multiple users »Unauthorized reception resistant »Interference into other systems reduced §Costs »Code synchronization »More complex system realization

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Radioelektronika 200554 Spread Spectrum Signals

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