Synchronization - Digital Communication Chapter 6 & 7 - Unik

SynchronizationOla JetlundIntroductionSynchronizationDigital CommunicationChapter 6 & 7SynchronizationPhase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’Ola JetlundNovember 20, 2007

definitionsSynchronizationOla JetlundIntroduction◮ Coherent versus noncoherent demodulation◮ Reference signal◮Must be generated (PLL)◮ Subcarrier synchronization◮ Frequency synchronization◮ Phase synchronization - phase lock◮ Reference signal is sync’ed in freq. and phase◮ Symbol synchronization◮ Frame synchronization◮ Receiver versus Network synchronizationSynchronizationPhase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’

costs and benefitsSynchronizationOla JetlundIntroductionCosts◮ hardware and software◮ processing time - communication delay◮ increased receiver powerBenefits◮ possible reduction in transmit power◮ synchronization allows advanced techniques as◮◮◮error-control codingmultiple access techniquesspread spectrumSynchronizationPhase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’

linear loop continuedSynchronizationOla JetlundIntroductionThe closed-loop transfer function:The phase error:H(ω) = ˆΘ(ω)Θ(ω) =K 0F (ω)K 0 F (ω) + jωSynchronizationPhase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’E(ω) =jωΘ(ω)K 0 F (ω) + jωθ(t)−F (ω)K 0 /jωˆθ(t)

steady-state of the linear loopSynchronizationOla JetlundIntroductionSynchronizationSteady-state is found by looking atlim e(t)t→∞From the final value theorem:Phase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’−ω 2 Θ(ω)lim e(t) = lim E(ω) = limt→∞ ω→0 ω→0 K 0 F (ω) + jωNow, if lim t→∞ e(t) = 0 the PLL will eventually lock thephase

performance in presence of noiseNow the received signal isr(t) = cos(ω 0 t + θ(t)) + n(t)rewriting the zero-mean Gaussian noise:n(t) = n c (t) cos(ω 0 t) + n s (t) sin(ω 0 t)SynchronizationOla JetlundIntroductionSynchronizationPhase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’we get the following error signale(t) =x(t)r(t)= sin(θ(t) − ˆθ(t)) + n ′ (t) + 2 sin(2ω 0 + . . .)wheren ′ (t) = n c (t) cos(ˆθ(t)) + n s (t) sin(ˆθ(t))

complete linear model of the PLLSynchronizationOla JetlundIntroductionSynchronizationθ(t)−F (ω)K 0 /jωˆθ(t)Phase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’n ′ (t)Network sync’NB! Assumessin(θ(t) − ˆθ(t)) ≈ θ(t) − ˆθ(t)which is only true for small phase errors!

nonlinear PLL modelSynchronizationOla JetlundIntroductionθ(t)−sin(·) F (ω) K 0 /jωˆθ(t)SynchronizationPhase syncPLLlinear loop modelnonlinear PLL modelSymbol syncNown ′ (t)Frame sync’Network sync’∆ω(t) = d dt {ˆθ(t)} = K 0 y(t)= K 0(sin(ω0 t + ˆθ(t)) ∗ f (t) + n ′ (t) ∗ f (t) )

acquisition - going into lockSynchronizationOla JetlundAssume that n ′ (t) = 0 and F (ω) = 1 and that the inputphase isθ(t) = ω i t.Then the output phase can be denotedˆθ(t) = ω o t +∫ t0K 0 sin e(t)dt + ˆθ(0)where ω i is the frequency of the input signal and ω o thefrequency of the output signal and the difference isdenoted∆ω = ω i − ω oIntroductionSynchronizationPhase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’

acquisition continuedSynchronizationOla Jetlundthe phase error becomese(t) = θ(t) − ˆθ(t) = ∆ω i t −differentiating gives∫ t0K 0 sin e(t)dt − ˆθ(0)IntroductionSynchronizationPhase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’de(t)dt= ∆ω − K 0 sin eFor the loop to be in lock we must havede(t)dt= 0

symbol synchonizationSynchronizationOla JetlundIntroductionSynchronizationPhase syncPLLlinear loop modelnonlinear PLL modelSymbol sync◮ Non-data aided versus data-aided◮ Open versus closed loop symbol syncFrame sync’Network sync’

open-loop sync’All open-loop synchronizers produce some informationon the frequence of the incoming symbols:◮ Example - autocorrelation of the input shapes(t)MatchedFilterEven-lawnonlinearity◮ Example - Fourier component of the data clockBPFsgnSynchronizationOla JetlundIntroductionSynchronizationPhase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’s(t)BPFsgnDelayT /2◮ Example - an edge detectors(t)LPF d/dt (·) 2 BPF sgn

closed-loop sync’SynchronizationOla JetlundIntroductionSynchronizationUses a local data clock. Example:R Tddt| · |Phase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’s(t)VCOF (ω)−+R T −d0 dt| · |

frame synchronizationSynchronizationOla JetlundIntroductionSynchronization◮ applies when the transmitted data have some sortof block or frame structure◮ application dependent◮ examples◮ frame marker◮ codeword transmissionPhase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’

network synchronizationSynchronizationOla JetlundIntroductionSynchronization◮ Receiver sync’◮ Coherent modulation◮ Broadcast (one direction communication)◮ single-link communication◮ Terminal sync - transmission parameters arechanged to obtain sync◮ Noncoherent modulation◮ multi user systems◮ satellite communication◮ TDMA systemsPhase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’

SynchronizationOla JetlundIntroductionSynchronizationPhase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’

SynchronizationOla JetlundIntroductionSynchronizationPhase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’

SynchronizationOla JetlundIntroductionSynchronizationPhase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’

SynchronizationOla JetlundIntroductionSynchronizationPhase syncPLLlinear loop modelnonlinear PLL modelSymbol syncFrame sync’Network sync’