Outline Transmitters (Chapters 3 and 4, Source Coding and Modulation) (week 1 and 2) Receivers (Chapter 5) (week 3 and 4) Received Signal Synchronization (Chapter 6) (week 5 ) Channel Capacity (Chapter 7) (week 6) Error Correction Codes (Chapter 8) (week 7 and 8) Equalization (Bandwidth Constrained Channels) (Chapter 10) (week 9) Adaptive Equalization (Chapter 11) (week 10 and 11) Spread Spectrum (Chapter 13) (week 12) Fading and multi path (Chapter 14) (week 12)

Received Signal Synchronization (Chapter 6) (week 5) Receiver needs Carrier Phase Estimation –Phase Locked Loops –Decision Directed Loops Symbol Timing Estimation

Digital Communication System: Transmitter Receiver

Signal Parameter Estimation Propagation Delay: phase and timing error received signal delay noise large, so phase very sensitive

Need separate estimators Phase Estimation: very narrow bandwidth - slow - tracks sending f c – very accurate Timing Estimation: - tracks changes in delay, , - faster – less accurate Select s i for which Phase Estimation Timing Estimation QAM

Maximum Likelihood Estimates Likelihood function, maximized if best estimate made Assume white Gaussian noise

Maximum Likelihood Carrier Phase Estimate Assume Then ML function is

Maximum Likelihood Carrier Phase Estimate A necessary condition yields:

Maximum Likelihood Carrier Phase Estimate Implementing this: If the loop is stable, then this is a ML estimate

Maximum Likelihood Carrier Phase Estimate Phase Locked Loop: Loop filter Voltage Controlled Oscillator (VCO)

Phase Locked Loop Using an unmodulated carrier for s(t) and a simple loop filter

Phase Locked Loop Using the phase of low pass equivalents and linearizing Stable second order system

Effect of noise on phase estimate Gaussian noise added at input Equivalent linear system

Phase Locked Loop Nice damping and

Phase Locked Loop Stable second order system Pole and zero cancel Not second order

Phase Locked Loop Effect of noise on phase estimate Gain large noise bandwidth small

Phase Locked Loop Nice damping and

Phase Locked Loop Conditions for nice damped system or

Phase Locked Loop Effect of noise on phase estimate Gain very large noise bandwidth OK

Phase Locked Loop Effect of noise on phase estimate Gain low noise bandwidth high

Phase Locked Loop Summary of effect of noise on phase estimate Best two cases

Decision Directed Loops PLLs have problems when the signal is imposed on the carrier and carrier is no longer part of signal –This is very efficient for power so is usually the case in power limited systems! –SSB PAM, QAM, NRZ like this? –Need to create carrier or remove symbols –Removing symbols is Decision Directed

Decision Directed Loops Maximum Likelihood Number of symbols used = K

Decision Directed Loops Maximum Likelihood

Decision Directed Loops Maximum Likelihood

Decision Directed Loops PAM implementation

Decision Directed Loops QAM implementation (get 2 phase estimates) y cn y sn

Non-Decision Directed Loops (Nonlinearity Loops) Ad-hoc use of nonlinearity to “create” carrier Have worse noise that decision directed

Non-Decision Directed Loops (Nonlinearity Loops) Averaging the Likelihood function over all symbols get:

Non-Decision Directed Loops (Nonlinearity Loops) Averaging the Likelihood function over all symbols get:

Symbol Timing Estimation Assume only time has error

Symbol Timing Estimation Assume only time has error

Symbol Timing Estimation Realizing a loop from this: VCC = Voltage Controlled Clock = VCO

Joint Timing and Phase Estimation Maximum Likelihood:

Joint Timing and Phase Estimation Maximum Likelihood:

Joint Timing and Phase Estimation General Case (but not QAM):

Joint Timing and Phase Estimation Realization:

Joint Timing and Phase Estimation QAM Realization: Noise dependant gain?

Joint Timing and Phase Estimation QAM Realization: –Maybe integral in front of VCC can take care of sum over K? –There is a Simulink™ issue with zero delay loops so may need to add loop filter with delay just to get it to work.

Joint Timing and Phase Estimation QAM Realization: –From Kobayashi 1971 IEEE Tran. Comm. Referenced in book p 368. Results in a different structure to book!

Joint Timing and Phase Estimation QAM Realization: –From Kobayashi 1971 IEEE Tran. Comm. –Optimum gain coefficients