Timing Synchronization with Band Edge Filters fred harris 11-15 September, 2017

What The Customer Wants

What the Customer Will Pay

When the Customer wants it.

The Size Customer Wants.

Timing and Carrier Synchronization of Digital Modems

Timing and Carrier Synchronization of Digital Modems Momma’s Middle name is Synchronizer

A Common Line in Adventure Movies!

Find Peak of Correlation Function Filter can’t answer the question: “Am I standing at the highest level?” She can only see the level where you are standing. A Better question to ask. and one she can answer is: “What’s the slope where I am standing?” Zero Slope Positive Slope Negative Slope f<fopt f=fopt f>fopt

Derivative with Help of Nearby Neighbors (Early and Late)

Maximizing Output of Correlation Receiver Same as Seeking Zero Derivative

To Determine Which Direction is the Peak of the Correlator, Qualify the Derivative with Polarity of the Correlator Output

Early-Late Gate Derivative

Combining Early and Late Gates in a One Derivative Filter

Slide Sampler to Input and Perform Timing Offset with Polyphase Digital Filter

We can do the same for phase offsets with a system that measures phase errors and adjusts a VCO to move the phase angle error towards 0. What is one to do when the phase offset is changing faster than the PLL can correct? You change loops to measure frequency offset and adjust VCO to move frequency error towards 0.

Frequency Matched Filter Output Times Derivative Output

Time and Frequency Response, Matched Filter and Frequency Derivative Matched Filter

Frequency Matched Filter Non Data Aided Frequency Acquisition

Band Edge Filter

Spectra of Input Signal and Band Edge Filter Outputs

Frequency Locked Loop with Band Edge Filters Maximum Likelihood Minimum Variance

Frequency Locked PLL

Spectra of Signals From Band Edges Combined to form Two New Signals

Conjugate Product of Sum and Difference Band Edge Filters Imaginary Part, Sinusoid at Symbol Frequency. Phase Related to Time offset between Samples and Signal. Real Part DC Proportional to Energy Difference

Equivalent Band Edge Options for Frequency Lock Loop

Eye Diagrams of Matched Filter, Band-Edge Filter Sum, Difference, and Product

Eye Diagrams of Matched Filter, Band-Edge Filter Sum, Difference, and Product with Timing Offset

Spectra of SQRT Nyquist Shaped Modulation Signals over Range of Excess BW

Eye Diagrams Matched Filter Output

Cyclostationary Mean and Variance Eye Diagrams Magnitude Matched Filter Output

Spectral Lines from Excess BW: MF(t) x dMF(t)* Modulation Noise

Eye Diagrams Band Edge Difference Filter Output

Cyclostationary Mean and Variance Eye Diagrams Magnitude Band Edge Difference Filter

Spectra of BEsum(t) x BEdiff(t)* No Modulation Noise)

Homework Problem

Band Edge Filter Carrier Frequency and Timing Acquisition 4-samples per symbol

Band Edge Filter Carrier Frequency and Timing Acquisition 2-samples per symbol

Gardner Loop (MINL) Timing Error Detector Timing Error(n) =[ydet(n-1)-ydet(n+1)]y(n)

Gardner Loop Track Zero Crossings y ydot = 0 when y = 0 Timing Error(n) =[ydet(n-1)-ydet(n+1)]y(n)

That’s all Folks

SOFTWARE DEFINED RADIO MAN Is Open For Questions