kautilya said:
Hi there.
I am working on a study-oriented university project on digital modulation techniques. I am trying to implement a scheme of early-late gate synchronizer to latch on to the pulse instant. Can you help me with the different ways of doing it? along with any suitable analysis and waveforms obtained.
will highly appreciate if u do it.
regards
kautilya
Suppose someone sends you a single rectangle pulse, and you want to know when it was received. You can implement a matched filter, and the output signal will then be a triangle. From the time offset of the peak of that triangle, you can infer the time (with respect to your local clock) at which the pulse was received.
An early-late architecture is simply one way of answering the question "when did the peak occur"? The idea is to sample the output of the matched filter at two times, one nominally before the expected peak and one after, at some known time delay between the two samples. (A typical delay may be the length of the bit.)
In any case let's assume you know exactly, with respect to your local clock, the times at which you sample the matched filter output. Call them T_early and T_late. Let's call the sample values themselves M(T_early) and M(T_late) where M(t) is the magnitude of the matched filter output at time t. Let's also define T_prompt = 0.5*(T_early + T_late) = the midpoint between T_early and T_late.
If the triangle peak is exactly at T_prompt, you would expect M(T_early) = M(T_late).
In general, if you compute delta = M(T_early) - M(T_late), then delta is proportional to the offset of the triangle peak, relative to the T_prompt.
If delta < 0, then the peak lies to the right of (later than) the midpoint. If delta > 0, then the peak lies to the left of (earlier than) the midpoint.
Thus delta acts as a discriminator: you hypothesize that the triangle peak is at T_prompt, and delta is proportional to the signed error of that hypothesis. (You can work out the constant of proportionality without too much difficulty: it depends on the height and width of the triangle.)
You can also generalize this idea: if someone sends you a known sequence of pulses of arbitrary shape, you can use a similar idea based on the matched filter and early-late sampling to create an error signal, which can then be used to drive a feedback loop to achieve correct synchronization.
If you want more information, look in a digital communication textbook that covers either pilot symbol-based synchronization, or code-division spread spectrum, which works very similarly. Another example is the construction of timing measurements in a GPS receiver, which again involves correlating a received signal with a matched filter and estimating the time of the peak.
