Exercise 2: Definition and measurement of time variance of a fiber optic channel’s Impulse Response
Define the time variance of a fiber optic channel’s Impulse Response, and suggest a method of measuring it.
Adaptive Equalizers don’t need a channel to be Linear or Time Invariant. But based on the limits of today’s DSP and IC technologies, we can assume that if the channel’s impulse response varies at a rate faster than 1 MHz, it can’t be adaptively equalized, and so will degrade the performance of the link. Therefore, it is important to know what portion of a channel’s impulse response variation, if any, falls above the 1 MHz band.
For the purpose of this exercise, it’s not necessary to know the type of laser, wavelength of operation or the type of fiber (singlemode or multimode). Those differences may produce different behaviors of the channel, but at the moment we are interested in figuring out how to define and measure the channel’s behavior in general. By channel, we mostly mean the fiber, but strictly speaking, it is the composite behavior of the transmitter, fiber, and the analog front end of the receiver, which in this exercise can also be substituted by the plug-in module of the test instrument.
As you think about the details of this exercise, you will be faced with several questions … At what channel bandwidth should this experiment be conducted, and why? How do we distinguish between the variations of a channel’s impulse response and noise? How to overcome the limitations imposed by the test instruments?
One approach may be to shoot narrow (impulse-like) pulses at the transmit end, separated by sufficient time (period) to allow the impulse response to reach a negligible value at the end of each period. Suppose that period is T.
Suppose we take n samples in a period T. Then we can suggest a measure of how much the impulse response has varied from one period to another – for each of the n samples, compute the square of the difference of values between the first pulse and second pulse. Then sum it over n samples. If the two received pulses are identical, this sum will be zero, otherwise it will be some positive number, a measure of the variance from first pulse to second. Now repeat this procedure for first pulse and third pulse, then first pulse and fourth pulse, and so on. By repeating this experiment over many periods, we can collect data that can be processed and interpreted for how large are “slow” and “fast” variations.
One problem with this method maybe that it makes it impossible to measure variations faster than frequency = 1/T. By summing the square of n differences (over T), information about sub-T-rate variations is lost. But if we have collected all this data in a file, we can extract information using other algorithms – what are the possibilities?
We must also consider practical limitations imposed by test instruments. Surely, real time sampling scopes that sample at 100 GHz, and have huge memory, will be available some day !! But until then, how do we make do with the scopes that do “interleaved” sampling – the kind most of us are likely to find in our labs? Can we assume that interleaved sampling will provide the same information, provided the experiment is repeated over large enough number of pulses?
Another possibility to consider is to use signal processing techniques to ease the burden on experimental setup. Is it really necessary to send very narrow pulses through the fiber, in order to achieve our objectives here? How about sending a 5 GHz or even 1 GHz clock?
You may email your reply to the Equalization Ad Hoc reflector, or send a file to me, and I will arrange to post it on the web.
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Last Update: 15 Oct 00