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Norm Swenson, Paul Voois, Tom Lindsay, Steve Zeng
ClariPhy Communications, Inc.
23 December 2004
version 0.1
Submitted to IEEE 802.3aq
This document outlines a TP2 test methodology for measuring a penalty for purposes of determining compliance with 10GBASELRM specifications. For the purposes of this document, it is assumed that an upper limit on penalty thus measured will be specified by 802.3aq. The penalty is defined as the difference (in dB) of the equivalent signal to noise ratios (SNR) at the slicer input for the reference ideal channel model and for the measured waveform after propagation through a simulated fiber channel model.
1. Reference Channel Model
For the reference channel, rectangular onoff keyed pulses are transmitted and the laser and fiber are assumed perfect. The received pulse is a rectangular pulse with an amplitude measured in OMA of OMARCV and time duration of one bit period T. The receiver has a perfect matched filter front end matched to the rectangular receive pulse. The output of the matched filter is sampled once per bit period (without timing error) and presented to the decision element (binary slicer).
The signal to noise ratio at the slicer input determines the reference bit error rate (BER). The bit error rate is given by
BERREF = Q(OMARCV(T/2N0)1/2)
where N0 is the onesided power spectral density of the additive white Gaussian noise assumed for the receiver, and Q( ) is the Gaussian error probability function
Q(y) = EMBED Equation.3 .
N0 is set 12 dB electrical (6 dB optical) below the level required to give a BER of 1e12. Hence
10 log10(OMARCV(T/2N0)1/2) = 8.47+6 = 14.47 dB = SNRREF
Without loss of generality, OMARCV is normalized to 1, and N0 is set accordingly.
2. Waveform Measurement and Processing
The waveform for the transmitter device under test (DUT) is captured with a sampling oscilloscope. The data sequence driving the DUT is a PRBS9 or similar data pattern. The scope is set to capture at least one complete cycle of the data pattern, with at least seven or eight samples per bit period. (Fewer samples per bit period may be used depending on the high frequency content of the signal. The effective sampling rate must be high enough to avoid aliasing.) The scope includes a fourthorder Bessel Thompson filter with 3dB electrical bandwidth of 7.5 GHz to filter the captured waveform. The scope is set to average over at least 16 patterns to average out noise in the captured waveform.
The captured data and known data sequence are processed as follows:
The measured waveform is resampled to synchronize with a reference clock for the simulation. The timing of the data is normalized by the known duration of the sequence (e.g., 511 bits/10.3125 Gbits per second).
The measured waveform is passed through the simulated fiber channels (Cambridge 2.1 or simulated channels equivalent to the channels in the TP3 test).
The OMA of the waveform is scaled to 1 to match the reference channel model. DC bias is removed from the waveform. (Note: this effectively sets the ratio of received OMA to N0 to the minimum allowed by the link budget.)
Alternative 1:
Fit a pulse shape to the received waveform using a linear approximation and the known data sequence. The pulse shape thus derived is used in a matched filter front end. The signal passes through the matched filter and is sampled at integer multiples of T.
The signal goes through a standard symbolspaced MMSEDFE receiver with 50 feedforward taps and 50 feedback taps.
Alternative 2:
The simulated channel output signal is passed through an antialiasing filter, for example a fourthorder Butterworth filter of bandwidth 7.5 GHz
The antialiasing filter output signal is sampled at rate 2/T.
The sampled signal is processed by a standard fractionallyspaced MMSEDFE receiver with 100 feedforward taps (at T/2 spacing) and 50 feedback taps.
For either Alternative (1) or (2), the feedforward and feedback tap coefficients are computed using a standard leastsquares approach in order to minimize the meansquared error at the slicer input for the particular periodic data sequence that generated the measured waveform, and for the particular N0 defined in Section 1.
The biterror rate is calculated by the semianalytic method
The Gaussian noise variance at the input to the slicer is calculated. Note the noise variance is calculated accordingly when the noise passes through the matched filter (Alternative 1) or antialiasing filter (Alternative 2), and the feedforward filter.
For each bit in the data sequence, the equalized input to the slicer is calculated. For each input (bit) to the slicer (over one complete period of the data sequence), the probability of error is calculated based on the variance of the filtered Gaussian noise and the distance from the slicer input to the decision threshold.
The probabilities of error are averaged over all slicer inputs (bits) to compute a total probability of error BERDUT
The equivalent SNR in optical dB is deduced from the BERDUT as follows:
SNREQUIV = 10 log10(Q1 ( BERDUT))
The penalty p is equal to the difference (in optical dB) between the equivalent SNR and SNRREF from the reference model. Hence
p = SNRREF  SNREQUIV
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