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Proposed TP2 Test Methodology
Norm Swenson, Paul Voois, Tom Lindsay, Steve Zeng
ClariPhy Communications, Inc.
6 January 2005
version 0.2
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 13 dB electrical (6.5 dB optical) below the level required to give a BER of 1e12. Hence
10 log10(OMARCV(T/2N0)1/2) = 8.47+6.5 = 14.97 dB = SNRREF
Without loss of generality, OMARCV is normalized to 1, and N0 is set accordingly.
2. Waveform Measurement and Processing
The TP2 penalty is calculated by Matlab code using a model as shown in Figure 1.
Figure 1. Model for TP2 Penalty Calculation
The measured 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 inputs to the Matlab code are the following:
The captured waveform (resampled, if necessary) corresponding to one complete cycle of the data sequence. The resampled waveform has 16 samples per bit period.
The measured OMA of the sampled waveform, and the measured off power level (i.e., the steady state power level corresponding to a string of transmitted zeroes). Refer to the off power level as the bias.
The data sequence used to generate the transmitted sequence. The data sequence must be aligned with the captured waveform (i.e., a rectangular pulse train based on the data sequence is aligned with the captured waveform within one bit period).
The captured waveform is processed as follows:
The waveform is passed through the simulated fiber channel(s) (Cambridge 2.1 or simulated channels equivalent to the channels in the TP3 test).
The bias is removed from the waveform and the OMA of the waveform is scaled to 1 to match the reference channel model. (Note: Scaling the OMA to 1 effectively sets the ratio of received OMA to N0 to the minimum allowed by the link budget.)
The simulated channel output signal is passed through an antialiasing filter. A fourthorder Butterworth filter of bandwidth 7.5 GHz is used for this purpose. (Note: removal of this filter is under consideration, since the signal has already been filtered by the BesselThompson filter when it was captured.)
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. The feedforward and feedback tap coefficients are calculated using a leastsquares approach that minimizes the meansquared error at the slicer input for the given measured waveform, assuming the noise properties defined in Section 1. Figure 1 shows the channel and equalizer model used for the leastsquares calculation. The channel input is a periodic data sequence EMBED Equation.3 , where N is the length of one period (e.g. 511 for PRBS9). The measured waveform is assumed to be the output of an arbitrary laser response. According to the steps described above, the measured waveform is propagated through the fiber model and antialiasing filter, and then sampled at rate 2/T. (The periodicity of the measured waveform is utilized in the simulated propagation order to avoid edge effects caused by filter memory.) The reference DFE consists of a feedforward filter EMBED Equation.3 and a feedback filter EMBED Equation.3 . Note that the feedforward filter is fractionally spaced and consists of 50 anticausal taps and 50 causal taps (including the tap at k=0). The feedback filter is symbol spaced and strictly causal, and does not have a tap at k=0. The input to the slicer is the periodic sequence EMBED Equation.3 .The leastsquares solution for the feedforward and feedback filters minimizes the quantity EMBED Equation.3 , where the expectation operator refers to the random sequence generated by the additive white Gaussian noise, filtered through the antialiasing filter and feedforward filter. (The periodicity of the inputs to both the feedforward and feedback filters is utilized in order to avoid edge effects caused by filters memories.)
The biterror rate is calculated by the semianalytic method
The Gaussian noise variance at the input to the slicer is calculated.
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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