mohatta2015.pdf

THE MATH 137
sometimes inaccurate when approximations are made. Only in special cases is performance
accurately predicted by a relatively simple analysis. An example is linear
equalization of CDM signals with large spreading factors, in which SINR expressions
are easy to compute, and performance is related directly to SINR because ISI
can be accurately modeled as Gaussian, similar to the noise.
A second approach is to measure performance at the output of the equalizer and
map the result to an effective SINR. Here we will measure symbol error rate. Using
the relations in (A.6) and (A.7), we can determine an effective E s /Nn, which we
will define as output SINR. In practice, these equations are used to generate a table
of SINR and SER values. Interpolation of table values is then used to determine
an effective SINR from a measured SER.
This second approach also has limitations. One limitation is that enough symbols
must be simulated at each fading realization to obtain an accurate estimate of SER.
This can be challenging when the instantaneous SINR is high, so that few, if any,
symbols are in error. This also gives rise to a granularity issue, as we can only
measure error rates of the form 0, 1/N S , 2/N s , etc., where N s is the number of
symbols simulated. These limitations can be overcome by ensuring that N s is large
so that the range of interesting SINR. values corresponds to many error events (recall
the 100 error events rule).
Effective SINR. results were obtained for the TwoTSfade channel by generating
1000 symbols (plus edge symbols not counted) for each of 2000 fading realizations.
In Fig. 6.15, cumulative distribution functions (CDFs) are provided for various
receivers for a 6 dB average received Eb/Na level (9 dB E s /No). Recall that the
CDF value (y-axis) is the probability that the effective SINR is less than or equal
to a particular SINR value (z-axis). Thus, smaller is better. For the MFB, output
SINR was determined via measurement rather than semi-analytically.
Observe that equalization provides a rightward shift in the CDF, making smaller
SINR values less likely (larger SINR values more likely). As expected, the MMSE
DFE provides higher SINR values than the MMSE LE. While difficult to see, the
CDFs cross at low SINR, so that the MMSE DFE has more lower SINR values due
to error propagation. The MFB acts as a lower bound CDF.
Results with power control are given in Fig. 6.16. Relative to the previous
results, there is less variation in effective SINR (quicker transition from 0 to 1) as
expected. For the MFB, power control ensures that the effective SINR is the same
for each fading realization (9 dB). However, because we used measured results, we
see a slight variation. Similar to the previous results, the MMSE DFE provides
more higher SINR values than MMSE LE. At low SINR, there is no crossover, as
power control and the high target value ensure few decision errors.
Sometimes certain receivers work well under certain fading conditions, whereas
other receivers work well under other conditions. Such behavior can be identified
using a scatter plot, plotting the effective SINR of one receiver against the effective
SINR of the other receiver. Scatter plots can also be useful in determining behaviors
under different fading scenarios.
In Fig. 6.17, a scatter plot of MMSE DFE effective SINR vs. MMSE LE effective
SINR is given. While the simulation was run for 2000 fading realizations, only the
first 1000 realizations are used to generate the scatter plot (making the individual