mohatta2015.pdf

46 MATCHED FILTERING
IQ" 1
Œ
LU
m
IQ" 2
10' 3 -2 0 2 4 6 8 10 12 14
Eb/N0 (dB)
Figure 2.4 BEI? vs. Ει,/Νο for QPSK, root-raised-cosine pulse shaping (0.22 rolloff),
static, two-tap. symbol-spaced channel. with relative path strengths 0 and —1 dB, and path
angles 0 and 00 degrees.
ensure that the channel does not give a gain in Eb, as we normalize the path
coefficients so their powers sum to one. Thus, by defining TwoFS as having paths
90 degrees apart, we do not have to account for any channel gain. For consistency,
the TwoTS channel is also defined as having two paths, 90 degrees apart.
In certain cases, the transmitted Eb may be the same for each bit, but the
received Eb may be different, even when the channel is static. An example is CDM,
in which different symbols use different symbol waveforms that interact differently
with a dispersive channel. In this case, we would like to plot BER vs. average
received Eb/N^. For traditional TDM, the symbol waveforms are time shifts of a
common waveform, so that they interact with a static channel the same way. If the
channel block fading or time-varying, then we need to average over the fading. For
a static channel and TDM case considered in this section, the Eb/No is the same
for all symbols (average = individual SNR).
Notice that when the paths create orthogonal copies of a bit, we can simply
account for the energy in each copy and then use analytical results for an AWGN
channel to determine matched filter bound performance. Analytical MFB results
are also possible when nonorthogonal copies are created.