mohatta2015.pdf
signal processing from power amplifier operation control point of view
signal processing from power amplifier operation control point of view
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46 MATCHED FILTERING<br />
IQ" 1<br />
Œ<br />
LU<br />
m<br />
IQ" 2<br />
10' 3 -2 0 2 4 6 8 10 12 14<br />
Eb/N0 (dB)<br />
Figure 2.4 BEI? vs. Ει,/Νο for QPSK, root-raised-cosine pulse shaping (0.22 rolloff),<br />
static, two-tap. symbol-spaced channel. with relative path strengths 0 and —1 dB, and path<br />
angles 0 and 00 degrees.<br />
ensure that the channel does not give a gain in Eb, as we normalize the path<br />
coefficients so their powers sum to one. Thus, by defining TwoFS as having paths<br />
90 degrees apart, we do not have to account for any channel gain. For consistency,<br />
the TwoTS channel is also defined as having two paths, 90 degrees apart.<br />
In certain cases, the transmitted Eb may be the same for each bit, but the<br />
received Eb may be different, even when the channel is static. An example is CDM,<br />
in which different symbols use different symbol waveforms that interact differently<br />
with a dispersive channel. In this case, we would like to plot BER vs. average<br />
received Eb/N^. For traditional TDM, the symbol waveforms are time shifts of a<br />
common waveform, so that they interact with a static channel the same way. If the<br />
channel block fading or time-varying, then we need to average over the fading. For<br />
a static channel and TDM case considered in this section, the Eb/No is the same<br />
for all symbols (average = individual SNR).<br />
Notice that when the paths create orthogonal copies of a bit, we can simply<br />
account for the energy in each copy and then use analytical results for an AWGN<br />
channel to determine matched filter bound performance. Analytical MFB results<br />
are also possible when nonorthogonal copies are created.