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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52 MATCHED FILTERING<br />
k — ko, we have<br />
ΛΤΛ,Β-1<br />
(2.90)<br />
which can be modeled as<br />
κ-\<br />
z k „ h (y/E a /N c )(l/y/Ñ¿¿) Σ s k(0)h k<br />
ΛΓΛΙΟ-1<br />
£ fkU)fkU)<br />
3=0<br />
+ U k<br />
(2.91)<br />
\= \/Ee/ifc„Sfc„(0) +w fc ,<br />
where<br />
E„ =<br />
NMI<br />
NMB + NCP<br />
E s , (2.92)<br />
and Uk is complex, Gaussian noise with zero mean and variance iV () . We used the<br />
orthogonality property in (1.42), which removed ISI from other symbols in the same<br />
symbol period (k φ fco). To complete the matched filtering operation, we would<br />
multiply by VË s h* ku .<br />
In this example, we saw that for OFDM, by keeping a certain NMB samples<br />
of the partial matched filter, completing the matched filtering operations leads to<br />
complete elimination of ISI. Keep in mind that we assumed the delay spread was<br />
no more than the length of the CP.<br />
2.4.2 The matched filter bound<br />
When different symbols use different symbol waveforms, there is a MFB for each<br />
symbol. These symbol-specific bounds can be quite different, depending on how<br />
the medium response interacts with the transmit symbol waveform.<br />
Often an average of the bound is taken, as it provides a bound on the average<br />
SINR or error rate. Ideally, to obtain the average SINR or average error rate,<br />
averaging should be performed after determining the SINR or error rate for each<br />
symbol waveform. In practice, a looser bound is often used based on assuming that<br />
each symbol waveform has ideal properties. For example, for CDM, we can assume<br />
the spreading sequence has an idealized autocorrelation function, in that the correlation<br />
of the sequence with a shift of itself is zero. As a result, the autocorrelation<br />
function for the symbol waveform is simply the chip pulse shape autocorrelation<br />
function. This provides a looser bound on the average SINR or error rate.<br />
This looser bound is not a bound on the individual symbol MFBs. The idealized<br />
autocorrelation function is only ideal when one must consider performance over a<br />
variety of medium responses. For a given medium response, performance is best<br />
for the symbol waveform that is most closely matched to the medium response.