mohatta2015.pdf

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