Digital Signal Processing Reference
In-Depth Information
the possibilities to control the spectrum of the single-carrier qpsk modulation
used by the phy layer of 802
.
11b do not even come close to the fine-grained
spectral control offered by multicarrier modulation. However, it is important to
recognize that in the case of a single-carrier system, the
energy spectral density
(esd) of one single qpsk symbol out of the received symbol stream is spread
across the entire frequency band of the signal. Therefore, the exact location of
the spectral energy of a single sample cannot be determined and is dependent
of the surrounding symbol stream. It should be clear that the disposal of only
a limited portion of the spectral information does not necessarily result in the
loss of all energy or information related to a particular qpsk symbol. There-
fore, it must be theoretically possible to recover at least part of the original
data from an isi- or interferer-distorted symbol stream. For this purpose, the
following information is at the disposal of the issr algorithm in the receiver:
The received signal, distorted by interference or isi due to fading
The location of the affected frequency bands
The modulation type (i.e. qpsk in this particular case)
The statement that it is possible to reconstruct the original signal only using
the aforementioned intelligence is intuitively confirmed by the following rea-
soning. Suppose that the back-end of the receiver is processing the received
symbol stream using blocks of
n
qpsk samples. The receiver converts the in-
coming qpsk-modulated data entities to the frequency domain, in order to in-
spect the spectral characteristics of the signal. Most of the time, subbands that
are affected by narrowband interference are easily identified thanks to the con-
siderably higher spectral density in comparison with unaffected bands in the
spectrum. The same strategy can also be used to identify frequency-selective
fading: averaged over a certain frequency span, subbands that are affected by
destructive fading are very likely to display a reduced energy spectral density.
After removing those parts that are affected by fading or interference from the
baseband spectrum, the signal is again converted to the time domain repre-
sentation. The resulting symbol stream still has sufficient snr, but is heavily
affected by isi due to the loss of some of the non-crucial information in the
frequency domain.
If enough processing power is available, it would be possible to regenerate the
spectral footprint of all of the 4
n
symbol combinations (Figure 3.2). Subse-
quently, the unaffected parts of the spectrum from the received symbol stream
are compared to the spectral footprint of each of the locally generated streams.
The local symbol stream which produces the best cross-correlation result
with the received signal has the best chance to be the originally transmitted
signal. Obviously, the enormous amount of possible combinations makes this
