mohatta2015.pdf

110 MMSE AND ML DECISION FEEDBACK EQUALIZATION
5.4.5 Group decision feedback equalization
As with linear equalization, group DFE is possible. The approach is similar, except
that the ISI from groups already detected is subtracted rather than suppressed
linearly.
5.5 AN EXAMPLE
US TDMA is sometimes used to refer to the second generation (2G) cellular system
also known as IS-54, IS-136, American Digital Cellular (ADC), or digital AMPS
(D-AMPS) [Rai91, Goo91]. The modulation is π/4-shift Differential Quadrature
Phase Shift Keying (DQPSK)(2 bits per symbol), and root-Nyquist pulse shaping
is employed. The symbol rate is 24.3 kbaud, giving a large symbol period (41.2 μβ)
relative to typical delay spreads. In [Pro91] a variety of equalization approaches
are reviewed, and a DFE design is developed. DFE with multiple receive antennas
is considered in [Li99].
Because of the long symbol period, path delays are on the order of a fraction of
a symbol period. Because of the ringing of the pulse shape, this causes ISI between
both future and past symbols. Fortunately the pulse shape ringing dies out quickly,
so that a DFE with a small number of forward filter and feedback filter taps makes
sense.
If the receiver is not in motion, the decision error rate at typical SNR operating
levels is low enough that error propagation is not severe. However, if the receiver
is moving quickly (in a vehicle), the fading can change rapidly within a burst of
data. Such fading can cause decision errors which then propagate. Bidirectional
equalization techniques have been developed to address this issue [Ari92, Nag95,
Hig89]. Another option, maximum likelihood sequence detection, is discussed in
the next chapter.
5.6 THE LITERATURE
Early work on DFE can be found in [Aus67]. An early survey of the DFE literature
is given in [Bel79]. In [Sme97] it is shown that with the perfect decision
feedback assumption, the FFF and FBF filters can be optimized separately. While
we have focused on ZF and MMSE designs for the FF, a WMF design can also be
used [Cio95]. DFE with multiple receive antennas is explored in [Mon71, Mon84],
considering self-interference as well as cochannel interference.
DFE works well when the channel is minimum phase. Roughly speaking, this
means that the energy is concentrated in the earlier arriving path delays. Thus,
for a two-path channel, the channel is minimum phase when the first tap is larger.
When the channel is minimum phase, the FF collects more of the signal energy.
If the channel is or might be nonminimum phase, there are several solutions.
One solution is bidirectional equalization, in which the received signal samples are
equalized forward in time, backward in time, or both. Equalization is performed
either forward or backward, depending on an MSE measure after training [Ari92]
or after equalizing a little bit of the data [Nag95]. According to [Nag95], equalizing