11-02-2013, 03:31 PM
Block FIR Decision-Feedback Equalizers for Filterbank Precoded Transmissions with Blind Channel Estimation Capabilities
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Abstract
—In block transmission systems, transmitter-induced
redundancy using finite-impulse response (FIR) filterbanks can
be used to suppress intersymbol interference and equalize FIR
channels irrespective of channel zeros. At the receiver end, linear
or decision-feedback (DF) FIR filterbanks can be applied to
recover the transmitted data. Closed-form expressions are derived
for the FIR linear or DF filterbank receivers corresponding to
varying amounts of transmission redundancy. Our framework
encompasses existing block transmission schemes and offers
low implementation-cost equalization techniques both when
interblock interference is eliminated, and when IBI is present as,
e.g., in orthogonal frequency-division multiplexing with insufficient
cyclic prefix. By applying blind channel estimation methods,
our filterbank transmitters–receivers (transceivers) dispense with
bandwidth consuming training sequences. Extensive simulations
illustrate the merits of our designs.
Index Terms—Estimation, decision-feedback equalizer, FIR digital
filters.
INTRODUCTION
RANSMISSION precoding is proposed in this paper along
with decision-feedback equalization (DFE) in order to suppress
intersymbol interference (ISI) in block transmission systems.
Equalization targets such “structured” ISI-induced errors that
are caused by multipath-induced frequency-selective channels.
If the (presumed linear and time-invariant) channel is known,
then its structured, deterministic effect on the transmitted signal
can be removed (or significantly reduced) by properly designed
equalizers at the receiver end. On the other hand, channel
coding techniques (e.g., convolutional codes) are effective for
“unstructured” (noise-like) symbol errors. As a result, even
when the channel cannot be completely equalized, or when the
noise cannot be suppressed (as with zero-forcing equalization
of a channel with nulls close to the unit circle), channel coding
lowers (but does not remove) the error floor in the bit-error rate
(BER) performance at the expense of introducing redundancy.
To combat fading effects in frequency-selective channels, the
transmitter does not have only channel coding at its disposal.
Redundant block transmission systems such as orthogonal
Paper approved by R. A. Kennedy, the Editor for Data Communications,
Modulation and Signal Design of the IEEE Communications Society. Manuscript
This paper was presented in part at the Workshop on Signal Processing Advances
in Wireless Communications, Annapolis, MD, May 1999.
The authors are with Department of Electrical and Computer Engineering,
University of Minnesota, Minneapolis, MN 55455 USA (e-mail:
frequency-division multiplexing (OFDM) rely on inverse fast
Fourier transform precoding to cope with ISI. Among the
ways to model block transmission of data is the unifying
framework of [10] that enables most of the currently used block
transmission systems to be realized using pairs of filterbank
transmitters and receivers (transceivers). By introducing very
modest redundancy relative to channel coding, transmitter
precoding also enables blind channel estimation and block
synchronization [11]. The redundancy is in the form of cyclic
prefix or zero padding (which acts as “guard interval”) and
offers degrees of freedom that can be exploited when designing
transceivers under BER and information rate (throughput)
constraints.
However, BER performance of the equalization process
depends critically upon the receiver structure. Serial decision-
feedback (DF) receivers have been shown to exhibit
superior BER performance (when compared to linear receivers)
and have the potential to achieve (under certain conditions)
the performance of the maximum-likelihood receiver (see,
e.g., [1] and [18] for details). Moreover, with adaptive DFE
techniques, the DFE receiver structure lends itself naturally
to decision-directed channel estimation [8, pp. 649–650],
[9]. Blind DFE channel estimation methods have been also
proposed (see [16] and references therein).
As their name suggests, serial DF receivers apply the same
filters to every received symbol. Though serial DF receivers can
be used in block transmission systems, they do not fully exploit
the structure of the received blocks. On the other hand,
block DF receivers apply different filters to symbols of the received
block and can result in improved BER performance. Unlike
serial zero-forcing (ZF) DF receivers, which entail infinite-
impulse response (IIR) feedforward and feedback structures,
we showin this work that block ZF-DF receivers are given
by closed-form expressions, which can be implemented exactly
using finite-impulse response (FIR) filterbanks. Consequently,
block DF receivers outperform serial DF receivers as we illustrate
in the simulations section.
FIR EQUALIZING WHEN IBI IS PRESENT
In Section III it was shown that to eliminate IBI, has to be
chosen so that . Given the fact there are channels
where can be quite high (for example, in ADSL the channel
may have 100 taps), having redundant symbols may lead to a
substantial decrease in information rate, unless high values for
are assumed (which will lead however to longer decoding delays).
This imposes an inherent tradeoff between longer blocks
(i.e., decoding delays) and information rate. One can dispense
with this tradeoff by using less than redundant symbols either
through padding less than trailing zeros, or, by using a
cyclic prefix of length smaller than . Both cases however, will
lead to IBI which can be removed using a more complex receiver
structure than that described in Section III. Hence, the
tradeoff “longer blocks versus information rate” can be replaced
by the tradeoff “small transmit-redundancy versus receiver complexity;”
the latter does not possess only theoretical interest but
holds practical importance as well. For example, allowing for
IBI in OFDM systems reduces the required redundancy (that
is the length of cyclic prefix) in long channels. In Section IV,
we compare our block DF approach with recent approaches to
handling long channels in OFDM [15]. But first, let us describe
how IBI is removed using either a linear or a DFE receiver. As
in Section III, we assume here that CIR is available only at the
receiver. Section V with the blind channel estimation algorithms
dispenses with this assumption.