Cryptography Reference
In-Depth Information
11.1.6 MMSE turbo equalization
The increase in data rates, in response to current multimedia service require-
ments, combined with the infatuation with mobility and wireless infrastructures,
present receivers with severe propagation conditions. Thus, if we take the ex-
ample of the radio interface of the Wireless MAN (
Metropolitan Area Network
)
802.16a standard normalized by IEEE during 2003 and operating in the 2-11
GHz band, the ISI encountered is likely to recover up to 50 symbol durations,
or even more. Underwater acoustic communications is another example. The
application of turbo equalization to such scenarios involves using low complex-
ity SISO equalizers. MMSE turbo equalization is an attractive solution in this
context.
In contrast with the approaches described in the previous section, MMSE
turbo equalization mainly involves substituting for the MAP equalizer an equal-
izer structure based on digital filters, optimized according to the minimum mean
square error criterion
4
. This solution presents a certain number of advantages.
First of all, simulations show that the MMSE turbo equalizer gives very good
performance on average, sometimes very close to the performance offered by
MAP turbo equalization. On the other hand, the complexity of the MMSE
equalizer increases linearly (and not exponentially) with the length of the chan-
nel impulse response, independently of the order of the modulation. Finally,
as we shall see in what follows, this approach naturally lends itself well to an
implementation in adaptive form, appropriate for tracking the time variations
of the channel.
Historically, the first MMSE turbo equalization scheme was proposed by
Glavieux
et al.
in 1997 [11.20, 11.32, 11.34]. This original contribution laid
down the bases of MMSE turbo equalization, particularly for the design of a
filter-based soft-input soft-output equalizer. Indeed, classical equalizers based
on digital filters do not naturally lend themselves to handling probabilistic infor-
mation. This diculty was overcome by inserting a binary to
M
-ary conversion
operation at the input of the equalizer, in charge of rebuilding a soft estimation
of the symbols transmitted using the
a priori
information sent by the decoder.
In addition, a SISO demapping module placed at the output of the equalizer
converts the equalized data (complex symbols) into extrinsic LLR on the coded
bits, which are then sent to the decoder. This initial scheme relied on the imple-
mentation of an equalization structure of the interference canceller type, whose
coecients were updated adaptively thanks to the
Least Mean Square
(LMS)
algorithm.
Least Mean Square
Remarkable progress was then achieved with the
work of Wang and Poor [11.56], taken up by Reynolds and Wang [11.47] then
by Tüchler
et al.
[11.51, 11.50]. These contributions have made it possible to
4
Equalizers optimized according to the Zero Forcing criterion could also be envisaged. How-
ever these equalizers usually introduce significant noise enhancement on channels with deep
nulls in their frequency response, and thus generally turn out to be less ecient than MMSE
equalizers.
