29-10-2012, 02:27 PM
Blind Recognition of Linear Space–Time Block Codes: A Likelihood-Based Approach
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Abstract
Blind recognition of communication parameters
is a research topic of high importance for both military and
civilian communication systems. Numerous studies about carrier
frequency estimation, modulation recognition as well as channel
identification are available in literature. This paper deals with the
blind recognition of the space–time block coding (STBC) scheme
used in multiple-input–multiple-output (MIMO) communication
systems. Assuming there is perfect synchronization at the receiver
side, this paper proposes three maximum-likelihood (ML)-based
approaches for STBC classification: the optimal classifier, the
second-order statistic (SOS) classifier, and the code parameter
(CP) classifier. While the optimal and the SOS approaches require
ideal conditions, the CP classifier is well suited for the blind
context where the communication parameters are unknown at
the receiver side. Our simulations show that this blind classifier
is more easily implemented and yields better performance than
those available in literature.
INTRODUCTION
BLIND recognition of communication parameters is an
intermediate step between signal detection and signal decoding/
demodulation. In civilian applications, blind recognition
algorithms are used in software-defined radio (SDR) to cope
with a large panel of communication systems. In electronic
warfare, these algorithms are required for signal interception
and processing, two tasks of key importance in tactical operations.
Usually, the largest part of the algorithms is devoted
to the blind recognition of single-input–single-output (SISO)
communication parameters. Other investigations have dealt
with the development of new technologies aimed at enhancing
the reliability of data transmission in wireless communication
systems.
Discussion
One should note that, though this classifier maximizes the average
probability of correct classification, it has several drawbacks.
First, the log-likelihood function is computation time
consuming. Let us denote by the complexity of the elementary
operations. It can be shown that the computation of
the likelihood function has complexity .
Therefore, the optimal classifier is computationally too complex
in the case of high-order modulation and/or a large number
of symbols per block [21]. Furthermore, the computation of
requires the knowledge of several parameters,
which are usually unknown in a noncooperative environment.
When these parameters are unknown, this classifier
is impractical since the maximization of the likelihood function
with respect to , , , and is computationally cost prohibitive.
THE SOS-STBC CLASSIFIER
The i.i.d. assumption AS3) and the signal model in (12) both
show that the received vector is the sum of i.i.d. random
variables plus the additive noise. According to the central
limit theorem, the distribution of can be approximated by
a Gaussian distribution for whatever the modulation
[13]. Although this approximation is only strictly correct in the
asymptotic case, a recent study [29] showed that the Gaussian
approximation provides the optimum second-order solution
when: 1) the SNR is very low or 2) the symbols belong to a
multilevel constellation. These considerations lead us to relax
the finite alphabet constraint of the sources, which are modeled
as i.i.d. Gaussian variables. One should note that this relaxation
has been previously used with success in SOS-based channel
estimation problems [11], [13]. In this study, this relaxation is
employed to propose an SOS-STBC classifier.
THE CP CLASSIFIER
In many STBC classification problems, the blind identification
of the three code parameters , , and is sufficient to
distinguish between several STBCs. For example, the Alamouti
code and an OSTBC3 can be distinguished through detection
of the number of transmitter antennas . Furthermore, the spatial
multiplexing and the Alamouti code can be differentiated by
their code length . Finally, two codes with the same code length
and using the same number of antennas at the transmitter side
can be identified through detection of the number of symbols
per space–time block. The blind detection of the number of
transmitter antennas is a well-known problem, which has been
investigated in numerous papers and reviewed in [6]. This section
focuses on the blind recognition of both code length and
on the number of encoded symbols per block . This CP classifier
only exploits a small portion of the redundancy introduced
by the STBC, but it is well suited for the blind scenario.
CONCLUSION
The investigations reported in this paper concerned the recognition
of STBCs by likelihood-based classifiers. Three newly
developed classifiers referred to as optimal, SOS-STBC, and CP
classifiers were presented. Though the first classifier is optimal
in an ideal context, it is impractical when the communication
parameters are unknown at the receiver side. In the blind scenario,
the SOS-STBC proved to outperform the CP classifier in
low SNR regions, but its application requires the channel to be
estimated. On the other hand, the knowledge of this parameter is
not a prerequisite for the CP classifier, which can be employed
to distinguish between several STBCs with different CPs. The
simulations carried out in this study showed that the SOS-STBC
and CP classifiers lead to a better average probability of correct
recognition than the classifiers described in literature. Future investigations
will focus on the theoretical analysis of the classifier
performances