30-06-2012, 01:29 PM
Designing Low-Complexity Equalizers for Wireless Systems
[attachment=26280]
ABSTRACT
The demand on wireless communications to provide
high data rates, high mobility, and high quality
of service poses more challenges for designers.
To contend with deleterious channel fading
effects, both the transmitter and the receiver
must be designed appropriately to exploit the
diversity embedded in the channels. From the
perspective of receiver design, the ultimate goal
is to achieve both low complexity and high performance.
In this article, we first summarize the
complexity and performance of low-complexity
receivers, including linear equalizers and decision
feedback equalizers, and then we reveal the fundamental
condition when LEs and DFEs collect
the same diversity as the maximum-likelihood
equalizer.
INTRODUCTION
Wireless communications have become the fastest
growing industry and are ubiquitous in almost all
areas of our daily life, encompassing radio and
television broadcasting, mobile phones, and satellite
communications. The increasing demand for
wireless services for voice, multimedia, and data
transmissions results in a continually expanding
market. Clearly, the development of solid-state
technology and digital-signal-processing (DSP)
devices contributes significantly to this growth
because such technology makes low-cost and feature-
rich communication devices feasible. More
importantly, however, the globalization of wireless
transmission standards accelerates the spread of
wireless services.
LOW-COMPLEXITY EQUALIZERS
In addition to near-MLEs, there are other equalizers
that usually are characterized and referred to
as low-complexity equalizers: the previously mentioned
LEs and DFEs. LEs, as depicted in Fig. 1b,
are in the form sˆ = Q(Gy), where Q(×) corresponds
to the Decision block and denotes quantization to
the nearest constellation point for a given modulation
scheme. Two LEs that often are adopted are
the zero-forcing (ZF) equalizer, where G is the
Moore-Penrose pseudo-inverse of the channel
matrix, and the linear minimum mean-square
error (MMSE) equalizer, where G is constructed
to minimize the noise effect [3, Eq. (6)]. The ZF
equalizer aims to cancel the channel effect by
assuming a noiseless environment, whereas the
MMSE equalizer further takes into account the
noise effect.
LATTICE REDUCTION ALGORITHMS
LR techniques have been studied by mathematicians
for decades, and many LR algorithms have
been proposed. Gaussian reduction, Minkowski
reduction, and Korkine-Zolotareff (KZ) reduction
algorithms find the optimal basis for a lattice
based on the successive minimal criteria, but
these algorithms are highly complex and therefore
infeasible for communications systems (see
[6] and references therein). The well-known
Lenstra-Lenstra-Lovász (LLL) algorithm does
not guarantee finding the optimal basis with
minimal od, but it guarantees in polynomial time
to find a basis within a factor to the optimal one
[6]. Seysen’s algorithm reduces Seysen’s metric
to perform LR [4].
CONCLUSIONS
Among different detectors for linear block transmissions,
traditional low-complexity equalizers
are favored for their cubic order polynomial
complexity, but they often suffer from diversity
loss. When the channel is constrained within a
certain distance from orthogonality, low-complexity
equalizers achieve the same diversity as
MLE. LR techniques are one approach to
impose a constraint on the orthogonality of the
channel matrix while maintaining the low-complexity
property. After a thorough investigation
of LR algorithms, the CLLL algorithm with
SQRD is selected to be implemented in VLSI.
[attachment=26280]
ABSTRACT
The demand on wireless communications to provide
high data rates, high mobility, and high quality
of service poses more challenges for designers.
To contend with deleterious channel fading
effects, both the transmitter and the receiver
must be designed appropriately to exploit the
diversity embedded in the channels. From the
perspective of receiver design, the ultimate goal
is to achieve both low complexity and high performance.
In this article, we first summarize the
complexity and performance of low-complexity
receivers, including linear equalizers and decision
feedback equalizers, and then we reveal the fundamental
condition when LEs and DFEs collect
the same diversity as the maximum-likelihood
equalizer.
INTRODUCTION
Wireless communications have become the fastest
growing industry and are ubiquitous in almost all
areas of our daily life, encompassing radio and
television broadcasting, mobile phones, and satellite
communications. The increasing demand for
wireless services for voice, multimedia, and data
transmissions results in a continually expanding
market. Clearly, the development of solid-state
technology and digital-signal-processing (DSP)
devices contributes significantly to this growth
because such technology makes low-cost and feature-
rich communication devices feasible. More
importantly, however, the globalization of wireless
transmission standards accelerates the spread of
wireless services.
LOW-COMPLEXITY EQUALIZERS
In addition to near-MLEs, there are other equalizers
that usually are characterized and referred to
as low-complexity equalizers: the previously mentioned
LEs and DFEs. LEs, as depicted in Fig. 1b,
are in the form sˆ = Q(Gy), where Q(×) corresponds
to the Decision block and denotes quantization to
the nearest constellation point for a given modulation
scheme. Two LEs that often are adopted are
the zero-forcing (ZF) equalizer, where G is the
Moore-Penrose pseudo-inverse of the channel
matrix, and the linear minimum mean-square
error (MMSE) equalizer, where G is constructed
to minimize the noise effect [3, Eq. (6)]. The ZF
equalizer aims to cancel the channel effect by
assuming a noiseless environment, whereas the
MMSE equalizer further takes into account the
noise effect.
LATTICE REDUCTION ALGORITHMS
LR techniques have been studied by mathematicians
for decades, and many LR algorithms have
been proposed. Gaussian reduction, Minkowski
reduction, and Korkine-Zolotareff (KZ) reduction
algorithms find the optimal basis for a lattice
based on the successive minimal criteria, but
these algorithms are highly complex and therefore
infeasible for communications systems (see
[6] and references therein). The well-known
Lenstra-Lenstra-Lovász (LLL) algorithm does
not guarantee finding the optimal basis with
minimal od, but it guarantees in polynomial time
to find a basis within a factor to the optimal one
[6]. Seysen’s algorithm reduces Seysen’s metric
to perform LR [4].
CONCLUSIONS
Among different detectors for linear block transmissions,
traditional low-complexity equalizers
are favored for their cubic order polynomial
complexity, but they often suffer from diversity
loss. When the channel is constrained within a
certain distance from orthogonality, low-complexity
equalizers achieve the same diversity as
MLE. LR techniques are one approach to
impose a constraint on the orthogonality of the
channel matrix while maintaining the low-complexity
property. After a thorough investigation
of LR algorithms, the CLLL algorithm with
SQRD is selected to be implemented in VLSI.