Abstract—Theoretical and experimental studies have shown
that layered space-time architectures like the BLAST system can
exploit the capacity advantage of multiple antenna systems in
rich-scattering environments. In this paper, we present a new
efficient algorithm for detecting such architectures with respect
to the MMSE criterion. This algorithm utilizes a sorted QR
decomposition of the channel matrix and leads to a simple suc-
cessive detection structure. The algorithm needs only a fraction
of computational effort compared to the standard V-BLAST
algorithm and achieves the same bit error performance.
Index Terms—BLAST, MIMO systems, Zero-Forcing and
MMSE detection, wireless communication.
I. INTRODUCTION
In rich-scattering environments the use of multiple antenna
systems provides an enormous increase in spectral efficiency
compared to single antenna systems [1]. A multiple-input
multiple-output (MIMO) system that exploits this potential
is the V-BLAST (Vertical Bell Labs Layered Space-Time)
architecture proposed in [2]. It uses a vertically layered coding
structure, where independent code blocks (called layers) are
associated with a particular transmit antenna. At the receiver,
these layers are detected by a successive interference cancella-
tion technique which nulls the interferers by linearly weighting
the received signal vector with a zero-forcing nulling vector
(ZF-BLAST). A very efficient detection algorithm utilizing the
QR decomposition of the channel matrix was proposed by the
authors in [3], [4]. It jointly calculates an optimized detec-
tion order and the QR decomposition of the channel matrix
and is called ZF-SQRD (ZF Sorted QR Decomposition). An
adaption of the original ZF-BLAST to the MMSE criterion
was presented in [5] and a phiên bản with lower complexity was
introduced in [6].
In this paper, we propose an extension of the ZF-SQRD
algorithm to the MMSE solution called MMSE-SQRD. As
it does not always find the optimal detection order, a per-
formance degradation may occur. If this drawback is not
acceptable for the specific application, MMSE-SQRD can be
used as a pre-ordering for the optimal strategy, leading to the
ideal detection sequence with reduced computational effort.
This work was supported in part by the German ministry of education and
research (BMBF) under grant 01 BU 153.
The remainder of this paper is organized as follows. In
Section II, the system model is introduced. In Section III, sev-
eral ZF detection algorithms are reviewed. MMSE extensions
of these detection algorithms are investigated and the new
MMSE-SQRD is described in Section IV. The performances
of the different methods are compared in Section V and
concluding remarks can be found in Section VI.
II. SYSTEM DESCRIPTION
We consider a multiple antenna system with nT transmit
and nR ≥ nT receive antennas as shown in Fig. 1. The data
is demultiplexed into nT substreams of equal length (called
layers). These substreams are mapped onto M-PSK or M-
QAM symbols s1,...,snT and simultaneously transmitted
over the nT antennas.
Data
Transmitter Receiver
1 x
1 n
R n x
R n n
1 s
T n s
m s
1,m h
, R nm h
estim.
Data
Detector
Fig. 1. Model of a MIMO system with nT transmit and nR receive antennas.
In order to describe the MIMO system, one time slot of
the time-discrete complex baseband model is investigated.
Let
1
=[s1 ... snT ]
T denote the nT ×1 vector of transmit
symbols, then the corresponding nR×1 receive signal vector
=[x1 ... xnR]
T is given by
= + . (1)
In (1), =[n1 ... nnR]
T represents the white gaussian noise
of variance σ2
n observed at the nR receive antennas while the
1Throughout this paper, (·)T and (·)H denote matrix transposition and
hermitian transposition, respectively. Furthermore Iα indicates the α × α
identity matrix and 0α,β denotes the α × β all zero matrix.
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that layered space-time architectures like the BLAST system can
exploit the capacity advantage of multiple antenna systems in
rich-scattering environments. In this paper, we present a new
efficient algorithm for detecting such architectures with respect
to the MMSE criterion. This algorithm utilizes a sorted QR
decomposition of the channel matrix and leads to a simple suc-
cessive detection structure. The algorithm needs only a fraction
of computational effort compared to the standard V-BLAST
algorithm and achieves the same bit error performance.
Index Terms—BLAST, MIMO systems, Zero-Forcing and
MMSE detection, wireless communication.
I. INTRODUCTION
In rich-scattering environments the use of multiple antenna
systems provides an enormous increase in spectral efficiency
compared to single antenna systems [1]. A multiple-input
multiple-output (MIMO) system that exploits this potential
is the V-BLAST (Vertical Bell Labs Layered Space-Time)
architecture proposed in [2]. It uses a vertically layered coding
structure, where independent code blocks (called layers) are
associated with a particular transmit antenna. At the receiver,
these layers are detected by a successive interference cancella-
tion technique which nulls the interferers by linearly weighting
the received signal vector with a zero-forcing nulling vector
(ZF-BLAST). A very efficient detection algorithm utilizing the
QR decomposition of the channel matrix was proposed by the
authors in [3], [4]. It jointly calculates an optimized detec-
tion order and the QR decomposition of the channel matrix
and is called ZF-SQRD (ZF Sorted QR Decomposition). An
adaption of the original ZF-BLAST to the MMSE criterion
was presented in [5] and a phiên bản with lower complexity was
introduced in [6].
In this paper, we propose an extension of the ZF-SQRD
algorithm to the MMSE solution called MMSE-SQRD. As
it does not always find the optimal detection order, a per-
formance degradation may occur. If this drawback is not
acceptable for the specific application, MMSE-SQRD can be
used as a pre-ordering for the optimal strategy, leading to the
ideal detection sequence with reduced computational effort.
This work was supported in part by the German ministry of education and
research (BMBF) under grant 01 BU 153.
The remainder of this paper is organized as follows. In
Section II, the system model is introduced. In Section III, sev-
eral ZF detection algorithms are reviewed. MMSE extensions
of these detection algorithms are investigated and the new
MMSE-SQRD is described in Section IV. The performances
of the different methods are compared in Section V and
concluding remarks can be found in Section VI.
II. SYSTEM DESCRIPTION
We consider a multiple antenna system with nT transmit
and nR ≥ nT receive antennas as shown in Fig. 1. The data
is demultiplexed into nT substreams of equal length (called
layers). These substreams are mapped onto M-PSK or M-
QAM symbols s1,...,snT and simultaneously transmitted
over the nT antennas.
Data
Transmitter Receiver
1 x
1 n
R n x
R n n
1 s
T n s
m s
1,m h
, R nm h
estim.
Data
Detector
Fig. 1. Model of a MIMO system with nT transmit and nR receive antennas.
In order to describe the MIMO system, one time slot of
the time-discrete complex baseband model is investigated.
Let
1
=[s1 ... snT ]
T denote the nT ×1 vector of transmit
symbols, then the corresponding nR×1 receive signal vector
=[x1 ... xnR]
T is given by
= + . (1)
In (1), =[n1 ... nnR]
T represents the white gaussian noise
of variance σ2
n observed at the nR receive antennas while the
1Throughout this paper, (·)T and (·)H denote matrix transposition and
hermitian transposition, respectively. Furthermore Iα indicates the α × α
identity matrix and 0α,β denotes the α × β all zero matrix.
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