MMSE Extension of V-BLAST based on
Sorted QR Decomposition
Dirk W
¨
ubben, Ronald B
¨
ohnke, Volker K
¨
uhn, and Karl-Dirk Kammeyer
Department of Communications Engineering
University of Bremen
Otto-Hahn-Allee, D-28359 Bremen, Germany
Email: {wuebben, boehnke, kuehn, kammeyer}@ant.uni-bremen.de
Abstract— In rich-scattering environments layered space-time
architectures like the BLAST system may exploit the capacity ad-
vantage of multiple antenna systems. In this paper, we present a
novel, computationally efficient algorithm for detecting V-BLAST
architectures with respect to the MMSE criterion. It utilizes a
sorted QR decomposition of the channel matrix and leads to a
simple successive detection structure. The new algorithm needs
only a fraction of computational effort compared to the standard
V-BLAST algorithm and achieves the same error performance.
Index Terms— BLAST, MIMO systems, Zero-Forcing and
MMSE detection, wireless communication.
I. INTRODUCTION
In rich-scattering environments the V-BLAST (Vertical Bell
Labs Layered Space-Time) architecture proposed in [1] ex-
ploits the capacity advantage of multiple antenna systems. 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 cancellation technique which
nulls the interferers by linearly weighting the received signal
vector with a zero-forcing nulling vector (ZF-BLAST). This
successive detection requires multiple calculations of pseudo-
inverses, being a computational expensive task. A reduced
complexity detection algorithm utilizing a sorted QR decom-
position of the channel matrix was proposed by the authors
in [2], [3]. It jointly calculates an optimized detection 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
[4] and a version with lower complexity was introduced in [5].
In this paper, we extend the ZF-SQRD algorithm to the
MMSE solution, called MMSE-SQRD. Similar to ZF-SQRD it
does not always find the optimal detection order and from there
a performance degradation may occur. If this drawback is not
acceptable for the specific application, a post-sorting algorithm
(PSA) can be used, leading to the ideal detection sequence
and thus to the performance of MMSE-BLAST. However,
the combination of MMSE-SQRD and PSA requires only
a fraction of computational effort compared to the BLAST
detection algorithm.
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 as follows. In Section II,
the system model and notation is introduced. In order to
simplify later derivation we recall the linear ZF and MMSE
filter and introduce an extended system model in Section III.
The detection of BLAST systems using the QR decomposition
of the channel matrix is investigated in Section IV. The
computational effort and the performance analysis are given
in Section V and VI, respectively. Concluding remarks can be
found in Section VII.
II. S
YSTEM DESCRIPTION
We consider a multiple antenna system with n
T
transmit
and n
R
≥ n
T
receive antennas. The data is demultiplexed
into n
T
data substreams of equal length (called layers). These
substreams are optionally encoded by a convolutional code
(CC), bit-interleaved, mapped onto M -PSK or M-QAM sym-
bols s
i
and transmitted over the n
T
antennas simultaneously.
For simplicity we will assume uncoded substreams for the
derivation of the detection algorithms, but will investigate the
performance of coded and uncoded systems in Section VI.
Data
Transmitter Receiver
1
x
1
n
R
n
x
R
n
n
1
s
1,1
h
,
RT
nn
h
estim.
Data
Detector
&
Decoder
T
n
s
1,
T
n
h
,1
R
n
h
CC
P
P
CC
Fig. 1. Model of a MIMO system with n
T
transmit and n
R
receive antennas.
In order to describe the MIMO system, one time slot of
the time-discrete complex baseband model is investigated.
Let
1
s =[s
1
... s
n
T
]
T
denote the n
T
× 1 transmit signal
vector, then the corresponding n
R
× 1 receive signal vector
x =[x
1
... x
n
R
]
T
is given by
x = Hs + n . (1)
In (1), n =[n
1
... n
n
R
]
T
represents white gaussian noise
of variance σ
2
n
observed at the n
R
receive antennas while
1
Throughout this paper, (·)
T
and (·)
H
denote matrix transpose and
hermitian transpose, respectively. Furthermore, I
α
indicates the α×α identity
matrix and 0
α,β
denotes the α × β all zero matrix.
0-7803-7954-3/03/$17.00 ©2003 IEEE. 508
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