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Abstract—This paper presents an in-depth analysis of the zero
forcing (ZF) and minimum mean squared error (MMSE) equal
izers applied to wireless multiinput multioutput (MIMO) systems
with no fewer receive than transmit antennas. In spite of much
prior work on this subject, we reveal several new and surprising
analytical results in terms of output signal-to-noise ratio (SNR),
uncoded error and outage probabilities, diversity-multiplexing
(D-M) gain tradeoff and coding gain. Contrary to the common
perception that ZF and MMSE are asymptotically equivalent at
high SNR, we show that the output SNR of the MMSE equalizer
(conditioned on the channel realization) is ,
where is the output SNR of the ZF equalizer and that the gap
is statistically independent of and is a nondecreasing func
tion of input SNR. Furthermore, as , converges with
probability one to a scaled random variable. It is also shown
that at the output of the MMSE equalizer, the interference-to-noise
ratio (INR) is tightly upper bounded by
. Using the decomposi
tion of the output SNR of MMSE, we can approximate its uncoded
error, as well as outage probabilities through a numerical integral
which accurately reflects the respective SNR gains of the MMSE
equalizer relative to its ZF counterpart. The -outage capacities of
the two equalizers, however, coincide in the asymptotically high
SNR regime. We also provide the solution to a long-standing open
problem: applying optimal detection ordering does not improve
the D-M tradeoff of the vertical Bell Labs layered Space-Time
(V-BLAST) architecture. It is shown that optimal ordering yields
a SNR gain of dB in the ZF-V-BLAST architecture
(where is the number of transmit antennas) whereas for the
MMSE-V-BLAST architecture, the SNR gain due to ordered
detection is even better and significantly so.
Index Terms—Diversity gain, error probability, MIMO, min
imum mean squared error, outage capacity, outage probability,
spatial multiplexing gain, tradeoff, V-BLAST, zero forcing.
Manuscript received March 01, 2007; revised August 24, 2010; accepted
September 14, 2010. Date of current phiên bản March 16, 2011. Y. Jiang and
M. K. Varanasi were supported in part by the National Science Foundation
Grants CCF-0423842 and CCF-0434410. Y. Jiang was also supported in
part by the National Natural Science Foundation of China NSFC-61071094
during his scholarly visit to the University of Science and Technology of
China in Spring 2010. This work was presented in part at Globecom 2005,
St. Louis, MO.
Y. Jiang is with Qualcomm Corporate Research and Development, San
Diego, CA 92121 USA (e-mail: [email protected]).
M. K. Varanasi is with the Department of Electrical and Computer
Engineering, University of Colorado, Boulder CO 80309 USA (e-mail:
J. Li is with the Department of Electrical and Computer Engineering, Univer
sity of Florida, Gainesville, FL 32611 USA (e-mail: [email protected]).
Communicated by G. Taricco, Associate Editor for Communications.
Color versions of one or more of the figures in this paper are available online
at Bấm vào đây để đăng nhập và xem link!.
Digital Object Identifier 10.1109/TIT.2011.2112070
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