Optimal superimposed training design for

3206 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 8, AUGUST 2008

Optimal Superimposed Training Design for

Spatially Correlated Fading MIMO Channels

Vu Nguyen, Hoang D. Tuan, Member, IEEE, Ha H. Nguyen, Senior Member, IEEE

and Nguyen N. Tran, Student Member, IEEE

Abstract—The problem of channel estimation for spatially cor￾related fading multiple-input multiple-output (MIMO) systems

is considered. Based on the channel’s second order statistic, the

minimum mean-square error (MMSE) channel estimator that

works with the superimposed training signal is first developed.

The problem of designing the optimal superimposed signal

is then addressed and solved with an iterative optimization

algorithm. Results show that under the constraint of equal

training power and bandwidth efficiency, our optimal design of

the superimposed training signal leads to a significant reduction

in channel estimation error when compared to the conventional

design of time-multiplexing training, especially for slowly time￾varying channels with a large coherence time. The issue of power

allocation between the information-bearing and training signals

for detection enhancement is also investigated. Simulation results

demonstrate excellent bit-error-rate performance of orthogonal

space-time block codes with our proposed channel estimation.

Index Terms—MIMO channel, spatial correlation, channel

estimation, MMSE estimation, training signal, training design,

time-multiplexing training, superimposed training.

I. INTRODUCTION

T

HE use of multiple antennas at both the transmitter

and the receiver to create the so-called multiple-input

multiple-output (MIMO) communication systems has been

shown to greatly increase the data rate of the wireless trans￾mission medium [21], [30]. This is especially true when the

channel fades among the transmitter-receiver pairs are inde￾pendently Rayleigh distributed [5], [30], [38]. In particular, it

is shown in [30] that the capacity of a MIMO wireless channel

increases linearly with the number of antennas.

The assumption of independent fades requires that the

antennas be placed sufficiently far apart, both at the transmitter

and the receiver. In many practical applications, meeting such

requirements might be very expensive and impractical (such

as for the antennas in hand-held mobile units). It is therefore

more practical and useful to consider spatial correlations

Manuscript received March 2, 2007; revised August 1, 2007; accepted

October 1, 2007. The associate editor coordinating the review of this paper

and approving it for publication is D. Dardari. This work is supported by the

Australian Research Council under grant ARC Discovery Project 0556174. A

part of this work was presented at the IEEE Second International Workshop on

Computational Advances in Multi-Sensor Adaptive Processing, St. Thomas,

U.S. Virgin Islands, USA, 12-14 December 2007.

Vu Nguyen, Hoang D. Tuan, and Nguyen N. Tran are with the

School of Electrical Engineering and Telecommunications, the University

of New South Wales, Sydney, NSW 2052, Australia (e-mail: {q.nguyen,

nam.nguyen}@student.unsw.edu.au, [email protected]).

Ha H. Nguyen is with the Department of Electrical and Computer Engi￾neering, University of Saskatchewan, 57 Campus Dr., Saskatoon, SK, Canada

S7N 5A9 (e-mail: [email protected]).

Digital Object Identifier 10.1109/TWC.2008.070250.

among different sub-channels of the MIMO channel matrix

[5], [13], [28]. Compared to an independent fading MIMO

channel, the results in [3], [10]–[12], [28] show that the

capacity of a spatially-correlated fading MIMO channel is

substantially reduced.

Capacity reduction due to spatially-correlated fading can be

partially alleviated by precoding the transmitted signal [20].

This technique however requires the knowledge of the channel

state information at the transmitter, which is not always

available. Furthermore, the MIMO channel capacity can be

further reduced if inaccurate channel state information is

obtained at the receiver [30]. In other words, accurate channel

estimation is very important to fully exploit the advantages

of MIMO wireless communications. The correlated fading

channel is often estimated by a training sequence, which

can be either time-multiplexing (TM) training (see e.g., [26],

[32] for single-input multiple-output (MISO) channels and

[7], [19] for MIMO channels), frequency-multiplexing [14],

[18] or superimposed (SP) training (see e.g., [17], [36] for

single-input single-output (SISO) channels and [33] for MISO

channels). In superimposed traning, the training symbols are

superimposed on the precoded data for transmission. In fact,

superimposed traning includes both time-multiplexing and

frequency-multiplexing as special cases, which correspond

to sending the non-zero training symbols when the data

symbols are zero or sending the non-zero training symbols

over subcarriers that are not occupied by the data symbols

(i.e., pilot subcarriers). Because superimposed training is a

general and powerful framework, it has recently received a

growing interest in the research community [14], [15], [18],

[33].

In SP training, since the received signal is a superposition

of the data-bearing signal, training signal and noise, a popular

design approach is to decouple channel and symbol estimation

[14], [18], [22], [37]. This can be done by designing the

precoding and training matrices so that the data-bearing and

training signals belong to complementary signal subspaces.

Then, the data-bearing signal, which is considered as the

unwanted noise in channel estimation, can be completely

removed and channel estimation is carried out based on

the training symbols. An alternative approach is to perform

joint channel/symbol estimation at the receiver and design

the training signal accordingly. Due to its more complicated

processing and marginal advantage [37], joint channel/symbol

estimation is less preferred than decoupled channel and sym￾bol estimation. This paper, therefore, is only concerned with

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