STC-MIMO Block Spread OFDM in Frequency
Selective Rayleigh Fading Channels
Le Chung Tran, Xiaojing Huang, Eryk Dutkiewicz and Joe Chicharo
Wireless Technologies Laboratory (WTL)
Telecommunications & Information Technology Research Institute
Faculty of Informatics, University of Wollongong
Wollongong, NSW 2522, Australia
Email: {lct71,huang,eryk,chicharo}@uow.edu.au
Abstract— In this paper, we expand the idea of spreading the
transmitted symbols in OFDM systems by unitary spreading ma-
trices based on the rotated Hadamard or rotated Discrete Fourier
Transform (DFT) matrices proposed in the literature to apply
to Space-Time Coded Multiple-Input Multiple-Output OFDM
(STC-MIMO-OFDM) systems. We refer the resulting systems
to as STC-MIMO Block Spread OFDM (STC-MIMO-BOFDM)
systems. In the proposed systems, a multi-dimensional diversity,
including time, frequency, space and modulation diversities, can
be used, resulting in better bit error performance in frequency
selective Rayleigh fading channels compared to the conventional
OFDM systems with or without STCs. Simulations carried out
with the Alamouti code confirm the advantage of the proposed
STC-MIMO-BOFDM systems.
I. INTRODUCTION
Orthogonal Frequency Division Multiplexing (OFDM) has
been intensively considered in the literature for transmitting
signals over frequency selective fading channels. The main
advantage of the OFDM technique compared to a single
carrier modulation is that it facilitates the use of high data
rates with a relatively low complexity receiver, which requires
only a Fast Fourier Transform (FFT) processor followed by
single tap equalizers across all subcarriers. OFDM systems
possess a diversity gain over single carrier systems since
the orthogonality of the subcarriers prohibits multipaths from
being combined across the channel at the symbol level.
The use of spreading matrices to mix the transmitted
symbols linearly across the subchannels has been considered
for single antenna wireless communications systems in the
literature, such as in [1], [2]. The main advantage of using
spreading matrices is that it allows us to achieve a diversity
over the frequency selective fading channels. The use of
unitary spreading matrices based on the rotated Hadamard or
rotated Discrete Fourier Transform (DFT) matrices to improve
the performance of single antenna OFDM systems was firstly
introduced by Bury et.al. [2] and further studied by McCloud
[3].
It is well known that the use of multiple transmit and/or
receive antennas can significantly improve the capacity of
wireless communications systems. Such systems are called
Multiple Input Multiple Output (MIMO) systems. Space-Time
Codes (STCs) are the codes designed for the use in MIMO
systems. Space-Time Block Codes (STBCs) [4], [5], [6],
Space-Time Trellis Codes (STTCs) [7], Bell Lab Layered
Space-Time (BLAST) [8] are among various types of STCs.
The combination of MIMO systems using STCs with the
OFDM technique has received a fair amount of attention in
the literature, such as in [9], [10], [11], [12], [13]. However,
the combination of MIMO systems using STCs with the block
spread OFDM technique has not been considered yet. This
combination is expected to improve further the performance
of the whole system at the cost of slightly more complicated
transmitter and receiver structures.
In this paper, we expand the idea of Block Spread OFDM
(BOFDM) mentioned in [2], [3] to apply to the MIMO-OFDM
systems using STCs. We call the resultant technique STC-
MIMO-BOFDM to distinguish it from the normal MIMO-
OFDM without block spreading. It is noted that the term
“spreading” is inherited from [2] to express the modulation
alphabet expansion, rather than the bandwidth expansion as
the normal meaning of this term.
The novel contributions of this paper include 1) the ap-
plication of the block spreading technique to the conven-
tional STC-MIMO-OFDM systems to improve further the
error performance of the STC-MIMO-OFDM systems; 2) the
derivation of the more detailed Simple Maximum Likelihood
(SML) decoding method [14] for the proposed STC-MIMO-
BOFDM systems using the Alamouti code [4]; and 3) the
error performance comparison between the proposed STC-
MIMO-BOFDM systems and the conventional OFDM systems
(without STCs or block spreading), BOFDM systems (without
STCs) [3] and STC-MIMO-OFDM systems (without block
spreading) [14], [15].
The paper is organized as follows. In Section II, we derive
the baseband model of an STC-MIMO-BOFDM system. Sec-
tion III derives a detailed decoding algorithm, namely Simple
Maximum Likelihood (SML), which was originally derived in
[14], for a particular example of the Alamouti code. Simulation
results are given in Section IV, and the paper is concluded by
Section V.