Coon, J., Siew, J., Beach, MA., Nix, AR., Armour, SMD., &
McGeehan, JP. (2003). A comparison of MIMO-OFDM and MIMO-
SCFDE in WLAN environments. In
Global Telecommunications
Conference, 2003 (Globecom 2003)
(Vol. 6, pp. 3296 - 3301). Institute
of Electrical and Electronics Engineers (IEEE).
https://doi.org/10.1109/GLOCOM.2003.1258845
Peer reviewed version
Link to published version (if available):
10.1109/GLOCOM.2003.1258845
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A Comparison of MIMO-OFDM and
MIMO-SCFDE in WLAN Environments
J. Coon, J. Siew, M. Beach, A. Nix, S. Armour, and J. McGeehan
Centre for Communications Research, University of Bristol
Merchant Venturers Building, Woodland Road, Bristol BS8 1UB, UK
Email: {Justin.Coon, Jiun.Siew}@bristol.ac.uk
Abstract— Recent developments in orthogonal frequency divi-
sion multiplexing (OFDM) and single-carrier frequency-domain
equalization (SCFDE) have sparked debate about the superiority
of one method over the other. In this paper, we further this
debate by comparing the theoretical performance of OFDM
and SCFDE when each is implemented in one of two different
multiple-input multiple-output (MIMO) architectures: spatial
multiplexing and space-time block codes. This study focuses on
the use of MIMO-OFDM and MIMO-SCFDE in wireless local
area network (WLAN) applications. Performance is given in
terms of the packet error rate (PER) and the throughput of
the systems.
I. INTRODUCTION
Lately, much attention has been focused on physical layer
(PHY) techniques that are suitable for high-data-rate multiple-
input multiple-output (MIMO) wireless communications sys-
tems. Of special interest are techniques that minimize the
complexity of the multi-dimensional equalization process that
is required in a wideband MIMO system. In this paper,
we present arguments both for and against the use of two
techniques, namely orthogonal frequency division multiplex-
ing (OFDM) and single-carrier frequency-domain equalization
(SCFDE). These arguments are presented in the form of a
theoretical performance comparison.
In single-antenna systems, OFDM is well-documented and
is favored among many in academia as well as in indus-
try [1]. SCFDE, a PHY technique of similar complexity, has
received much attention of late and has recently stimulated
much “single-carrier vs multi-carrier” debate [2]. Both of
these techniques utilize signal processing in the frequency
domain to provide relatively low-complexity solutions to the
problem of equalization. In [2], a comparison of these two
technologies was conducted with a focus on single-antenna
systems employed in fixed broadband wireless applications
(IEEE 802.16) where the multipath spread of the channel is
only a few non-zero discrete taps. However, to the best of our
knowledge, an OFDM/SCFDE performance comparison has
not been conducted for MIMO systems employed in wireless
local area network (WLAN) applications where the effects of
multipath propagation in the channel can be much greater.
In this paper, we present an investigation of the perfor-
mance of several different MIMO-OFDM and MIMO-SCFDE
systems in WLAN environments. In section II, an overview
of the chosen MIMO-OFDM and MIMO-SCFDE systems
is presented. In section III, the selected wireless channel
models are discussed. The results that were obtained in this
investigation are illustrated in section IV. Finally, conclusions
are given in section V.
II. S
YSTEM DESCRIPTION
OFDM and SCFDE were applied to two MIMO baseband
architectures: spatial multiplexing (SM) and space-time block
coding (STBC). Two transmit antennas and two receive anten-
nas were used in all systems. A generalized block diagram of
the systems under investigation is shown in Figure 1.
The key architectural difference between a MIMO-OFDM
system and a MIMO-SCFDE system, namely the order in
which the IFFT operation is executed, is depicted in Figure 1.
Other differences between the SCFDE and OFDM architec-
tures include the implementation of the Viterbi decoder, the
designs of the transmit and receive filters, and the structure of
the frequency-domain equalizers. We address these dissimilar-
ities below.
A. Viterbi Decoder Implementation
All MIMO architectures were simulated with and without a
half-rate convolutional code with random bit interleaving fol-
lowing the encoder as depicted in Figure 1. The convolutional
code used in this study is specified in [3], [4]. At the receiver,
½-rate
conv.
enc.
Π
Space-Time
Processing
(SM, STBC)
CP
CP
TX
Filter
TX
Filter
IFFT
IFFT
OFDM
only
½-rate
conv.
enc.
Π
Space-Time
Processing
(SM, STBC)
CP
CP
TX
Filter
TX
Filter
IFFT
IFFT
OFDM
only
Viterbi
decoder
Π
-1
P/S
CP
removal
CP
removal
RX
Filter
RX
Filter
SCFDE
only
FFT
FFT
Space-Time
Processing
(Decouple,
Equalize)
IFFT
IFFT
AWGN
AWGN
Viterbi
decoder
Π
-1
P/S
CP
removal
CP
removal
CP
removal
CP
removal
RX
Filter
RX
Filter
RX
Filter
RX
Filter
SCFDE
only
FFT
FFT
FFT
FFT
Space-Time
Processing
(Decouple,
Equalize)
IFFT
IFFT
IFFT
IFFT
AWGN
AWGN
Fig. 1. Generalized block diagram of MIMO-OFDM and MIMO-SCFDE
systems.
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the equalized symbols were mapped to soft bits that were then
passed through a soft-input hard-output Viterbi decoder as
illustrated in Figure 1. The OFDM systems utilize channel
state information (CSI) to weight the branch metrics, thus
enhancing the performance of the Viterbi decoder. However,
single-carrier systems are generally unable to utilize CSI in
this fashion because the energy in each transmitted bit is
spread across the entire bandwidth of the system. As a result,
a standard soft-input hard-output Viterbi decoder was used in
the SCFDE systems.
B. TX and RX Filter Design
In general, the transmit and receive filters in OFDM systems
can be much tighter than those used in single-carrier systems.
Consequently, we implemented root-raised-cosine filters with
a roll-off factor of 0.4 at the transmitter and the receiver of
each SCFDE system studied and root-raised-cosine filters with
a roll-off factor of 0.025 at the transmitter and the receiver
of each OFDM system [5]. Additionally, the bandwidth used
by the simulated systems was kept as close to 20 MHz as
possible. Therefore, to avoid the introduction of intersymbol
interference (ISI) by the filters, the symbol periods for the
OFDM and SCFDE systems were set equal to 50 ns and
70 ns, respectively. The full specifications of these filters are
presented in Table I.
C. Equalizer Design
In each MIMO system, two factors affect the design of the
frequency-domain equalizer: the PHY technique (i.e. OFDM
or SCFDE) and the MIMO architecture (i.e. SM or STBC).
Throughout this study, zero forcing (ZF) equalizers were
implemented in the OFDM systems whereas minimum mean-
squared error (MMSE) equalizers were employed in the
SCFDE systems. Both of these common linear equalization
techniques have similar complexity in the context of MIMO
applications. Before discussing each system in turn, some
notation is defined. The matrix I
q
is the q × q identity
matrix, 0
q
is the q × q zero matrix, ⊗ denotes the Kronecker
product, and (·)
K
, (·)
∗
, (·)
T
, (·)
H
, and E{·} denote the modulo-
K, complex conjugate, transpose, conjugate transpose, and
expectation operations, respectively.
1) SM-OFDM: The SM-OFDM equalized symbol vector ˜x
is given by
˜
x = W
SM
(Λx + η) (1)
where
Λ =
Λ
1,1
...
Λ
1,n
t
.
.
.
.
.
.
.
.
.
Λ
n
r
,1
...
Λ
n
r
,n
t
(2)
is the overall channel matrix of a system with n
t
trans-
mit antennas and n
r
receive antennas and W
SM
is the ZF
equalizer matrix. As previously mentioned, n
t
= n
r
=2in
this study. The sub-matrix
Λ
i,j
is a diagonal matrix defining
the frequency response of all K subcarriers between the jth
transmit antenna and the ith receive antenna. The vector x is a
2K ×1 vector of transmitted symbols and η is a 2K ×1 vector
of white Gaussian noise samples. The ZF equalizer W
SM
=
Λ
−1
removes the channel distortion from the received symbols
at the expense of possibly enhancing the noise as seen in (1).
2) STBC-OFDM: For STBC-OFDM systems, equalization
is performed after the received signals are combined [6]. If s
is the stacked 2K × 1 vector of symbols after maximum ratio
combining (MRC), the equalized symbol vector
˜
x is given by
˜
x = W
STBC
(s +˜η) . (3)
In (3), W
STBC
=
¯
Λ
−1
is the ZF equalizer matrix where
¯
Λ = diag
i,j
h
(1)
i,j,1
2
,...,
i,j
h
(p)
i,j,k
2
is a diagonal matrix and h
(p)
i,j,k
is the channel gain between the
jth transmit antenna and the ith receive antenna on subcarrier
k for the pth MRC signal. The vector ˜η is the noise after MRC.
3) SM-SCFDE: For SM-SCFDE systems, the vector ˜x of
equalized symbols at both receive antennas is given by
˜x = D
−1
F
W
SM
(ΛD
F
x + D
F
η) (4)
where D
F
= I
2
⊗ F. The matrix F is the K × K FFT matrix
where K is the length of each transmitted block in the SCFDE
system. In (4),
W
SM
is the MMSE equalizer matrix defined
in [7] and reproduced below for convenience.
W
SM
= Λ
H
ΛΛ
H
+
σ
2
η
σ
2
x
I
2K
−1
. (5)
The quantity σ
2
η
is the total variance of the complex Gaussian
noise process at one receive antenna, σ
2
x
is the total power of
the complex transmitted signal from one transmit antenna, and
Λ is defined in (2). As observed in (4), the equalizer spans both
receiver branches to separate the transmitted symbol streams
and equalize the received symbols simultaneously.
4) STBC-SCFDE: The MMSE equalizer used in the STBC-
SCFDE systems, first discussed in [8], is different from that
employed in the SM-SCFDE systems in that the decoupling
and equalization processes are performed separately. To il-
lustrate, let x
(1)
and x
(2)
be the two K × 1 symbol vectors
transmitted from the first and second antennas respectively at
time . Then the two vectors transmitted at time +1, directly
after the first two vectors, are defined by
x
(1)
+1
(k)=−x
∗
(2)
((−k)
K
)
x
(2)
+1
(k)=x
∗
(1)
((−k)
K
)
for k =0, 1,..., K − 1. At the receiver, the vectors corre-
sponding to those transmitted during the (+1)th time slot are
conjugated, after which each received vector is transformed
into the frequency domain and MRC is implemented to
decouple the transmitted sequences. The resulting length-2K
vector of symbols prior to equalization is given by
Y =
2
i=1
Λ
H
(i)
Λ
(i)
D
F
x + D
F
η
(i)
(6)
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where
Λ
(i)
=
Λ
i,1
Λ
i,2
Λ
∗
i,2
−
Λ
∗
i,1
,
Λ
i,j
is defined in (2), x =(x
T
(1)
, x
T
(2)
)
T
, and η
(i)
represents
the noise contribution from the ith receive antenna. The
sequence Y is then passed through an MMSE equalizer. The
equalizer matrix
W
STBC
for this system is obtained by solving
the equation
W
STBC
= arg min
W
E
|x − ˜x|
2
(7)
where ˜x = D
−1
F
WY represents the equalized symbols in the
time domain. It can be shown that the solution to (7) is [6],
[8]
W
STBC
=
˘
Λ +
σ
2
η
σ
2
x
I
2K
−1
(8)
where
˘
Λ =
2
i=1
2
j=1
Λ
i,j
2
0
K
0
K
2
i=1
2
j=1
Λ
i,j
2
. (9)
III. C
HANNEL DESCRIPTION
In [9], five different indoor WLAN channel models are
described. For this study, the channel models with the shortest
and the longest RMS delay spreads were chosen. The ETSI
A model corresponds to a typical office environment and has
an RMS delay spread of 50 ns, whereas the ETSI E model
corresponds to a typical large open space environment with
an RMS delay spread of 250 ns. Both of these channels
represent non-line-of-sight (NLOS) conditions in their respec-
tive environments. In the simulations, statistically independent
Rayleigh fading channel realizations were generated, and the
receiver was assumed to have complete knowledge of the
channel. Although these models are specified for 100 MHz
bandwidth, the filters discussed in section II-B were employed
to give an RF bandwidth of 20 MHz.
IV. S
IMULATION RESULTS
To provide a fair comparison, several system parameters
were held constant in the simulations. A complete list of the
simulation parameters is given in Table I. It is important to
note that the number of bits in a packet specified in Table I
includes six tail bits used to return the encoder to the zero
state for the systems implementing the convolutional code.
As metrics of performance, packet error rate (PER) and
throughput were used. To simulate the PER of a system,
one packet was transmitted for each independent channel
realization. The transmission of one packet was assumed to
be well within the coherence time of the channel. The PERs
of systems employing QPSK and 16-QAM in the ETSI A
channel are shown in Figure 2. Likewise, the PERs of systems
employing QPSK and 16-QAM in the ETSI E channel are
shown in Figure 3. Figures 4 and 5 show the throughputs of
TABLE I
S
IMULATION PARAMETERS.
SCFDE Parameters OFDM Parameters
Bandwidth 20 MHz 20.5 MHz
Modulation QPSK & 16-QAM QPSK & 16-QAM
Channels simulated ETSI A & E ETSI A & E
Convolutional (2,1,6) [3], [4] (2,1,6) [3], [4]
encoder
Viterbi decoder soft-input hard-output soft-input hard-output
(standard) (weighted metrics)
Equalization MMSE ZF
Bits per packet 1024 1024
No. of subcarriers 64 64
(symbols per block)
TX filter RRC RRC
Sample rate 7 samples/symbol 5 samples/symbol
Filter span 10 symbols 10 symbols
Roll-off factor 0.4 0.025 [5]
RX filter RRC RRC
Sample rate 7 samples/symbol 5 samples/symbol
Filter span 10 symbols 10 symbols
Roll-off factor 0.4 0.025 [5]
Symbol period 70 ns 50 ns
Cyclic prefix 12 sym.
840 ns 17 sym.
850 ns
the simulated systems in the ETSI A and ETSI E channels,
respectively. In Figures 2 through 5, cd signifies a system in
which the convolutional code is employed, uncd signifies a
system that does not utilize the code; curves related to SCFDE
systems are solid lines, and curves related to OFDM systems
are dot-dashed lines.
A. PER Analysis
The graphs presented in Figures 2 and 3 show a number
of interesting trends. Firstly, as expected, the uncoded SM-
OFDM systems perform extremely poorly and are, in general,
outperformed by the SM-SCFDE systems. This is most obvi-
ous in Figure 2(a) where the SNR gain of the uncoded SM-
SCFDE system is about 10 dB at a PER of 0.3. Secondly, the
best PER performance is achieved by concatenating a channel
code with STBC. This is also expected since this arrangement
exploits spatial diversity and coding. Furthermore, the perfor-
mance difference between the OFDM and SCFDE system with
this particular architecture is at most 0.5 dB.
It is interesting to note that results published in [2] for
single-input single-output (SISO) systems with linear equali-
zation show that for a sufficiently strong channel code, OFDM
systems outperform SCFDE systems. In the MIMO case,
however, this trend appears to be reversed as shown by the
coded SM and uncoded STBC curves in Figures 2 and 3.
An exception to the trend is seen in Figure 2(b), where it is
shown that the SM-SCFDE system performs approximately
2 dB worse than the SM-OFDM system in the ETSI A
channel when a 16-QAM constellation is used. This behavior
is most likely due to the limitations of MMSE equalization
when dense signal constellations are used. Identical behavior
is not observed for transmissions in the ETSI E channel
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0 5 10 15 20 25 30
10
−3
10
−2
10
−1
10
0
SNR per RX Antenna (dB)
Probability of Packet Error
SCFDE STBC: uncd
OFDM STBC: uncd
SCFDE STBC: cd
OFDM STBC: cd
SCFDE SM: uncd
OFDM SM: uncd
SCFDE SM: cd
OFDM SM: cd
(a) QPSK
0 5 10 15 20 25 30
10
−3
10
−2
10
−1
10
0
SNR per RX Antenna (dB)
Probability of Packet Error
SCFDE STBC: uncd
OFDM STBC: uncd
SCFDE STBC: cd
OFDM STBC: cd
SCFDE SM: uncd
OFDM SM: uncd
SCFDE SM: cd
OFDM SM: cd
(b) 16-QAM
Fig. 2. Packet error rates for STBC and SM systems in the ETSI A channel (n
t
= n
r
=2).
0 5 10 15 20 25 30
10
−3
10
−2
10
−1
10
0
SNR per RX Antenna (dB)
Probability of Packet Error
SCFDE STBC: uncd
OFDM STBC: uncd
SCFDE STBC: cd
OFDM STBC: cd
SCFDE SM: uncd
OFDM SM: uncd
SCFDE SM: cd
OFDM SM: cd
(a) QPSK
0 5 10 15 20 25 30
10
−3
10
−2
10
−1
10
0
SNR per RX Antenna (dB)
Probability of Packet Error
SCFDE STBC: uncd
OFDM STBC: uncd
SCFDE STBC: cd
OFDM STBC: cd
SCFDE SM: uncd
OFDM SM: uncd
SCFDE SM: cd
OFDM SM: cd
(b) 16-QAM
Fig. 3. Packet error rates for STBC and SM systems in the ETSI E channel (n
t
= n
r
=2).
due to SCFDE’s efficient utilization of frequency diversity
and OFDM’s sensitivity to the loss of orthogonality between
subcarriers, which is caused by an insufficient cyclic prefix.
The results also show the trade-off between SM and STBC
schemes for wideband systems. For example, in the ETSI A
channel, the coded SM and uncoded STBC-OFDM systems
perform almost identically as shown in Figure 2(a). However,
in the ETSI E channel, the SM-OFDM system outperforms
the STBC-OFDM system in Figure 3(a) by approximately
3 dB at a PER of 0.01. A similar trend can be seen for
the same systems with 16-QAM modulation in Figures 2(b)
and 3(b). These trends imply that the exploitation of frequency
diversity can potentially provide better performance gains for
MIMO-OFDM systems than the utilization of spatial diversity
alone. In practical terms this means that importance should be
placed on the type of channel code employed over the type of
diversity scheme used. Frequency diversity can be exploited
further by increasing the number of subcarriers used in the
system, which decreases the subcarrier spacing thus causing
small perturbations in the channel to become significant. The
practical trade-off here is that the OFDM system becomes
more sensitive to synchronization errors and imperfect channel
knowledge as the number of subcarriers increase.
In the SCFDE systems, the trade-off between SM and
STBC is most obvious in the ETSI A channel where the
coded SM-SCFDE systems perform better at low SNR while
the STBC-SCFDE systems perform better at high SNR as
shown in Figures 2(a) and 2(b). The crossover occurs at
an SNR of approximately 12 dB (PER = 0.025) for the
QPSK modulation and at an SNR of 15 dB (PER = 0.5)
for 16-QAM, which suggests that spatial diversity exploited
through the STBC significantly aids the detection process in
a channel with low frequency selectivity such as the ETSI A
channel. Additionally, in rich scattering environments, SCFDE
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