Int. J. Communications, Network and System Sciences, 2009, 2, 903-911
doi:10.4236/ijcns.2009.29105 Published Online December 2009 (http://www.SciRP.org/journal/ijcns/).
903
Efficient Time/Frequency Permutation of MIMO-OFDM
Systems through Independent and Correlated Nakagami
Fading Channels
Khodr A. SAAIFAN, Emad K. AL-HUSSAINI
Department of Electronics and Communications, Cairo University, Giza, Egypt
Received August 16, 2009; revised September 28, 2009; accepted November 4, 2009
Abstract
Space-Time Frequency (STF) codes for MIMO-OFDM over block-fading channel can achieve rate Mt and
full-diversity Mt Mr Mb L which is the product of the number of transmit antennas Mt, receive antennas Mr,
fading blocks Mb and channel taps L. In this article, time permutation is proposed to provide independent
block-fading over Jake’s Doppler power spectrum channel. Moreover, we show the performance variations
of STF code as channel delay spread changes. Therefore, we introduce a frequency/time permutation tech-
nique in order to remove the frequency correlation among sub-carriers, which subsequently increases the
coding gain and achieves maximum diversity. Finally, the symbol error rate (SER) performance of the pro-
posed time/frequency permuted STF codes over independent and correlated MIMO antenna branches under
Nakagami fading channel is simulated. We show that the proposed systems provide better performance and
more robust to large values of antennas correlation coefficients in comparison with the un-interleaved one.
Keywords: MIMO, OFDM, Space-Time Frequency Coding, Nakagami Fading Channel, Time/Frequency
Interleaving
1. Introduction
Achieving high data rate, full diversity gain and higher
network capacity becomes the major requirements of wire-
less system providers. MIMO-OFDM system is one of the
most attractive techniques to provide these capabilities.
Recently, some attention has been devoted to design
STF codes for MIMO-OFDM system with Mt transmit
antennas, Mr receive antennas, and N-OFDM tones through
L multi-path fading channel. There are several papers,
which discussed the code structure to provide full diver-
sity gain and high data rate. In [1], W. Su et al. proposed
the design of full diversity space frequency block code
(SFBC) with rate-1 for any number of transmit antennas
and arbitrary power delay profiles. The rate-Mt full di-
versity SFBC was proposed in [2] for any arbitrary
number of transmit antennas. However, because a zero-
padding matrix has to be used when N is not an integer
multiple of Mt L, the symbol transmission rate Mt cannot
be always guaranteed.
In [3], better diversity gains through block-fading
channels can be obtained, that was done by spreading the
coding across multiple fading blocks. In [4], they studied
the error performance results of STF codes in MIMO-
OFDM systems for a variety of system configurations
and channel conditions. The maximum diversity is the
product of time diversity, frequency diversity and space
diversity as shown in [5]. Recently in [6], W. Zhang et al.
proposed a systematic design of high-rate STF codes for
MIMO frequency-selective block-fading channels. By
spreading the algebraic coded symbols across different
OFDM sub-channels, transmit antennas and fading blocks,
the proposed STF codes can achieve a rate-Mt and a full
diversity of Mt Mr Mb L, where Mb is the number of in-
dependent fading blocks in the code-words. To achieve
the full-diversity performance of STF code, maximum-
likelihood (ML) decoding must be employed. In order to
decrease the large complexity of ML decoding, sphere
decoder can be considered to achieve near-ML perform-
ance [7,8]. For block-fading channels, the performance
of STF-coded OFDM is much better than SF coding as
demonstrated in [9].
In MIMO-OFDM systems, the DFT operation intro-
duces correlation into the channel frequency response at
different sub-carriers [10,11], making its performance var-

K. A. SAAIFAN ET AL. 904
ies as the delays between paths vary.
The outline of the paper is as follows. Section 2 de-
scribes the channel statistics and system model. The
suggested time/frequency permutations of high rate STF
codes structure proposed in [6] for independent and cor-
related Nakagami fading are introduced in Section 3. In
Section 4, we provide simulation results for the per-
formance of the proposed scheme. Finally, some conclu-
sions are made in Section 5.
2. Channel Statistics and System Models
Before investigating permutation schemes for MIMO-
OFDM systems equipped with Mt transmit antennas, Mr
receive antennas in mobile radio channels, we briefly de-
scribe the channel statistics, emphasizing the separation
property of mobile wireless channels, which is crucial for
simplifying our time/frequency permutation. In this sec-
tion we also briefly describe a MIMO-OFDM system.
2.1. Statistics of Mobile Radio Channels
The channels between each pair of transmit and receive
antennas are assumed to have L independent delay paths
and the same power delay profile. The channel impulse
response between mt
th
transmit antenna and mr
th receive
antenna can be modeled as




1
0
,, )()();(
L
l
l
l
mmmm ttth rtrt

(1)
where τl is the delay of the lth path, and is
complex amplitude of the lth path between mt
th transmit
antenna and mr
th receive antenna. ’s are mod-
eled as a complex random fading signals with Nakagarni-m
distributed fading amplitudes and uniform phases. Na-
kagami m-distribution fading model [12] is one of the
most versatile, in the sense that it has greater flexibility
and accuracy in matching some experimental data than
Rayleigh, log-normal, or Rician distributions. The Rayleigh
distribution is a special case when the fading parameter
m=1. It can approximate Rice distribution for m＞1.
Moreover, it is assumed that all path gains between any
pair of transmit and receive antennas follow the same
power profile, i.e.,
)(
,t
l
mm rt

)(
,t
l
mm rt

0
2
l
 )( 2
,





l
mm tErt
 for any given
. The powers of the paths are normalized such
that . Using Equation (1), the frequency re-
sponses of the time-varying radio channel at time t is
),,( lmm rt
1
0
2



L
l
l
 1
)2exp()(),(
1
0
,, l
L
l
l
mmmm fjtftH rtrt
  


(2)
The MIMO channel is assumed to be spatially corre-
lated for any (mt, mr), where mt =1,…Mt, mr =1,…Mr, and
independent for any l where, l=0,…L-1. Let de-
notes the spatial correlation coefficient between
and defined as
TX
mm tt  ,

,
l
m
t
 )(t
m
r
)(
,t
l
mmrt


)(),( ,,, tt l
mm
l
mm
Tx
mmrtrttt  
 (3)
The spatial correlation coefficient observed at the re-
ceiver has also been extensively studied in the literature
and is given as
)(),( ,,, tt l
mm
l
mm
Rx
mm rtrtrr  
 (4)
Given Equations (3) and (4), the symmetrical correla-
tion matrices at transmitter and the receiver can be de-
fined respectively as
tt
tttt
t
t
MM
Tx
MM
Tx
M
Tx
M
Tx
M
TxTx
Tx
M
TxTx
Tx























21
22221
11211
R (5)
and,
rr
rrrr
r
r
MM
Rx
MM
Rx
M
Rx
M
Rx
M
RxRx
Rx
M
RxRx
Rx























21
22221
11211
R (6)
The spatial correlation matrix R of the MIMO radio
channel is the Kronecker product of the spatial correla-
tion matrix at the transmitter and the receiver and is
given by [13]
RxTx RRR 

(7)
where

denotes the Kronecker product.
The correlation function of the frequency response for
different times and frequencies is









1
0
,
*
,
,
*
,,
)2exp()]()([
),(),(),(
L
l
l
l
mm
l
mm
mmmmmm
fjtttE
ffttHftHEft
rtrt
rtrttt

(8)
Assume Jake’s Doppler power spectrum [14], there-
fore the correlation of the l th path is given by
)2()]()([ 0
2
,,
*
,tfJtttE Dl
Tx
mm
l
mm
l
mm ttrtrt  
 (9)
where represents the power of l th path, fD is the
Doppler frequency, and JO(x) is the zero order Bessel
function of the first kind. Substitute Equation (9) in
Equation (8), then Equation (8) can be rewritten as
2
l


K. A. SAAIFAN ET AL. 905
)()(
)2exp()2(
),(
,
1
0
2
0,
,
ft
fjtfJ
ft
ft
Tx
mm
L
l
llD
Tx
mm
mm
tt
tt
tt










 (10)
where Φt(Δt) is the time domain correlation function
and Φf (Δf) is the frequency domain correlation function.
From Equation (10), the time-frequency domain chan-
nel correlation function of Hmt,mr(t,f) can be separated as
the product of the spatial correlation coefficient, the
time domain channel correlation, and the frequency
domain channel correlation, which are dependent on the
antenna separation, the Doppler frequency, and
multi-path delay spread respectively.
For an OFDM system with block length T and tone
spacing (sub-channel spacing) Δf=1/T, the correlation
function for different blocks and tones can be written as
)()(),(
,TnkTftft
Tx
mmmm tttt  
 (11)
2.2. MIMO-OFDM System Model
Consider a STF-coded MIMO-OFDM system with Mt
transmit antennas, Mr receive antennas and N sub-carriers
operating over a frequency-selective multi-path fading
channel. The MIMO-OFDM system with code permuta-
tions considered in this paper is shown in Figure 1.
The source S generates Ns=N Mt Mb information sym-
bols from the discrete alphabet A, which are quadrature
amplitude modulation (QAM) normalized into the unit
power. Using a mapping f: S→C, an information symbol
vector S∈ANs is parsed into blocks and mapped onto a
STF codeword to be transmitted over the Mt transmit
antennas and Mb OFDM blocks. Each STF codeword C
can be expressed as a N ×Mb Mt matrix.


b
M
CCCC 
21
 (12)
where the N×Mt matrix


b
t
bb bm
M
mm mcccC 
21
 for
mb=1,...Mb denotes the sub-codeword ready to be sent
during the time epoch mb. The mt
th (mt=1,...Mt) column of
Figure 1. MIMO-OFDM system with code permutation to
combat channel correlation.
Cmb denoted by is sent to the OFDM block at the
mt
th transmit antenna during the time epoch mb. After
inverse fast Fourier transform (IFFT) modulation and
cyclic prefix (CP) insertion, OFDM symbols are sent
from all transmit antennas simultaneously.
b
t
m
m
c
At the receiver, after matched filtering, removing the
cyclic prefix, and applying FFT, the received signal at
the received signal at the mr
th receive antenna during the
time epoch mb is given by
b
r
t
t
b
rt
b
t
b
r
m
m
M
m
m
mm
m
m
t
m
mMZHcY  
1
,
)(diag

(13)
where


T
m
mm
m
mm
m
mm
m
mm NHHH b
rt
b
rt
b
rt
b
rt )1()1()0(,,,,  H
b
t
m
m
Z
is the mb
th OFDM block channel frequency response
vector between mt
th transmit antenna and mr th receive
antenna and denotes the complex discrete
AWGN process with zero mean and unit variance at the
mr
th receive antenna. The factor t
M 
in Equation (13)
ensures that the average SNR at each receive antenna is
independent on the number of transmit antennas.
3. Time/Frequency Permuted STF Codes
STF coding proposed in [6] can achieve rate of Mt and
full diversity for any number of transmit antennas and
any arbitrary channel power delay profiles. It was con-
structed by applying the layering concept along with
algebraic code components, which was introduced in the
design of threaded algebraic space-time (TAST) code
[15]. The STF code structure spreads the algebraic code
components in adjacent sub-carriers and adjacent time
slots that suffer from high correlation introduced by DFT
operation and time correlation respectively. In this sec-
tion, time/frequency permuted STF code structure is in-
troduced into STF code structure of [6] in order to re-
move the effect of channel correlation among the code
components and achieve better diversity order.
3.1. STF Codes Structures
Let , , and ,
then a block of Ns transmitted information symbols
S=[S1,S2,...SNMtMb]T are parsed into J(J=N/K) equal size
sub-blocks. Each sub-block Sj∈AKMtMb (j=1,2…, J) is
respectively encoded into an STF code matrix Bj of size
K×MtMb through the following steps:

L
p
N2
log
2
 t
M
q
N2
log
2

qp NNK
1) Each subblock Sj (j=1,2…, J) are parsed into Nq in-
formation vector.
btp
q
MMN
nAs),,2,1( qq Nn 

K. A. SAAIFAN ET AL. 906
2) Generate algebraic code sub-block q
n
X by apply-
ing a fully-diverse unitary transformations into each
information vector to generate Nq
threads by
Θ
),2,1( qqn Nn
q
s



q
qqq
b
Lq
b
q
Lqqq
n
nnn
M
Nn
M
n
Nnnn
NXXX
Θs
XXXXX



)()2()1(
,1,
1
,
1
1,


(14)
where btp MMNN , and is the first principal
Θ
NN  unitary matrix of the following matrix


1
,,,1  MH
Mdiag
 FΨ (15)
where

N
M
2
log
2, H
N
F is the
M
M
 discrete Fou-
rier transform (DFT) matrix, and


Mj 42exp  .
3) Applying the layering concept to construct the en-
coder sub-matrices b
p
m
n
X(and ).
pp Nn,1bbMm,1
1
1, 2,,
1
12
1
12
1
12
(1) (1)(1)
(2) (2)(2)
()() ()
q
bb bb
pp pqp
q
bb b
pp qp
q
bb b
pp qp
q
bb b
pp qp
N
mm mm TT T
nn nNn
N
mm m
nn Nn
N
mm m
nn Nn
N
mm m
nt ntNnt
XkXkX k
XkXkX k
Xk MXkMXk M











 


 




 

XX XX




(






where and
4) Re-arrange the elements of
16)
q
N/1
 tpbtp
m
nMNmMnk b
p)1()1(  .
b
p
m
n
X by ),(qt
m
nnm
b
p
 X
),( qt
u
mnmX:



mod
21
t
qtq M
nmn

, and













1
t
q
M
n
tt mm , for tt Mm 1, qNn 1q

1
12
12
1
1
2
23
(1) (1)(1)
1(2) (2
()() ()
bbtb
pp tp
qbb b
T
qppt p
q
bb b
pp qp
mmMm
nn Mn
Nmm m
M
NnnM n
N
mm m
nt ntNnt
XkXkX k
XkXkX k
Xk MXk MXk M


 




  













1
)









(17)
then, the code matrix is constructed as
bt MMK i
B







b
M
X
21








b
L
LL
b
M
N
NN
M
i
XXX
XXX
XX
B



21
2
2
2
1
2
1
11
(18)
The STF coding applies the same coding strategy to
every sub-block ),,2,1( Jj
jB, then the rate-Mt STF
code tMMN C Cb is of the form


T
T
J
BBBC 
21

TT (19)
It is clear that, each thread of codeword )(nX
nnq
(qq Nn ,2,1 and Nnn,2,1) is spread ove
tiency dimerefore, the STF code
structure is not optimum in spreading the code compo-
nents of each thread on adjacent sub-carriers that suffer
from high correlation introduced by DFT operation.
However, if the power delay profile of the channel is
available at the transmitter side, further improvement can
be achieved by developing an interleaving strategy (can
reduce the correlation between adjacent sub-carriers)
which explicitly considers the power delay profile. In
addition, since the STF code structure maintains its di-
versity gain from sending the OFDM blocks through
independent fading blocks, we shall introduce time per-
mutation to achieve independent fading blocks through
MIMO channels that suffer from high correlation intro-
duced by Doppler power spectrum.
r space,
me and frequensions. Th
3.2. Time/Frequency Permutation Schemes
he assumption of independent fading at the branches is
to the autocorrelatio
(20)
Obviously, the sources of channel correlation are
ca
T
acceptable if the antennas are spaced sufficiently apart
with respect to the radio frequency (RF) carrier wave-
length. In this case, tt
TX
mm mm
t

,0

, and
TX 
  ,theuced
n function [10]
1L
t
n Equation (11) will be red
ttmm mm
tt ,1
)/2exp()2(),(
0
2
0, TnjkTfJnk l
l
lDmm tt
  

used by the time domain channel correlation, and the
frequency domain channel correlation. Our objective is
to find the separation parameters k and n for MIMO-
OFDM system which produce zero time and frequency
correlations then permute the algebraic code components
of Bj (j=1,…J) at zero time frequency correlation to
maximize the diversity gain.

 )2(
0kTfDkc minJK


(21)
(22)
The zeros of the Bessel functions (Equation (21)) play
a







 


 )/2exp(min
1
0
2
10 TnjN l
L
l
lNnc

dominant role in our applications. The Bessel functions
have infinite number of zeros. The maxima and minima
of J0 steadily decrease in absolute value as k increases.

K. A. SAAIFAN ET AL. 907
The first five zeros of J0 are 2.4048, 5.5201, 8.6537,
11.7915, and 14.9309. The interval between the last two
is 3.1394, which is already close to π. The larger roots
are approximately



4
1
v, where v is the number of
the root. To break correlation of the channel,
verify independent fading block and realize high-rate
full-diversity STC of [6], the Mb-OFDM blocks of STC
matrix Bj (j=1,…J) should be transmitted at time differ-
the time
ence of 

4048.2
leaving size is required to break the memory of the channel.
The optimum sub-carriers separation factor Nc (see


Tf K
D
c
 2. For large coherence time or
equivalently low Doppler spread of the fading, high inter-
Eq
annel separations factors
N
independent fading
bl
2) Apply fruency permutation into each pair of code
m
uation (22)) can be easily found via low-complexity
computer search. However, closed-form solutions for spe-
cific cases are reported in [1].
Based on the knowledge of ch
c and Kc, time/frequency permuted STF code can be
introduced using the following steps:
1) Distribute the STC blocks over
ocks by permuting the u-OFDM blocks of STC ma-
trix Bj (j=1,…J) withhose blocks at time uKc,
),2( b Mu .
eq
t
atrices Bj and Bj’, where b Njj 
, KNNcb

,
bbb NnNj)1(2],,1[  and bb
n,1NJ 2.., b ,.2 y
permuting rows K, oows K,12 f Bj with the r
2,,1K of Bj’.
her perm3) Furtutation should be done to break the rest
of channel frequency correlation by permuting each pair of
rows ),( 21 nn , where2,2
1Kn and KKn ,22
2


for alatrices Bjwith
ing pair of rows at bloccb KMu )1(  where
l code m the correspond- ),1( Jj 
k distances
)2,,2( Ku .
By performing the abgure 2,
th
ove steps as shown in Fi
e code components )(nn nX q (qq Nn ,2,1 and
Nnn,2,1) of each t
pendent fading blocks which subsequently
achieve maximum diversity gain.
Examples of STF codes and pe
hread of code m are af-
fected by inde
rmuted STF codes for
M
d
tim
4. Simulation Results
In this section, we simulated the proposed permutation
atrix Bj
t=2, L=2 are shown Figures 3 and 4. For Mb=1, STF
codes will be, in fact, the SF codes of [16]. The rate-2 SF
code structure and the suggested time/frequency permu-
tation (antenna 1 is shown only) are shown in Figure 3.
The rate-2 STF code structure and the suggeste
e/frequency permutation for Mb=2 are shown in
Figure 4.
Figure 2. The suggested time/frequency permutation of STF
codes.
Figure 3. Rate-2 time/frequency permuted SF code (T/FP- S F).
Figure 4. Rate-2 time/frequency permuted STF code (T/FP-STF).
cheme and compared with the non-permuted STF codes s
for different power delay profiles of the channel. We
present average symbol-error rate (SER) curves as func-
tions of the average SNR. Then we illustrate the per-
formance of the proposed permutation for SF codes
through correlated Nakagami fading channels. To inves-
tigate the performance of the proposed time/frequency
permutation of STF codes over frequency-selective fad-
ing channels, we perform the simulation experiments and
compare with the STF codes [6] for MIMO-OFDM sys-
tems. In the simulation, we use a 2×2 system with 128
OFDM tones and 4QAM transmission scheme, thus the
spectral efficiency is 4 bit/s/Hz, ignoring the cyclic pre-
fix. The bandwidth of OFDM system is 1 MHz and the
length of the cyclic prefix is 32, i.e., 32μs. Hence the
duration of one OFDM symbol (cyclic prefix excluded)
is T=128μs. A two-ray Nakagami fading channel statis-

K. A. SAAIFAN ET AL. 908
d-
in
.1. Performance Comparison for Different
he first set of experiments is conducted to compare the
pict the improvement in SER
pe
tics model is considered with the equal gain, Doppler
spread fD=200Hz, and fading depth m = 0.5, 1 and 2.
It is to be noted that m = 0.5 represents the worst fa
It can be observed from these figures that the SER per-
formance of STF codes [6] varied as the delay spread of
the channel changed. The SER performance of STF
codes is further improved as delay spread of the channel
increased. Such an improvement is attributed to the large
coding gain induced by multi-path fading channels with
a larger delay spread. The performance of the STF code
degraded significantly from the 20μs case to the 8μs case,
whereas the performance of the STF code using time/
frequency permutation was almost the same for the
two delay profiles.
g situation that can be represented by Nakagami dis-
tribution. This case can be countered in bad urban mobile
radio. When m=1, we obtain Rayleigh fading channel.
Finally, m=2 represents the best considered situation in
which the fading is less than that of Rayleigh.
4
Delay Spreads
We can see that the T/FP-STF codes have better SER
performance than the non-permuted STF codes. For τ=8μs
case, there is an improvement of about 3.2 dB for SF
codes and an improvement of about 1.8 dB for the STF
codes at a SER of 10-4 when m=1. Therefore; the pro-
posed interleaving method offering higher code gains
making it more robust to small delay spread. This con-
firms that by careful interleaver design, the performance
of the STF codes can be significantly improved.
T
performance of the proposed scheme with STF codes for
different path delay of the two-ray model. A simple
two-ray, equal-power delay profile, with a delay τ mi-
croseconds between the two rays is assumed. Simulation
is carried out for two cases: 1) 8μ sec (optimum permuta-
tion Nc=8) and 2) 20μ sec (optimum permutation Nc=16).
For Doppler spread fD=200Hz the optimum time separa-
tion is 14 OFDM symbols to ensure independent fading
blocks, therefore the interleaved STF code is spanned
over 56 OFDM symbols.
Figures 5, 6 and 7 de
From Table 1, it is clear that the SNR decreases with
the increase of m. The performance of the interleaved
codes is not sensitive to the variation in the channel
time delay spread. In all of cases considered, the re-
quired SNR of the time/frequency interleaved codes is
lower than that needed for the un-interleaved one to
achieve the same SER.
rformance offered by the proposed time/frequency
permutations through independent Nakagami fading
channel with different m. The values of the fading depth
considered are m = 0.5, 1, and 2 respectively.
Figure 5. Average SER versus SNR of 2×2, MIMO-OFDM system through independent Nakagami fading channel m=0.5 with
different delay spread.

K. A. SAAIFAN ET AL. 909
Figure 6. Average SER versus SNR of 2×2, MIMO-OFDM system through independent Nakagami fading channel m=1 with
different delay spread.
Figure 7. Average SER versus SNR of 2×2, MIMO-OFDM system through independent Nakagami fading channel m=2 with
different delay spread.

K. A. SAAIFAN ET AL. 910
Table 1. SNR required to obtain a SER=10-4 for STFC and T/FP-STFC at different time delay spread.
SFC T/FP-SFC STFC T/FP-STFC
M 8μsec 20μsec 8μsec 20μsec 8μsec 20μsec 8μsec 20μsec
0.5 20.8 dB 19.4 dB 18 dB 16.3 dB 15.8 dB 14.7dB
1 18.1 dB 16.2 dB 14.9 dB 14.9 dB 13.8 dB 13.13 dB
2 17.4 dB 15.2 dB 13.9 dB 14.3 dB 13.1 dB 12.53 dB
4.2. Performance Comparisons over Correlated
Nakagami Fading Channels
MIMO system with closely spaced antenna elements is
considered here. Our aim is to analyze the influence of
the Nakagami-m fading parameter and the effect of
antenna correlation on the SER performance of the
rate-2 SF code, and the proposed T/FP-SF code de-
picted in Figure 3.
Figure 8 shows the SER degradation as the correlation
coefficients between the transmitting antenna branches ρ
vary from 0 up to 0.8. Similar correlation is assumed
between receiving antenna branches. Simulation is car-
ried out for two cases: 1) Transmitter correlated Naka-
gami MIMO fading channel case: , and
, and 2) Doubly correlated Nakagami
MIMO fading channel case: , and
. The values of the fading depth consid-
ered are m=0.5, 1, and 2 respectively. It is clear that the
SER increases with the increase of correlation coeffi-
cient ρ. At ρ=0, the received signals are independent
and the codes practically achieves full diversity recep-
tion gain. It is clear that the probability of error de-
creases with the increase of m, which is with the de-
crease of the severity of fading.






1
1


t
R






1
1


t






10
01
r
R






1
1


r
R
R
From these figures, it is clear that the systems under
consideration appreciably dominate the systems con-
sidered in [6].
5. Conclusions
Figure 8. Average SER versus correlation coefficients for
2×2 MIMO-OFDM systems at SNR=14dB.
In this paper, the limitation for achieving full-diversity of
STF-coded OFDM is introduced. The limitation arises
due to the fact that the algebraic code components are
spread in adjacent sub-carriers that suffer from high cor-
relation introduced by DFT operation. Assuming that the
power delay profile of the channel is available at the trans-
mitter, we proposed an efficient time-frequency interleav-
ing scheme to further improve the performance. Based on
simulation results, we can draw the following conclusions.
First, the proposed time/frequency permutations STF
codes offer considerable performance improvement over
previously reported results. Second, the applied inter-
leaving scheme can have a significant effect on the over-
all performance of the STF code through correlated and
independent Nakagami fading channels.

K. A. SAAIFAN ET AL. 911
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