Performance of wideband CDMA using spacetime spreading over multipath Nakagami fading channels
07 Aug 2002Vol. 1, pp 626630
TL;DR: The analysis and numerical results suggest that significant diversity gain can be achieved by employing several transmit antennas or/and by combining several multipath components.
Abstract: In this contribution the performance of wideband codedivision multipleaccess (WCDMA) systems using spacetime spreading (STS) based transmit diversity is investigated, when frequencyselective Nakagamim fading channels, multiuser interference and background noise are considered. The analysis and numerical results suggest that significant diversity gain can be achieved by employing several transmit antennas or/and by combining several multipath components. Furthermore, both the transmit diversity and the frequencyselective diversity appear to have the same order of importance.
Summary (1 min read)
Jump to: [I. INTRODUCTION] – [B. Channel Model] – [III. DETECTION OF SPACETIME SPREAD] and [V. CONCLUSIONS]
I. INTRODUCTION
 The capacity and the achievable data rate of wireless communication systems is limited by the timevarying characteristics of the channels.
 In recent years, spacetime coding has received much attention as an effective transmit diversity technique used for combating fading in wireless communications [1] , [2] .
 In [5] the performance of CDMA systems using STS has been investigated, when the channel is modeled either as a flat or as a frequencyselective Rayleigh fading channel in the absence of multiuser interference.
 Therefore, in this contribution, the authors investigate the performance.
 This work has been funded in the framework of the IST project IST199912070 TRUST, which is partly funded by the European Union.
B. Channel Model
 The complex lowpass equivalent representation of the impulse response experienced by the uth parallel signal component of user k is given by [7].
 EQUATION where Γ represents the gamma function [7] , and m (u) kl is the Nakagamim fading parameter, which characterizes the severity of the fading over the lth resolvable path between the uth transmission antenna and user k.
 The authors support K asynchronous CDMA users in the system and assume perfect power control.
III. DETECTION OF SPACETIME SPREAD
 With the aid of the Gaussian approximation and after some arduous analysis, it can be shown that the average BER of the STSassisted WCDMA system using U transmission antennas can be expressed as EQUATION where EQUATION ) Again, (19) shows that the diversity order achieved is LU .
 In Figs. 2 5 the authors compare the BER performance of the STSassisted WCDMA system transmitting over flatfading channels and that of the conventional RAKE receiver using only one transmission antenna, but communicating over frequencyselective fading channels.
 Evaluated from (19) by assuming appropriate parameters, which are explicitly shown in the corresponding figures.
 4 and 5 the BER was drawn against the number of users, K, supported by the system.
 For transmission over general Nakagamim fading channels, if the first resolvable path is less severely faded, than the other resolvable paths, such as in Figs.
V. CONCLUSIONS
 When multipath Nakagamim fading, multiuser interference and background noise induced impairments are considered.the authors.
 The authors analysis and numerical results demonstrated that significant diversity gain can be achieved by using several transmit antennas or/and by combining several multipath components.
 Furthermore, both the transmit diversity and the frequencyselective diversity have a similar influence on the BER performance of the WCDMA systems considered.
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Performance of Wideband CDMA Using SpaceTime Spreading over Multipath
Nakagami Fading Channels
LieLiang Yang and Lajos Hanzo
Dept. of Electronics and Computer Sciences
University of Southampton, SO17 1BJ, UK.
Tel: +44703593 125, Fax: +44703594 508
Abstract— In this contribution the performance of wideband
codedivision multipleaccess (WCDMA) systems using space
time spreading (STS) based transmit diversity is investigated,
when frequencyselective Nakagamim fading channels, multiuser
interference and background noise are considered. The analysis
and numerical results suggest that signiﬁcant diversity gain can
be achieved by employing several transmit antennas or/and by
combining several multipath components. Furthermore, both the
transmit diversity and the frequencyselective diversity appear to
have the same order of importance.
I. INTRODUCTION
The capacity and the achievable data rate of wireless commu
nication systems is limited by the timevarying characteristics
of the channels. An efﬁcient technique of combating the time
varying effects of wireless channels is employing diversity. In
recent years, spacetime coding has received much attention
as an effective transmit diversity technique used for combating
fading in wireless communications [1], [2]. Spacetime block
coding [2] assisted transmit diversity has now been adapted as
an optional diversity mode in the thirdgeneration (3G) wire
less systems known as IMT2000 using wideband codedivision
multipleaccess (WCDMA) [3], [4]. Inspired by spacetime
codes, in [5] an attractive transmit diversity scheme based on
spacetime spreading (STS) has been proposed for employ
ment in CDMA systems. More speciﬁcally, a STS scheme de
signed for supporting two transmission antennas and one re
ceiver antenna has been included in the cdma2000 WCDMA
standard [4]. In [5] the performance of CDMA systems using
STS has been investigated, when the channel is modeled ei
ther as a ﬂat or as a frequencyselective Rayleigh fading chan
nel in the absence of multiuser interference. It was argued that
the proposed STS scheme is capable of attaining the maximal
achievable transmit diversity gain without using extra spreading
codes and without an increased transmit power. Furthermore,
the results recorded for transmission over frequencyselective
Rayleigh fading channels (Fig.4 of [5]) show that when there
is a sufﬁciently high number of resolvable paths, a CDMA sys
tem using a single transmit antenna and a conventional RAKE
receiver is capable of achieving an adequate diversity gain.
Wideband CDMA channels are typically frequency selec
tive fading channels, having a number of resolvable paths.
Therefore, in this contribution, we investigate the performance
This work has been funded in the framework of the IST project IST1999
12070 TRUST, which is partly funded by the European Union. The authors
would like to acknowledge the contributions of their colleagues.
of WCDMA systems using STS based transmit diversity, when
encountering multipath Nakagamim fading channels, mul
tiuser interference and background noise. A Bit Error Ratio
(BER) expression is derived, when Gaussian approximation [6]
of the multiuser interference and that of the multipath interfer
ence is invoked. The analysis and the numerical results show
that both the STS and the frequencyselectivity of the chan
nel appear to have the same order of importance, especially,
when the power decay factor of the multipath intensity proﬁle
(MIP) [7] is low.
II. S
YSTEM MODEL
A. Transmitted Signal
The WCDMA system considered in this paper consists of U
transmitter antennas and one receiver antenna. The transmitter
schematic of the kth user and the receiver schematic of the ref
erence user are shown in Fig.1, where realvalued data symbols
using BPSK modulation and realvalued spreading [5] were as
sumed. As shown in Fig.1(a), at the transmitter side the binary
input data stream having a bit duration ofT
b
is serialtoparallel
(S/P) converted to U parallel substreams. The new bit duration
of each parallel substream, in other words the symbol duration
becomes T
s
= U T
b
. After S/P conversion, the U number of
parallel bits are directsequence spread using the STS schemes
proposed in [5] with the aid ofU number of orthogonal spread
ing sequences  for example Walsh codes  having a period of
UG, where G = T
b
/T
c
represents the number of chips per
bit and T
c
is the chipduration of the orthogonal spreading se
quences. As seen in Fig.1(a), following STS, theU parallel sig
nals to be mapped to theU transmission antennas are scrambled
using the kth user’s pseudonoise (PN) sequence PN
k
(t), in or
der that the transmitted signals become randomized, and to en
sure that the orthogonal spreading sequences employed within
the STS block of Fig.1 can be reused by the other users. Fi
nally, after the PN sequence based scrambling, the U number
of parallel signals are carrier modulated and transmitted by the
corresponding U number of antennas.
As described above, we have assumed that the number of
parallel data substreams, the number of orthogonal spreading
sequences used by the STS block of Fig.1 and the number of
transmission antennas is the same, namelyU . This speciﬁc STS
scheme constitutes a speciﬁc subclass of the generic family of
STS schemes, where the number of parallel data substreams,
the number of orthogonal spreading sequences required by STS
626
0780374002/02/$17.00 © 2002 IEEE
block and the number of transmission antennas may take dif
ferent values. The study conducted in [5] has shown that the
number of orthogonal spreading sequences required by STS is
usually higher, than the number of parallel substreams. The
STS scheme having an equal number of parallel substreams,
orthogonal STSrelated spreading sequences as well as trans
mission antennas constitutes an attractive scheme, since this
STS scheme is capable of providing maximal transmit diversity
without requiring extra spreading codes for STS. Note that for
the speciﬁc values of U = 2, 4 the above mentioned attractive
STS schemes have been speciﬁed in [5]. In this contribution,
we only investigate these attractive STS schemes.
......
......
......
......
......
......
......
......
S/P
+
+
+
PSfrag replacements
Input
Data
b
k1
b
k2
b
kU
SpaceTime
Spreading
×
×
×
×
×
××
×
PN
k
(t)
cos(2πf
c
t)
cos(2πf
c
t)
s
k1
(t)s
k2
(t) s
kU
(t)
[c
1
(t), c
2
(t), . . . , c
U
(t)]
Antenna:
PN(t − τ
l
)
r(t)
SpaceTime
Despreading
Z
1l
Z
2l
Z
U l
Z
11
Z
1L
Z
21
Z
2L
Z
U 1
Z
U L
Z
1
Z
2
Z
U
ˆ
b
1
ˆ
b
2
ˆ
b
U
(a) Transmitter
(b) Receiver
≷ 0
≷ 0
≷ 0
Fig. 1. Transmitter and receiver block diagram of the WCDMA system using
spacetime spreading.
Based on the philosophy of STS as discussed in [5] and re
ferring to Fig.1(a), the transmitted signal of thekth user can be
expressed as
s
k
(t) =
r
2P
U
2
c(t)B
U
(t) × PN
k
(t) cos(2πf
c
t), (1)
where P represents each user’s transmitted power, which is
constant for all users, s
k
(t) = [s
k1
(t) s
k2
(t) ... s
kU
(t)] rep
resents the transmitted signal vector of the U transmission
antennas, while PN
k
(t) and f
c
represent the DS scrambling
based spreading waveform and the subcarrier frequency, re
spectively. The scrambling sequence waveform is given by
PN
k
(t) =
P
∞
j=−∞
p
kj
P
T
c
(t−jT
c
), where p
kj
assumes values
of +1 or 1 with equal probability, whileP
T
c
(t) is the rectangu
lar chip waveform, which is deﬁned over the interval [0, T
c
).
In (1) the vector c(t) = [c
1
(t) c
2
(t) ... c
U
(t)] is constituted
by the U number of orthogonal signals assigned for the STS,
c
i
(t) =
P
∞
j=−∞
c
ij
P
T
c
(t − jT
c
), i = 1, 2, . . . , U denotes the
individual components of the STSbased orthogonal spread sig
nals, where {c
ij
} is an orthogonal sequence of period UG for
each index i; B
U
(t) represents the U × U dimensional trans
mitted data matrix created by mapping U input data bits to the
U parallel substreams according to speciﬁc design rules [5],
so that the maximum possible transmit diversity is achieved,
while using relatively lowcomplexity signal detection algo
rithms. Speciﬁcally, B
U
(t) can be expressed as
B
U
(t) =
a
11
b
k,11
a
12
b
k,12
. . . a
1U
b
k,1U
a
21
b
k,21
a
22
b
k,22
. . . a
2U
b
k,2U
.
.
.
.
.
.
.
.
.
.
.
.
a
U1
b
k,U 1
a
U2
b
k,U 2
. . . a
UU
b
k,U U
(t), (2)
where the time dependence of the (i, j)th element is indicated
at the right of the matrix for simplicity. In (2)a
ij
represents the
sign of the element at the ith row and the jth column, which is
determined by the STS design rule, while b
k,ij
is the data bit
assigned to the (i, j)th element, which is one of the U input
data bits { b
k1
, b
k1
, . . . , b
kU
} of user k. Each input data bit of
{b
k1
, b
k2
, . . . , b
kU
} appears only once in any a given row and
in any given column.
B. Channel Model
The U number of parallel signal components s
k
(t) =
[s
k1
(t) s
k2
(t) ... s
kU
(t)] are transmitted by the U number of
antennas over frequencyselective fading channels, where each
parallel signal component experiences independent frequency
selective Nakagamim fading. The complex lowpass equiva
lent representation of the impulse response experienced by the
uth parallel signal component of user k is given by [7]
h
u
k
(t) =
L
X
l=1
h
u
kl
δ(t − τ
kl
) exp (jφ
u
kl
) , (3)
where h
u
kl
, τ
kl
and ψ
u
kl
represent the attenuation factor, delay
and phaseshift of the lth multipath component of the channel,
respectively, while L is the total number of resolvable multi
path components and δ(t) is the Kronecker Deltafunction. We
assume that the phases {ψ
u
kl
} in (3) are independent identically
distributed (iid) random variables uniformly distributed in the
interval [0, 2π), while the L multipath attenuations {h
u
kl
} in (3)
are independent Nakagami random variables with a Probability
Density Function (PDF) of [6]
p(h
u
kl
) = M(h
u
kl
, m
(u)
kl
, Ω
u
kl
),
M(R, m, Ω) =
2m
m
R
2m−1
Γ(m)Ω
m
e
(−m/Ω)R
2
, (4)
where Γ(·) represents the gamma function [7], and m
(u)
kl
is the
Nakagamim fading parameter, which characterizes the sever
ity of the fading over the lth resolvable path between the uth
transmission antenna and user k. The parameter Ω
u
kl
in (4) is
the second moment of h
u
kl
, i.e. we have Ω
u
kl
= E[(α
u
kl
)
2
]. We
assume a negative exponentially decaying multipath intensity
proﬁle (MIP) given by Ω
u
kl
= Ω
u
k1
e
−η(l−1)
, η ≥ 0, where Ω
u
k1
is the average signal strength corresponding to the ﬁrst resolv
able path and η is the rate of average power decay.
627
We support K asynchronous CDMA users in the system
and assume perfect power control. Consequently, when the K
users’ signals obeying the form of (1) are transmitted over the
frequencyselective fading channels characterized by (3), the
received complex lowpass equivalent signal at a given mobile
station can be expressed as
R(t) =
K
X
k=1
L
X
l=1
r
2P
U
2
c(t − τ
kl
)B
U
(t − τ
kl
)h
kl
× PN
k
(t − τ
kl
) + N(t), (5)
where N (t) is the complex valued lowpassequivalent Ad
ditive White Gaussian Noise (AWGN) having a doublesided
spectral density of N
0
, while
h
kl
=
h
1
kl
exp(jψ
1
kl
)
h
2
kl
exp(jψ
2
kl
)
. . .
h
U
kl
exp(jψ
U
kl
)
,
k = 1, 2, . . . , K;
l = 1, 2, . . . , L
(6)
represents the channel’s complex impulse response in the con
text of the kth user and the lth resolvable path, where ψ
u
kl
=
φ
u
kl
− 2πf
c
τ
kl
.
C. Receiver Model
Let the ﬁrst user be the userofinterest and consider a re
ceiver using spacetime despreading as well as diversity com
bining, as shown in Fig.1(b), where the subscript of the ref
erence user’s signal has been omitted for notational conve
nience. The receiver of Fig.1(b) carries out the inverse pro
cessing of Fig.1(a), in addition to multipath diversity combin
ing. In Fig.1(b) the received signal is ﬁrst downconverted
using the carrier frequency f
c
, and then descrambled using
the DS scrambling sequence of PN(t − τ
l
) in the context of
the lth resolvable path, where we assumed that the receiver
is capable of achieving nearperfect multipathdelay estima
tion for the reference user. The descrambled signal associ
ated with the lth resolvable path is spacetime despread us
ing the approach of [5], in order to obtain U separate vari
ables, {Z
1l
, Z
2l
, . . . , Z
Ul
}, corresponding to theU parallel data
bits {b
1
, b
2
, . . . , b
U
}, respectively. Following spacetime de
spreading, a decision variable is formed for each parallel trans
mitted data bit of {b
1
, b
2
, . . . , b
U
} by combining the corre
sponding variables associated with the L number of resolvable
paths, which can be expressed as
Z
u
=
L
X
l=1
Z
ul
, u = 1, 2, . . . , U. (7)
Finally, the U number of transmitted data bits {b
1
, b
2
, . . . , b
U
}
can be decided based on the decision variables{Z
u
}
U
u=1
using
the conventional decision rule of a BPSK scheme.
III. D
ETECTION OF SPACETIME SPREAD WCDMA
S
IGNALS
Let d
l
= [d
1l
d
2l
. . . d
Ul
]
T
, l = 1, 2, . . . , L  where T de
notes vector transpose  represent the correlator’s output vari
able vector in the context of thelth (l = 1, 2, . . . , L) resolvable
path, where
d
ul
=
Z
UT
b
+τ
l
τ
l
R(t)c
u
(t − τ
l
)PN(t − τ
l
)dt. (8)
When substituting (5) into (8), it can be shown that
d
ul
=
√
2P T
b
a
u1
b
u1
h
1
l
exp
jψ
1
l
+ a
u2
b
u2
h
2
l
exp
jψ
2
l
+ . . . + a
uU
b
uU
h
U
l
exp
jψ
U
l
+ J
u
(l) (9)
for u = 1, 2, . . . , U, where
J
u
(l) = J
Su
(l) + J
Mu
(l) + N
u
(l), u = 1, 2, . . . , U (10)
and J
Su
(l) is due to the multipathinduced selfinterference of
the signalofinterest inﬂicted upon the lth path signal, where
J
Su
(l) can be expressed as
J
Su
(l) =
L
X
j=1,j6=l
r
2P
U
2
Z
UT
b
+τ
l
τ
l
c(t − τ
j
)B
U
(t − τ
j
)h
j
×PN(t − τ
j
)c
u
(t − τ
l
)PN(t − τ
l
)dt, (11)
while J
Mu
(l) represents the multiuser interference due to the
signals transmitted simultaneously by the other users, which
can be expressed as
J
Mu
(l) =
K
X
k=2
L
X
j=1
r
2P
U
2
Z
UT
b
+τ
l
τ
l
c(t − τ
kj
)B
U
(t − τ
kj
)
×h
kj
PN
k
(t − τ
kj
)c
u
(t − τ
l
)PN(t − τ
l
)dt. (12)
Finally N
u
(l) is due to the AWGN, which can be written as
N
u
(l) =
Z
UT
b
+τ
l
τ
l
N(t)c
u
(t − τ
l
)PN(t − τ
l
)dt, (13)
which is a Gaussian distributed variable having zero mean and
a variance of 2UN
0
T
b
.
Let J(l) = [J
1
(l) J
2
(l) . . . J
U
(l)]
T
. Then, the correlator’s
output variable vector d
l
can be expressed as
d
l
=
√
2P T
b
B
U
h
l
+ J(l), l = 1, 2, . . . , L, (14)
where B
U
is the reference user’s U ×U dimensional transmit
ted data matrix, which is given by (2), but ignoring the time de
pendence, while h
l
is the channel’s complex impulse response
between the base station and the reference user, as shown in (6)
in the context of the reference user.
Attractive STS schemes have the property [5] of B
U
h
l
=
H
U
b, i.e., Equation (14) can be written as
d
l
=
√
2P T
b
H
U
b + J(l), (15)
where b = [b
1
b
2
. . . b
U
]
T
represents the U number of trans
mitted data bits, while H
U
is a U ×Udimensional matrix with
elements from h
l
. Each element of h
l
appears once and only
628
once in a given row and also in a given column of the matrix
H
U
[5]. The matrix H
U
can be expressed as
H
U
(l) =
α
11
(l) α
12
(l) . . . α
1U
(l)
α
21
(l) α
22
(l) . . . α
2U
(l)
.
.
.
.
.
.
.
.
.
.
.
.
α
U1
(l) α
U2
(l) . . . α
UU
(l)
, (16)
where α
ij
(l) takes the form of d
ij
h
m
l
exp(jψ
m
l
), and d
ij
∈
{+1, −1} represents the sign of the (i, j)th element of H
U
,
while h
m
l
exp(jψ
m
l
) belongs to the mth element of h
l
.
With the aid of the analysis in [5], it can be shown that
the matrix H
U
(l) has the property of Re
n
H
†
U
(l)H
U
(l)
o
=
h
†
l
h
l
· I, where † denotes complex conjugate transpose and I
represents a U × Udimensional unity matrix. Letting h
u
(l)
denote the uth column of H
U
(l), the variable Z
ul
in (7) can be
expressed as [5]
Z
ul
= Re
h
†
u
(l)d
l
=
√
2P T
b
b
u
U
X
u=1
h
u
l

2
+Re
h
†
u
(l)J(l)
, u = 1, 2, . . . , U. (17)
Finally, according to (7) the decision variables associated with
the U parallel transmitted data bits {b
1
, b
2
, . . . , b
U
} of the ref
erence user can be expressed as
Z
u
=
√
2P T
b
b
u
L
X
l=1
U
X
u=1
h
u
l

2
+
L
X
l=1
Re
h
†
u
(l)J(l)
, (18)
which shows that the receiver is capable of achieving a diversity
order of UL, as indicated by the related sums of the ﬁrst term.
With the aid of the Gaussian approximation and after some
arduous analysis, it can be shown that the average BER of the
STSassisted WCDMA system using U transmission antennas
can be expressed as
P
b
(E) =
1
π
Z
π/2
0
L
Y
l=1
U
Y
u=1
m
(u)
l
sin
2
θ
γ
lu
+ m
(u)
l
sin
2
θ
!
m
(u)
l
dθ, (19)
where
γ
lu
=
1
U
"
(2K + 1)q(L, η) − 3
3G
+
Ω
1
E
b
N
0
−1
#
−1
×e
−η(l−1)
. (20)
Again, (19) shows that the diversity order achieved isLU .
IV. NUMERICAL RESULTS
In Figs. 2  5 we compare the BER performance of the STS
assisted WCDMA system transmitting over ﬂatfading chan
nels and that of the conventional RAKE receiver using only
one transmission antenna, but communicating over frequency
selective fading channels. The results in these ﬁgures were all
Fig. 2. BER versus the SNR per bit, E
b
/N
0
, performance comparison be
tween the spacetime spreading based transmit diversity scheme and the con
ventional RAKE receiver arrangement using only one transmission antenna
when communicating over ﬂatfading (for spacetime spreading) and multipath
( for RAKE) Rayleigh fading (m
l
= m
c
= 1) channels by assuming that the
average power decay rate was η = 0.
Fig. 3. BER versus the SNR per bit, E
b
/N
0
, performance comparison be
tween the spacetime spreading based transmit diversity scheme and the con
ventional RAKE receiver arrangement using only one transmission antenna
when communicating over ﬂatfading (for spacetime spreading) and multipath
(for RAKE) Nakagamim fading channels by assuming that the average power
decay rate was η = 0.2, where m
1
= 2 indicates that the ﬁrst resolvable path
constitutes a moderately fading path, while the other resolvable paths experi
ence more severe Rayleigh fading (m
c
= 1).
629
evaluated from (19) by assuming appropriate parameters, which
are explicitly shown in the corresponding ﬁgures. In Figs. 2
and 3 the BER was drawn against the SNR/bit, namelyE
b
/N
0
,
while in Figs. 4 and 5 the BER was drawn against the number of
users, K, supported by the system. From the results we observe
that for transmission over Rayleigh fading channels (m
l
= 1),
as characterized by Figs. 2 and 4, both the STS based transmit
diversity scheme transmitting over the frequency nonselective
Rayleigh fading channel and the conventional RAKE receiver
scheme communicating over frequencyselective Rayleigh fad
ing channels having the same number of resolvable paths as the
number of transmission antennas in the STSassisted scheme
achieved a similar BER performance, with the STS scheme
slightly outperforming the conventional RAKE scheme. For
transmission over general Nakagamim fading channels, if the
ﬁrst resolvable path is less severely faded, than the other re
solvable paths, such as in Figs. 3 and 5 where m
1
= 2 and
m
2
= m
3
= . . . = m
c
= 1, the STS based transmit diver
sity scheme communicating over the frequency nonselective
Rayleigh fading channel may signiﬁcantly outperform the cor
responding conventional RAKE receiver assisted scheme com
municating over frequencyselective Rayleigh fading channels.
This is because the STS based transmit diversity scheme com
municated over a single nondispersive path, which beneﬁtted
from having a path experiencing moderate fading. However,
if the number of resolvable paths is sufﬁciently high, the con
ventional RAKE receiver scheme is also capable of achieving a
satisfactory BER performance.
V. C
ONCLUSIONS
In this contribution we have investigated the performance of
STSassisted WCDMA systems, when multipath Nakagami
m fading, multiuser interference and background noise induced
impairments are considered. Our analysis and numerical results
demonstrated that signiﬁcant diversity gain can be achieved by
using several transmit antennas or/and by combining several
multipath components. Furthermore, both the transmit diversity
and the frequencyselective diversity have a similar inﬂuence on
the BER performance of the WCDMA systems considered.
R
EFERENCES
[1] V. Tarokh, N. Seshadri, and A. R. Calderbank, “Spacetime codes for high
data rate wireless communication: performance criterion and code con
struction,” IEEE Transactions on Information Theory, vol. 44, pp. 744–
765, March 1998.
[2] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Spacetime block cod
ing for wireless communications: performance results,” IEEE Journal on
Selected Areas in Communications, vol. 17, pp. 451–460, March 1999.
[3] Proposed TDOC: 662/98 to ETSI SMG2 UMTS Standards, Spacetime
block coded transmit antenna diversity for WCDMA, December 1998.
[4] Telcomm. Industry Association (TIA), TIA/EIA Interim Standard: Phys
ical Layer Standard for cdma2000 Standards for Spread Spectrum Sys
tems, 2000.
[5] B. Hochwald, T. L. Marzetta, and C. B. Papadias, “A transmitter diversity
scheme for wideband CDMA systems based on spacetime spreading,”
IEEE Journal on Selected Areas in Communications, vol. 19, pp. 48–60,
January 2001.
[6] T. Eng and L. B. Milstein, “Coherent DSCDMA performance in Nak
agami multipath fading,” IEEE Transactions on Communications, vol. 43,
pp. 1134–1143, Feb./Mar./Apr. 1995.
[7] J. G. Proakis, Digital Communications. McGraw Hill, 3rd ed., 1995.
Fig. 4. BER versus the number of users, K, performance comparison be
tween the spacetime spreading based transmit diversity scheme and the con
ventional RAKE receiver arrangement using only one transmission antenna
when communicating over ﬂatfading (for spacetime spreading) and multipath
(for RAKE) Rayleigh fading channels by assuming that the average power de
cay rate was η = 0.
Fig. 5. BER versus the number of users, K, performance comparison between
the spacetime spreading based transmit diversity scheme and the conventional
RAKE receiver arrangement using only one transmission antenna when com
municating over the ﬂatfading (for spacetime spreading) and multipath (for
RAKE) Nakagamim fading channels by assuming that the average power de
cay rate was η = 0.2, where m
1
= 2 indicates that the ﬁrst resolvable path
constitutes a moderately fading path, while the other resolvable paths experi
ence more severe Rayleigh fading (m
c
= 1).
630
Citations
More filters
•
07 Oct 1999
TL;DR: A circuit is provided to improve a receiving efficiency by offering at least 2L diversity covering a time and a space, not to need an additional transmitting power or a band width, and to be balanced the power covering both ends of a multiplex antenna.
Abstract: PURPOSE: A circuit is provided to improve a receiving efficiency by offering at least 2L diversity covering a time and a space, not to need an additional transmitting power or a band width, and to be balanced the power covering both ends of a multiplex antenna. CONSTITUTION: A mobile communications system is equipped an inputting circuit contacted to receive first plural signals for a first time(T0,T1) from an outer source and contacted to receive second plural signals from the outer source. The inputting circuit receives each first and second plural signals according to each first and a second paths(j). The inputting circuit generates a first inputting signal(610) and a second inputting signal(614) from each first and second plural signals. A correcting circuit generates a first evaluation of symbol by answering a first and a second evaluating signals and the first and the second inputting signals. The correcting circuit generates a second evaluation of symbol by answering the first and the second evaluating signals and the first and the second inputting signals.
28 citations
References
More filters
01 Nov 1985
TL;DR: This month's guest columnist, Steve Bible, N7HPR, is completing a master’s degree in computer science at the Naval Postgraduate School in Monterey, California, and his research area closely follows his interest in amateur radio.
Abstract: Spread Spectrum It’s not just for breakfast anymore! Don't blame me, the title is the work of this month's guest columnist, Steve Bible, N7HPR (n7hpr@tapr.org). While cruising the net recently, I noticed a sudden bump in the number of times Spread Spectrum (SS) techniques were mentioned in the amateur digital areas. While QEX has discussed SS in the past, we haven't touched on it in this forum. Steve was a frequent cogent contributor, so I asked him to give us some background. Steve enlisted in the Navy in 1977 and became a Data Systems Technician, a repairman of shipboard computer systems. In 1985 he was accepted into the Navy’s Enlisted Commissioning Program and attended the University of Utah where he studied computer science. Upon graduation in 1988 he was commissioned an Ensign and entered Nuclear Power School. His subsequent assignment was onboard the USS Georgia, a trident submarine stationed in Bangor, Washington. Today Steve is a Lieutenant and he is completing a master’s degree in computer science at the Naval Postgraduate School in Monterey, California. His areas of interest are digital communications, amateur satellites, VHF/UHF contesting, and QRP. His research area closely follows his interest in amateur radio. His thesis topic is Multihop Packet Radio Routing Protocol Using Dynamic Power Control. Steve is also the AMSAT Area Coordinator for the Monterey Bay area. Here's Steve, I'll have some additional comments at the end.
8,781 citations
••
TL;DR: In this paper, the authors consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas and derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective.
Abstract: We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 23 dB of the outage capacity for these channels using only 64 state encoders.
7,105 citations
•
01 Jan 1999TL;DR: It is shown that using multiple transmit antennas and spacetime block coding provides remarkable performance at the expense of almost no extra processing.
Abstract: We document the performance of spacetime block codes, which provide a new paradigm for transmission over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a spacetime block code, and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. Maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection. This uses the orthogonal structure of the spacetime block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver. We review the encoding and decoding algorithms for various codes and provide simulation results demonstrating their performance. It is shown that using multiple transmit antennas and spacetime block coding provides remarkable performance at the expense of almost no extra processing.
1,958 citations
••
TL;DR: The technique, called spacetime spreading (STS), improves the downlink performance by using a small number of antenna elements at the base and one or more antennas at the handset, in conjunction with a novel spreading scheme that is inspired by space time codes.
Abstract: We present a transmit diversity technique for the downlink of (wideband) directsequence (DS) code division multiple access (CDMA) systems. The technique, called spacetime spreading (STS), improves the downlink performance by using a small number of antenna elements at the base and one or more antennas at the handset, in conjunction with a novel spreading scheme that is inspired by spacetime codes. It spreads each signal in a balanced way over the transmitter antenna elements to provide maximal path diversity at the receiver. In doing so, no extra spreading codes, transmit power or channel information are required at the transmitter and only minimal extra hardware complexity at both sides of the link. Both our analysis and simulation results show significant performance gains over conventional singleantenna systems and other openloop transmit diversity techniques. Our approach is a practical way to increase the bit rate and/or improve the quality and range in the downlink of either mobile or fixed CDMA systems. A STSbased proposal for the case of two transmitter and singlereceiver antennas has been accepted and will be included as an optional diversity mode in release A of the IS2000 wideband CDMA standard.
446 citations
"Performance of wideband CDMA using ..." refers background or methods in this paper
...Therefore, in this contribution, we investigate the performance This work has been funded in the framework of the IST project IST199912070 TRUST, which is partly funded by the European Union....
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...In recent years, spacetime coding has received much attention as an effective transmit diversity technique used for combating fading in wireless communications [1], [2]....
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