2.
1, ejΔθk
, ...ej(N−1)Δθk
[11], [13], where Δθk may be ex-
pressed as
Δθk =
2πk
N k = 1, 2, . . . N
2πk
N + π
N k = N + 1, N + 2, . . . 2N
(1)
In the receiver, while making the decision of kth
user, in
parallel interference cancellation, we have to subtract the esti-
mated value of (K-1) users’ information that creates multiple
access interference (MAI). The received signal r(t) can be
written as,
r(t) =
K
k=1
N−1
i=0
αi,kak[n].exp j(2πfit + iΔθk + βi,k)
.p(t − nTb) + η(t)(2)
where, αi,k is the complex-valued channel gain and βi,k is
the uniformly distributed phase offset for the kth
user in ith
subcarrier. For BPSK modulation, ak[n] = ±1 represents nth
bit of kth
user. {fi = fc + iΔf, (i = 0, 1, . . . N − 1)} is the
frequency of ith
narrow band subcarrier with center frequency
fc and Δf is selected such that orthogonality between carrier
frequencies can be maintained. Typically Δf = 1/Tb, where
Tb is bit duration of Nyquist pulse shape p(t). η(t) represents
AWGN at the multiuser receiver.
The received signal r(t) is projected onto N orthogonal
subcarriers and is despread using kth
user’s CI code. The ith
subcarrier component of received signal r(t) can be written as
yi =
2
N0Tb
Tb
0
r(t)exp − j(2πfit) dt (3)
The decision variables for kth
user at different subcarriers
may be expressed as
rk
= rk
0 , rk
1 , . . . rk
N−1 (4)
rk
i,iter = α∗
i,k.exp − j(iΔθk) yi
+
K
m=1,m=k
2Eb
N0
ˆa(iter−1)
m α∗
i,kαi,mexp j(i(Δθm − Δθk)
+ ˆβi,m − βi,k + ηiexp − j(iΔθk) (5)
where, rk
i,iter is decision variable for kth
user at ith
subcarrier
in iterth
iteration stage. Here, ∗
denote the complex conjugate
and yi is the projected N-orthogonal subcarriers component
of the received signal r(t). ηi is a Gaussian random variable
with zero mean and variance of N0/2. For simpliﬁcation of
analysis, the transmission is assumed to be synchronous i.e.,
ˆβi,m = βi,k. Further, we assumed that the received power of
every user is same, so that |αi,k| = 1. Eb is the transmitted bit
energy and ˆa
(iter)
k is the estimated data of kth
user at iterth
iteration stage.
When yi is multiplied by kth
user’s spreading code, the
expression becomes:
N−1
i=0
exp − j(iΔθk) yi
=
2Eb
N0
ak[n]
+
N−1
i=0
K
m=1,m=k
2Eb
N0
amexp j(i(Δθm − Δθk))
+
N−1
i=0
ηiexp − j(iΔθk) (6)
Taking the real part,
Yk =
2Eb
N0
ak[n] + Ik + Nk (7)
Yk
∼=
2Eb
N0
ak[n] + ˆIk + Wk
where,
Yk =
N−1
i=0
exp − j(iΔθk) yi (8)
Nk =
N−1
i=0
ηiexp − j(iΔθk) (9)
Nk is zero mean Gaussian random variable with variance of
N0/2 for kth
user. Ik is the MAI experienced by kth
user due
to (K-1) users and ˆIk is denoted as estimation of Ik based on
other users’ information.
Wk = Ik − ˆIk + Nk (10)
In conventional PIC scheme, the estimated interference is
directly subtracted from r(t). But in case of Sub-PIC, the
received signal is projected onto N orthogonal subcarrier and
the interference due to other users is subtracted at subcarrier
level. Wk arises due to imperfect cancellation which reduces
with iterative receiver structure. Now, (7) can be written as
Yk =
2Eb
N0
ak[n] + ˆIiter
k + Witer
k (11)
and ˆIiter
k is the estimated MAI experienced by kth
user due
to (K-1) users at iterth
iteration.
ˆIiter
k =
N−1
i=0
K
m=1,m=k
2Eb
N0
ˆaiter−1
m exp j(i(Δθm − Δθk))
(12)
For synchronous transmission between transmitter and re-
ceiver and assuming spreading code availability at the receiver,
only uncertainty lies in ˆIk. The term (Ik − ˆIk) represents
the residual or uncancelled interference power. For initial
769
3.
estimation, after forming the decision variables rk
, minimum
mean square error combiner (MMSEC) is employed to get
decision in an AWGN channel [16]. So, for ˆa0
k[n], Yk = rk
ω,
where ω is the weight vector of the combiner [16]. The
decision of kth
user information at iterth
iteration:
ˆaiter
k [n] ∼= sgn Yk − ˆIiter
k (13)
ˆa0
k[n] = sgn Yk
The scheme represented by (13) referred is as hard deci-
sion subcarrier parallel interference cancellation technique
(HDSub-PIC) [15].
III. SOFT DECISION SUBCARRIER PIC (SDSUB-PIC)
In SDSub-PIC the received signal is ﬁrst projected onto
N orthogonal subcarrier, and the interference is cancelled in
the subcarrier level as discussed earlier. The estimation of
the transmitted data is performed by taking soft decisions
using nonlinear function [8]. The soft decision of ak[n] is
given by ˜ak[n] = φ{(Yk − ˆIiter
k ); iter}, where the nonlinear
function φ{(x); iter} may depend on the iteration number
‘iter’. Different types of nonlinearities like dead-zone non-
linearities, hyperbolic tangent, Piecewise linear approximation
of hyperbolic tangent can be used for φ{(x); iter}.
i. Dead-Zone Nonlinearity:
φ(x) =
sgn(x) |x| ≥ λ
0 |x| < λ
(14)
If λ = 0 then it becomes similar to hard decision based
estimation in (13).
ii. Hyperbolic Tangent:
φ(x) =
sgn(x) |x| ≥ λ
tanh(x/λ) |x| < λ
(15)
iii. Piecewise linear approximation of Hyperbolic Tangent:
In piecewise linear approximation, for all iteration the
function φ{(x); iter} can be written as
φ(x) =
sgn(x) |x| ≥ λ
x/λ |x| < λ
(16)
The nonlinear parameter λ is selected such that minimum BER
can be obtained for iterated IC process. Here in SDSub-PIC
technique, we have considered piecewise linear approximation
of Hyperbolic Tangent [3] as a nonlinear function of soft
decision IC process. In the last stage of iteration, the ﬁnal
decision is made by hard detector, ˆak[n] = sgn{Yk − ˆIiter
k }.
IV. SIMULATION RESULTS
In this section we present the BER performance results
of the SDSub-PIC scheme for CI/MC-CDMA system under
different conditions (λ, N, number of iterations, and loading
conditions) using Monte Carlo simulation. The simulations
have been carried out in MATLAB. We have assumed syn-
chronous uplink transmission with BPSK modulation.
1 2 3 4 5 6 7 8 9 10
10
−5
10
−4
10
−3
10
−2
10
−1
SNR (in dB)
BER
Single User Bound
2.0N λ=0.9
2.0N λ=0.7
1.5N λ=0.4
1.5N λ=0.7
Fig. 1. Performance of the SDSub-PIC with different λ value after 8th
iteration with subcarrier (N) = 64
1 2 3 4 5 6 7 8 9 10
10
−4
10
−3
10
−2
10
−1
SNR (in dB)
BER
Single User Bound
2.0N (N=64) after 3
rd
iteration
2.0N (N=64) after 8
th
iteration
2.0N (N=64) after 10
th
iteration
Fig. 2. Performance of the SDSub-PIC with different iteration for 2N system;
subcarrier (N) = 64, and λ = 0.7
A. Simulation for getting optimum value of λ and number of
iterations
Fig. 1 shows the performance of SDSub-PIC with different
λ values (soft decision parameter (16) after 8th
iteration.
2N and 1.5N overloaded systems are being analyzed with
subcarrier N = 64. In the simulation, we have kept same
value of λ in all iteration. From the ﬁgure it can be said
that if we take λ = 0.7 then it gives better performance
compared to other λ values. So, we have taken λ = 0.7
for the soft decision parameter. Fig. 2 and 3 represent BER
performance after different iteration for 2N and 1.5N system.
This performance shows that if we increase the number of
iteration, BER performance improves. As iteration increases
the estimated MAI becomes more closer to actual MAI so
the residual part of MAI (Ik − ˆIiter
k ) becomes less and the
subtraction of estimated MAI provides improvement in BER.
After a certain number of iteration, we see that performance
770
4.
1 2 3 4 5 6 7 8 9 10
10
−5
10
−4
10
−3
10
−2
10
−1
SNR (in dB)
BER
Single User Bound
1.5N (N=64) after 4
th
iteration
1.5N (N=64) after 8
th
iteration
1.5N (N=64) after 10
th
iteration
Fig. 3. Performance of the SDSub-PIC with different iteration for 1.5N
system; subcarrier (N) = 64, and λ = 0.7
does not improve by increasing the number of iteration. The
residual part can not be removed further by using this type
of iterative interference cancellation process. From the ﬁgure
we observe that there is a BER improvement when number of
iteration is increased from 3 to 8 (Fig. 2) and 4 to 8 (Fig. 3) in
case of 2N and 1.5N respectively. So, we have taken number
of iteration as 8 so that lowest BER performance is achieved.
The system is tested at 100% overloading, so it is quite obvious
that it can ensure acceptable BER at lower loading conditions.
B. Comparison of Block-PIC and Sub-PIC with SDSub-PIC
1 2 3 4 5 6 7 8 9 10
10
−4
10
−3
10
−2
10
−1
SNR (in dB)
BER
Single User Bound
Block PIC [14]
Sub−PIC [15]
SDSub−PIC
Fig. 4. Comparison of SDSub-PIC with Sub-PIC and BlockPIC with
subcarrier = 64 for 2N system
Other PIC techniques like Block PIC [14], Sub-PIC [15]
have been compared with the proposed SDSub-PIC scheme
in Fig. 4 and 5. Those ﬁgures illustrate the comparison of
other two schemes with SDSub-PIC. We have considered λ =
0.7 and 8 iteration. In Sub-PIC the MAI is cancelled out at
1 2 3 4 5 6 7 8 9 10
10
−5
10
−4
10
−3
10
−2
10
−1
SNR (in dB)
BER
Single User Bound
Block PIC [14]
Sub−PIC [15]
SDSub−PIC
Fig. 5. Comparison of SDSub-PIC with Sub-PIC and BlockPIC with
subcarrier = 64 for 1.5N system
subcarrier level before taking the ﬁnal decision. This scheme
offers improvement over Block-PIC [14]. We have shown that
SDSub-PIC offers better BER performance than hard decision
based Sub-PIC. In SDSub-PIC, soft decision is involved for
the interference cancellation process. This technique ensures
BER of the order 5e-04 at 10 dB SNR with N = 64 subcarrier
for 128 users (i.e., 100% overloaded system). In Sub-PIC,
we observed that BER is 3e-03 at 10 dB SNR. Fig. 5 shows
that if we reduce the overloading to 1.5N, BER performance
improves considerably compared to other two schemes. Here
we obtained a BER of 1e-04 at 10 dB SNR with SDSub-
PIC. So, this technique can be utilized for high data rate
communication with some penalty in SNR (∼1.5 dB). For
Block-PIC BER is about 5.5e-03 for 2N system and 4.5e-
03 for 1.5N system. In case of SDSub-PIC the BER goes
down from 5e-04 (2N) to 1e-04 (1.5N) at 10 dB SNR with
subcarrier (N) = 64. It is also observed that Sub-PIC and
Block-PIC result a bit error ﬂoor.
C. Different loading condition
In real time communication, it is desirable to make cellular
system overloaded. The system is said to be more bandwidth
efﬁcient when it can handle extra active simultaneous users
with a desirable BER performance. When the active user gets
reduced (i.e., 1.2N, 1.4N system), it is interesting to observe
that (Fig. 6), system performance is closer to single user
bound.
D. Performance in frequency selective channel
We have also considered slow frequency selective Rayleigh
fading chananel with four-fold diversity [14] for subcarrier
(N) = 64 and 128 users (K). In the Fig. 7, we have shown
the performance comparision among Block PIC [14], Sub-PIC
[15], and proposed SDSub-PIC technique. In Block PIC [14]
BER is 6e-04 at 25 dB SNR after 10th
iteration. We can get
BER of 3e-04 using Sub-PIC [15] after 10th
iteration. It is
771
5.
1 2 3 4 5 6 7 8 9 10
10
−5
10
−4
10
−3
10
−2
10
−1
SNR (in dB)
BER
Single User Bound
2.0N
1.5N
1.4N
1.2N
Fig. 6. Different loading condition with subcarrier = 64, λ = 0.7, after 8th
iteration
5 10 15 20 25
10
−5
10
−4
10
−3
10
−2
10
−1
SNR (in dB)
BER
Single User Bound
Block PIC [14]
Sub−PIC [15]
SDSub−PIC
Fig. 7. Comparison of SDSub-PIC (After 8th iteration) with Sub-PIC (After
10th iteration) and BlockPIC (After 10th iteration) with subcarrier = 64
for 2N system with four-fold diversity in slow frequency selective Rayleigh
fading chananel
interesting to observe that (Fig. 7), the SDSub-PIC performs
considerably better than other two interference techniques.
In case of SDSub-PIC, BER of 4e-05 is obtained after 8th
iterations only at 25 dB of SNR. So, it is clear that, SDSub-
PIC scheme performs better than other two schemes even on
slow frequency selective channel.
E. Multirate Transmission and Peak-to-average power ratio
(PAPR)
Modern digital communication needs multimedia transmis-
sion. For this type of transmission, users have to transmit data
simultaneously at different data rates depending upon voice,
video or multimedia data. So, multiple access schemes like
CDMA should be able to support multimedia communication.
CI/MC-CDMA system can be designed to support ‘N’ high
data rate users with ‘N’ subcarriers each and lesser number
1 2 3 4 5 6 7 8 9 10
10
−5
10
−4
10
−3
10
−2
10
−1
SNR (in dB)
BER
Single User Bound
2.0N (64 HDR + 32x2 LoDR)
1.4N (64 HDR + 13x2 LoDR)
1.2N (64 HDR + 6x2 LoDR)
Fig. 8. Performance of SDSub-PIC in multirate transmission after 8th
iteration, subcarrier (N) = 64, λ = 0.7 in AWGN channel
10 15 20 25 30 35
10
−15
10
−10
10
−5
10
0
PAPR (in dB)
ProbabilityofPAPR
conventional
Partition(all PO−CI Shift π/N)
Partition(osc π/N, esc π/2N)
Partition(osc π/2N, esc π/N )
Proposed phase shift
Fig. 9. Complementary cumulative distribution of PAPR for 2N system with
N = 64
of subcarriers to low data rate users. In this paper, the
implementation is done by allocating all sub-carriers to the
users who transmit high-data-rate (HDR) and alternate odd
and even subcarriers are assigned to the other set of users
who need to transmit at low data-rate (LoDR). The usage of
alternate sub-carriers suggests to split CI codes in odd and
even parts leading to increase in capacity. Fig. 8 illustrates the
BER performance of three multirate systems where N users
transmit at high data rate with N = 64 available subcarrier. For
1.2N multirate system, the BER is 3.7e-05 after 8th
iteration
at 10 dB SNR which is 1 dB away from single user permance
in an AWGN channel.
Multicarrier systems, like OFDM and MC-CDMA, support
high data rate transmission with an increased peak-to-average
power ratio (PAPR). In multicarrier transmission, when the
subcarriers are superimposed in same phase, then probability
of getting high PAPR becomes more. PAPR not only affects
772
6.
the power ampliﬁer at transmitter section, it also deteriorates
BER performance. The transmitted signals get distorted due
to high PAPR. Further, the information signal is lost due to
the non-linear operation of power ampliﬁer. Here, reduction
in PAPR value is achieved through the phase shift of even
CI code using odd sub-carriers by an amount of π/2 and
odd CI code using even sub-carriers by −π/2, all measured
with respect to the orthogonal codes supporting high data rate
transmission. From the Fig. 9 it is observed that the proposed
system also ensures low probabilty of PAPR, which reduces
the effect of power ampliﬁer. So, in our proposed CI/MC-
CDMA system it is clear that the probability of high PAPR
becomes less compared to other schemes [14].
F. Complexity
Conventional PIC has the complexity of O(2N-1) for ‘N’
length of CI code. In case of Block-PIC [14], the complexity
reduces to 2O(N). Our proposed SDSub-PIC provides consid-
erably better BER performance at complexity of O(N) which
is much lower than other two previous schemes.
V. CONCLUSION
In this paper, a new soft decision based subcarrier PIC
scheme has been introduced for CI/MC-CDMA system. We
have observed that the SNR penalty is about 1.6 dB at a BER
of 1e-04 with proposed SDSub-PIC scheme for N = 64 and
96 users in an AWGN channel. In slow frequency selective
Rayleigh fading channel, SDSub-PIC ensures a BER of 4e-05
at 25 dB SNR with four-fold diversity at 100% overloading.
Block PIC [14] and Sub-PIC [15] result in a BER of 6e-
04 and 3e-04 respectively after 10th
iteration at 25 dB of
SNR. Hence, the proposed receiver scheme provides improved
BER performance with less complexity. It will be interesting
to evaluate the performance of this scheme under non ideal
channel conditions. The SNR penalty can be reduced further
by using suitable error correcting codes.
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