International Journal of Advanced Research in Electronics and Communication Engineering (IJARECE)
Volume 3, Issue 2, February 2014
203
ISSN: 2278 – 909X All Rights Reserved © 2014 IJARECE
Abstract— MC-CDMA is the most promising technique for
high bit rate and high capacity transmission in wireless
communication.Multicarrier code-division multiple-access
(MCCDMA) system performance can severely be degraded by
multiaccess interference (MAI) due to the carrier frequency
offset (CFO). We argue that MAI can more easily be reduced
by employing complex carrier interferometry (CI) codes. We
consider the scenario with spread gain N, multipath length L,
and N users, i.e.,a fully loaded system. It is proved that, when CI codes are used, each user only needs to combat 2(L − 1) (rather than N − 1) interferers, even in the presence of CFO. It
is shown that this property of MC-CDMA with CI codes in a
CFO channel can be exploited to simplify three multiuser
detectors, namely, parallel interference cancellation (PIC),
maximum-likelihood, and decorrelating multiuser detectors.
The bit-error probability (BEP) for MC-CDMA with binary
phase-shift keying (BPSK) modulation and single-stage PIC
and an upper bound for the minimum error probability are
derived. Finally, simulation results are given to corroborate
theoretical results. Index Terms— Multi-carrier code division multiple access
(MCCDMA), Multiple access interference (MAI).
I. INTRODUCTION
MULTICARRIER code-division multiple access
(MCCDMA) has emerged as a promising multi-access
technique [2, 3].Multicarrier systems like CDMA and
OFDM are now days being implemented commonly. MC-
CDMA (or OFDM-CDMA) multiple access has become a
most likely technique for future generation broadband
wireless communication system such as 4G. This scheme is
a combination of both OFDM and CDMA that can provide
protection against frequency selective fading and time
dispersion. The CDMA part of this scheme provides
multiple access ability as well as spread each user signal
over the frequency domain to reduce the impact of frequency selective fading. On the other hand OFDM
provides spreading across time domain of each spreading
code’s chip which reduces the impact of inter-symbol
interference. This achieves in fulfilment of high data rate
transmission, so the number of subcarrier and spreading
codes must be carefully selected according to worst channel
conditions [1][2].
.
Biru S. Bhanvase, Department of Electronic&Telecommunication,
Mumbai University/Ramrao Adik institute of technology college,
Mumbai, India, Mobile No-9029287647
Bipeen B. patil, Department of Electronic&Telecommunication ,
Mumbai University / Ramrao Adik institute of technology College,
Kolhapur, India, Mobile No7709724988.
V.R.Dahake, Department of Electronic&Telecommunication ,
Mumbai University / Ramrao Adik institute of technology , Mumbai,,
India, Phone Mobile No.,9220803271.
Although MC-CDMA is a powerful multiple access
technique but it is not problem free. MC-CDMA is
inherently more robust to inter symbol interference (ISI) than conventional CDMA system due to the use of the
OFDM (Orthogonal Frequency Division Multiplexing)
structure. Furthermore, the full diversity gain can be
achieved if the maximum ratio combining (MRC) is used in
MC-CDMA. However, the multipath and/or the carrier
frequency offset (CFO) effects tend to destroy orthogonality
among users and lead to MAI. Thus, the performance of
MC-CDMA can be greatly degraded. Therefore it is
desirable to reduce MAI by means of MAI reduction
schemes. There are number of proposed technique that is
capable of reducing MAI for DS-CDMA system. These technique involve mainly the application of optimal
spreading sequence, multiuser detection and multiuser
detection. There has been research on MAI suppression
using single user detection (SUD) techniques. For example,
the structural differences of interfering users caused by CFO
were exploited at the receiver to suppress MAI in
[4].However, this MAI suppression technique imposes a
computational burden on the receiver since a discrete
Fourier transform (DFT) of size larger than N is required
due to the oversampling of the received signal in the
frequency domain. Another way to reduce MAI is achieved
by code design while keeping the structure of MCCDMA unchanged [5]. In [5], a code-design method based on real
Hadamard–Walsh (HW) codes was proposed and shown to
achieve zero MAI in a multipath environment in MC-
CDMA. However, not all users can enjoy MAI-free
communications with this design. In addition, suppression of
the MAI due to the CFO effect was not considered in this
paper. Multiuser detection (MUD) [6] or related signal-
processing techniques have been developed to mitigate
MAI. However, their complexity is usually high, and this
imposes a computational burden on the receiver. Moreover,
the channel information is needed for the application of the MUD scheme so that effective channel estimation plays an
essential role in the system [7]. Recently, multicarrier
CDMA (MC-CDMA) has been proposed as a promising
multiaccess technique. MC-CDMA systems can be divided
into two types [2]. For the first type, one symbol is
transmitted per time slot. The input symbol is spread into
several chips, which are then allocated to different
subchannels. The number of subchannels is equal to the
number of chips [8], [9]. For the second type, a vector of
symbols is formed via the serial-to-parallel conversion, and
each symbol is spread into several chips. The chips
corresponding to the same symbol are allocated to the same subchannel [10], which is often called MC-DS CDMA.
When compared with conventional CDMA systems, MC-
CDMA can combat intersymbol interference (ISI) more
Multiaccess Interference Reduction Technique For MC-CDMA
With Carrier Frequency Offsets By Carrier Interferomatory code
Biru S. Bhanvase, Bipeen B. Patil, V.R. Dahake
International Journal of Advanced Research in Electronics and Communication Engineering (IJARECE)
Volume 3, Issue 2, February 2014
204
ISSN: 2278 – 909X All Rights Reserved © 2014 IJARECE
effectively. Moreover, the frequency diversity gain can be
fully exploited if the maximum ratio combing (MRC)
technique [2], is used at the receiver in MC-CDMA systems.
Despite the above advantages, the performance of MC-
CDMA systems is still limited by MAI in a multipath
environment. Even though MAI can be reduced by MUD [6]
and other signal-processing [10] techniques, the diversity
Fig. 1. Block diagram of the uplink transmission of the ith user in an MC-CDMA system
gain provided by multipath channels could be sacrificed
since the received chips are no longer optimally combined
channel estimation is under MRC. Furthermore, channel
status information is needed for MRC and MUD. In a
multiuser environment, multiuser more complicated and its.
accuracy degrades as the number of users increases, which
will in turn degrade the system performance In this paper,
we approach the MAI reduction problem for MC-CDMA systems from another angle. That is, we investigate a novel
way to select a set of ―good‖ spreading codes so as to
completely eliminate the MAI effect while keeping the
transceiver structure simple and the computational burden
low. Some earlier work has been done along this direction.
For conventional CDMA systems, Scaglione et al. [11] used
a code to reduce MAI in a multipath environment. However,
since the performance curves in [11] have a slope similar to
the orthogonal frequency-division multiple-access
(OFDMA) system, this code design does not offer a full
diversity gain. Oppermann et al. [12] examined several code
sequences and selected some code words to reduce MAI by experiments with little theoretical explanation of the MAI
reduction performance. Chen et al. [13] proposed a code
scheme based on the complementary code to achieve an
MAI-free CDMA system in a flat fading channel. Even
though the number of supportable users is much less than
the codeword length, this scheme can achieve higher
spectrum efficiency than conventional CDMA system with a
successive transmitting structure. In a multipath
environment, this scheme is no longer MAI-free, and a
recursive receiver structure is demanded for symbol
detection. A large-area synchronized (LAS) code was proposed by LinkAir and was examined in [14] to design a
code that has an area with zero off-peak autocorrelation and
zero cross correlation for CDMA. This code scheme has
zero ISI and MAI in a multipath environment. The number
of supportable users to achieve ISI- and MAI-free
conditions depends on the multipath length. The LAS code
is generalized to MC-DS-CDMA systems in [15]. As for
MC-CDMA systems, Shi and Latva-aho [20] proposed a
code scheme for downlink MC-CDMA with little theoretical
analysis. Moreover, this scheme is not optimal in
minimizing the bit error probability in both uplink and downlink directions. Cai et al. [4] proposed a group-
orthogonal (GO-) MC-CDMA scheme. By assigning only
one user to each group, this scheme can be MAI-free and
with a maximum channel diversity gain. Moreover, in a
heavily loaded situation, the required computation for MUD
to achieve the MAI-free property is small. However, in a
CFO environment which causes MAI, relatively
complicated multiuser CFO estimation methodology is
demanded to estimate every user’s CFO.
In this paper, we discuss the various MAI reduction technique.
II. SYSTEM MODEL
Suppose that there are T users in an MC-CDMA system.
The block diagram of the uplink transmission of the ith user
is shown in Fig. 1. As shown in the figure, symbol xi is
spread by N code words in the frequency domain to yield an
N × 1 vector:
𝑦𝑖 𝑘 = 𝑤𝑖[𝑘]𝑥𝑖 0 ≤ k ≤ N− 1
(1)
Where wi[k] is the kth component of the ith orthogonal code.
The spreading code of a user is the same along time. The
resulting block of length N is passed through an N × N IDFT
matrix. After the parallel-to-serial conversion, a cyclic prefix is added to mitigate ISI. Then, symbols are fed into
the multiple access channels. Since the uplink scenario is
considered, it is reasonable to assume that each user
experiences a different fading channel with a different
amount of CFO.
At the receiver, the cyclic prefix is removed. After the
serialto-parallel conversion, the block is passed through the
N×N DFT matrix. The kth component of the DFT output, ŷ,
can be expressed by
ŷ = 𝑟𝑗 [𝑘] + 𝑛[𝑘]
𝑇−1
𝑗=0
(2)
where n[k] is the DFT of additive noise, and rj [k] is the received signal contributed from the jth user due to the
channel fading and CFO effects. Suppose that user j has a
normalized CFO ∈ 𝑗 , i.e. the actual CFO normalized to the
subcarrier spacing. rj [k] can be written as [16], [17]
International Journal of Advanced Research in Electronics and Communication Engineering (IJARECE)
Volume 3, Issue 2, February 2014
205
ISSN: 2278 – 909X All Rights Reserved © 2014 IJARECE
𝑟𝑗 [𝑘]=𝛼𝑗 ⋋𝑗 [𝑘]𝑦𝑗 [𝑘] + 𝛽𝑗 ⋋𝑗 𝑚 𝑦𝑗 𝑚 𝑔𝑗 [𝑚 −𝑁−1
𝑚=0,𝑚≠𝑘
𝑘]
(3)
where⋋j [m] is the mth component of N-point DFT of the
Channel impulse response of user j, and
𝛼𝑗 = sin𝜋𝜖𝑗
𝑁 sin𝜋𝜖𝑗
𝑁
𝑒𝑗𝜋 𝜖𝑗𝑁 − 1
𝑁
𝛽𝑗 = sin(𝜋𝜖𝑗 ) 𝑒𝑗𝜋 𝜖
𝑗𝑁−1𝑁
𝑔𝑗 [𝑚 − 𝑘]= 𝑒
−𝑗𝜋𝑚−𝑘
𝑁
𝑁 sin𝜋(𝑚 −𝑘+𝜖𝑗 )
𝑁
Note that, when there is no CFO, i.e. ∈ 𝑗 = 0. rj [k] =⋋j[k]yj
[k]. However, in the presence of CFO, there are two terms.
The first term is ⋋j[k]yj [k] distorted by 𝛼𝑗 and the second
term is the ICI caused by CFO. Finally, the ith transmitted
symbol is detected by multiplying the received symbol ŷ[k]
of user i by 𝑤𝑖∗ [k] and performing MRC on ŷ[k] 𝑤𝑖
∗[k], i.e.,
𝑥𝑖 = ŷ 𝑘 ⋋𝑖∗ 𝑘 𝑤𝑖
∗[𝑘]
𝑁−1
𝑘=0
= 𝑠𝑖 + 𝑀𝐴𝐼𝑖←𝑗𝑘−1𝑗 =0,𝑗≠𝑖 + 𝑛[𝑘] ⋋𝑖
∗𝑁−1𝑘=0 𝑘 𝑤𝑖
∗ 𝑘
(4)
where si consists of the distorted chip and the ICI caused by
CFO for the desired user given by
𝑠𝑖 = 𝑟𝑖[𝑘] ⋋𝑖∗
𝑁−1
𝑘=0
𝑘 𝑤𝑖∗[𝑘]
(5)
and 𝑀𝐴𝐼𝑖←𝑗 is the MAI of user i due to the jth user’s CFO
𝑀𝐴𝐼𝑖←𝑗 = 𝑟𝑗 𝑘 ⋋𝑖∗ 𝑘 𝑤𝑖
∗[𝑘]
𝑁−1
𝑘=0
(6)
Using Eqs. (3) and (6), we can show that the MAI term is
given by
𝑀𝐴𝐼𝑖←𝑗 = 𝑀𝐴𝐼𝑖←𝑗(0)
+ 𝑀𝐴𝐼𝑖←𝑗(1)
(7)
Where
(8)
and
(9)
Eq. (8) can be expressed in matrix form as [6]
(10)
Where
and
and where F is the N×N DFT matrix whose element at the
kth row and the nth column is [𝐹]𝑘 ,𝑛 =1
𝑁𝑒−𝑗 𝑘𝑛𝑁
2𝜋 Also, † in
Eq. (10) denotes the matrix Hermitian operation. It was
shown in [6] that 𝑀𝐴𝐼𝑖←𝑗(1)
given by (9) can be rewritten as
(11)
where
(12)
International Journal of Advanced Research in Electronics and Communication Engineering (IJARECE)
Volume 3, Issue 2, February 2014
206
ISSN: 2278 – 909X All Rights Reserved © 2014 IJARECE
(13)
and
(14)
III. ORTHOGONAL CODES FOR
MULTIACCESSINTERFERENCE-FREE
MULTICARRIER CODE-DIVISION MULTIPLE ACCESS
WITH CARRIER FREQUENCY OFFSET
A. Requirements on MAI-Free Codes
Theoretical requirements on codes to produce MAI-free
MC-CDMA system in the presence of CFO are implied by
(4). That is, to have zero MAI in a frequency-selective
channel with CFO, we demand 𝑀𝐴𝐼𝐼←𝐽=0. Define
(15)
It is well known that D𝑖𝑗(𝑝)
is a circulant matrix [9]. N-point
inverse DFT (IDFT) of ri,j(p)
, where 𝑟𝑖 ,𝑗
𝑝 =𝑤𝑖
(𝑝)[k]𝑤𝑗
∗[k].and
𝑤𝑖(𝑝)
[k]=𝑤𝑖[(N-p+k)],for k=0,1….
N-1 where ((n))N denotes n modulo N. It was shown in [19]
that condition MAIi←j = 0 is equivalent to
(16)
B. CI Orthogonal Codes
In this section, we study the CI codes of size N, which is of
the following form:
𝑤𝑖 𝑘 = 𝑒 𝑗2𝜋
𝑁𝑘𝑖
, 𝑘, 𝑖 = 0,1, … . , 𝑁 − 1 [17]
Then, the MAI-free property of this code can be stated as
follows.
Theorem 1: Let the channel length be 𝐿, and let G = 2q ≥L.
There exist N/G CI codewords such that the corresponding
MC-CDMA is MAI free in a CFO environment. Theorem 2 : For an MC-CDMA system in a CFO
environment consisting of N active users with CI codes, if L ≤ N/2, each user has 2(L − 1) interfering users only.
IV.REDUCED-COMPLEXITY PARALLEL INTERFERENCE
CANCELLATION FOR CARRIER INTERFEROMETRY
MULTICARRIER CODE-DIVISION MULTIPLE ACCESS
The receiver for the𝑖𝑡ℎ user in an MC-CDMA system with
PIC is depicted in Fig. 2. It is assumed that the exact
knowledge of channel gains and CFO values of all users is available in the receiver. First, initial bit estimates for all
users are derived from the SUD receivers, which is basically
the same as that depicted in Fig. 1. We call this stage as
stage 0 of the PIC detector and denote detected symbols
by𝑥 0𝑖 , 𝑖 = 0, … , 𝐾 − 1. Let and . From (3)–(9) and (12), we
can express the detected symbol for user i at the zeroth stage
of PIC as
(18)
Where
and 𝑛𝑖 = 𝑛 𝑘 ⋋𝑖
∗ 𝐾 𝑊𝑖∗[𝐾]𝑁−1
𝐾=0 . Tentative hard
decisions are made on 𝑥 0𝑗 , 𝑗 = 1,2, … . 𝐾,𝑗 ≠ 𝑖, to produce
initial bit estimates, namely, 𝑠𝑔𝑛[ℜ{𝑥 0𝑗 }]. Then, theMAI
estimate for the desired user i is generated and subsequently
subtracted from its received signal𝑦 . The new detected
symbol at stage 1 of the PIC detector is given by
(19)
We know from Theorem 2 and its corollary that, if
MCCDMA employs CI codes in fading and CFO
environments with multipath length L, every user only has
2(L − 1) interferers. Hence, the PIC complexity with CI
codes linearly increases with 2L − 1 instead of N. Since L N, in practice, this implies huge savings in the
computational cost by employing the CI codes in association
with the PIC detector.
If a correct decision is made on a particular interferer’s bit,
the interference from that user to the ith user can completely
be cancelled. On the other hand, if an incorrect decision is
made, the interference from that user will be enhanced
rather than cancelled. By substituting 𝑥 0𝑖 from (23) in (24),
we obtain
International Journal of Advanced Research in Electronics and Communication Engineering (IJARECE)
Volume 3, Issue 2, February 2014
207
ISSN: 2278 – 909X All Rights Reserved © 2014 IJARECE
(20)
If 𝑥𝑗 is a binary phase-shift keying (BPSK) symbol, 𝑥𝑗 −
𝑠𝑔𝑛[ℜ{𝑥 0𝑗 }] is a three-valued random variable (0, 2, −2)
whose magnitude represents whether a tentative decision is
correctly made on the 𝑗𝑡ℎ user’s bit at the previous stage. It
can easily be shown that, given ⋋𝑖 , 𝑛𝑖 is a circularly
symmetric zero-mean Gaussian random variable with
variance equal to𝜎2 ⋋𝑖 [𝑘] 2𝑁−1𝑘=0 . The random vector ⋋𝑖
consists of N correlated Rayleigh random variables. In other
words, ⋋𝑖 is a multivariate Gaussian random vector with
zero mean and covariance matrix 𝑅𝑖 whose elements are
given by
Fig. 2. MCCDMA receiver with single stage PIC for the ith user
The probability of error for user i at state 0 of the
PICdetector using (23) can be written as
(22)
IV. SIMULATION RESULTS
The Monte Carlo simulation was conducted to corroborate
the theoretical results derived in the previous sections. In the
simulation, channel taps were generated as independent
identically distributed random variables with zero mean and
unit variance. Every user had his/her own CFO value. To compute the analytical BEP, the Monte Carlo integration
method was used [18]. That is, random variables λi[k], k = 0,
1, . . .,N − 1 are generated by taking the DFT of complex
Gaussian-distributed channel taps M times. Then, computer
generated samples of λi[k], k = 0, 1, . . .,N − 1 are
substituted in the Q-function, and the sum of trials is divided
by M.
Example 1: Theoretical Versus Simulated BEP of Fully
Loaded MC-CDMA With Single-Stage PIC: In this example,
we evaluate the BEP performance of MC-CDMA with PIC
in the presence of CFO and examine both analytical and
simulated BEP results.We employ two orthogonal codes,
namely, orthogonal HW codes and CI codes. Fig. 6 depicts
the analytical and simulated BEP results for a fully loaded
MC-CDMA system with CI and HW codewords as a
function of the SNR value Eb/N0 under the setting of N = 16, L = 2, K = 16, and CFO = ±0.1. To shorten the simulation
time, only the BEP results for the first users were compared.
Since L = 2, we can use (22) as the analytical BEP
expressions of CI-MCCDMA. For this case, we observe
close agreement between the analytical BEP expression and
simulation results. For MCCDMA with HW codes, the
approximate BEP expression, as shown in (21), was used.
Due to a higher number of interfering users employing HW
codes, the analytical Gaussian model for the total residual
user interference can be used. However, the analytical and
simulation results for HW codes (the last two curves in the
figure) do not have strong agreement, particularly in the high-SNR regime, as shown in Fig.3.
International Journal of Advanced Research in Electronics and Communication Engineering (IJARECE)
Volume 3, Issue 2, February 2014
208
ISSN: 2278 – 909X All Rights Reserved © 2014 IJARECE
Fig. 3. Analytical and simulated BEP results versus Eb/N0
with N = 16, L = 2, and CFO = ±0.1.
. Example 2: ML-MUD BEP Versus Minimum Probability of Error: Fig. 4 shows the upper bound to the BEP as a
function of the SNR value Eb/N0 for CI-MC-CDMA under
the setting of N = 8, L = 2, and K=8 for both zero CFO and
CFO=±0.3 cases. The upper bound curves in each case are
plotted against their corresponding simulated BEP. To
obtain the simulated BEP,𝑁𝑟𝑜𝑢𝑛𝑑 = 1.5 and Δ = 2 for zero
CFO, and 𝑁𝑟𝑜𝑢𝑛𝑑 = 1.5 and Δ = 3 for nonzero CFO values.
To shorten the simulation and computation time, only the
BEP for the first user was computed. We can see close
agreement between the performance of the ML-MUD BEP
Fig. 4. Upper bound and simulation of the BEP for N = 8,
L = 2, and CFO = 0,±0.3.
and the upper bound for the minimum BEP. It is also clear
from the figure that ML-MUD performs better in the
absence of CFO than in the presence of CFO. This can be
explained by noting the fact that the denominator in (49) for
the upper bound on the minimum BEP with CFO
is 𝑒𝑇𝐻†𝐻 𝐻𝑒𝜎 , as opposed to just σ in the denominator of (23) for the upper bound on the minimum BEP with no CFO
Example 3—ML-MUD Performance: Fig. 5 shows a
significant performance improvement of the ML detector,
where the performance of CI-MC-CDMA with ML-MUD is
compared with CI-MC-CDMA with single-user MRC
detection. The parameters for the simulated CI-MC-CDMA
system were N = 16, L = 2, and K = 16. As compared with
Fig. 4 with N = 8, we can see that ML-MUD performs better
since there were more pair wise MAI-free users. Separate
simulations were performed to acquire the BEP performance
for CFO = 0 and CFO = ±0.3.We can see that the BEP achieved by ML for both systems is very low when the SNR
is close to 10 dB. Again, we can see that the performance of
ML-MUD is better with no CFO that in the presence of
CFO.
Fig. 5. ML-MUD BEP performance versus Eb/N0 with N = 16, L = 2,
and CFO = ±0.3.
Example 4—Decorrelating Detector Performance: Fig. 6
shows the theoretical and simulated BEP results as a
function of the SNR value𝐸𝑏 𝑁0 in the presence of CFO =
±0.5 with a decorrelating detector with N = 21, L = 4, and K
= 18. To shorten the simulation time, only the BEP for the
first user was computed. We can see that simulated and
analytical BEP results are in good agreement. The average
BEP performance of CI-MC-CDMA and with N = 16, L = 3,
and K = 14 is also shown in Fig. 9. We can see that, as the
number of users increases from 14 to 18, the BEP
performance degrades up to 2.5 dB for 𝐸𝑏 𝑁0 < 8dB and
around 5 dB for 𝐸𝑏 𝑁0 > 8dB.
Fig. 6. Analytical and simulated BER performance of the decorrelating
detector with the reduced-complexity Gaussian elimination algorithm for
MCCDMAwith CFO = ±0.5
International Journal of Advanced Research in Electronics and Communication Engineering (IJARECE)
Volume 3, Issue 2, February 2014
209
ISSN: 2278 – 909X All Rights Reserved © 2014 IJARECE
V.CONCLUSION
For an MC-CDMA system with spread gain N, multipath
length L, and N users, when CI codes are used, a proper
subset of CI codes leads to a completely MAI-free MC-CDMA system in a CFO environment and each user only
has to combat 2(L − 1) (rather than N − 1) interferers, even
in the presence of CFO. We analyzed the BEP of MC-
CDMA in a CFO environment with PIC, ML, and
decorrelating multiuser detectors. We also demonstrated that
the sparse cross-correlation matrix of the CI codes can be
used to considerably reduce the complexity of the
aforementioned multiuser detectors.
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