Multiaccess Interference Reduction Technique For MC-CDMA ...ijarece.org/wp-content/uploads/2014/02/IJARECE-VOL-3-ISSUE-2-203... · Index Terms— Multi-carrier code division multiple

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



204


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]



205


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)



206


(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



207


(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.



208


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



209


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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