Adnan Ahmed Khan, Sajid Bashir, Syed Ismail Shah

IEEE --- 2005 International Conference on Emerging Technologies 

September 17-18, Islamabad 

Adnan Ahmed Khan 

Centre for Advanced Studies in 

Engineering, Islamabad. 

adkhan100@gmail.com 

Sajid Bashir 

Centre for Advanced Studies in 

Engineering, Islamabad. 

sajidbashir.1@gmail.com 

Syed Ismail Shah 

Iqra University 

Islamabad Campus. 

syedismailshah@gmail.com 

Abstract 

Multiple Access Interference (MAI) is the most 

significant limiting factor on the capacity of the 

conventional DS-CDMA systems. In this paper an analysis 

of the character of MAI is carried out. The main causes of 

intra-cell MAI and their effects on the system are 

highlighted through simulation and analysis. A 

considerable research effort in the development of 

efficient Multiple User Detection (MUD) techniques is in 

progress, however no concrete analysis of MAI and its 

character modeling is found in the literature. In this paper 

numerous factors which result in MAI enhancement like 

asynchronous reverse channel, semi-orthogonal long PN 

codes and increase in users are analyzed. This 

quantification of MAI character will result in its clearer 

understanding and will lead to a more realistic and 

efficient MUD algorithms. 

1. Introduction 

Frequency spectrum is one of the most precious 

resources. Efforts are directed towards its efficient 

utilization. Spread spectrum systems serve this goal and 

have, therefore, received considerable attention during 

recent years [1]. Total capacity increase of a spread 

spectrum communications system can be over 10-fold in 

cellular mobile telephone applications compared with the 

narrowband frequency-division multiple-access (FDMA) 

systems [2]. 

In direct sequence code division multiple access (DS- 

CDMA) spreading codes are used for channelization of 

users. When the DS-CDMA system can be guaranteed to 

be synchronous it is preferable to use orthogonal sequences 

(Walsh codes) for spreading in CDMA-2000 based 

systems orthogonal Walsh codes are used in the forward 

synchronous link. The reverse asynchronous link utilizes 

semi-orthogonal partial long PN codes with variable offset 

and spreading gain. These codes have larger cross 

correlation values when used in asynchronous environment 

where users are not time aligned [3,13]. This is really why 

Walsh codes are used in forward link while PN codes are 

used in the reverse link. In CDMA-2000 the long PN code 

used in reverse link has a length of 2 42 -1 = 4.4 x10 12 chips 

long and repeats after 41 days [4]. Each user generates its 

spreading code from a particular offset. The user data bits 

get spread with the segments of the running long PN 

sequence. The spreading of user bits with the PN code 

segments and the asynchronous channel leads to MAI in 

the reverse link. 

MAI is the interference between direct-sequence users, it 

limits the capacity and performance of DS-CDMA systems. 

The MAI caused by any one user is generally small, 

however with the increase in number of interferers or their 

powers, MAI becomes significant [13]. The knowledge of 

the partial-correlation properties of known PN sequences 

and their influence on system performance either on the bit 

error probability or on the signal-to-noise ratio is difficult 

but essential to analyze in order to mitigate MAI effects on 

system performance [5-12]. 

The first section of this paper illustrates the DS-CDMA 

system model. Section 3 elaborates the reasons of MAI. 

This section also highlights the main causes such as 

asynchronous reverse link, non-orthogonal PN codes, 

larger partial cross correlation, multipath and near far 

effects. Section 4 aims at quantifying these effects through 

simulations and analysis. Results that help in the 

understanding and characterization of MAI structure within 

a cell are also presented in this section. We conclude the 

paper in section 5. 

2. System Model 

The system model consists of N users transmitting BPSK 

signals to a single receiver. The individual user data is 

spread using a segment of the long PN code generated with 

a particular offset. The data signals d 1 (t), d 2 (t) up to d n (t) 

include the data symbols spread by the random sequences 

P 1 (t), P 2 (t) up to P n (t) as shown in Figure 1. The spreading 

sequences are periodic extension of single periods as 

shown below. 

N 

∑ 

Pi( t) 

= CimP( 

t − ( m −1) 

Tc) 

(1) 

M = 1 

Where C im is the m th chip of the spreading sequence, N is 

0-7803-9247-7/05/$20.00 ©2005 IEEE 

182



the spreading gain, P(t) is the chip pulse shape that is 

assumed to be rectangular for our simulations and Tc is the 

chip duration. 

The channel introduces delays τ to signals from different 

users. The signals also undergo fading before they are 

summed up and received by the system receiver. The 

received signal r(t) can be written as. 

r( t) 

= ∑ Ak( 

t −τ ) Pk( 

t −τ 

) dk( 

t −τ 

) + n( 

t) 

) (2) 

Where A k , P k and d k are the delayed amplitude, 

signature code waveform and data signal of the k th user 

respectively, n(t) 

is the Additive White Gaussian Noise 

(AWGN). 

and partial cross-correlation values of the spreading 

sequences. 

Partial cross-correlation values among the spreading 

sequences are dependent upon how much one symbol 

overlaps with the other symbol, which in turn depends 

upon the transmission instants of the individual users 

(which is a random) instant and their distances from the 

base station (channel delays). Interfering portions of two 

symbols from each interfering user can be thought of as 

just one symbol. For example, in figure 2, portions of S 21 

and S 22 that interfere with S 12 can be regarded as a single 

interfering symbol. Thus, with random spreading 

sequences, the asynchronous and the synchronous systems 

will exhibit the same average bit error rate. 

S11 S12 S13 

S21 S22 S23 

Figure 2. MAI for two asynchronous users. Each 

symbol from a user is affected by two different symbols 

from the other users. 

Figure 1. CDMA generic Reverse link model, 

demonstrating a typical CDMA transmitter and a 

channel. 

The spreading sequence for all the mobile users when 

time aligned correlate with each other to give the symbol 

period correlation matrix. 

Rij(t) = ∫ Pi(t)Pj(t) 

(3) 

Rij(t) is the element of symbol period correlation matrix 

in the i th row and j th column obtained by taking the inner 

product of the PN sequence of the i th user with that of the 

j th user. 

3.2 Effects of partial Correlation of PN Codes 

At present the DS-CDMA systems employ Single User 

Match Filter (SUMF) detection. The detection is 

performed by correlating a locally generated replica of the 

spreading sequence of the user of interest with the 

incoming signal, as shown in Figure 3. The correlation is 

performed over a symbol period and it is assumed that the 

symbol-long portion of the locally generated spreading 

sequence correlates weakly with the spreading sequences 

of the other users. 

3. MAI Reasons Analysis 

3.1 Effects due to Asynchronous Link 

The reverse link of DS-CDMA behaves asynchronously 

as the received symbols from different users are not 

aligned to a single time base [13]. In an asynchronous 

system, one symbol of each user is contaminated by at 

most two symbols of the other users. So an N-user system, 

there will be (N−1) interfering symbols in the synchronous 

case and up to 2(N−1) interfering symbols in the 

asynchronous case. Figure 2 shows the interfering symbols 

in an asynchronous system with two users. It should be 

noted that an increase in the number of interfering symbols 

from (N−1) to 2(N−1) does not imply an increase in MAI 

in an asynchronous system compared with the synchronous 

system, because the cross-correlation products are 

computed only over the overlapping portion of the 

symbols. MAI and the bit error probability in this case are 

dependent upon relative magnitudes of the received signals 

Figure 3. SUMF Receiver. A typical CDMA uplink 

model with distinct single user matched filters for N 

users. 

For a particular symbol, the output of the SUMF is given 

as 

∫ 

Yi (t) = r(t)P i(t) 

(4) 

symbol period 

Long PN sequences are based on the statistical quasiorthogonality. 

Since spreading segments are distinct for 

183



each consecutive data bit, the cross-correlation value 

changes from bit to bit. The correlation value depends on 

the partial cross correlation between long sequences. The 

absolute maximum partial cross-correlation value between 

two spreading segments is occasionally larger compared 

with the maximum periodic cross-correlation value of short 

CDMA sequences. However, the partial correlation value 

is a random variable with distribution similar to the sum of 

binary independent, identically distributed (iid.) variables 

[20]. The cross-correlation value between two spreading 

segments {x} and {y} of length N can be expressed with 

the aid of the Hamming distance between corresponding 

binary code words [7,12]. 

Cx, y = N − 2HD( 

x, 

y) 

(5) 

The absolute maximum periodic cross-correlation values 

for some well-known PN sequence families have been 

computed in [14-16]. However, the point of concern is that 

how the length of the long PN code segment affects the 

generation of MAI. It is obvious that as the number of 

chips in each bit is lowered according to systems spreading 

gain the magnitude of MAI increase correspondingly. This 

has been simulated and analyzed in the next section. 

3.3 Increasing users 

The effects due to increase in the number of direct 

sequence interfering users in understandable [6], however 

its quantification to characterize MAI pattern is essential. 

The cross correlation of each interfering users spreading 

sequence is amplified and added to give the resultant MAI 

for the reference user. Thus the increase in the number of 

interferers will increase MAI. The existing systems 

capacity can be enhanced by overcoming the MAI. In the 

next section we have analytically quantified the effects on 

MAI for a reference user with increasing systems load. The 

results are also confirmed through simulation in the last 

section. 

3.4 Multipath and Near far effects 

The power unbalance is yet another problem with DS- 

CDMA. If there are more than one active users, the 

transmitted power of the non-referenced users is 

suppressed by a factor dependent on the partial crosscorrelation 

between the code of the reference user and the 

code of the non-reference user. However when a nonreference 

user is closer to the receiver than the reference 

user, it is possible that the interference caused by this nonreference 

user has more power than the reference user. 

Therefore, only non-reference user will be received 

causing near far effect. 

When signals from multiple paths arrive at the receiver 

the fingers of rake receiver locks on to the best signals 

arriving through multipaths. The MAI from all the locked 

paths produces an additive effect. These effects on MAI 

due to power unbalance and multipath need to be analyzed 

which is done in subsequent section. 

4. Simulation Results Analysis and MAI 

Quantification 

4.1 Asynchronous channel 

The asynchronous nature of reverse link results in 

correlation of logically shifted PN codes, where the shift 

depends upon the difference between users transmission 

time measured in chip duration. In our simulation we have 

found the partial correlation of the users spreading 

sequences with respect to a reference user. The results 

shown in the figure 4 and figure 5 depict that with a fixed 

spreading gain (127 for simulation) for each user and 

keeping the PN offset an integer multiple of a reference 

value (255) the partial cross correlation achieves a 

deterministic pattern. The X-Axis shows the time 

difference in multiples of chip duration Tc between the 

transmission instants of any two users. Y-Axis shows the 

pattern that the partial cross correlation values will follow. 

The PN code with shift registers length 10, 15 and 20 

respectively are used. 

Let the PN offset be ‘K’ and spreading gain ‘S’ then the 

starting chip ‘C 1n ’ for the spreading code of n th user can be 

found by using Eq.(6) which gives the value of ‘i’ that 

determines ‘ Pi ’. ‘N’ is the index of user and varies from 

‘0’ to ‘maximum users -1’. 

i = (N + 1)* K where N ≥ 0 

(6) 

Long PN code is represented as. 

Pi = {P 1,P 2,........P k} 

(7) 

Now C 1n =P i , ‘i’ can vary from ‘1’ to ‘k’ the length of 

the long PN Code in chips. The length of patterns in figure 

5 and figure 6 is (2*S – 1) where the patterns in figure 5 

shows the variation of cross correlation when N ref > N async 

and the reference user transmission instant is before the 

interferer. Similarly the pattern in figure 5 shows the 

variations for N ref < N async and the reference user starts 

transmission before the interferer. The interesting 

observation is that this pattern remains the same for a given 

long PN Code, spreading gain and PN offset. Hence the 

max MAI which results from these cross correlation values 

at chip delay become deterministic. 

4.2 Integration over symbol period. 

The long PN sequences are designed to have balance, 

run, shift and add properties [4] which lead to a low partial 

cross correlation values. These properties are however lost 

when the length of the PN sequences are altered while 

selecting spreading sequences for different mobile users. 

The integration done in the receiver is at the symbol period 

Eq.(3) which includes the segment of the long PN sequence 

equal to the spreading gain. The autocorrelation of the 

spreading sequence is linearly related with its length 

whereas the cross correlation is a random quantity. The 

normalized cross correlation values for PN sequence for 

three different lengths is shown in figure 6. It can be 

inferred from the results that greater the length of PN 

184


sequence more stable is the correlation curve, whereas with 

shorter PN codes the MAI behavior becomes increasingly 

random. 

The soft decision at the end of the Matched Filter is also 

effected by the number of chips per symbol and it moves 

away from the correct symbol in the constellation diagram 

with decrease in number of chips per symbol as observed 

in figure 7. It can also be deduced that the longer the 

spreading sequence more is the error margin available 

hence reducing the effects of MAI. 

4.3 Number of users 

With the increase in number of users cumulative C x,y 

Eq.(5) increases the variation in MAI. Figure 8 and figure 

9 show the designed cross correlation values for a 

reference user with that of other users for with spreading 

gain of 64 chips figure 8 and spreading gain of 128 chips 

figure 9. The first value being the auto-correlation of the 

reference user’s spreading code with itself resulting in a 

peak. Rests of the values are the cross-correlations with the 

remaining users. The difference between the autocorrelation 

and cross correlation is the available margin for 

error. 

It can be seen that the cross-correlation values for 

different users may be positive or negative which depends 

upon the assigned spreading codes. In case of BPSK (the 

modulation technique for our simulation) the data bit may 

only invert the cross correlation. If data bit is ‘0’ the 

transmitted signal is the same assigned spreading code and 

for data bit ‘1’ the spreading code is inverted. This 

inversion modulation changes the polarity of the resulting 

cross correlation. Assuming each user transmits data bit ‘0’ 

the cross correlations at the receiver will be the same as 

that of the transmitter. In this case all those users having 

cross correlation in the same coordinates as the reference 

user will correlate constructively while the users from other 

half will correlate destructively. The available data for 

decision at the receiver is [6]. 

Y 

∑ 

= Akdk 

+ i, 

k + 1/ Tb 

n( 

t) 

gk( 

t dt 

k ) 

We can re-write this equation as. 

Y 

or 


∫ 

ρ (8) 

∑dnkAndn 

+ ∑ dmkAmdm 

+ 

= AkdK 

+ 

n 

k (9) 

MAI MAI + MAI 

k = n m 

(10) 

Where ‘n’ users correlate constructively and ‘m’ is the 

total number of users which correlate destructively. The 

MAI to be eliminated for getting correct decision is only 

MAI m i.e the destructive interference. In a constellation 

diagram for BPSK we have a single decision boundary for 

the two transmitted symbols. The users with MAI n that 

result in constructive interference will force the estimated 

symbol away from the decision boundary deep into the 

correct decision region. Whereas the users that result in 

MAI m will drag the decision out of the correct decision 

region. The identification of users causing destructive 

interference will not only reduce the complexity of the 

MUD algorithm but will also reduce the computational 

overheads. Figure 8 and 9 differentiates between the users 

causing the two types of MAI. The worst case scenario of 

MAI is seen when all the users are causing destructive 

interference as shown in figure 10 that depicts an increase 

in MAI with increase in the number of users. Where as for 

a practical scenario when random data is transmitted by 

each mobile user the behavior of MAI curve is not linear as 

observed earlier. 

The algorithm shown below, if used before MUD can be 

helpful in deciding weather MUD is indeed required or it 

can be avoid, thus reducing computational complexity of 

the system. When the two positive and negative MAIs are 

equal they cancel each others effects, therefore there is no 

need for MUD algorithm. In the second case the MUD will 

only be required when the destructive interference exceeds 

the constructive interference by a pre decided threshold. 

The threshold will be selected on the basis of the channel 

conditions, possible maximum users and partial crosscorrelation 

values of the spreading sequences. 

If 

MAIn = MAIm 

then 

MAI = 0,MUD_Algorithm_not_needed 

elseif 

Abs(MAIm) − Abs(MAIn) > Threshold 

then 

Need MUD_Algorithm 

4.4 Multipath and Near far effects. 

In multipath scenario the signal from reference user is 

received from different paths. The rake receiver resolves 

these signals from different paths and presents a stronger 

received signal. This increased amplitude ‘A k ’ reduces the 

impact of MAI in having a soft decision Eq.(8). Similarly 

in near far effect, the amplitude variations for the 

interfering user ‘Ai’ and reference user ‘A k ’ also effect the 

soft decision. The amplitudes of the received signals from 

different interfering mobile users result in cumulative MAI 

variations which effects the soft decision for the reference 

user as shown in Eq.(8). The cross correlation value 

is scaled by the amplitude of received signal for the i th 

interfering user Ai as given by the following relation. 

k th 

∑ 

MAI , 

k = i kAidi 

ρ 

i, k 

ρ (11) 

ρ i, k is the cross correlation of the PN sequences of the 

user (reference) with the i th user (interfering). While 

studying the effects of MAI we may ignore noise then 

Eq.(8) can be written as. 

Y k = ρ k, kAkdk 

+ ρi, 

kAidi 

(12) 

ρ 

Where k, k is the autocorrelation value for the reference 

user which is equal to the length of the spreading sequence 

185



‘L’. The normalized correlation results in the following 7. References 

relation. 

[1] W C Y. Lee, "Overview of cellular CDMA", IEEE 

Y k = Akdk 

+ (ρi,k/L)Aidi 

(13) Trans.Veh. Tech., vol. V T 4 , no. 2, pp. 291-302, May 1991. 

In case of BPSK the data results in change of the 

polarity without affecting the amplitudes. The case of 

destructive interfering user can be written as. 

Y 

k = Ak 

−(ρi,k/L)Ai 

(14) 

In our simulation the threshold for decision is Y k = 0. In 

the above scenario when the reference user transmits bit‘0’ 

the correct decision is for Y k > 0. The minimum amplitude 

for one interfering user that can results in incorrect 

decision is shown below, also verified in figure 11. 

Ai ( Ak * L) / ρi, 

k 

= (15) 

Figure 11 also illustrates the simulation results for 

multipath and near far effects. The effect on the energy 

available for soft decision with amplitude variations of 

interfering signal is also depicted. When the amplitude of 

the interfering user crosses certain level with reference to 

the user under detection the probability of correct decision 

minimizes. The spreading gain in our simulation is 255 and 

the normalized cross correlation values of the interfering 

users are 0.0745 and 0.0510. The curves cross the decision 

threshold at the minimum amplitude required for incorrect 

decision is evident from Eq.(15). The curve of the user 

with larger cross correlation has a steeper slope. This 

suggests that spreading sequences with smaller cross 

correlation values should be used in the system. 

5. Conclusion 

In this paper we have quantified the character of MAI 

with the aim to have a clear understanding of its behavior 

in an asynchronous channel. We quantified that the MAI 

behaves deterministically in asynchronous channel. 

Increase in the length of PN code segments and code itself 

results in a more stable MAI pattern. In addition we have 

showed that MUD algorithm is only required once the 

resultant MAI crosses a pre-defined threshold. The 

relationship amongst the signal amplitude and the 

spreading codes correlation has also been quantified. This 

analysis will help mitigating MAI effects and improving 

system capacity. These MAI parameters will also be 

helpful in reducing the complexity of MUD algorithms 

which will ultimately result in computationally efficient 

and fast converging MUD algorithms in DS-CDMA 

systems. 

6. Acknowledgement 

The authors acknowledge the enabling role of the Higher 

Education Commission Islamabad, Pakistan and appreciate 

its financial support through "Merit and Indigenous 

Scholarship Scheme for PhD Studies in Science and 

Technology ". 

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186

0 20 40 60 80 100 120 140 



20 

'N' REFERENCE USER > 'N' ASYNCRONOUS USER SPREADING GAIN =127 

PN SEQUENCE LENGTH = 1023 CHIPS 

PN OFFSET = 255 

VARIATION IN PN CROSS CORRELATION 

10 

0 

-10 

-20 

-30 

30 

20 

10 

0 

-10 


-20 

0 20 40 60 80 100 120 140 


20 

CORRELATION VALUE 

70 

60 

50 

40 

30 

20 

10 

0 

CORRELATION OF FIRST 64-CHIPS OVER ENTIRE LENGTH OF PN SEQ 

SHORT PN SEQUENCE 

MAX USERS = 511 

OFFSET = 64 

SPREADING GAIN = 64 

MAX CROSS CORR = 36 

0 

-10 

-20 

-20 

Variation in Cross Correlation 

-40 

0 20 40 60 80 100 120 140 

RELAVITIVE DELAY BETWEEN TRANSMISSIONS (MEASURED IN Tc) 

Figure 4. Variation of Cross Correlation when Nref>Nasync 

'N' Reference User < 'N' Interfering User SPREADIN GAIN = 127 


PN OFFSET = 255 

20 

10 

0 

-10 

-20 

-30 

0 20 40 60 80 100 120 140 


30 

20 

10 

0 

-10 

-20 

0 20 40 60 80 100 120 140 


40 

20 

0 

-20 

-40 

0 20 40 60 80 100 120 140 

Overlap of Spreading in Chip Duration(Tc) 

Figure 5. Variation of cross correlation when Nref

Adnan Ahmed Khan, Sajid Bashir, Syed Ismail Shah

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