Adnan Ahmed Khan, Sajid Bashir, Syed Ismail Shah

September 17-18, Islamabad
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
IEEE --- 2005 International Conference on Emerging Technologies
∫
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
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