Adnan Ahmed Khan, Sajid Bashir, Syed Ismail Shah

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