Reduction of Computational Complexity in Multistage
DS-CDMA System
J. RAVINDRABABU
1
, DASI SWATHI
1
, J. V. RAVI TEJA
2
, J. V. RAVI CHANDRA
3
,
S. PUJITHA BHAVANI1, S. SWEEKAR1, A. NAGA SREEJA1
1E.C.E. Department, P.V.P. Siddhartha Institute of Technology,
Vijayawada,
INDIA
2
Software Engineer-1, FactSet Systems Pvt. Ltd,
Hyderabad,
INDIA
3
C.S.E. Department, V. R. Siddhartha Engineering College,
Vijayawada, Andhra Pradesh,
INDIA
Abstract: - Multiple Access Interference (MAI) is one of the major problems that limit the system capacity of
Direct Sequence-Code Division Multiple Access (DS-CDMA) Wireless Communication Systems. The
reduction of MAI to improve system capacity without increasing computational Complexity is the motivation
to do this work. The objective of this paper is to develop efficient multiuser detection algorithms that improve
the DS-CDMA system performance i.e., to achieve a low Bit Error Rate (BER) and high Signal to Noise Ratio
(SNR) with less computational complexity. The BER performance of the multistage multiuser detection
schemes using Kasami spreading sequences and MMSE detector is found to be better than that of a
conventional Matched Filter detector in a single-stage multiuser detection scheme but the Computational
Complexity increases with the number of stages and the number of users. The BER performance of the
multistage multiuser PIC detection scheme is found to be better than that of a single-stage multiuser PIC
detection scheme but at the cost of computational complexity increasing with a number of stages and users. It is
found that the BER performance of the multistage multiuser PPIC detection scheme is better than that of the
multistage multiuser PIC detection scheme but the computational complexity increases. Though the
computational complexity is found reduced in the multistage multiuser DPIC when compared to the multistage
multiuser PIC, the BER performance remains almost the same as that in multistage multiuser PIC.
Key-Words: - Multiuser Detection, MAI, PIC, PPIC, DPIC, Computational Complexity.
Received: August 29, 2023. Revised: July 15, 2024. Accepted: August 21, 2024. Published: September 5, 2024.
1 Introduction
As limited bandwidth is allocated for various
wireless services and as many users as possible are
required to be accommodated which has to be
achieved by effectively sharing the allotted
bandwidth, multiple access techniques need to be
used in the field of communications for a minimum
degradation in the system performance, [1], [2], [3],
[4]. Since the spectrum utilization in Frequency
Division Multiple Access (FDMA) is not efficient
and exact synchronization is needed in Time
Division Multiple Access (TDMA), one has to go in
for a Code Division Multiple Access (CDMA)
technique. In this users can occupy the entire
channel at all times unlike in FDMA and TDMA
and the users are recognized by their a-priori codes
assigned uniquely. The users can be recognized at
the receiver by using a correlator treating the
remaining users' signal energies as noise. The
CDMA has more spectral efficiency and user
capacity when compared to FDMA and TDMA.
CDMA uses a "spread spectrum" technology where
in a large bandwidth spreading signal multiplies the
narrowband message signal and the users are
differentiated by their unique codes, [5], [6], [7], [8],
[9], [10].
In a perfect synchronous DS-CDMA
transmission, the spreading codes retain their
orthogonality whereas in the asynchronous case they
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J. Ravindrababu, Dasi Swathi, J. V. Ravi Teja,
J. V. Ravi Chandra, S. Pujitha Bhavani,
S. Sweekar, A. Naga Sreeja
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exhibit non-zero off peak auto-correlation and cross-
correlation values. However a perfect synchronous
DS-CDMA system may not be possible to realize in
practice and thus suffers from MAI as well as from
near-far effects, [11], [12], [13], [14], [15].
In a mobile environment, MAI can exist in a
single-user conventional detection at the receiver
even though mutually orthogonal codes are
employed for all the users at the transmitter end.
The single-user conventional detector can also
suffer from near-far effect in practice. The received
signal contains the desired signal, thermal noise, and
the MAI. In a single-user conventional detector, the
signal from each user at the receiver end is
demodulated independently of other users whereas
in MAI is treated as additional noise adding to
thermal noise and hence limiting the system
capacity, [16], [17], [18].
In a multiuser detection scheme, the received
signals from all the users with the presence of MAI
are demodulated simultaneously and hence also
known as joint detection. The receiver has a priori
knowledge of the spreading codes of each user and
MAI is not treated as additional noise in multiuser
detection. When optimum MUD systems are used
no power control is required but the computational
complexity increases. Hence, sub-optimum
approaches are being sought, [19].
2 Literature Review
[20], a low-complexity hybrid analog-digital signal
detector for uplink multiuser massive multiple-input
multiple-output (MIMO) systems. In particular, both
the hardware cost and computation load can be
reduced.
[21], Sparse-aware (SA) detectors have
attracted a lot of attention due to their significant
performance and low complexity, in particular for
large-scale multiple-input multiple-output (MIMO)
systems. Similar to the conventional multiuser
detectors, the nonlinear or compressive sensing-
based SA detectors provide better performance but
are not appropriate for the over-determined
multiuser MIMO systems in the sense of power and
time consumption. The linear SA detector provides
a more elegant tradeoff between performance and
complexity compared to the nonlinear ones.
After the review of the existing relevant
literature, the following observations are being
made:
i. The overall BER performance among all the
multi-user detectors was found better in the
maximum likelihood detector/the optimum
detector at the cost of very high
computational complexity and thus not
realistic for implementation.
ii. Reduced computational complexity exists in
decorrelating detectors and MMSE
detectors. However in these linear detectors,
the calculation of the inverse cross-
correlation matrix is difficult.
iii. The computational complexity increases
linearly with the number of users in SIC,
PIC, HIC, and PPIC techniques. Each type
of interference cancellation detector has its
level of complexity, processing time, and
BER performance.
Given the above observations, there exists a
need to make studies to enhance visual DS-CDMA
system performance and reduce the difficulty of
computing. Further, interference cancellation
methods other than the existing ones are to be
explored for DS-CDMA systems.
The CDMA signal and channel model are
covered in the following chapter. Standard single-
user and multiuser detection methods are covered in
Section 3. The fourth section describes multiple
phases of detection techniques and noise. Simulation
results on the performance comparison of several
multistage multiuser identification approaches are
presented in Section 5. An overview of the results is
provided in Chapter 6's results.
3 Multistage Multiuser Detection
Techniques
3.1 Multistage Multiuser PIC with MMSE
Detector
Data bit estimation and interference cancellation
need to be done for each user at every stage in
multistage PIC schemes. The MMSE detector
estimates data bits and subtracts interference from
the first stage onwards in this Multistage Multiuser
PIC scheme. The Multistage Multiuser PIC with
MMSE Detector is shown in Figure 1.
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J. Ravindrababu, Dasi Swathi, J. V. Ravi Teja,
J. V. Ravi Chandra, S. Pujitha Bhavani,
S. Sweekar, A. Naga Sreeja
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Fig. 1: Multistage Multiuser PIC with MMSE
Detector
Algorithm for Multistage Multiuser PIC
with MMSE detector:
(1)
1 mmse
b sgn(y )
For s=2 to S %/ Cancellation of
Interference s-1 stages/
For k=1 to K %/ The interference is subtracted
from every user signal at each stage /
(s)
(s-1)
k m m s e j jk j
j=1
jk
Z =y - A ρb
K
where
kj kj
kj R - diag(R )ρ
End
()
( -1)
sgn( )
s
s
k
kz
b
%/ Decision /
End
3.2 Computational Complexity of PIC
Computational Complexity involves the amount of
time taken to accomplish the multiuser detection
starting from the time of arrival of the transmitted
signal at the first stage of the detector of the
receiver. Therefore, the time required to perform the
number of multiplications and the wide variety of
additions in the detection process need to be
calculated to arrive at the computational complexity.
The cancellation of MAI from the stronger user
every time until the closing user requires the
multiplication of two matrices. To accomplish the
multiplication of an (A1×B1) matrix with a (B1×C1)
matrix, A1B1C1 multiplications and A1B1C additions
are needed.
Therefore, assuming K users in the system
wherein the transmission is a burst waveform, each
user transmits D data symbols in the burst, B
represents the number of chips in the spreading code
for every user, and U is the complicated matrix
which includes the factors that describe the channel
impulse response, then one needs DB instances of
multiplications and DB instances of additions for
each user for one data symbol in a single path burst.
If the bursts arrive along L multi-path channels, then
the receiver would require DBL instances of
multiplications and DBL instances of addition for
one data symbol. Combine the D symbols
transmitted from the dispersive paths, requires in
addition DL instances of multiplications and DL
instances of additions. Therefore, DBL+DL times of
multiplications and DBL+DL times of additions are
required to get the data estimates from the receiver.
In the signal reconstruction process, the data
estimates need to be respread with the spreading
code first and then convolved with the
corresponding channel impulse response, which
leads to DBL multiplications and (DB+U−1)
additions. To get the data estimate for every user,
the effects of remaining users need to be subtracted.
To cancel one user’s MAI, it needs (DB+U−1)
subtractions. Therefore, for every user,
(K−1)(DB+U−1) subtractions are needed. For a
system supporting K users, the whole number of
mathematical operations are SPIC1 = K
[DBL+DL+DBL+DL+DBN+DBL+DB+U-1+(K-1)
(DB+D-1)]
= K [3DBL+2DL+DB+K(DB+U-1)] for first
stage
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Therefore, for two-stage,
SPIC2 = 2 K [3DBL+2DL+DB+K(DB+U-1)]
Therefore, the number of operations needed by the
two-stage PIC detector for every one symbol is
SPIC2 /symbol = SPIC2 / KD
3.3 Multistage Multiuser PPIC with MMSE
Detector
In this scheme, the MAI Cancellation is
implemented using a weight factor at every stage to
decide about the amount of cancellation to be
implemented, [14], [15], [16].
In a Multistage Multiuser PPIC scheme, the
weight factor used for interference cancellation
affects a biased selection statistic. The bias has its
strongest effect on the first stage of interference
cancellation. In the subsequent stages, its effect
decreases. However, if the biased selection statistic
is unfair at the first stage leading to a wrong
cancellation, then the effects of these errors can
escalate in the subsequent stages, [13], [14], [16].
One way to mitigate the effect of the biased
selection statistic to enhance the overall
performance of multistage PPIC is to multiply the
amplitude estimates with a partial cancellation
factor, CK(s) lying between 0 and 1 [i.e.,
()
01
s
KC
]
which varies with the stage of cancellation ‘s’ and
the number of users ‘K’.
In this scheme also, various stages are involved
for interference estimation and cancellation. The
MMSE is used in the first stage to estimate the
information bits whereas the subsequent stages also
use MMSE detectors. The signal reconstruction and
subtraction of the predicted interference from other
users obtained by weighting the estimates of the
information bit of the user in question is carried out
at all stages . The multistage multiuser PPIC with
MMSE detector is shown in Figure 2.
Fig. 2: Partial PIC detector
Algorithm for Multistage Multiuser PPIC
with MMSE detector:
(1)
1sgn( )
mmse
by
For s=2 to S %/ Cancellation of
Interference s-1 stages /
For k=1 to K %/ The interference is
subtracted from every
user signal
at each stage /
K()
(s-1) (s)
k m m s e k j kj j
j=1
jk
z =y - c A ρb
s
where
kj ()ρij ij
R diag R
()
(s-1) (s)
k m m s e k j ij ij j
j=1
jk
=y - c A (R -diag(R )) b
Ks
z
End
(s) (s-1)
kk
b sgn( )z
%/
Decision /
End
3.4 Computational Complexity of PPIC:
For this case, assuming K users in the system where
the transmission is a burst waveform, each user
transmits D data symbols in the burst, n represents
the number of chips in the spreading code for every
user, C represents the partial cancellation factor and
U is the complicated matrix which includes the
factors that describe the channel impulse response,
then one needs CDBinstances of multiplications and
CDB instances of additions for each user for one
data symbol in a single path burst. If the bursts
arrive along L multi-path channels, then the receiver
would require CDBL instances of multiplications
and CDBL instances of additions for one data
symbol. Combining the q symbols transmitted from
the dispersive paths requires CDL instances of
multiplications and CDL instances of additions.
Therefore, to get the data estimates from the
receiver, CDBL+CDL times of multiplications and
CDBL+CDL times of additions are required. In the
signal reconstruction part, the detected data have to
be re-spread with the spreading code first leading to
CDB instances of multiplications and then convolve
with the corresponding channel impulse response
resulting in DBL times of multiplications and
C(DB+U−1) times of additions. To get the estimate
for every user, all of the different users' affects need
to be subtracted. To cancel one user’s MAI, it will
need C(DB+U−1) instances of subtraction.
Therefore, for every user, (K−1)C(DB+U−1)
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instances of subtractions are needed. For a system
supporting K users, the whole number of
mathematical operations are
SPPIC1 = KC
[DBL+DL+DBL+DL+DB+DBL+DB+U-1+(K-1)
(DB+U-1)]
= KC [3DBL+2DL+DB+K(DB+U-1)] for first stage
Therefore, for two-stage,
SPPIC2 = 2 KC [3DBL+2DL+DB+K(DB+U-1)]
Therefore, the number of operations needed by the
two-stage PIC detectors for every symbol is
SPPIC2 /symbol = SPPIC2/ KD .
3.5 Multistage Multiuser Differencing PIC
with MMSE Detector
In PIC schemes, the component of MAI from
different users is eliminated from the acquired signal
to get a higher-anticipated signal for a specific user
in parallel. As the exact bit statistics for any user are
not known, the anticipated bits are made use of at
each stage . As this process is iterative, it's highly
possible to have
(s) (s-1)
kk
b =b
after sth iteration. Instead
of managing with an estimated bit vector
(s)
k
b
at
each stage s, one can calculate the difference of the
estimated bits in two consecutive stages. Then input
at each stage s becomes
(s) (s) (s-1)
k k k
e = b - b

and is called
the differencing technique.
The multistage multiuser DPIC with MMSE
detector is shown in Figure 3.
The first stage of this DPIC scheme remains
the same as in DPIC with an MMSE detector. This
scheme makes use of an MMSE detector from the
second stage onwards also wherein the preceding
estimations from stage-1 are utilized to generate a
new vector of signals. Then sum up all the
interfering users and subtract them from the MMSE
output signal.
Fig. 3: Difference PIC detector using MMSE
The first stage of this DPIC scheme remains the
same as that in DPIC with an MMSE detector. This
scheme makes use of MMSE detector from the
second stage onwards also wherein the preceding
estimations from stage-1 are utilized to generate a
new vector of signals. Then sum up all the
interfering users and subtract them from the MMSE
output signal.
Algorithm for Multistage Multiuser DPIC with
MMSE detector:
(1)
1 mmse
b sgn(y )
For k=1 to K %/Interference is subtracted from
each user at every stage /
(2) (1)
1
( ( ))
K
k m m s e j ij ij
j
jk
z y A R diag R b
End
(2) (2)
11
sgn( )bZ
%detection/
For s = 2 to S %/ second and next stages:
Subtracting multistage
For k = 1 to K
K
(s-1) (s) (s)
k k j kj kj j
j=1
jk
z =z - A (R -diag(R ))e
where
( ) ( ) ( 1)
j j j
s s s
e b b

End
() ( 1)
1k
sgn( )
ss
bZ
%/decision/
End
3.6 Computational Complexity of DPIC
The computational complexity of this DPIC system
can be arrived at on similar lines to that for PIC and
PPIC as discussed respectively in sections 3.3 and
3.4 previously. That is, it is based on the total
number of multiplications and additions involved in
this scheme. The procedure is similar to that in the
first stage of PIC except only DB times more
additions are required in differencing PIC. Since for
a PIC system supporting K users, the total number
of mathematical operations are
SPIC= K [DBL +DL+ DBL +DL+DN+ DBL
+DB+U-1+(K-1)(DB+U-1)]
=K[3DBL+2DL+DB+K(DB+U-1)] for first
stage of PIC.
Therefore, for a single-stage DPIC,
SDPIC1 = K[3DBL+2DL+DB+K(DB+U-1)] + DB
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Therefore, the number of operations needed by the
single-stage DPIC detector for every symbol is
SDPIC1/symbol = SDPIC1/ KD
Similarly, for a two-stage DPIC
SDPIC2 = 2{K[3DBL+2DL+DB+K(DB+U-1)] + DB}
and the number of operations needed by the two-
stage DPIC detector for every symbol is
SDPIC2/symbol = SDPIC2/ KD
4 Simulation Results
The DS-CDMA basic multistage multiuser discrete
time paradigm was applied. The customer's data is
disseminated via BPSK modulation and Kasami odd
spreading sequence.
It is evident from the below simulation results
that with an increasing number of stages, the
system's overall BER performance is improved as
PIC with MMSE detector. However, the
computational complexity also increases. The BER
performance did not alternate dramatically beyond
4thstage (not shown here). Three stages are only
considered for simplicity. BER performance is
better at the 3rdstage when compared to that at the
1ststage and 2nd stage for all the cases like PIC,
PPIC, and DPIC from Figure 4, Figure 7 and Figure
10 for clarity.
It is evident from the simulation results shown
in Figure 5, Figure 8 and Figure 11, that the BER
performance degrades with an increasing number of
users. But at the same time, the computational
complexity increases with an increasing number of
users as shown in Figure 6, Figure 9 and Figure 12.
0 5 10 15 20 25 30 35 40 45 50
10-6
10-5
10-4
10-3
10-2
10-1
100
BER
Eb/No
PIC with MMSE
stage 1
stage 2
stage 3
Fig. 4: Bit-Error-Rate performance of PIC with
MMSE for K=10 users
0 5 10 15 20 25 30 35 40 45 50
10-6
10-5
10-4
10-3
10-2
10-1
BER
Eb/No
BER performance of three stage PIC with MMSE
K=10
K=15
K=20
K=25
K=30
Fig. 5: Bit-Error-Rate performance of three-stage
PIC with MMSE different users
101102
0
0.5
1
1.5
2
2.5
3
3.5 x 105Computational complexity of PIC
Number of users (K)
No.of Computations(S)
PIC
Fig. 6: Computational complexity of PIC
0 5 10 15 20 25 30 35 40 45 50
10-6
10-5
10-4
10-3
10-2
10-1
100
BER
Eb/No
PPIC with MMSE
stage 1
stage 2
stage 3
Fig. 7: Bit-Error-Rate performance of PPIC with
MMSE for K=10
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0 5 10 15 20 25 30 35 40 45 50
10-6
10-5
10-4
10-3
10-2
10-1
BER
Eb/No
PPIC with MMSE stage 3
K=10
K=15
K=20
K=25
K=30
Fig. 8: Bit-Error-Rate performance of PPIC with
MMSE for K=No.of users
101102
0
0.5
1
1.5
2
2.5
3
3.5
4x 105Computational Complexity comparison
No.of users (K)
No.of Computations (S)
PIC
PPIC
Fig. 9: Computational complexity of PIC and PPIC
0 5 10 15 20 25 30 35 40 45 50
10-6
10-5
10-4
10-3
10-2
10-1
100
BER
Eb/No
DPIC with MMSE
stage 1
stage 2
stage 3
Fig. 10: Bit-Error-Rate performance of DPIC with
MMSE for K=10
0 5 10 15 20 25 30 35 40 45 50
10-6
10-5
10-4
10-3
10-2
10-1
BER
Eb/No
BER performance of three stage DPIC with MMSE
K=10
K=15
K=20
K=25
K=30
Fig. 11: Bit-Error-Rate performance of DPIC with
for MMSE K=No.of users
101102
0
0.5
1
1.5
2
2.5
3
3.5
4x 105Computational Complexity comparison
No.of users (K)
No.of Computations (S)
PIC
PPIC
DPIC
Fig. 12: Computational complexity of PIC, PPIC &
DPIC
5 Conclusions
Employing multiple-stage multiuser approaches in
DS-CDMA systems can also minimize the
complexity of computation and Multiple Access
Interference. In the multistage PIC approach, bit
error rate (BER) drops and detection becomes more
dependable as the number of stages rises. The ability
to increase in subsequent phases cannot be
guaranteed by the PIC. In a DS-CDMA system, the
effectiveness of the Partial Parallel Interference
Cancellation (PPIC) technique is assessed. However
there is no improvement in computational
complexity. The computational complexity
decreased by using DPIC. Ultimately, it may be
concluded that DPIC outperforms PIC and PPIC.
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WSEAS TRANSACTIONS on COMMUNICATIONS
DOI: 10.37394/23204.2024.23.7
J. Ravindrababu, Dasi Swathi, J. V. Ravi Teja,
J. V. Ravi Chandra, S. Pujitha Bhavani,
S. Sweekar, A. Naga Sreeja
E-ISSN: 2224-2864
50
Volume 23, 2024
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
- J Ravindra Babu, D. Swathi Identified the
problem statement and done the mathematical
Analysis.
- J V Ravi Teja,J V Ravi Chandra have
implemented the Algorithms in section 3.
- S.Pujitha Bhavani, S.Sweekar A.Naga Sreeja
carried out the simulation in section 5 using
MATLAB.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
WSEAS TRANSACTIONS on COMMUNICATIONS
DOI: 10.37394/23204.2024.23.7
J. Ravindrababu, Dasi Swathi, J. V. Ravi Teja,
J. V. Ravi Chandra, S. Pujitha Bhavani,
S. Sweekar, A. Naga Sreeja
E-ISSN: 2224-2864
51
Volume 23, 2024