Performance comparison of blind adaptive multiuser detection algorithms

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 02 Issue: 11 | Nov-2013, Available @ http://www.ijret.org 454
PERFORMANCE COMPARISON OF BLIND ADAPTIVE MULTIUSER
DETECTION ALGORITHMS
Khalifa Hunki1
, EhabM. Shaheen2
, Mohamed Soliman3
, K. A. El-Barbary4
1, 2, 3
Military Technical College, Cairo, Egypt
4
Suez Canal University, Suez, Egypt
hunki07@gmai.com, efareed2007@yahoo.com, mnna3000@yahoo.com, khbar2000@yahoo.com
Abstract
Blind multiuser detection algorithms are used to eliminate the Multiple Access Interference (MAI) and the Near-Far effect in mobile
communication systems. Four kinds of blind multiuser detection algorithms applied to code-division multiple-access (CDMA)
communication system are studied in this paper. Those algorithms are the Least Mean Squares (LMS), Recursive Least Squares
(RLS), Kalman filter and subspace-based Kalman filter algorithms. The resultant signal to interference ratio (SIR) at the output of the
receivers controlled by the four kinds of multi-user detection algorithm has been discussed in this paper. Simulation results show that
the subspace based Kalman filter algorithm outperforms all other three algorithms. Subspace-based Kalman filter algorithm has
faster convergence speed, more practical and the capability of CDMA system can be increased.
Keywords: Blind multiuser detection, Code-division multiple access, Mean output energy, Adaptive filtering.
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1. INTRODUCTION
Direct-sequence code-division multiple-access (DS-CDMA)
has been widely studied in the literatures. Recently, adaptive
interference suppression techniques based on multiuser
detection have been considered as powerful methods for
increasing the quality, capacity, and coverage of CDMA
systems [1].
The mitigation of MAI in CDMA systems is a problem of
continuing interest since MAI is the dominant impairment for
CDMA systems. It is widely recognized that MAI exists even
in perfect power-controlled CDMA systems [2]. Multiuser
detectors perform better than the conventional detector under
all power distributions, except in pathological cases, such as
the decorrelating detector in extremely low signal to noise
ratio (SNR) [2]. Therefore, multiuser detection is not only a
solution to the near-far problem but is also useful even with
power control.
In order to successfully eliminate the MAI and detect the
desired user‟s information bits, one or more of the following is
usually required at the receiver end:
1) Spreading waveform of the desired user;
2) Spreading waveforms of the interfering users;
3) Propagation delay (timing) of the desired user;
4) Propagation delays of the interfering users;
5) Received amplitudes of the interfering users (relative to that
of the desired user);
6) Training data sequences for every active user
The “blind” adaptive multiuser detectors require only the
knowledge of (1) and (3), which is, the same knowledge as the
conventional receiver.
Previous work on blind adaptive multiuser detection dates
back to a 1995 paper by Honig et al. [3], who established a
canonical representation for blind multiuser detectors and used
stochastic gradient algorithms such as LMS to implement the
blind adaptive mean output energy (MOE) detector. As
elegantly shown by Roy [4], the blind adaptive MOE detector
has a smaller eigenvalue spread than the training-based
adaptive LMS detector; hence, the blind LMS algorithm
always provides (nominally) faster convergence than the
training driven LMS-MMSE receiver but at the cost of
increased tap-weight fluctuation or misadjustment.
It is well-known that the RLS algorithm and the Kalman
filtering algorithm are better than the LMS algorithm in
convergence rate and tracking capability [2]. Using the
exponentially weighted sum of error squares cost function,
Chen and Roy [5] proposed an RLS algorithm that requires the
knowledge of (1)–(4) and, thus, is not a blind multiuser
detector. Later, Poor and Wang [6] proposed an exponentially
windowed RLS algorithm for blind multiuser detection
requiring only the knowledge of (1) and (3).
On the other hand, the RLS is a special case of the Kalman
filter [7], [8], whereas the Kalman filter is known to be a
linear minimum variance state estimator [7], [9] and [10].
Motivated probably by these two facts, some attention has
been focused on Kalman filter-based adaptive multiuser

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detection [11]–[15]. In particular, it is shown in [13] that when
applied in an asynchronous CDMA system, the RLS algorithm
performs more poorly than the more general Kalman filter
algorithm.
Zhang and Wei [2] proposed a simple and effective state space
model for the multiuser detection problem in a stationary or
slowly fading channel and employed Kalman filter as the
adaptive algorithm. Compared with the LMS approach in [3]
and the RLS approach in [6], this detector demonstrates lower
steady-state excess output energy in adaptation. Interestingly,
though the state space model for the Kalman filter was devised
under a time-invariant assumption, the resulting algorithm
could work well in a slowly time-varying environment.
Motivated by the signal subspace concept in [16], Zhou et al.
[17] proposed a modified version of this blind adaptive
multiuser detector by modeling the detector as a vector in the
signal subspace and employing a Kalman filter philosophy
similar to that in [2] to derive the coefficients adaptively.
Compared with the full-rank approach in [2], despite some
similarity in the state-space model, this new subspace-based
multiuser detector has some significantly important merits.
First it has lower computational complexity and faster
convergence rate in terms of SIR. Secondly, it is less
conditioned on some system parameters such as the desired
users‟ signal amplitude than the full-rank method, thus it is a
blind detection method in a more strict sense. Additionally, the
detection effectiveness is maintained both in additive Gaussian
noise channels and in slowly time-varying Rayleigh fading
channels. In a dynamical system where users can enter and
leave at random, the structure of the signal subspace is also
time-varying. In this case a subspace tracking algorithm is
seamlessly integrated into the proposed detector to track the
changes and provide an online estimation of the signal
subspace.
To this end; this paperpresents and comparesthe four
mentioned algorithms.Their performances in the case of static
and dynamic channels are presented and comments are
provided to fulfill the comparative study.
2. SIGNAL MODEL
Consider an antipodal K-user synchronous DS-CDMA system
signaling through an additive white Gaussian noise channel.
By passing through a chip-matched filter, followed by a chip-
rate sampler, the discrete-time output of the receiver during
one symbol interval can be modeled as
𝑟 𝑛 = 𝐴 𝑘 𝑏 𝑘 𝑛 𝑠 𝑘 𝑛 + 𝜎𝑣 𝑛 , (1)
𝐾
𝑘=1
𝑛 = 0,1, … … . 𝑇𝑠 − 1
Where
𝑣 𝑛 ambient channel noise;
𝐾number of users;
𝐴 𝑘received amplitude of the kth
user;
𝑏 𝑘 𝑛 information symbol sequence from the kth
user,
chosen independentlyand equally from {-1,+1} ;
𝑠 𝑘 𝑛 signature waveform of the kth
user;
It is assumed that𝑠 𝑘 𝑛 is supported only on the
interval[0, 𝑇𝑠 − 1],
Where
𝑇𝑠 = 𝑁𝑇𝑐 symbol interval;
𝑇𝑐chip interval;
Nprocessing gain.
Defining
𝒓 𝑛 = 𝑟 0 , 𝑟 1 , … , 𝑟 𝑁 − 1 𝑇
𝒗 𝑛 = [𝑣 0 , 𝑣 1 , … , 𝑣 𝑁 − 1 ] 𝑇
(2)
We can express (1) in vector form
𝒓 𝑛 = 𝐴1 𝑏1 𝑛 𝒔1 + 𝐴 𝑘 𝑏 𝑘(𝑛)𝒔 𝑘
𝐾
𝑘=2
+ 𝜎𝒗 𝑛 (3)
Where
𝒔 𝑘 = (1/ 𝑁)[𝑠 𝑘 0 , 𝑠 𝑘 1 , … , 𝑠 𝑘 𝑁 − 1 ] 𝑇
is the code
sequence assigned to the kth
user.
For convenience, we will assume that the desired user is k=1.
It is well known that any linear multiuser detector for user 1
can be characterized by the tap-weight vector 𝒄1(𝑛) such that
the decision on 𝑏1 𝑛 during the nth
symbol interval is given by
𝑏1 𝑛 = 𝑠𝑔𝑛 𝒄1, 𝒓 = 𝑠𝑔𝑛 𝒄1
𝑇
, 𝒓 𝑛 (4)
Where 𝒂, 𝒃 denotes the dot product of the vectors 𝒂, 𝒃
3. BLIND ADAPTIVE MULTIUSER DETECTORS
3.1 Blind LMS Multiuser Detector
The canonical representation of a linear blind adaptive
multiuser detector for user 1 was firstly established [3] as
follows:
𝒄1 𝑛 = 𝒔1 + 𝒙1 𝑛 (5)
Subject to
𝒔1, 𝒙1 = 0 (6)

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Where𝒔1 is the spreading vector of the first user and 𝒄1(𝑛) is
the adaptive part of the detector. By minimizing a MOE cost
function of the form.
𝑀𝑂𝐸 𝒄1 = 𝐸 𝒓, 𝒄1
2
(7)
Honig et al. [3] have proposed a blind LMS based algorithm to
update the adaptive
𝒙1 𝑛 = 𝒙1 𝑛 − 1 − 𝜇𝑧 𝑛 𝒓 𝑛 − 𝑧 𝑀𝐹 𝑛 𝒔1 (8)
Where𝑧 𝑛 = 𝒓 𝑛 , 𝒔1 + 𝒙1(𝑛 − 1) is the output of the
detector 𝑧 𝑀𝐹 𝑛 = 𝒓 𝑛 , 𝒔1 is the output of the conventional
matched-filter, and 𝜇is the step-size that controls the
adaptation speed. The step size is given by (70) in [3], when
implementing the LMS algorithm, the step-size must satisfy
the stability condition of convergence of output MSE:
𝜇 <
2
𝐴 𝑘
2
+ 𝑁𝜎2𝐾
𝑘=1
(9)
3.2 Blind RLS Multiuser Detector
Using the minimum output energy criterion, Poor and Wang
[6] proposed a RLS algorithm for blind multiuser detection.
The exponentially windowed RLS algorithm selects the
weight vector to minimize the sum of exponentially weighted
output energy, namely
minimize 𝜆 𝑛−1
𝒄1
𝑇
𝑛 𝒓(𝑛) 2
𝑛
𝑖=1
(10)
Subject to
𝒔1
𝑇
𝒄1 𝑛 = 1 (11)
Where0 < 𝜆 > 1 is the forgetting factor. The solution to this
constrained optimization problem yields the linear MMSE
detector, which is given by [4], [11]
𝒄1 𝑛 =
𝑹−1
(𝑛)𝒔1
𝒔1
𝑇
𝑹−1(𝑛)𝒔1
(12)
Where
𝑹 𝑛 = 𝜆 𝑛−𝑖
𝒓(𝑖)𝒓 𝑇
(𝑖)
𝑛
𝑖=1
(13)
A recursive procedure for 𝒄 𝑛 updating can be obtained as
follows:
𝒌 𝑛 ≜
𝑹−1
𝑛 − 1 𝒓 𝑛
𝜆 + 𝒓 𝑇 𝑛 𝑹−1 𝑛 𝒓 𝑛
(14)
𝒉 𝑛 ≜ 𝑹−1
𝑛 𝒔1 =
1
𝜆
𝒉 𝑛 − 1 − 𝒌 𝑛 𝒓 𝑇
𝑛 𝒉(𝑛 − 1) (15)
𝒄 𝑛 =
1
𝒔 𝑇 𝒉 𝑛
𝒉 𝑛 (16)
𝑹−1
𝑛 =
1
𝜆
𝑹−1
𝑛 − 1 − 𝒌(𝑛)𝒓 𝑇
(𝑛)𝑹−1
(𝑛 − 1) (17)
3.3 Blind Multiuser Detection Based on Kalman
Filtering
In [2], Zhang et al. have proposed to use an alternative
standard representation for the blind adaptive multiuser
detector:
𝒄1 𝑛 = 𝒔1 − 𝑪1,𝑛𝑢𝑙𝑙 𝒘1 𝑛 (18)
Where the columns of the N × N− 1 matrix 𝑪1,𝑛𝑢𝑙𝑙 span the null
space of𝒔1, i.e
𝒔1
𝑇
𝑪1,𝑛𝑢𝑙𝑙 = 0 (19)
It should be noted that 𝑪1,𝑛𝑢𝑙𝑙 can be pre-computed off-line via
one of many orthogonalization procedures such as the Gram-
Schmidt orthogonalization. Unlike (5), the adaptive part
𝒘1 𝑛 in (18) is now of size (N − 1) × 1 and has the advantage
of being unconstraint. Let us define the output of the detector
as follows:
𝑧 𝑛 = 𝒄1
𝑇
𝑛 𝒓 𝑛 (20)
Then 𝑧 𝑛 has zero-mean and its variance is given by
Paragraph comes content here.
𝐸 𝑧2
(𝑛) = 𝑀𝑂𝐸 𝒄1(𝑛) = 𝑀𝑆𝐸 𝒄1 𝑛 + 𝐴1
2
(21)
Thus, when the detector is optimal (i.e., 𝑀𝑆𝐸 𝒄1(𝑛) attains
its MMSE value), the variance of 𝑧 𝑛 corresponds to the
minimum MOE and is dominated by the power of the desired
user 𝐴1
2
.
Substituting (18) in (20) yields
𝑧 𝑛 = 𝒔1
𝑇
𝒓 𝑛 − 𝒓 𝑇
𝑛 𝑪1,𝑛𝑢𝑙𝑙 𝒘1 𝑛 (22)
Put 𝑧 𝑀𝐹 (𝑛) = 𝒔1
𝑇
𝒓(𝑛)and 𝒅 𝑇
𝑛 = 𝒓 𝑇
(𝑛)𝑪1,𝑛𝑢𝑙𝑙 . If
𝒘1achieves 𝒘 𝑜𝑝𝑡 1, then (22) can be rewritten as the following
measurement equation:
𝑧 𝑀𝐹 𝑛 = 𝒅 𝑇
𝑛 𝒘 𝑜𝑝𝑡 1 𝑛 + 𝑧 𝑛 (23)

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If the detector is assumed to be time-invariant, one can write:
𝒘 𝑜𝑝𝑡 1 𝑛 = 𝒘 𝑜𝑝𝑡 1 𝑛 − 1 (24)
As (23) and (24) define a state-space representation of the
adaptive part of the detector, Kalman filtering makes it
possible to recursively update 𝒘 𝑛 [2].
𝒈 𝑛 = 𝑲 𝑛, 𝑛 − 1 𝒅 𝑛
× 𝒅 𝑇
𝑛 𝑲 𝑛, 𝑛 − 1 𝒅 𝑛 + 𝜉 𝑚𝑖𝑛
−1
(25)
𝑲 𝑛 + 1, 𝑛 = 𝑲 𝑛, 𝑛 − 1
−𝒈 𝑛 𝒅 𝑇
𝑛 𝑲 𝑛, 𝑛 − 1 (26)
𝒘 𝑜𝑝𝑡 1 𝑛 = 𝒘 𝑜𝑝𝑡 1 𝑛 − 1
+𝒈 𝑛 𝑧 𝑀𝐹 𝑛 − 𝒅 𝑇
𝑛 𝒘 𝑜𝑝𝑡 1 𝑛 − 1 (27)
𝒄1 𝑛 = 𝒔1 − 𝑪1,𝑛𝑢𝑙𝑙 𝒘 𝑜𝑝𝑡 1 𝑛 (28)
Where 𝒈(𝑛) is (N-1)×1 Kalman gain vector, 𝐾(𝑛 + 1, 𝑛) is
(N-1)×(N-1) correlation matrix of predicted state error and
𝜉 𝑚𝑖𝑛 = 𝑀𝑂𝐸(𝒄1(𝑛)) is the minimum MOE of the dynamical
system of user 1. The initial value𝒘 𝑜𝑝𝑡1 0 = 0and 𝑲 1,0 =
𝑰.
3.4 Subspace-based Blind Multiuser Detector using
Kalman Filter
Based on the signal model (3) and the associated independent
assumptions, the autocorrelation matrix of the received signal
𝒓(𝑛)can be expressed as
𝑹 = 𝐸 𝒓 𝑛 𝒓 𝑛 𝑇
= 𝐴 𝑘
2
𝒔 𝑘 𝒔 𝑘
𝑇
+ 𝜎2
𝑰 𝑁
𝐾
𝑘=1
= 𝑺𝑨𝑺 𝑇
+ 𝜎2
𝑰 𝑁 (29)
Where 𝑺 = 𝒔1 𝒔2 … 𝒔 𝐾 denotes the signature matrix, and
𝑨 = 𝑑𝑖𝑎𝑔 𝐴1
2
𝐴2
2
… 𝐴 𝐾
2
denotes the diagonal matrix of the
signal amplitude. On the other hand, applying an eigende
composition to the matrix 𝑹 yields
𝑹 = 𝑼𝜦𝑼 𝑇
= 𝑼 𝑠 𝜦 𝑠 𝑼 𝑠
𝑇
+ 𝑼 𝑛 𝜦 𝑛 𝑼 𝑛
𝑇
(30)
where 𝑼 = 𝑼 𝑠 𝑼 𝑛 , 𝜦 = 𝑑𝑖𝑎𝑔 𝜦 𝑠 𝜦 𝑛 . 𝚲s =
diag λ1λ2 … λK contains the K largest eigenvalues of 𝑹in
descending order, and 𝑼 𝑠contains the corresponding
orthonormal eigenvectors. 𝜦 𝑛 = 𝜎2
𝑰 𝑁−𝐾contains another N–K
eigenvalues of 𝑹and 𝑼 𝑛 contains the corresponding N–K
orthonormal eigenvectors. The column vectors of 𝑼 𝑠 and 𝑼 𝑛
span two orthogonal subspaces, namely, the signal subspace
and the noise subspace with𝑼 𝑠
𝑇
𝑼 𝑛 = 0.
In [17], Zhou et al. have proposed a new blind adaptive
multiuser detection scheme based on a hybrid of Kalman filter
and subspace estimation. The detector can be expressed as an
anchored signal in the signal subspace as follows
𝒄1 = 𝒔1 + 𝒔1𝑛𝑢𝑙𝑙 𝒘1 (31)
Subject to
𝒄1
𝑇
𝒔1 = 1 (32)
Where the column vectors of the matrix 𝒔1 𝒔1𝑛𝑢𝑙𝑙 compose
the signal subspace basis set and 𝒘1is a weight vector.
Now,𝒔1𝑛𝑢𝑙𝑙 its columns span the null space of𝒔1, i.e.
𝒔1
𝑇
𝒔1𝑛𝑢𝑙𝑙 = 0 , and they are orthonormal, i.e. 𝒔1𝑛𝑢𝑙𝑙
𝑇
𝒔1𝑛𝑢𝑙𝑙 =
𝑰 𝐾−1 . Since 𝒔1is assumed to be known and 𝒔1𝑛𝑢𝑙𝑙 can be
obtained, for example, by applying eigenvalue decomposition
(EVD) to the autocorrelation matrix𝑹.
In order to find the optimal weight vector 𝒘1that minimizes
the MAI. It is demonstrated this vector can be estimated by
using the Kalman filter method [2]. The Subspace Kalman
blind adaptive algorithm is summarized in Table-1.
Table -1: Subspace-Based Kalman Filtering Estimation for
Blind Multiuser Detection
Step 1:
Signal Subspace Estimation:
*Compute autocorrelation matrix 𝑹 for a batch of J
symbols
𝑹 =
1
𝐽
𝒓𝑗 𝒓𝑗
𝑇
𝐽
𝑗=1
* Perform eigenvalue decomposition of 𝑹
𝑹 = 𝑼𝜦𝑼 𝑇
= 𝑼 𝑠 𝜦 𝑠 𝑼 𝑠
𝑇
+ 𝑼 𝑛 𝜦 𝑛 𝑼 𝑛
𝑇
* From matrix
𝒁 = 𝒔1 𝒖1 … 𝒖 𝐾−1
where
𝒖𝑖 is the ith
column vector of 𝑼 𝑠, ∀𝑖 = 1, … , 𝐾 − 1
* Apply Gram-Schmidt method on 𝒁 to obtain an
orthonormal matrix
𝒀 = 𝒔1 𝒚1 … 𝒚 𝐾−1
* Let
𝒔1𝑛𝑢𝑙𝑙 = 𝒚1 … 𝒚 𝐾−1
be the null signal subspace of 𝒔1
Step 2:
Kalman Filtering Estimation in Symbol-rate Adaptation:
* For n=1, 2, …

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* Implement Kalman filter algorithm according to
(25)-(27)
* Signal detection
𝒄1(𝑛) = 𝒔1 + 𝒔1𝑛𝑢𝑙𝑙 𝒘 𝑜𝑝𝑡 1(𝑛)
𝑏1(𝑛) = 𝑠𝑔𝑛 𝒄1
𝑇
(𝑛), 𝒓(𝑛)
* End
4. COMPUTATION COMPLEXITY
We now compare the computational complexity of LMS [3],
RLS [6], Kalman [2], and Subspace Kalman blind adaptive
algorithms [17]. The computational complexities of four
algorithms are compared in term of the number of
multiplications and additions per adaptation iteration as shown
in Table-2.
Table -1: Comparison of Computational Complexity
Algorithm Computational
Complexity
LMS algorithm [3] O(N)
RLS algorithm [6] O(N2
)
Kalman filtering algorithm [2] O(N2
)
Subspace Kalman filtering
algorithm [17] O(NK)
Generally, N>>K; thus, Subspace Kalman has much less
computational complexity than the RLS and Kalman filtering
algorithms.
5. SIMULATION RESULTS
In this section, several simulation results that compare among
the four algorithms for blind multiuser detection are presented.
As a figure of merit for assessing the MAI suppression
capability of the blind LMS, RLS, Kalman filtering, and
subspace-based Kalman filtering algorithms, the time-
averaged SIR (in decibels) at the nth
iteration is given by [3]
𝑆𝐼𝑅 𝑛 = 10𝑙𝑜𝑔
𝒄1𝑙
𝑇
𝑛 𝒔1
2𝑀
𝑙=1
𝒄1𝑙
𝑇
𝑛 𝒓𝑙 𝑛 − 𝑏1,𝑙 𝑛 𝒔1
2𝑀
𝑙=1
(33)
Where 𝑀 is the number of independent runs, and the subscript
𝑙 indicates that the associated variable depends on the
particular run. All signal energies are given in decibels relative
to the background noise variance 𝜎2
, i.e., the SNR of user 𝑘 is
defined by 𝑆𝑁𝑅 = 10𝑙𝑜𝑔 𝐸𝑘 𝜎2
, where 𝐸𝑘 = 𝐴 𝑘
2
is the bit
energy of user 𝑘. In all simulations, user 1 is assumed to be
the desired user that has the unit energy 𝐴1
2
= 1 and an SNR of
20 dB (i.e., 𝜎2
= 0.01), and the processing gain 𝑁 = 31. In
the following, the data in each plot are the average over 500
independent runs.
5.1 Convergence Rate Comparison
In Example 1, DS-CDMA systems in a Gaussian channel are
simulated, and there are nine multiple-access interfering users
among which five users have an SNR of 30 dB each, three
users have SNR of 40 dB each, and another user has an SNR
of 50 dB, i.e., 𝐴2
2
= … = 𝐴6
2
= 10, 𝐴7
2
= 𝐴8
2
= 𝐴9
2
= 100, and
𝐴10
2
= 1000. Then, from (9), it follows that the step size
should satisfy 𝜇 < 1.47 × 10−3
, and thus, μ = 3 × 10−4
was
used in the LMS algorithm. When applying the RLS
algorithm, the initial value 𝑹−1
0 = 𝛿−1
𝑰takes 𝛿 = 0.01, and
the forgetting factor 𝜆 = 0.997 is taken. In Kalman filtering,
we used, the estimate 𝜁 𝑚𝑖𝑛 = 1in (25),
The time-averaged SIR versus iteration numbers for the four
algorithms is plotted in Fig. 1. It is seen that the performance
of the subspace-based Kalman filtering algorithms outperform
the rest. When n is sufficiently large subspace-based Kalman
filtering algorithm approach SNR=19dB. This means that the
MAI in the SIR has been eliminated almost completely.
However, note that the subspace-based algorithm achieves this
near-optimum performance at a significantly reduced
computational complexity compared with the full-rank
algorithm. Fig. 2 shows the mean square error (MSE) versus
iteration number (time) for the four algorithms applied in a
synchronous CDMA system. The most slow algorithm is the
LMS while the other three algorithms reach the minimum
MSE faster than LMS.
Fig -1: Time-averaged SIR versus time for 500 runs when
using the four algorithms to a synchronous CDMA system
with processing gain N = 31.

__________________________________________________________________________________________
Fig -2: MSE versus time for 500 runs when using the four
algorithms to a synchronous CDMA system with processing
gain N = 31.
5.2 Tracking Dynamical Environment
In Example 2, we compare the tracking capabilities of the
LMS, RLS, Kalman filtering, and subspace-based Kalman
filtering algorithms in a dynamical environment with a time-
varying number of users for DS-CDMA systems in a Gaussian
channel. When 𝑛 < 600, the configuration is the same as
Example 1. At 𝑛 = 600, three interfering users with SNR of
40 dB are added to the CDMA system at the same time. At
𝑛 = 1200, four interfering users with SNR of 40 dB and one
interfering user with SNR of 50 dB are removed from the
system. The subspace-based Kalman filter use projection
approximation subspace tracking with deflation (PASTd)
algorithm to track the rank and signal subspace with the
forgetting factor 𝛽 = 0.997. Fig. 3 show the tracking
behaviors of the four blind adaptive algorithms in a
synchronous system.
In Fig. 3, It is also seen that the Kalman filter tracks faster
than the subspace approaches due to the reason that in the
subspace tracking strategy, the subspace-based algorithm
includes two adaptation phases, that is, adaptive subspace
tracking and then adaptive signal detection, whereas the full-
rank detector includes only one adaptation phase.
using the four algorithms to a synchronous CDMA system
with processing gain N = 31 and the time-varying number of
users.
5.3 Slowly Time-Varying Environment
Example 3 is a synchronous DS-CDMA system in a Rayleigh
fading channel. We assume a single-path Rayleigh-fading
channel with a Doppler frequency of 22 Hz, which is obtained
based on Jakesmodel [18]. The signal model is expressed by
𝑟 𝑛 = 𝐴 𝑘 𝑏 𝑘 𝑛 ℎ 𝑘 𝑠 𝑘 𝑛 + 𝜎𝑣 𝑛 , (34)
𝐾
𝑘=1
𝑛 = 0,1, … , 𝑇𝑠 − 1
Where ℎ 𝑘 is the channel coefficient for the kth
user and is a
random variable following Rayleigh distribution The
convergence curves for the subspace-based Kalman filter, the
Kalman filter and the RLS are plotted in Fig. 4. The results
show that all algorithms can track the slow channel
fluctuation, and the subspace-based Kalman filtering detector
still yields better performance than the other two detectors.
The MSE curves of the three algorithms are shown in Fig. 5.
The curves show that all of them have the same residual error
while the subspace-based Kalman filter is the faster algorithm.
5.4 BER Performance Comparison
In Example 4, we evaluate the BER performance of the four
algorithms versus SNR in Rayleigh fading channel, the
configuration is the same as Example 1. The receivers process
10000 symbols and averaged over 100 independent runs for all
BER simulations. The results in Fig. 6 indicate that the
subspace-based Kalman filter and the full-rank Kalman
filtering algorithms outperform the RLS and LMS algorithms.
The performance of the subspace-based Kalman filter

__________________________________________________________________________________________
algorithm is close to the Kalman filtering algorithm but with
much lower complexity.
using the three algorithms with 𝜆 = 0.997 to a synchronous
CDMA system in Rayleigh fading channel; the processing
gain is N = 31.
Fig -5: MSE versus time for 500 runs when using the three
algorithms with 𝜆 = 0.997 to a synchronous CDMA system in
Rayleigh fading channel; the processing gain is N = 31.
Fig -6: BER versus SNR for 100 runs when using the four
algorithms to a synchronous CDMA system in Rayleigh
fading channel.
CONCLUSIONS
In this paper, we have analyzed the SIR and MSE performance
of four blind-adaptive algorithms. Subspace-based Kalman
filter has near-far resistant, lower computational complexity,
and better convergence performance compared with another
algorithms. It is effective in both AWGN channel and slowly
time-varying Rayleigh-fading channel. It is also a blind
detection method in a stricter sense because it is less
conditioned on the knowledge of the signal amplitude of the
desired user. Adaptation in the dynamic environment with
variable number of users is enabled by seamlessly integrating
a subspace tracking methodology at the cost of slight
increment in computational complexity.
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BIOGRAPHIES
KhalifaHunkireceived the B.S. degree in
electronic engineering from Engineering
Academy Tajoura, Tajoura, Libya, in 2001
and the M.Sc. degree in electronic engineering
from the Military Technical College, Cairo,
Egypt, in 2008.Currently, he is working
toward the Ph.D. degree with the Department of Electronic
Warfare, Military Technical College, Egypt. His research
interests include multiuser detection, and adaptive signal
processing.
Ehab M. Shaheenwas born in Cairo, Egypt,
on March 16, 1973 Obtained the B.Sc. and
M.Sc. in electrical engineering in 1995 and
2000 respectively, both from Military
Technical College in Cairo, Egypt, and the
Ph.D. in Computer and Electrical Engineering
from Carleton University, Ottawa, Ontario, Canada in
2010.He joined the Military Technical College in 2011 and he
is currently astaff in the Electronic Warfare Department where
his current research interests include ultra-wideband (UWB)
radio communications, spread-spectrum and secure
communication signalsand digital communications over multi-
path fading channels.
Mohamed Soliman received the BEng.
degree in Comunication and the Master of
Science degree from the Military Technical
College, Egypt 1993 and 2001, respectively.
Between 1993 and 2006, he was an
engineering officer in Egyptian armed forces. Since 2006, he
has been a PhD student in the School of Electrical and
Electronic Engineering, University of Manchester. He
received his PhD from the Manchester University in January
2009.
K.A. El-Barbary received the B. S. degree
(with Average Grade Very Good) in Electric
Engineering from Military Technical
College, Egypt , the M.S. degree in Electric
Engineering from Military Technical
College, Egypt, the Ph.D. degree in
Communications from George Washington University,
Washington DC, USA, in 1981, 1986 and 1993, respectively.
He was faculty member at Military Technical College, Egypt
in the Electric Engineering Department (Chair of
communications and Electronic warfare) (1994-2010). There
he became a professor of Electric Engineering (2009), Head of
Electronic Warfare Engineering Department (2000), and Head
of Electrical Engineering Department (2009). He has been a
professor of signal and systems and Communications at Suez
Canal University, Egypt in Electric Engineering Department.
Currently he is the Head of Electric Engineering Department,
Suez Canal University, Egypt. His research interests include
Statistical signal and array processing and related applications
in communications, radar, Electronic Intelligence, Multi user
Detectors and wideband systems.

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