AL-DooriVian S.1
JamelThamer M.2
MansoorBashar M.2
-
(Al-Rafidain university college, Baghdad, Iraq vian.kasim@ruc.edu.iq)
-
(University of Technology-Iraq, Department, of the Communications Engineering, Baghdad
{thamer.m.jamel, 30024}@uotechnology.edu.iq
)
Copyright © The Institute of Electronics and Information Engineers(IEIE)
Keywords
Block least mean square (BLMS), Speedy euclidian direction search (SEDS), Space division multiple access (SDMA), Single cell MISO downlink channels
1. Introduction
Each mobile user within a wireless communication network is connected to and effectively
communicates with at least one base station in a geographical region called a cell
[1]. The antennas of these cellular base stations are Space Division Multiple Access
(SDMA) antennas (also called smart antennas), which have an adjustable radiation pattern
according to the environment. The SDMA’s antenna radiation patterns direct the main
beam towards a desired user and attenuate or cancel out undesired users or interference
depending on the channel environments and the user's location, as shown in Fig. 1 [2]. An SDMA antenna can update the antenna weight coefficients by using an adaptive
algorithm that beamforms or steers the radiation patterns towards a desired user and
cancels out interference in a cell [3].
SDMA has two different beamforming arrangements: one for producing downlink beams
and a second one for producing uplink beams [1]. In this study, single-cell downlink beams are used such that a base station having
M elements in a uniform linear array (ULA) is connected with different users, such
that each user has a single antenna. In this case, Multiple-Input Single-Output (MISO)
links are obtained. A block adaptive algorithm is applied to perform the smart operation
of the system. This is done to manage the long channel impulse response of some wireless
communication channels such as massive MIMO using a block coding for a 5G system,
such as Low-Density Parity-Check (LDPC) code, which is the best error-correcting code
[4].
To our knowledge, there is no study or analysis on the performance of a time-domain
block adaptive LMS algorithm in SDMA. All previous research compared between the SEDS
(also known as FEDS) algorithm and sequential or traditional algorithms like Recursive
Least Square (RLS), Least Mean Square (LMS), and Normalized Least Square (NLMS) [5-8]. The SEDS algorithm is a block adaptive algorithm. Therefore, it is fair to compare
its performance with block algorithms like BLMS. An SDMA antenna was simulated using
MATLAB, and we modeled three different multipath fading wireless communications channels,
which represent indoor and outdoor environments.
Section 2 presents a literature review, while section 3 provides an overview of time-domain
block adaptive algorithms. Section 4 presents the two-block adaptive algorithms BLMS
and SEDS and how to choose the block length. In section 5, simulation results are
presented, and finally, section 6 concludes the study.
Fig. 1. Concept of SDMA base station.
2. Literature Review
As mentioned previously, very few works in the literature studied the performance
of the SEDS algorithm applied to an SDMA system and compared it with other algorithms
that use sequential time processing (i.e., not block processing). The authors of article
in [5] compared the performance of SEDS algorithm with classical algorithms like LMS, RLS,
and NLMS. Another research [6] was study the effect of choosing the window length parameter (L) of the SEDS algorithm
over the AWGN channel only. In another study [7], the author repeats the previous study [6] but for a Rayleigh channel. Finally, the authors in another study [8] used different channels to demonstrate the results of the outcome in the previous
study [7]. All previous studies used both classical sequential time processing and a traditional
SDMA system, while in this study, block data processing and a single-cell MISO downlink
channel were used.
3. Method of Time -Domian Block Adaptive Algorithms
Some wireless communications channels such as massive-MIMO channels (or those using
an LDPC for a 5G system) have a long impulse response, so the traditional or sequential
adaptive algorithms like LMS or RLS are not sufficient or are expensive to use [9]. In order to reduce the computational complexity of adaptive filters, block implementation
or block processing was proposed because using parallel processing of data samples
can lead to less computational complexity. Moreover, high computational efficiency
can be obtained due to sharing of the processing time among the samples in each block.
The computational complexity of block adaptive filtering can be defined as the operations
needed to process one block of data divided by the block length [9].
Due to a block of the input signal, samples must be gathered before starting block
processing, and then processing time delay will arise at the system output and should
be minimized. This processing delay increases with the block length. Of the possible
options for the limitations on the block size relevant to the length M of FIR filter,
choosing a block length equal to the filter order (M) represents the best choice from
the viewpoint of minimum computational complexity. A second option considers the reduction
of processing delay when choosing a block length less than the filter order. The third
choice is when the block length is larger than the filter order, which means processing
data will be redundant [9]. In this study, two-block adaptive algorithms were used: block LMS (BLMS) and SEDS
algorithms. The SEDS and BLMS algorithms are least square and mean square error algorithms,
respectively.
4. Block Adaptive Algorithms
4.1 Block Samples Processing
Fig. 2 shows the concept of block processing for block adaptive filtering, where the input
and desired output signals of the block adaptive filter are composed in order to have
a block of the output signal [10]. The symbol L refers to the length of the data blocks, which will be used to update
or modify the main filter’s parameters. Other symbols like u and W represent the input
and filter weight coefficients, respectively.
The parameters that are defined at time index n = k L + I are as follows: - u(k L
+ i) (the input signal); y(k L + i ) = wT (k) u(k L + i) (the output of the filter),
and finally, e(k L + i) (the error signal). The only parameter that is defined at
time instants Kl is the weight vector, W(k).
Fig. 2. Block filter parameters[10].
4.2 The BLMS Algorithm
Fig. 3 illustrates the adaptive block filter idea. It is clear that the input sequence (u)
enters the serial-to-parallel converter to divide into blocks of length L, and one
block at a time is used by the M-order FIR filter. After gathering each block of u
samples, the weight coefficients of the FIR filter are adjusted block by block instead
of conventional LMS, which uses a sample-by-sample process [11].
The block length index is k, and the sample time n is:
The input signal vector at time n for block k is defined by a set:
The output of the FIR filter will be calculated as:
where w ̂^T (k) denotes the tap-weight vector of the filter at time k. Let d(kL +
i) denote the desired response. Then, an error signal can be calculated as:
In a synchronous way with the input end of the FIR filter, the error signal is divided
into L point blocks to be used later to update the filter weight coefficients. Different
values of error signals will be used for each block of samples in the BLMS adaptive
algorithm. The weight coefficient vector of the BLMS algorithm will be adjusted over
all possible values of i according to the following formula after summation of the
product process u (kL+i)e(kL+i) [11].
where u is the BLMS step size. Table 1 shows the step sequence of BLMS.
Table 1. Step sequence of BLMS algorithm.
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Parameters
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Step 1: Initialize weight vector w(0)=0
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Step 2: for k=0,1,2,3,…..k_max, repeat (where parameter k referred to the block index)
and start ${\varphi}$ =0
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Step 3: for I =0,1,2,3,…... L-1, repeat (where parameter L referred to data block
length), a new data pair create which are (u(kL + i), d(kL+ i) ), u and d is input
data and desired vectors, respectively.
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Filter output: $y\left(kL+i\right)=w^{T}\left(k\right)~ u\left(kL+i\right)=~ $ \par
$~ \sum _{j=0}^{M-1}w_{j}\left(k\right)u\left(kL+i-j\right)$; M is the order of the
filter (number of weight coefficients)
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Error signal (e(kL+i)) = desired signal – filter output signal;
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Step 4: weight adaptation vector: w(k+1) = w(k) +u* ${\varphi}$;
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where M-by-1 vector ф(k) is a cross-correlation defined by
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$\varphi \left(k\right)=~ \sum _{i=0}^{L-1}e\left(kL+i~ \right)u~ \left(kL+i~ \right)$
and u is block step size.
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Fig. 3. Adaptive block filter idea[11].
4.3 Direction Search (DS) Algorithm
The first direction search (DS) algorithm was developed by Powell and Zangwill in
1964 and 1967 and is a least square algorithm [12]. Recently, a modified version of the DS algorithm called the Euclidean Direction
Search (EDS) algorithm was developed by Xu and Bose in 1999 [13]. When the N weights are updated by cyclically searching through the N Euclidean directions,
then the EDS algorithm is called the Fast EDS algorithm.
This fast EDS was named as Speedy Euclidean Direction Search (SEDS) in this study
[5-8]. Fig. 4 shows how DS family algorithms find a preferable estimated weight by searching in
the duration of each direction among a set of linearly independent directions. Then,
with every block of data, the weights will be reduced exponentially instead of with
discrete time or sample by sample as in conventional least square algorithms like
RLS (where ${\lambda}$ is the forgetting factor) [13]. Then, for every sample of data, only one Euclidean direction search is processed.
The SEDS algorithm steps are listed in Table 2. For each block index, k, the formulas in Table 2 are carried out. There are N data within each block. Items (1) through (8) are performed
for each data (index i). At the end of each block, both items (A) and (B) are processed.
For each Euclidean direction search (i.e., for each i), one row of Q (item (l) is
the first part of Q), one element of w, and one element of r (item (2) is the first
part of r) are updated. Items (3) and (4) are accumulations of Q and r within one
block. The update items of one row of Q and r are shown in items (5) and (6), respectively,
such that this one-row update is q$^{\mathrm{(i)}}$, and q~$^{\mathbf{(i)}}$for Q
and (r + r$^{\mathbf{\sim }}$) for r. The step size parameter a is set in items 5,
6, and 7. One element of the weight vector was updated in item (8). Finally, items
(A) and (B) represents an update of Q and r, and we also reset Q~ and r~ at the end
of each block [13].
Fig. 4. Weight searching direction in SEDS[13].
5. Results and Discussion
5.1 SDMA Base Station Simulation
As shown in Fig. 5, the SDMA base station with MISO (i.e., 16 X1) has a uniform linear antenna array
that consists of 16 receiving antennas separated by half a wavelength. Four users
transmit at a specified elevation angle such that the desired angle of the desired
user is 0$^{\circ}$, while the three other undesired or interference angles are 30$^{\circ}$,
-30$^{\circ}$, and 60$^{\circ}$ respectively. Two time-domain block adaptive algorithms
were used: BLMS and SEDS with a different block index K and different data length
L. Three different multipath fading propagation channel models were used according
to 3GPP [14].
Fig. 5. SDMA-MISO downlink block diagram.
Table 2. SEDS algorithm[13].
|
Parameters
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Initialization:
$w(0)=0 ; \tilde{Q}=0 ; Q=0 ; \tilde{r}=0 ; r=0$ : Discrete time index $n=k N+l ;
\mathrm{N}$ is block size; The $k$ is number of the full block within $\mathrm{n}$,
and $l$ is the number of sampling remaining, where
$1 \leq l \leq N$
For $k=1,2, \ldots \ldots .$
For $\mathrm{I}=1,2, \ldots \ldots N$
(1) $q^{i}=\lambda q^{i}$
(2) $(r)_{i}=\lambda(r)_{i}$
(3) $\tilde{Q}=\tilde{Q}+x(k N+l) x^{T}(k N+l)$
(4) $\tilde{r}=\tilde{r}+d(k N+l) x(k N+l)$
(5) $e=\left(q^{i}+\tilde{q}^{i}\right)^{T} w-(r+\tilde{r})_{i}$
(6) $a=q_{i}^{i}+\left(\tilde{q}^{i}\right)_{i} ; a$ is step size parameter calculated
as in DS algorithm
(7) if $a \neq 0, \alpha=\frac{-\varepsilon}{a}$
(8) $(w)_{i}=(w)_{i}+\alpha$
end $i$
(A) $Q=Q+\tilde{Q} ; \tilde{Q}=0$
(B) $r=r+\tilde{r} ; \tilde{r}=0$
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5.2 EPA Wireless Channel Model
Extended Pedestrian A model (EPA) has seven paths with gain equal to [0 -1 -2 -3 -8
-17.2 -20.8], and the corresponding delay for each path is [0 30 70 90 110 190 410]
*1e-9/Ts, such that the sampling frequency fs equals 7.68e6 Hz, and the sampling time
is Ts equals 1/fs [14]. This channel represents indoor environments with small cell sizes and a low delay
spread environment. Fig. 6 shows the EPA frequency response [14].
Fig. 7 shows MSE for both algorithms with L values and K equal to 100. It is clear that
the performance of the SEDS algorithm is better than BLMS in terms of fast convergence
and accurate estimation with minimum error. Also, we can notice that this performance
(both SEDS and BLMS) is enhanced when L is increased, and we have an accurate estimation
output signal when the input desire signal is a pure cosine wave, as illustrated in
Fig. 8.
Fig. 6. Frequency response of EPA channel[14].
Fig. 7. Mean square error (MSE) for both algorithms (EPA channel).
Fig. 8. Estimated output signal (EPA channel).
5.3 EVA Wireless Channel Model
Extended Vehicular A model (EVA) has nine paths with gain equal to [0 -1.5 -1.4 -3.6
-0.6 -9.1 -7 -12 -16.9], and the corresponding delay for each path is [0 30 150 310
370 710 1090 1730 2510] *1e-9/Ts. This channel represents urban environments with
large cells and has a medium delay spread model [14]. Fig. 9 shows the EVA frequency response.
Figs. 10 and 11 show the performance of two algorithms in terms of the MSE and estimation output
signal, respectively.
As shown in the aforementioned figures, when L is less than 40, the performance of
the SEDS algorithm is better than BLMS, but it starts to become unstable when L has
a value more than 40. Therefore, the performance of SEDS for L equal to 60 is omitted.
On the other hand, the performance of BLMS remains stable even when L has values more
than 40. This fact is also repeated for the next channel type (ETU). Therefore, one
way to solve the instability problem of the SEDS algorithm is to control or minimize
its step size.
Fig. 9. Frequency response of EVA channel[14].
Fig. 10. MSE for both algorithms (EVA channel).
Fig. 11. Estimated output signal (EVA channel).
5.4 ETU Wireless Channel Model
The Extended Typical Urban model has high delay spread environments, so it is used
to model urban environments with large cells [14]. Fig. 12 shows the ETU frequency response. ETU has nine paths with gain equal to [-1 -1 -1
0 0 0 -3 -5 -7], and the corresponding delay for each path is [0 50 120 200 230 500
1600 2300 5000] *1e-9/Ts [14]. The figure below shows the ETU frequency response [14].
Figs. 13 and
14 show the MSE and estimated output signal.
Figs. 15-17 depict beam patterns for both algorithms with different values of block lengths (L)
for the ETU channel. It is clear that the beam pattern of SEDS is better than the
BLMS in terms of null beamforming at interfering angles with no deviations from these
nulling angles (30$^{\circ}$, -30$^{\circ}$, and -60$^{\circ}$), while both algorithms
steer the main beam towards the desired user angle (0$^{\circ}$). Moreover, the beampattern
of BLMS is enhanced with increasing block length (L).
Fig. 12. Frequency response of ETU channel[14].
Fig. 13. MSE for both algorithms (ETU channel).
Fig. 14. Estimated output signal (ETU channel).
Fig. 15. Beam patterns k =100, L=10 (ETU channel).
Fig. 16. Beam patterns k =100, L=20 (ETU channel).
Fig. 17. Beam patterns k =100, L=40 (ETU channel).
6. Conclusion
The main contribution of this paper is to propose two adaptive time-domain blocks
for long-length wireless communication channels impulse response for future communications
systems. There has been no earlier works that employ or implement adaptive time-domain
block algorithms (such as BLMS or SEDS) for the SDMA system that we are aware of.
To our knowledge, no research has been done to evaluate or analysis the performance
of the time-domain block adaptive LMS algorithm in SDMA, or to compare it to the SEDS
method. These schemes are a mean and least squared error which includes BLMS and SEDS
algorithms respectively.
The performance of the base station SDMA system with MISO downlink channel (16 X 1)
was investigated using the above algorithms. The simulated results show that both
BLMS and SEDS algorithms have good performance when block size (L) increased. Moreover,
although the SEDS algorithm has accurate and better estimation compared with BLMS
in indoor environments SEDS’s performance is degraded for outdoor environments when
the block size was set to 60. On another side, the BLMS algorithm has stable performance
and is enhanced with increasing block length.
REFERENCES
Smith M. Stevens, Urquhart A. James, Robson J. George, Bevan D. Nicholas, 2013, Downlink
and uplink array and beamforming arrangement for wireless communication networks,
Apple, Inc., Cupertino, CA (US)
Mohamed Nadder, January 2016, Antenna myths for base station antennas, CommScope white
paper
Kumar, Vivek, Rajouria, Deepak, Jain, Manju, Kumar, Vikas , July - Sept 2013, Performance
Analysis of LMS Adaptive Beamforming Algorithm, International Journal of Electronics
& Communication Technology. (JECT), Vol. 4, No. issue spl - 5, pp. 47-51
Bashar M. Mansoor, Tarik Z. Ismaeel, 2019, Design and Implementation of an Improved
Error Correcting Code for 5G Communication System, Journal of Communications, Engineering
and Technology Publishing (ETP), Vol. 14, No. 2, pp. 88-96
Thamer m. Jamel, Bashar M. Mansoor, Application of Fast Euclidean Direction Search
(FEDS) method For Smart Antennas in Mobile Communications Systems, In Intelligent
Signal Processing (ISP) Conference, 2 - 3 December 2013 - Strand Palace Hotel, London,
UK.
Thamer m. Jamel, Performance Evaluation of the Fast Euclidean Direction Search Algorithm
for Adaptive Beamforming Applications, Al Sadiq International Conference on Multidisciplinary
in Information and Communication Technologies 2016 AIC -MITC 2016, IEEE Iraq Section,
9-10 May 2016, Baghdad- Iraq.
Thamer M. Jamel, July-2019, Optimal Window Length and Performance Analysis of FEDS
Based Adaptive Beam Forming Approach over Rayleigh Fading Channel, International Journal
of Computing and Digital Systems (IJCDS) Int. J. Com. Dig. Sys, Vol. 8, No. 4, pp.
397-404
Thamer m. Jamel, Ali N., Nov 1, 2020, ,Novelty Study of the Window Length Effects
on the Adaptive Beam-forming Based-FEDS Approach, International Journal of Computing
and Digital Systems, IJCDS-9-6
Behrouz Farhang-Boroujeny , 2013, Adaptive Filters Theory and Applications, 2$^{\mathrm{nd}}$
edition, John Wiley & Sons, Ltd.
Poularikas D., 2015, Fundamentals of Least Mean Squares with MATLAB Alexander, CRC
Press Taylor & Francis Group
Simon Haykin , 2014, Adaptive Filter Theory 5$^{\mathrm{th}}$ edition, Pearson Education
Limited
Mei-Qin Chen , Tamal Bose , Guo Fang Xu , Feb. 1999, A Direction Set Based Algorithm
for Adaptive Filtering, IEEE Trans.on Signal Processing, Vol. 47, No. 2
Tamal Bose , 2004, Digital Signal and Image Processing, John Wiley & Sons, Ltd
2008, 3GPP TS 36.104: Evolved Universal Terrestrial Radio Access (E-UTRA), Base Station
(BS) radio transmission and reception
Author
Vian S. Al-Doari is one of the staff at Al-Rafidain university college, Baghdad,
Iraq. She was graduated and had B.Sc., M.Sc. and Ph.D. degree awards in modern communications
systems from Al-Nahrian University, Engineering college, Baghdad, Iraq. Her field
study interest includes Adaptive Signal Processing, MIMO and OFDM systems.
Thamer M. Jamel graduated from the University of Technology with a Bachelor's degree
in electronics engineering. He received a Master's and a Doctoral degree in communi-cation
engineering in 1997. His scientific degree is Professor and currently, he is one of
the staff of the communication engineering department at University of Technology,
Baghdad, Iraq. His Research Interests are Adaptive Digital Signal Processing (Algorithms
and Applications) for modern and future Communications system.
Bashar M. Mansoor received the M.Sc. and B.Sc. degrees in communication engineering
from Electrical and Electronic Engineering (EEE) department at University of Technology,
Baghdad, Iraq, in 2008 and 2013, respectively. He gained a Ph.D. degree in Electrical
engineering from Engineering college at University of Baghdad in 2019. His research
interests are in Adaptive filtering, Digital wireless communication and Coding