Design of LMS based adaptive beamformer for ULA antennas
VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 71-78
Design of LMS Based Adaptive Beamformer
for ULA Antennas
Tong Van Luyen1, Truong Vu Bang Giang2,*
1Hanoi University of Industry, Hanoi, Vietnam
2VNU University of Engineering and Technology, 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam
Abstract
This paper proposes a design of an adaptive beamformer for arbitrarily Uniformly spaced Linear Array
(ULA) antennas. Least Mean Square (LMS), a prevalent adaptive beamforming algorithm, has been employed in
the beamformer for the ULA antennas. A procedure has been introduced to validate the proposed design.
Applying the proposal, a LMS based adaptive beamformer for 8×1 ULA antennas has been built and
implemented on Xilinx FPGA. The fundamental characteristics of the implemented beamformer have been
measured and verified. The experimental results show that the beamformer is capable of creating appropriate
weights in order to steer the main lobe of the ULA antennas to the desired direction and to place simultaneously
null points towards the interferences in case of NOAA LEO satellites system.
Received 01 October 2016, Revised 16 November 2016, Accepted 19 November 2016
Keywords: Beamformer design, Adaptive beamformer, Beamformer implementation, ULA antennas .
1. Introduction*
hardware, but the disadvantage of this LMS
algorithm is slow convergence [2-4].
Adaptive beamfomers utilizing beamforming
Recently, design of the beamformer has been
and beamsteering technique are widely applied for
extensively studied for a number of applications
smart antennas. These antennas are very useful to
with several results related to this field from the
increase the effectiveness of radio spectrum
literature. Design and FPGA implementation of
utilizing, interference rejection and reduce power
LMS adaptive algorithm for the beamformer have
consumption. Indeed, smart antennas are broadly
been done by using Xilinx System Generator in
applied in several applications such as radar,
[5], however, complete structrure and verification
sonar, wireless communications, radio astronomy,
of the beamformer have not been given. In [6],
direction finding, seismology and medical
FPGA implementation of a beamformer based on
diagnosis and treatment [1]. In terms of operation,
LMS has been built for radar applications. This
the beamformer is based on adaptive
paper has not presented the design and
beamforming algorithms such as LMS, SMI,
verification procedure of the implemented
RLS, etc. However, in comparison with the
beamformer. The work in [7] implemented a LMS
others, LMS is a popular adaptive algorithm
applying for the beamformer due to some benefits
such as simplicity and easily implementing on
based beamformer on FPGA for power analysis of
embedded
adaptive
beamforming.
The
beamformer has only been verified in a simple
model with input signals of square wave pulse
_______
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T.V. Luyen et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 71-78
72
and applied for power analysis of adaptive
beamforming.
antenna element spacing and
of incidence of incoming signal [10].
is the angle
In our previous papers [8-9], a procedure
of designing, verification the beamformer on
software has been given. In addition, the
design of a beamformer based on FPGA has
been shown, but this design has not been
implemented and verified on real systems.
This is the starting point for further works on
the beamformer’s hardware.
Theoretically, if the main lobe of the ULA
antennas is steered to direction of the
incoming signal, the optimum weights (
)
should be calculated according to mean-
squared error (MSE) criterion and can be
obtained by Wiener-Hopf equation [10].
(2)
In this paper, a design of LMS based
adaptive beamformer for arbitrary ULA
antennas will be proposed. A procedure for
verification of the beamformer will also be
introduced. The beamformer will be
implemented on Xilinx FPGA and verified in
the case of NOAA LEO (National Oceanic
and Atmospheric Administration Low-Earth
Orbiting) satellites system. The capabilities of
forming and steering the beam, operational
processes, and convergence characteristics of
the beamformer will be verified. The results
show that the beamformer operates well in
respect of its principal and meets the design’s
requirements.
The rest of this paper is organized as follows:
Section 2 presents LMS as an adaptive
beamforming algorithm for ULA antennas.
Design formulation of the adaptive beamformer is
introduced in details in Section 3. Section 4 will
validate the proposal. Finally, Section 5 will
conclude this paper.
where
is the covariance
matrix;
is the cross-correlation
vector.
LMS algorithm is invented by Widrow
and Hoff in 1960 and has become one of the
most widely adaptive algorithms used for
filtering [10-11]. The algorithm is based on
the steepest-descent method that recursively
computes and updates the weight vector
based on MSE criterion. MSE is calculated by
applying successive corrections to the weight
vector in the direction of the negative
gradient. The weights can then be updated as
(3)
The algorithm is utilized to compute the
instantaneous estimates of
and
instead
of their actual values. Eventually, the
calculating steps are as follows:
2. LMS algorithm for ULA Antennas
(
(
(
The ULA antennas can be constructed by
N identical directional elements with the
array factor calculated by:
4)
5)
6)
(1)
where
is the vector of input signals
receiving from the ULA antennas, H denotes
as Hermitian (complex conjugate) transpose,
where
is the free space wave number,
is the complex weight
is weight vector,
is the reference,
called step-size
corresponding to each element,
is the
is array output signal,
T.V. Luyen et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 71-78
73
parameter mainly affects the convergence
characteristics of the algorithm.
-
LMS
calculating three equation (4), (5), and (6)
until the error is less than or the
algorithm:
Consecutively
number of samples is equal to no_samples.
- Output: Obtaining data of the weights,
output signal and error.
3. Design Formulation
3.1. Objectives and Requirements
This work aims to:
- Design LMS based adaptive beamformer
for arbitrary ULA antennas.
- Implement a specific case based on the
design, a daptive beamformer for 8×1 ULA
antennas, on FPGA.
Start
Intialization:
; parameters:
, µ, no_samples,
,
,
- Verify the operation of the implemented
beamformer in a particular case.
Matching filter:
Cross-correlation of
and
The results are expected to meet some
requirements such as:
FALSE
Matching
- The implemented beamformer must
work well based on an adaptive beamforming
algorithm, LMS algorithm in particular.
- The beamformer can perform main
functions such as forming and steering the main
lobe to the desired signal, simultaneously placing
NULL points toward interferences in case of
NOAAsatellites system.
TRUE
LMS algoritm:
Calculating the equations (4), (5), and (6)
FALSE
or n = no_samples
TRUE
Output:
Weights, output signal and error for step
3.2. Structure of the beamformer
End
In this section a structure of the adaptive
beamformer based on the foundation given in
section 2 and subsection 3.1 will be built. First of
all, a flowchart of the LMS based adaptive
beamformer is being introduced and presented in
Figure 1. Operational principal of the beamformer
comprises of following steps:
Figure 1. Flow chart of the LMS based adaptive
beamformer.
Consequently, a structure of the adaptive
beamformer has been obtained as given in
Figure 2. The beamformer includes four
components as WeighMultiplier and Sum,
- Initialization: getting input data such as
ErrorSubtractor,
MatchedFilter.
The MatchedFilter detects the reference in
the header of wireless communication system
WeighCalculator,
and
;
initializing parameters for the
beamformer such as index of sampling point
, total number of samples for processing
(no_samples), µ, predefined threshold value
of error ( ), and
- Matching filter: calculating the cross-
correlation of and to detect the
(
frames. Then, the control signal (
generated to enable the Error Subtractor.
) is
.
The ErrorSubstractor calculates the
difference (
) between the reference signal
and the output signal and gives feedback to the
reference in the header of wireless
communication system frames. Then, if the
matching is found, a control signal is
generated to enable the LMS algorithm block.
WeightCalculator by
N weights (
the Weightcalculator have been multiplied by the
and
signal.
) created by
input signals at the
(
)
T.V. Luyen et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 71-78
74
WeightMultiplier to create N sub-products
corresponding to N inputs. These sub-products are
added together to give an output signal (
).
e
Figure 2. Structure of the LMS based adaptive beamformer for N×1 ULA antennas.
This beamformer will be implemented on
Virtex FPGA- xc5vsx50t-1ff1136
(XtremeDSP™ Development Kit) by Xilinx
beamformer gets convergence, these updated
weights will be used to form and steer the beam.
- Step 4 - Measuring and verifying: To
verify the beamformer, the weights, the
output signal, and the error of the
beamformer will be measured.
5
ISE 2015.01, and presented in section 4.
3.3. Verification Procedure
Figure 3 gives a procedure of verifying
the beamformer, in which following steps are
carried out:
Start
Step 1: Generating input data
Inputs of signals and parameters
- Step 1 - Generating input data:
• Input of signals such as desired signal,
interferences, and reference signal.
• Input of parameters such as angle of
arrival (AOA) for desired signal, angles of
interference (AOI) for interferences, µ for
LMS algorithm, and parameters of an 8×1
ULA antenna.
Step 2: Creating array response
Steering vector
Step 3: Executing beamformer
LMS based beamformer
Step 4: Mesuring and Verifying
Weights, output signal and error
- Step 2 - Creating array response: Getting
the output signal (
) of the array from the data
of step 1 using the steering vector.
End
- Step 3 - Executing beamformer: The
beamformer takes input signals from step 2. Then,
it utilizes LMS algorithm to produce
consecutively updated weights. When the
Figure 3. Verification procedure of the beamformer.
T.V. Luyen et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 71-78
75
beamforming (d(n))
Noise/Number of
Interferences
Processing time of
the matched filter
Processing time of
the LMS based
beamformer
100 words
4. Implementation and Experimental Results
AWGN/Up to three
interferences
315 samples
Using the above proposals, in this section,
the implementation and validation on FPGA
of the beamformer will be shown. Following
parameters will be used: the processing
frequency of 100 MHz (equivalent to a time-
unit of 10 ns), µ=0.001, and an ULA antenna
array consisting of 8 elements with spacing of
λ/2. Each signal is presented in 16 bit fixed-
point number. As the results, Xilinx Virtex 5
1685 samples for
getting convergence
and tracking
There
are
two
scenarios
being
investigated: Capability of beamforming and
beamsteeting; Convergence characteristics
with respect to different SNRs and step-sizes.
a) Capability of beamforming and
beamsteeting
FPGA
resource
utilization
for
the
implemented beamformer is summarized in
Table 1. Xilinx chipscope has been used to
obtain the measurement data.
Table 3. Parameters for four investigation cases
Cases
AOA
(degree)
10
AOI
SNR/SIR
Table 1. Virtex 5 resource ultilization
for the beamformer
(degree)
None
0
Case 1
Case 2
Case 3
Case 4
30dB
-45
-30
30
30dB/10
30dB/10
Virtex 5 Resource Used Available Percentage
0, 30
Number of
Slice Registers
Number of LUTs 24183
Number of
13877
32640
32640
8160
42%
74%
88%
-45,0,50 30dB/10
In this scenario, the implemented
beamformer has been used to form and steer
the beam of the ULA antenna arrays in four
cases which have detailed parameters in Table
3. The results including of weights, outputs
and errors have been measured and presented.
7219
Occupied Slices
Number of
bonded IOBs
Number of
FG/BUFGCTRLs
20
480
32
4%
3%
1
Number of
DSP48Es
Table 4. Normalized radiation intensities at AOA
and AOIs for four investigation cases
132
288
45%
NOAA LEO satellite system has been
used to investigate the beamformer following
the procedure presented in section 3. In order
to do that, the beamformer for 8×1 ULA
antennas has been applied for tracking NOAA
LEO satellites. The parameters of the satellite
communication system, which are given in
Table 2, are utilized as input data.
NRP
value
(dB)
0
NRP
value
(dB)
AOA
(degree)
AOI
(degree)
Cases
Case 1
Case 2
10
-45
None
0
0
30
-45
0
0
-23.98
-45.97
-50.65
-25.15
-45.97
-29.26
Case 3
-30
30
0
0
Case 4
Table 2. NOAA LEO satellite system parameters
[12] for verification of the beamformer
50
First of all, measurement weights of four
cases have been used to build corresponding
radiation patterns of the ULA antenna arrays
on MATLAB. These patterns have been
depicted in Figure 4. It can be seen that the
beamformer can form and steer the main
beam of the ULA antennas to the desired
Parameters
LEO satellite system
Standard
Value
NOAA
High Resolution
Picture Transmission
NOAA KLM and
NOAA-N,-P
Minor
Type of satellite
Frame format
Reference data for
Auxiliary Sync with
T.V. Luyen et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 71-78
76
direction and place simultaneously NULL
time, convergence time, and tracking time. It is
clear that the beamfomer operates correctly in
respect of the principal given in section 3.
points towards the directions of interferences.
Specific values of normalized radiation
intensities (NRI) at AOA and AOIs for four
cases are shown in Table 4.
b) Convergence characteristics with respect
to different SNRs and step-sizes
For
further
investigation,
weights
Figure 8 gives the error of the beamformer
with different SNRs of 10 dB, 20 dB, and 30 dB,
respectively, at a fixed step-size µ=0.001. It is
clear that the beamformer gets convergence with a
nearly constant speed while variance is inversely
proportional to SNRs. In addition, the beamformer
becomes more stable as the SNR increases.
Figure 9 indicates the error of the
beamformer with different step-sizes. It can be
observed from Figure 9 that the step-sizes have
significant influence on the convergence speed
of beamformer. The larger the value step-size
is, the faster the convergence but the less the
stability around the minimum value is obtained.
On the other hand, the smaller the value of step-
size is, the slower the convergence but the more
stable around the optimum value the
beamformer is given.
adaptation, error, output and reference in the
case 4 have been presented. The beamforming
process for NOAA LEO satellites have been
conducted by three periods: matching time for
correctly detecting the reference; convergence
time for getting the optimized weights
according to LMS algorithm; and tracking time
for maintaining the state of the pattern. These
results have been shown in Figure 5, 6, 7.
Figure 5 presents the measured results of
weights, w(n), for eight channels. It can be
observed that:
- Weights are zero in matching time
because the beamformer is waiting to detect
the reference for operation. It takes the
matching step 315 time-units to finish.
- Weights strongly vary during the
convergence time according to the LMS
algorithm.
- Weights are keeping around a mean
value with a small variance in tracking time.
These weights are stable over time for the rest
of time in the reference.
The corresponding error, e(n), is depicted in
Figure 6. It can be seen that the convergence
time is fewer than 435 time-units at the error
less than 0.05.
Figure 7 presents the reference, d(n), and
output signal, y(n), over time. It is clear that the
beamformer’s output can meet the reference
and keep tracking it over time after getting
convergence.
Without loss of generality, four cases have
been investigated to verify the operation of the
beaformer. The results demonstrate that the
beamformer is able to form and steer the main
lobe to the direction of the desired signal and
simultaneously place NULL points to various
interferences. Specifically, in the case 4,
completed operation of the beamformer has
been verified through three periods: matching
Figure 4. Radiation patterns of ULA antennas
in four cases.
5. Conclusion
This paper proposed a design of LMS based
adaptive beamformer for arbitrary ULA antennas
and introduced a verification procedure for the
design. In order to validate the design, a
beamformer for 8×1 ULA antennas has been
implemented on Xilinx FPGA chip. Verification
in the case of tracking the NOAA LEO satellites
has been done. The measured results show that
the beamformer operates well. In particular, the
T.V. Luyen et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 71-78
77
beamformer is able to form and steer the main
lobe to the desired user and simultaneously place
NULL points toward various interferences.
Besides, it operates correctly in term of the given
can be applied to design smart antennas for a
number of applications such as radar, wireless
communications, and directional Wi-Fi.
F
principal and the LMS algorithm. The proposal
Figure 5. Weights adaptation over time.
Figure 6. Error between output and reference signals over time.
Figure 7. Output and reference signals over time: 0 -1500th , and 316 - 800th time-unit.
H
Figure 8. Error over time with different SNRs.
Figure 9. Error over time with different step-sizes.
T.V. Luyen et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 71-78
78
Advanced
Electrical
and
Electronics
Acknowledgements
Engineering, vol. 2, no. 3, pp. 53-57, 2013.
2014 International Conf. on Commun. and
Melmaruvathur, India, Apr. 2014.
This work has been partly supported by
Vietnam National University, Hanoi (VNU),
under Project No. QG. 16.27.
of 2015 International Conf. on Commun.,
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