Design of LMS based adaptive beamformer for ULA antennas

ze 
 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 - LMS algorithm: Consecutively 
characteristics of the algorithm. calculating three equation (4), (5), and (6) 
 until the error is less than or the 
3. Design Formulation number of samples is equal to no_samples. 
3.1. Objectives and Requirements - Output: Obtaining data of the weights, 
 output signal and error. 
 This work aims to: 
 - Design LMS based adaptive beamformer Start 
 \
for arbitrary ULA antennas. 
 - Implement a specific case based on the Intialization: ; parameters: , , 
design, a daptive beamformer for 8×1 ULA , µ, no_samples, 
antennas, on FPGA. 
 - Verify the operation of the implemented Matching filter: 
beamformer in a particular case. Cross-correlation of and 
 The results are expected to meet some 
 FALSE 
requirements such as: Matching 
 - The implemented beamformer must TRUE 
work well based on an adaptive beamforming LMS algoritm: 
algorithm, LMS algorithm in particular. Calculating the equations (4), (5), and (6) 
 - The beamformer can perform main 
functions such as forming and steering the main FALSE 
 or n = no_samples 
lobe to the desired signal, simultaneously placing 
NULL points toward interferences in case of TRUE 
NOAA satellites system. Output: 
 Weights, output signal and error for step 
3.2. Structure of the beamformer 4 
 In this section a structure of the adaptive End 
beamformer based on the foundation given in Figure 1. Flow chart of the LMS based adaptive 
section 2 and subsection 3.1 will be built. First of beamformer. 
all, a flowchart of the LMS based adaptive Consequently, a structure of the adaptive 
beamformer is being introduced and presented in beamformer has been obtained as given in 
Figure 1. Operational principal of the beamformer Figure 2. The beamformer includes four 
comprises of following steps: components as WeighMultiplier and Sum, 
 - Initialization: getting input data such as ErrorSubtractor, WeighCalculator, and 
 ; initializing parameters for the MatchedFilter. 
beamformer such as index of sampling point The MatchedFilter detects the reference in 
 the header of wireless communication system 
( , total number of samples for processing 
(no_samples), µ, predefined threshold value frames. Then, the control signal ( ) is 
 generated to enable the Error Subtractor. 
of error ( ), and . 
 The ErrorSubstractor calculates the 
 - Matching filter: calculating the cross-
 difference ( ) between the reference signal 
correlation of and to detect the 
 and the output signal and gives feedback to the 
reference in the header of wireless 
communication system frames. Then, if the WeightCalculator by and signal. 
matching is found, a control signal is N weights ( ) created by 
generated to enable the LMS algorithm block. the Weightcalculator have been multiplied by the 
 input signals ( ) at the 
74 T.V. Luyen et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 71-78 
WeightMultiplier to create N sub-products added together to give an output signal ( ). 
corresponding to N inputs. These sub-products are 
e 
 Figure 2. Structure of the LMS based adaptive beamformer for N×1 ULA antennas. 
 This beamformer will be implemented on beamformer gets convergence, these updated 
Virtex 5 FPGA- xc5vsx50t-1ff1136 weights will be used to form and steer the beam. 
(XtremeDSP™ Development Kit) by Xilinx - Step 4 - Measuring and verifying: To 
ISE 2015.01, and presented in section 4. verify the beamformer, the weights, the 
 output signal, and the error of the 
3.3. Verification Procedure beamformer will be measured. 
 Figure 3 gives a procedure of verifying Start 
the beamformer, in which following steps are 
carried out: 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. Step 2: Creating array response 
 Steering vector 
 • Input of parameters such as angle of 
arrival (AOA) for desired signal, angles of 
interference (AOI) for interferences, µ for Step 3: Executing beamformer 
 LMS based beamformer 
LMS algorithm, and parameters of an 8×1 
ULA antenna. 
 - Step 2 - Creating array response: Getting Step 4: Mesuring and Verifying 
 Weights, output signal and error 
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, Figure 3. Verification procedure of the beamformer. 
it utilizes LMS algorithm to produce 
consecutively updated weights. When the 
 T.V. Luyen et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 71-78 75 
4. Implementation and Experimental Results beamforming (d(n)) 100 words 
 Noise/Number of AWGN/Up to three 
 Using the above proposals, in this section, Interferences interferences 
the implementation and validation on FPGA Processing time of 315 samples 
of the beamformer will be shown. Following the matched filter 
 Processing time of 1685 samples for 
parameters will be used: the processing 
 the LMS based getting convergence 
frequency of 100 MHz (equivalent to a time- beamformer and tracking 
unit of 10 ns), µ=0.001, and an ULA antenna There are two scenarios being 
array consisting of 8 elements with spacing of investigated: Capability of beamforming and 
λ/2. Each signal is presented in 16 bit fixed- beamsteeting; Convergence characteristics 
point number. As the results, Xilinx Virtex 5 with respect to different SNRs and step-sizes. 
FPGA resource utilization for the a) Capability of beamforming and 
implemented beamformer is summarized in beamsteeting 
Table 1. Xilinx chipscope has been used to 
obtain the measurement data. Table 3. Parameters for four investigation cases 
 Cases AOA AOI SNR/SIR 
 Table 1. Virtex 5 resource ultilization (degree) (degree) 
 for the beamformer 
 Case 1 10 None 30dB 
 Virtex 5 Resource Used Available Percentage Case 2 -45 0 30dB/10 
 Number of Case 3 -30 0, 30 30dB/10 
 13877 32640 42% 
 Slice Registers Case 4 30 -45,0,50 30dB/10 
 Number of LUTs 24183 32640 74% In this scenario, the implemented 
 Number of 
 7219 8160 88% beamformer has been used to form and steer 
 Occupied Slices the beam of the ULA antenna arrays in four 
 Number of 
 20 480 4% 
 bonded IOBs cases which have detailed parameters in Table 
 Number of 3. The results including of weights, outputs 
 1 32 3% 
 FG/BUFGCTRLs and errors have been measured and presented. 
 Number of 
 132 288 45% Table 4. Normalized radiation intensities at AOA 
 DSP48Es and AOIs for four investigation cases 
 NOAA LEO satellite system has been NRP NRP 
 AOA AOI 
used to investigate the beamformer following Cases value value 
 (degree) (degree) 
the procedure presented in section 3. In order (dB) (dB) 
to do that, the beamformer for 8×1 ULA Case 1 10 0 None 
antennas has been applied for tracking NOAA Case 2 -45 0 0 -23.98 
 0 -45.97 
LEO satellites. The parameters of the satellite Case 3 -30 0 
communication system, which are given in 30 -50.65 
Table 2, are utilized as input data. -45 -25.15 
 Case 4 30 0 0 -45.97 
 Table 2. NOAA LEO satellite system parameters 50 -29.26 
 [12] for verification of the beamformer 
 Parameters Value First of all, measurement weights of four 
 LEO satellite system NOAA cases have been used to build corresponding 
 Standard High Resolution radiation patterns of the ULA antenna arrays 
 Picture Transmission on MATLAB. These patterns have been 
 Type of satellite NOAA KLM and depicted in Figure 4. It can be seen that the 
 NOAA-N,-P beamformer can form and steer the main 
 Frame format Minor beam of the ULA antennas to the desired 
 Reference data for Auxiliary Sync with 
76 T.V. Luyen et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 71-78 
direction and place simultaneously NULL time, convergence time, and tracking time. It is 
points towards the directions of interferences. clear that the beamfomer operates correctly in 
Specific values of normalized radiation respect of the principal given in section 3. 
intensities (NRI) at AOA and AOIs for four b) Convergence characteristics with respect 
cases are shown in Table 4. to different SNRs and step-sizes 
 For further investigation, weights Figure 8 gives the error of the beamformer 
adaptation, error, output and reference in the with different SNRs of 10 dB, 20 dB, and 30 dB, 
case 4 have been presented. The beamforming respectively, at a fixed step-size µ=0.001. It is 
process for NOAA LEO satellites have been clear that the beamformer gets convergence with a 
conducted by three periods: matching time for nearly constant speed while variance is inversely 
correctly detecting the reference; convergence proportional to SNRs. In addition, the beamformer 
time for getting the optimized weights becomes more stable as the SNR increases. 
according to LMS algorithm; and tracking time Figure 9 indicates the error of the 
for maintaining the state of the pattern. These beamformer with different step-sizes. It can be 
results have been shown in Figure 5, 6, 7. observed from Figure 9 that the step-sizes have 
 Figure 5 presents the measured results of significant influence on the convergence speed 
weights, w(n), for eight channels. It can be of beamformer. The larger the value step-size 
observed that: is, the faster the convergence but the less the 
 - Weights are zero in matching time stability around the minimum value is obtained. 
because the beamformer is waiting to detect On the other hand, the smaller the value of step-
the reference for operation. It takes the size is, the slower the convergence but the more 
matching step 315 time-units to finish. stable around the optimum value the 
 - Weights strongly vary during the beamformer is given. 
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 Figure 4. Radiation patterns of ULA antennas 
 in four cases. 
beamformer’s output can meet the reference 
and keep tracking it over time after getting 
 5. Conclusion 
convergence. 
 Without loss of generality, four cases have This paper proposed a design of LMS based 
been investigated to verify the operation of the adaptive beamformer for arbitrary ULA antennas 
beaformer. The results demonstrate that the and introduced a verification procedure for the 
beamformer is able to form and steer the main design. In order to validate the design, a 
lobe to the direction of the desired signal and beamformer for 8×1 ULA antennas has been 
simultaneously place NULL points to various implemented on Xilinx FPGA chip. Verification 
interferences. Specifically, in the case 4, in the case of tracking the NOAA LEO satellites 
completed operation of the beamformer has has been done. The measured results show that 
been verified through three periods: matching 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 can be applied to design smart antennas for a 
lobe to the desired user and simultaneously place number of applications such as radar, wireless 
NULL points toward various interferences. communications, and directional Wi-Fi. 
Besides, it operates correctly in term of the given F 
principal and the LMS algorithm. The proposal 
 F 
 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. 
78 T.V. Luyen et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 71-78 
Acknowledgements Advanced Electrical and Electronics 
 Engineering, vol. 2, no. 3, pp. 53-57, 2013. 
 This work has been partly supported by [6] Anjitha D., and Shanmugha S.G.A., "FPGA 
Vietnam National University, Hanoi (VNU), Implementation of Beamforming Algorithm 
under Project No. QG. 16.27. for Terrestrial Radar Application”, in Proc. of 
 2014 International Conf. on Commun. and 
 Signal Processing (ICCSP), pp. 453-457, 
 Melmaruvathur, India, Apr. 2014. 
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