Wideband Adaptive LMS Beamforming Using QMF Subband ...
Wideband Adaptive LMS Beamforming Using QMF Subband Decomposition for Sonar H. Charafeddine, V. Groza University of Ottawa/School of Electrical Engineering and Computer Science Ottawa, Canada {HChar099,VGroza}@uOttawa.ca
∆
Abstract— This paper describes the utilization of wideband LMS adaptive beamforming with QMF filterbanks decomposition for sonar application. The obtained results showed that applying the new algorithm yields better results than the time domain LMS beamformer (TD). The subband LMS beamformer isolates the interference in its own band and uses that band beamformer to steer a null in its direction, this capability enables the other beamformers to adapt independently without been affected by the interference.
I.
1 cos
Where d is the distance between each two elements, and is equal to half a wavelength for uniform linear arrays (ULA). The phase rotation at each element is: ∆
∆ 2
Consider a linear array of N sensors, the signal arriving at each array element is time delayed due to the extra distance travelled by each plane wave which is equal to
1 cos
1 cos
∆
(5) 2 The antenna pattern is normalized to the number of elements N 1
(6)
Using the geometric series we get: 1
. .
1 Using the Euler formula we get:
. .
(1)
(2) 2 ∆ , The extra distance of every array element relative to the phase is
.
.
(8)
1 The time delay causes phase rotation in the frequency domain which can be expressed as
(7)
.
1 1
1 ,
(4)
2
In the rest of this section we review the beamforming concept, by focusing mainly on the uniform linear array (ULA) case.
∆
2
And the delay at each element is:
INTRODUCTION
The use of filterbanks decomposition in adaptive wideband beamforming is not novel as we can see in [3] and [4]. However, in both of the mentioned publications the wideband beamforming is done at very high frequencies where the narrow band approximation is valid and the delay at each array element is modeled as phase rotation. However, in sonar the narrow band approximation is no longer valid due to the fact that the carrier frequency is not much larger than the bandwidth of the transmitted signal. In addition the use of LMS in wideband beamforming enables efficient interference cancellation and reduces the hardware complexity.
∆
(3)
.
.
cos . cos
The first term can be dropped due to the fact that the physical array is centered at (N-1) d/2. Hence:
1
w
cos .
(9)
cos
The resulting minimum MSE is: (13)
The received signal at each array element is delayed according to equation (5). Each element delay corresponding amount of time is converted to samples by multiplying ∆ with the sampling frequency Fs. The result might contain a fractional part. Therefore, it is better to use a high sampling frequency relative to the operating frequency (in this paper the sonar waveform has a center frequency of about 80 KHz, a 20 KHz bandwidth, and a sampling frequency of 1.2 MHz). In addition to the utilization of a high sampling frequency, we also use a Lagrange polynomial fractional delay filter to compensate for the fractional sample delay in the simulated received signal. Additive white Gaussian noise (AWGN) is added to each antenna element according to pre-set signal to noise ratio (SNR). Interference is also added according to a pre-set signal to noise and interference ratio (SINAD). Hence, the output of the kth element is: (10) Where s is the delayed signal, n is the noise and i is the interference. The objective of the adaptive beamformer that is described in this paper is to steer the beam in the direction of the signal and place a null in the direction of the interference. II.
Instead of using the matrix inversion we use a gradient search to solve for Jmin, which is quadratic and will converge to a unique minimum. Using the steepest descent (SD) algorithm we define: 1 1
(14)
1 , 1,2, …
The LMS algorithm estimates and instantaneous values, where . Hence, and
based on ,
1
(15)
1 1 is the LMS adaptation step size.
Where, III.
Quadrature Mirror Filters (QMF)
It is desired that the QMF filters are designed to achieve perfect reconstruction (PR). The PR is desired because the reconstructed signal is used in various post processing algorithms such as Doppler analysis, target detection and tracking and many other processing blocks. The QMF aliasing constraint is: (16)
THE LMS ADAPTIVE ALGORITHM
The LMS algorithm minimizes the error iteratively between the output and the reference signal. The mean square error (MSE) cost function is,
Magnitude (dB)
|
0
| (11)
-20 -40 -60 -80 0.1
0.2
0.3
0.4 0.5 0.6 0.7 Normalized Frequency (×π rad/sample)
0.8
0.9
1
0
0
(12)
-1000 Phase (degrees)
is the variance of the desired signal, is the Where cross correlation between the input signal and the desired signal , is the autocorrelation of the input signal, and is the LMS weights. To minimize the cost function we find the gradient of with respect to , and set to 0.
-2000 -3000 -4000 -5000 -6000
0
0.1
0.2
0.3 0.4 0.5 0.6 0.7 Normalized Frequency (×π rad/sample)
Figure 1 Crochiere QMF.
0.8
0.9
1
shows a three level QMF wavelet packet, and Figure 3 shows the spectrum decomposition of the same wavelet packet.
The QMF filtering and aliasing constraint is: 1 2
(17)
To achieve perfect reconstruction we need to design the filter H0(z) to satisfy the constraint of equation (17).
h1 h1
y11
h1 h0
y1
h0
y10
h1 h0
h1 h0
y01
h1 h0
y0
h0
y00
h1 h0
y111 y110 y101 y100 y011
IV.
Time Domain LMS (TD)
In the baseband adaptive time domain LMS system the signal at the output of each array element is demodulated to baseband, then a low pass filter is applied to remove the images. The output of the filters (in-band and quadrature components) is then down sampled accordingly (optional) as described in Figure 4. The output of the downsampler is passed to the LMS adaptive system which multiplies each complex sample (I and Q components) by an adaptive weight that is calculated iteratively according to equation (15). The reference signal that is described in the same figure is the waveform that the sonar transmits, hence the LMS error can be derived from the received waveform and the transmitted one.
y010 y001 y000
Figure 2 QMF wavelet packet.
Figure 4 time domain adaptive beamformer.
Figure 3 The spectrum of a QMF wavelet packet with three stages.
The design procedure minimizes a weighted combination of the ripple energy and the stop band energy of the low pass prototype filter. The design procedure is motivated by a paper by Jain and Crochiere [1]. The QMF filters frequency responses is shown in Figure 1. A simple way to achieve multiband decomposition with perfect construction using QMF would be the use of a tree structure QMF, where the QMF filters are cascaded into many stages to achieve two to the power of the number stages (2stages) bands in decomposition. Figure 2
A. Performance with Gaussian noise The performance of the TD beamformer with various SNR is studied in this section, where it was demonstrated that the system was able to steer toward the signal direction of arrival (DOA) at 0 dB SNR value as shown in Figure 5. The performance was also studied at 10 dB and 20 dB SNR values, where signal DOA was set 20 degrees. The antenna beam pattern at 10 dB SNR is shown in Figure 6. The transmitted waveform is a linear FM chirp sweeping from 70 KHz to 90 KHz, the sampling frequency (Fs) is 1.2 MHz, and the pulse width is 1.7 ms. The LMS weights convergence over time is
shown in Figure 7 and Figure 8 for both SNR values of 0 dB, and 10 dB. The antenna beam pattern 0 Conventional TD LMS
-10
-20
dB
-30
-40
-50
-60
-70 -100
Figure 8 LMS weights convergence for 10 dB SNR (DOA is set to 20o). -80
-60
-40
-20 0 20 Angle in degrees
40
60
80
100
Figure 5 The LMS array pattern at 0dB SNR (the signal DOA is 20o). The antenna beam pattern 0 Conventional TD LMS -10
-20
B. Performance with interference The performance of the baseband time domain LMS with various signal to interference and noise ratio SINAD is presented in this section, where it was demonstrated that the system was able to steer toward the signal DOA and place a null in the interference DOA.
-30
The antenna beam pattern
dB
0 Conventional TD LMS
-40 -10
-50
-20
-60
dB
-30
-70
-80 -100
-40
-50
-80
-60
-40
-20
0 20 Angle in degrees
40
60
80
100 -60
Figure 6 The LMS array pattern at +10dB SNR (the DOA is 20o).
-70
-80 -100
-80
-60
-40
-20
0 20 Angle in degrees
40
60
80
100
Figure 9 Beam pattern with the signal DOA at 0o and the interference DOA at 50o, SINAD=-10 dB.
Figure 9 shows the LMS beam pattern with the signal DOA at 0o, the interference DOA at 50o, and the SINAD is 10dB. It can be noticed that the LMS algorithm placed a null in the direction of the interference with more than 35dB attenuation, while the signal main beam at 0o main beam was maintained. Figure 7 LMS weights convergence for 0 dB SNR (DOA is set to 20o).
The experiment was done using MATLAB, by simulating ten elements ULA, with AWGN and interference added to each antenna element according to the SNR, as discussed in section I.
The LMS weights convergence over time (iterations) is shown in Figure 10, where it can be noticed that the LMS system is placing a null in the interference direction at 50o. The null gets more and more attenuated with time (iterations).
The IQ demodulation of the high frequency signals is performed as described in Figure 4. The output of the downsampler is then passed to the analysis filter banks block of Figure 12, where each band is passed to an LMS adaptive beamformer. The outputs of the beamformers are then passed to the synthesis filter banks block to reconstruct the waveform.
Figure 10 LMS weights convergence (Notice the null placed in the interference direction at 50o).
The experiment was done using MATLAB, by simulating ten elements ULA, with AWGN added to each antenna element according to the SNR. Interference is also added according to a pre-set SINAD, as described in (10).
V.
QMF LMS adaptive beamforming
This system shares the baseband property with the baseband time domain beamformer. Only this time we down sample the signal I and Q components to have the baseband bandwidth limited to the signal bandwidth or a little bit higher to leave room for the relaxation of the low pass filter design (antialiasing filter). The baseband is divided into multiple bands, each having its own LMS system.
Figure 12 Wideband QMF Adaptive LMS System.
A. Performance with Noise Using a linear FM chirp sweeping from 70 KHz to 90 KHz, a sampling frequency Fs is 1.2 MHz, and a pulse width is 1.7 ms, the wideband QMF LMS system exhibited similar performance to the TD system, as demonstrated in Figure 13 and Figure 14. The antenna beam pattern 0 Conventional QMF LMS
-10
-20
-30
dB
-40
-50
-60
-70
-80
Figure 11 Adaptive LMS system using filter banks.
-90
-100 -100
The signal decomposition of each array element is done using a tree structure quadrature mirror filter (QMF) as described in Figure 2. Each analysis band is combined with its corresponding band from the other array elements to perform beamforming as described in Figure 11. The output of each beamformer is then passed to the synthesis filter banks block to reconstruct the waveform.
-80
-60
-40
-20
0 20 Angle in degrees
40
60
80
100
Figure 13 QMF beam pattern at 20dB SNR.
The performance similarity between the two systems in the AWGN environment make sense, because the two system match. However, the QMF LMS system will exhibit better performance in the presence of narrow band
interference, because the interference is isolated in its own band and a null is placed in its direction using the same band beamformer, while the other band beamformers are not affected. The antenna beam pattern 0 Conventional TD LMS -10
dB
-20
-30
-40
to each antenna element according to the SNR, as discussed in section I. B. QMF Performance with Interference Using a linear FM chirp sweeping from 70 KHz to 90 KHz, a sampling frequency of 1.2 MHz, a pulse width of 1.7 ms, a signal DOA of 0o, an interference DOA at 50o, and a SINAD of -10dB, the QMF LMS system exhibited higher performance than the TD system, where it can be noticed in Figure 15 that the null in the interference direction exceeds -45dB, so about 10 dB lower than the TD LMS. The convergence of the wideband QMF LMS system is shown in Figure 16. VI.
-50
-60 -100
-80
-60
-40
-20
0 20 Angle in degrees
40
60
80
100
Figure 14 QMF beam pattern at 20dB SNR. The antenna beam pattern 0 Conventional TD LMS -10
-20
dB
-30
-40
CONCLUSION
In this paper we studied and simulated a new wideband adaptive LMS beamformer with subband decomposition for Sonar application. It can be noticed from the simulation sections that the new system exhibits superior performance to the TD LMS beamformer in the presence of interference because of its capability to isolate the interference and steer a null in its direction using the beamformer that is employed in the same band, this capability also enables the other beamformers that are employed in different bands to adapt independently without been affected by the interference.
-50
REFERENCE
-60
[1]
-70
-80 -100
-80
-60
-40
-20
0 20 Angle in degrees
40
60
80
100
Figure 15 Beam pattern with the signal DOA at 0o and the interference DOA at 50o, the SINAD is -10 dB.
[2]
[3]
[4]
[5] [6] [7]
[8]
Figure 16 QMF convergence over time, with a SINAD of-10dB.
The experiment was done using MATLAB, by simulating ten elements ULA, with AWGN and interference added
[9]
V. K. Jain and R. E. Crochiere, "Quadrature Mirror Filter Design in the Time Domain", IEEE Trans. Acoustics, Speech, Signal Processing, vol. 32, no. 2, pp. 253-361, April 1984. J. An and B. Champagne, “GSC realisations using the twodimensional transform LMS algorithm,” IEE Proc. Radar, Sonar and Navig., vol.141, pp. 270–278, Oct. 1994. Wei Liu and Richard J. Langley, “An Adaptive Wideband Beamforming Structure With Combined Subband Decomposition,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 57, NO. 7, JULY 2009 Peter G. Vouras, and Trac D. Tran, “Wideband Adaptive Beamforming Using Linear Phase Filterbanks,” Signals, Systems and Computers, 2006. ACSSC '06. Fortieth Asilomar Conference on, Oct. 29 2006-Nov. 1 2006. S. Haykin, Adaptive Filter Theory, Prentice Hall, Upper Saddle River, NJ, 1996. P. P. Vaidyanathan, Multirate Systems and Filter Banks, Prentice Hall, NJ, 1993. Harry L. Van Trees, Detection, John Wiley & Sons, Estimation, and Modulation Theory, Part IV, Optimum Array Processing, 2002. Alan V. Oppenheim & Ronald W. Schafer, Discrete-time Signal Processing, Second edition, Prentice Hall Signal Processing series, 1999. H. Charafeddine, V. Groza, “Design and Simulation of a Variable Bit Load Adaptive OFDM Transceiver for Frequency Selective Channel”, Instrumentation & Measurement, Sensor Network and Automation (IMSNA), 2012 International Symposium on. 25-28 Aug. 2012 Sanya, China). 95-101. 25-28 Aug 2012
∆
Abstract— This paper describes the utilization of wideband LMS adaptive beamforming with QMF filterbanks decomposition for sonar application. The obtained results showed that applying the new algorithm yields better results than the time domain LMS beamformer (TD). The subband LMS beamformer isolates the interference in its own band and uses that band beamformer to steer a null in its direction, this capability enables the other beamformers to adapt independently without been affected by the interference.
I.
1 cos
Where d is the distance between each two elements, and is equal to half a wavelength for uniform linear arrays (ULA). The phase rotation at each element is: ∆
∆ 2
Consider a linear array of N sensors, the signal arriving at each array element is time delayed due to the extra distance travelled by each plane wave which is equal to
1 cos
1 cos
∆
(5) 2 The antenna pattern is normalized to the number of elements N 1
(6)
Using the geometric series we get: 1
. .
1 Using the Euler formula we get:
. .
(1)
(2) 2 ∆ , The extra distance of every array element relative to the phase is
.
.
(8)
1 The time delay causes phase rotation in the frequency domain which can be expressed as
(7)
.
1 1
1 ,
(4)
2
In the rest of this section we review the beamforming concept, by focusing mainly on the uniform linear array (ULA) case.
∆
2
And the delay at each element is:
INTRODUCTION
The use of filterbanks decomposition in adaptive wideband beamforming is not novel as we can see in [3] and [4]. However, in both of the mentioned publications the wideband beamforming is done at very high frequencies where the narrow band approximation is valid and the delay at each array element is modeled as phase rotation. However, in sonar the narrow band approximation is no longer valid due to the fact that the carrier frequency is not much larger than the bandwidth of the transmitted signal. In addition the use of LMS in wideband beamforming enables efficient interference cancellation and reduces the hardware complexity.
∆
(3)
.
.
cos . cos
The first term can be dropped due to the fact that the physical array is centered at (N-1) d/2. Hence:
1
w
cos .
(9)
cos
The resulting minimum MSE is: (13)
The received signal at each array element is delayed according to equation (5). Each element delay corresponding amount of time is converted to samples by multiplying ∆ with the sampling frequency Fs. The result might contain a fractional part. Therefore, it is better to use a high sampling frequency relative to the operating frequency (in this paper the sonar waveform has a center frequency of about 80 KHz, a 20 KHz bandwidth, and a sampling frequency of 1.2 MHz). In addition to the utilization of a high sampling frequency, we also use a Lagrange polynomial fractional delay filter to compensate for the fractional sample delay in the simulated received signal. Additive white Gaussian noise (AWGN) is added to each antenna element according to pre-set signal to noise ratio (SNR). Interference is also added according to a pre-set signal to noise and interference ratio (SINAD). Hence, the output of the kth element is: (10) Where s is the delayed signal, n is the noise and i is the interference. The objective of the adaptive beamformer that is described in this paper is to steer the beam in the direction of the signal and place a null in the direction of the interference. II.
Instead of using the matrix inversion we use a gradient search to solve for Jmin, which is quadratic and will converge to a unique minimum. Using the steepest descent (SD) algorithm we define: 1 1
(14)
1 , 1,2, …
The LMS algorithm estimates and instantaneous values, where . Hence, and
based on ,
1
(15)
1 1 is the LMS adaptation step size.
Where, III.
Quadrature Mirror Filters (QMF)
It is desired that the QMF filters are designed to achieve perfect reconstruction (PR). The PR is desired because the reconstructed signal is used in various post processing algorithms such as Doppler analysis, target detection and tracking and many other processing blocks. The QMF aliasing constraint is: (16)
THE LMS ADAPTIVE ALGORITHM
The LMS algorithm minimizes the error iteratively between the output and the reference signal. The mean square error (MSE) cost function is,
Magnitude (dB)
|
0
| (11)
-20 -40 -60 -80 0.1
0.2
0.3
0.4 0.5 0.6 0.7 Normalized Frequency (×π rad/sample)
0.8
0.9
1
0
0
(12)
-1000 Phase (degrees)
is the variance of the desired signal, is the Where cross correlation between the input signal and the desired signal , is the autocorrelation of the input signal, and is the LMS weights. To minimize the cost function we find the gradient of with respect to , and set to 0.
-2000 -3000 -4000 -5000 -6000
0
0.1
0.2
0.3 0.4 0.5 0.6 0.7 Normalized Frequency (×π rad/sample)
Figure 1 Crochiere QMF.
0.8
0.9
1
shows a three level QMF wavelet packet, and Figure 3 shows the spectrum decomposition of the same wavelet packet.
The QMF filtering and aliasing constraint is: 1 2
(17)
To achieve perfect reconstruction we need to design the filter H0(z) to satisfy the constraint of equation (17).
h1 h1
y11
h1 h0
y1
h0
y10
h1 h0
h1 h0
y01
h1 h0
y0
h0
y00
h1 h0
y111 y110 y101 y100 y011
IV.
Time Domain LMS (TD)
In the baseband adaptive time domain LMS system the signal at the output of each array element is demodulated to baseband, then a low pass filter is applied to remove the images. The output of the filters (in-band and quadrature components) is then down sampled accordingly (optional) as described in Figure 4. The output of the downsampler is passed to the LMS adaptive system which multiplies each complex sample (I and Q components) by an adaptive weight that is calculated iteratively according to equation (15). The reference signal that is described in the same figure is the waveform that the sonar transmits, hence the LMS error can be derived from the received waveform and the transmitted one.
y010 y001 y000
Figure 2 QMF wavelet packet.
Figure 4 time domain adaptive beamformer.
Figure 3 The spectrum of a QMF wavelet packet with three stages.
The design procedure minimizes a weighted combination of the ripple energy and the stop band energy of the low pass prototype filter. The design procedure is motivated by a paper by Jain and Crochiere [1]. The QMF filters frequency responses is shown in Figure 1. A simple way to achieve multiband decomposition with perfect construction using QMF would be the use of a tree structure QMF, where the QMF filters are cascaded into many stages to achieve two to the power of the number stages (2stages) bands in decomposition. Figure 2
A. Performance with Gaussian noise The performance of the TD beamformer with various SNR is studied in this section, where it was demonstrated that the system was able to steer toward the signal direction of arrival (DOA) at 0 dB SNR value as shown in Figure 5. The performance was also studied at 10 dB and 20 dB SNR values, where signal DOA was set 20 degrees. The antenna beam pattern at 10 dB SNR is shown in Figure 6. The transmitted waveform is a linear FM chirp sweeping from 70 KHz to 90 KHz, the sampling frequency (Fs) is 1.2 MHz, and the pulse width is 1.7 ms. The LMS weights convergence over time is
shown in Figure 7 and Figure 8 for both SNR values of 0 dB, and 10 dB. The antenna beam pattern 0 Conventional TD LMS
-10
-20
dB
-30
-40
-50
-60
-70 -100
Figure 8 LMS weights convergence for 10 dB SNR (DOA is set to 20o). -80
-60
-40
-20 0 20 Angle in degrees
40
60
80
100
Figure 5 The LMS array pattern at 0dB SNR (the signal DOA is 20o). The antenna beam pattern 0 Conventional TD LMS -10
-20
B. Performance with interference The performance of the baseband time domain LMS with various signal to interference and noise ratio SINAD is presented in this section, where it was demonstrated that the system was able to steer toward the signal DOA and place a null in the interference DOA.
-30
The antenna beam pattern
dB
0 Conventional TD LMS
-40 -10
-50
-20
-60
dB
-30
-70
-80 -100
-40
-50
-80
-60
-40
-20
0 20 Angle in degrees
40
60
80
100 -60
Figure 6 The LMS array pattern at +10dB SNR (the DOA is 20o).
-70
-80 -100
-80
-60
-40
-20
0 20 Angle in degrees
40
60
80
100
Figure 9 Beam pattern with the signal DOA at 0o and the interference DOA at 50o, SINAD=-10 dB.
Figure 9 shows the LMS beam pattern with the signal DOA at 0o, the interference DOA at 50o, and the SINAD is 10dB. It can be noticed that the LMS algorithm placed a null in the direction of the interference with more than 35dB attenuation, while the signal main beam at 0o main beam was maintained. Figure 7 LMS weights convergence for 0 dB SNR (DOA is set to 20o).
The experiment was done using MATLAB, by simulating ten elements ULA, with AWGN and interference added to each antenna element according to the SNR, as discussed in section I.
The LMS weights convergence over time (iterations) is shown in Figure 10, where it can be noticed that the LMS system is placing a null in the interference direction at 50o. The null gets more and more attenuated with time (iterations).
The IQ demodulation of the high frequency signals is performed as described in Figure 4. The output of the downsampler is then passed to the analysis filter banks block of Figure 12, where each band is passed to an LMS adaptive beamformer. The outputs of the beamformers are then passed to the synthesis filter banks block to reconstruct the waveform.
Figure 10 LMS weights convergence (Notice the null placed in the interference direction at 50o).
The experiment was done using MATLAB, by simulating ten elements ULA, with AWGN added to each antenna element according to the SNR. Interference is also added according to a pre-set SINAD, as described in (10).
V.
QMF LMS adaptive beamforming
This system shares the baseband property with the baseband time domain beamformer. Only this time we down sample the signal I and Q components to have the baseband bandwidth limited to the signal bandwidth or a little bit higher to leave room for the relaxation of the low pass filter design (antialiasing filter). The baseband is divided into multiple bands, each having its own LMS system.
Figure 12 Wideband QMF Adaptive LMS System.
A. Performance with Noise Using a linear FM chirp sweeping from 70 KHz to 90 KHz, a sampling frequency Fs is 1.2 MHz, and a pulse width is 1.7 ms, the wideband QMF LMS system exhibited similar performance to the TD system, as demonstrated in Figure 13 and Figure 14. The antenna beam pattern 0 Conventional QMF LMS
-10
-20
-30
dB
-40
-50
-60
-70
-80
Figure 11 Adaptive LMS system using filter banks.
-90
-100 -100
The signal decomposition of each array element is done using a tree structure quadrature mirror filter (QMF) as described in Figure 2. Each analysis band is combined with its corresponding band from the other array elements to perform beamforming as described in Figure 11. The output of each beamformer is then passed to the synthesis filter banks block to reconstruct the waveform.
-80
-60
-40
-20
0 20 Angle in degrees
40
60
80
100
Figure 13 QMF beam pattern at 20dB SNR.
The performance similarity between the two systems in the AWGN environment make sense, because the two system match. However, the QMF LMS system will exhibit better performance in the presence of narrow band
interference, because the interference is isolated in its own band and a null is placed in its direction using the same band beamformer, while the other band beamformers are not affected. The antenna beam pattern 0 Conventional TD LMS -10
dB
-20
-30
-40
to each antenna element according to the SNR, as discussed in section I. B. QMF Performance with Interference Using a linear FM chirp sweeping from 70 KHz to 90 KHz, a sampling frequency of 1.2 MHz, a pulse width of 1.7 ms, a signal DOA of 0o, an interference DOA at 50o, and a SINAD of -10dB, the QMF LMS system exhibited higher performance than the TD system, where it can be noticed in Figure 15 that the null in the interference direction exceeds -45dB, so about 10 dB lower than the TD LMS. The convergence of the wideband QMF LMS system is shown in Figure 16. VI.
-50
-60 -100
-80
-60
-40
-20
0 20 Angle in degrees
40
60
80
100
Figure 14 QMF beam pattern at 20dB SNR. The antenna beam pattern 0 Conventional TD LMS -10
-20
dB
-30
-40
CONCLUSION
In this paper we studied and simulated a new wideband adaptive LMS beamformer with subband decomposition for Sonar application. It can be noticed from the simulation sections that the new system exhibits superior performance to the TD LMS beamformer in the presence of interference because of its capability to isolate the interference and steer a null in its direction using the beamformer that is employed in the same band, this capability also enables the other beamformers that are employed in different bands to adapt independently without been affected by the interference.
-50
REFERENCE
-60
[1]
-70
-80 -100
-80
-60
-40
-20
0 20 Angle in degrees
40
60
80
100
Figure 15 Beam pattern with the signal DOA at 0o and the interference DOA at 50o, the SINAD is -10 dB.
[2]
[3]
[4]
[5] [6] [7]
[8]
Figure 16 QMF convergence over time, with a SINAD of-10dB.
The experiment was done using MATLAB, by simulating ten elements ULA, with AWGN and interference added
[9]
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