Barker coded excitation with linear frequency modulated carrier for ultrasonic imaging

Biomedical Signal Processing and Control 13 (2014) 306–312

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Barker coded excitation with linear frequency modulated carrier for ultrasonic imaging Juan Fu, Gang Wei, Qinghua Huang ∗ , Fei Ji, Yizhi Feng School of Electronic and Information Engineering, South China University of Technology, Guangzhou, China

a r t i c l e

i n f o

Article history: Received 12 February 2014 Received in revised form 26 May 2014 Accepted 8 June 2014 Available online 28 June 2014 Keywords: Ultrasound imaging Barker coded excitation LFM carrier Pulse compression Axial resolution and SNR improvements

a b s t r a c t A new Barker coded excitation using linear frequency modulated (LFM) carrier (called LFM-Barker) is proposed for improving ultrasound imaging quality in terms of axial resolution and signal-to-noise ratio (SNR). The LFM-Barker coded excitation has two independent parameters: one is the bandwidth of LFM carrier, and the other is the chip duration of Barker code. To improve the axial resolution, increase the bandwidth of LFM carrier; and to improve the SNR, increase the chip duration of Barker code. In this study, a LFM pulse with proper (<5.5) time–bandwidth product is considered as the carrier in order to avoid sidelobes inside the mainlobe of matched filtered output. A pulse compression scheme for the LFM-Barker coded excitation is developed, and it consists of the LFM matched filter and Barker code mismatched filter. In the simulations, the impulse response of transducer can be approximated by a Gaussian shaped sinusoid with 5 MHz central frequency of 60% −6 dB fractional bandwidth. The pulse compression filter is performed to suppress sidelobes below −40 dB roughly, which is acceptable in medical imaging. Simulation results show that in comparison with conventional Barker coded excitation using sinusoid carrier (called Sinusoid-Barker), the axial resolution of the LFM-Barker coded excitation system can be doubled, and the SNR can be improved by about 3 dB. Simulation of B-mode images with the Field II program demonstrates that the axial resolution is improved from 0.7 mm to 0.4 mm. In addition, the LFM-Barker coded excitation is robust for frequency dependent attenuation of tissues. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction Ultrasound imaging is an important medical imaging modality, and is often used for many diagnostic purposes, mostly considering that it is safe and produces real-time images [1], moreover less expensive and simpler in use than other imaging techniques [2,3]. Axial resolution and signal-to-noise ratio (SNR or penetration) are crucial factors to consider in evaluation of the image quality of ultrasound system. It is well known that the axial resolution can be improved by increasing the frequency of the transmitted ultrasound. Unfortunately, the energy of ultrasound is attenuated when propagating through tissues. Generally the attenuation of ultrasound in tissues is frequency dependent, and increases as the frequency increases. Therefore, the improvement in the axial resolution results in limited penetration depth and a decrease in SNR of the received signals due to the higher attenuation coefficients. On the other side, the improvement in SNR can be achieved by increasing the total ultrasound energy input into the system, by

∗ Corresponding author. Tel.: +86 20 87113540. E-mail address: [email protected] (Q. Huang). http://dx.doi.org/10.1016/j.bspc.2014.06.004 1746-8094/© 2014 Elsevier Ltd. All rights reserved.

increasing either the pulse amplitude or pulse duration. In medical ultrasound, safety requirements limit the peak amplitude of the pulse in order to avoid heating and cavitation damages within the insonated human body [4,5]. Therefore, the way to improve the SNR is to excite the transducer with a long and modulated pulse (coded excitation) in the transmitter, which allows increasing the average transmit power without increasing the peak amplitude of the pulse. Moreover, in the receiver, the echoes of the long pulses can be compressed (decoded) with pulse compression filter to restore the axial resolution. Coded excitation technique is often used in medical ultrasound for improving the SNR and increasing the penetration depth. It has been studied and applied to medical ultrasound for almost 10 years [6–14]. A variety of coded excitations have been developed, including the linear frequency modulated (LFM) signal or nonlinear frequency modulated signal [6–8], and the phase coded signal, such as Barker codes [9,10], m-sequences [11] and Golay complementary sequences [12], and the amplitude modulated signal [13,14]. They can be basically categorized according to their modulation functions into three types: frequency modulation, phase modulation and amplitude modulation. Generally, a coded waveform uses only one of modulation functions. For example, Barker coded signal uses

J. Fu et al. / Biomedical Signal Processing and Control 13 (2014) 306–312

the bi-phase modulation, and the LFM coded signal uses the linear frequency modulation. In this paper, we focus on improving the performance of Barker coded excitation. Conventionally Barker code is modulated with a single-frequency carrier of sinusoidal wave, and the Barker coded excitation using the sinusoid carrier (called Sinusoid-Barker) has the advantages of simpler pulser and lower cost compared with the LFM coded excitation [15]. However, its frequency spectrum cannot accord well with ultrasound transducer frequency spectrum. Moreover, the single-frequency carrier of sinusoidal wave has the time–bandwidth (TB) product on the order of one, and hence the gain in SNR (SNRG) through the Sinusoid-Barker coded excitation can be only achieved by Barker code length [16]. Theoretically, Barker coded waveforms with longer code length give better SNRG. Unfortunately, the Barker-13 (i.e. the code length is 13) is the longest Barker code available, and the Barker-13 coded excitation can achieve 11.1 dB SNRG [17]. Therefore the SNRG is limited for the Sinusoid-Barker coded excitation. In addition, the Sinusoid-Barker coded signal has frequency-shift sensitivity [9]. Because of frequency dependent attenuation of tissues, it cannot be well applied in medical ultrasound. Due to the drawbacks of conventional Sinusoid-Barker coded excitation, a new Barker coded excitation using the LFM pulse as the carrier (called LFM-Barker) is proposed in this paper. The LFMBarker coded signal uses two types of modulation functions. Within every chip of Barker code, it uses the linear frequency modulation. Between chips of Barker code, it uses the Barker phase modulation [18]. The LFM pulse as the carrier is flexible to control its frequency spectrum according to the impulse response of ultrasound transducer, and it has the TB product on the order of above one [7]. Hence, the SNRG through the LFM-Barker coded excitation can be achieved not only by the Barker code length but also by the TB product of LFM carrier. Moreover, the LFM signal has the advantage of frequency-shift tolerance [7]. However, the major problem associated with coded excitation is the range sidelobe artifacts [7–10,19]. In the Barker-13 coded excitation system, the peak sidelobe level (PSL) of matched filtered output is −22.3 dB below the mainlobe, which is not tolerated in medical ultrasound imaging. In this study, the mismatched filter for the LFM-Barker coded excitation is developed to decode the received echo and suppress the sidelobe level. In this paper, basic concepts and expected benefits of the LFMBarker coded excitation are presented. The two Barker coded excitations using the LFM carrier and sinusoid carrier, respectively, are compared in simulation experiments. Section 2 gives the representations of the LFM-Barker coded excitation and introduces the mismatched filter for pulse compression. The optimized coded excitation/pulse compression scheme was simulated to verify the quality of ultrasound imaging in Section 3. Section 4 draws the final conclusions.

307

as a convolution of a carrier sequence with an oversampled Barker code sequence [9,12]. The Barker coded signal can be expressed by s(n) = v(n) ∗ c(n)

(2)

where v(n) is the sample sequence of the carrier denoted as v(t), and c(n) is the oversampled Barker code sequence, as expressed by c(n) =

P−1 

ck ı(n − kTp fs )

(3)

k=0

where {ck = ±1, k = 0, 1, . . ., P − 1} is the original Barker code sequence before oversampling, P is the Barker code length, Tp is the chip duration of Barker code and fs is the system sampling rate. The total duration of the Barker coded signal is T = PTp . Generally one or multiple cycles of sinusoidal wave at the transducer central frequency is used as the carrier of conventional Sinusoid-Barker coded excitation, and thus v(t) can be expressed as

v1 (t) = sin(2f0 t),

t ⊂ [0, Tp ]

(4)

where f0 is the transducer central frequency. The sinusoid carrier is a broadband signal containing all frequencies in a bandwidth of 1/Tp around f0 [6,16]. It can be seen that the bandwidth of sinusoid carrier is determined by the chip duration of Barker code. In this study, the carrier of the LFM-Barker coded excitation is formed by the LFM pulse with most energy concentrated within the transducer bandwidth, and thus v(t) is expressed as





v2 (t) = sin 2 f0 −

B 2





t + t 2 ,

t ⊂ [0, Tp ]

(5)

2. Methods

where B is the bandwidth of LFM carrier, and  is the frequency sweep rate, which is  = B/Tp corresponding to the chip duration of Barker code Tp and the bandwidth of LFM carrier B. Generally the axial resolution of ultrasound imaging system is related to the bandwidth of transducer frequency response. Therefore, the bandwidth of the excitation signal should be as large as that of the transducer, resulting in the echoes with enlarged bandwidth, thereby improving the axial resolution. The bandwidth of Barker coded signal is basically determined by its carrier frequency spectrum [9]. In this study, the bandwidth of Barker coded signal must be redefined as the bandwidth of carrier, since the definition of bandwidth for a phase encoded signal is complex, due to the sharp phase transitions in the signal [16]. The sinusoid carrier has the TB product on the order of one. When the bandwidth of sinusoid carrier is increased to improve the axial resolution, the chip duration of Barker code is decreased and the SNR is deteriorated for the Sinusoid-Barker coded excitation. In contrast, the bandwidth of LFM carrier can be flexibly chosen regardless of the chip duration of Barker code because the LFM carrier has the TB product on the order of above one. It is feasible to broaden the bandwidth of the LFM-Barker coded signal in order to match the transducer bandwidth, thereby achieving the improvement in the axial resolution.

2.1. LFM-Barker coded excitation

2.2. Pulse compression scheme

The ultrasound imaging system can be mathematically expressed as

In an ultrasound coded excitation system, the returned echo is squeezed (decoded) into a short (compressed) pulse through pulse compression filter in the receiver [12]. Thus, the compressed (decoded) signal d(t) is

e(t) = s(t) ∗ H(t) + n(t)

(1)

where ∗ is the convolution operator, s(t) is the excitation pulse, H(t) is the system transfer function, e(t) is the received echo and n(t) is the additive noise [15]. In the Barker coded excitation system, Barker code is always modulated with a carrier. The encoding process can be described

d(t) = e(t) ∗ p(t)

(6)

where p(t) is the pulse compression filter. If the matched filter (the time inverse of the transmitted signal) is used for pulse compression, the output is an autocorrelation function (ACF) of the transmitted signal. The ACF envelopes

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J. Fu et al. / Biomedical Signal Processing and Control 13 (2014) 306–312

Normalized amplitude (dB)

0

-20

Fig. 3. The pulse compression scheme for the LFM-Barker coded excitation system which has no sidelobes inside the mainlobe of the matched filtered output.

-40

-60

0

10

25

Time (μs)

LFM-Barker

35

Sinusoid-Barker

Fig. 1. The autocorrelation function envelopes of the LFM-Barker and SinusoidBarker coded signals. The following parameters are used: P = 13, f0 = 5 MHz, Tp = 1.4 ␮s and B = 4 MHz. The time–bandwidth product of LFM carrier is 5.6.

of the LFM-Barker and Sinusoid-Barker coded signals are illustrated in Fig. 1, respectively. The following parameters for the two Barker coded signals are used: P = 13, f0 = 5 MHz (T0 = 1/f0 = 0.2 ␮s), Tp = 7T0 = 1.4 ␮s and B = 4 MHz (the bandwidth of LFM carrier). It should be noted that the LFM-Barker coded signal has good autocorrelation to ensure pulse compression. Fig. 1 shows that the matched filtered output for the LFM-Barker coded signal has one mainlobe and twelve sidelobes, the same as the Sinusoid-Barker coded signal. The shapes of the mainlobe and sidelobes are the same. Peak level of the twelve sidelobes is −22.3 dB because of the Barker code autocorrelation. Meanwhile, inside the mainlobe, the sidelobes of below −18 dB appear because of the LFM pulse autocorrelation. The sidelobes inside the mainlobe are related to the Fresnel ripples from the spectrum of the LFM carrier, and their number and intensity depend on the TB product of the LFM pulse [4]. In Fig. 1, the TB product of LFM carrier is 5.6, and there are two sidelobes in the mainlobe from the LFM pulse autocorrelation. When the following parameters of LFM carrier are used: Tp = 3T0 = 0.6 ␮s and B = 3 MHz, the matched filtered output is shown in Fig. 2. It reveals that the sidelobes inside the mainlobe in Fig. 1 disappear. The TB product of LFM carrier in Fig. 2 is 1.8. It can

be seen that when the TB product of LFM carrier is decreased, the sidelobes inside the mainlobe would be eliminated. If the TB product of LFM carrier is large (>5.5) enough to have the sidelobes inside the mainlobe of the matched filtered output, it is necessary for the LFM-Barker coded excitation that both sidelobes need to be suppressed from the LFM pulse and Barker code autocorrelations, respectively. First, the LFM mismatched filter is used to suppress the sidelobes from the LFM pulse autocorrelation. Then the Barker mismatched filter is used to suppress the sidelobes from the Barker code autocorrelation. The pulse compression filter can be expressed together by p(t) = p1 (t) ∗ p2 (t)

(7)

where p1 (t) is the LFM mismatched filter, and p2 (t) is the Barker mismatched filter. The design of the mismatched filter for the LFM pulse is straightforward by multiplying the matched filter with a proper window function [7]. The application of LFM mismatched filter leads to a SNR loss and broadens the mainlobe width for sidelobe suppression. In this study, the LFM pulse with proper (<5.5) TB product is considered as the carrier in order to avoid sidelobes inside the mainlobe of the matched filtered output, so the matched filter for the LFM carrier is only needed. The pulse compression scheme is displayed in Fig. 3. Solutions for designing the mismatched filter for Barker code can be derived using the amplitude-weighting network [20], the integrated sidelobe level criteria, or the PSL criteria [21]. In this study, the mismatched filter for Barker code is applied based on the lowest PSL criteria, which can be expressed by p2 (t) =

L−1 

bk ı(t − kTp )

(8)

k=0

where L is the filter length and bk is the filter coefficient. 2.3. SNRG and SNR improvements The SNRG is often used to describe the performance of coded excitation imaging system, and is defined as

Normalized amplitude (dB)

0

SNRG = -20

-40

-60

0

5

10

15

Time (µs) Fig. 2. The autocorrelation function envelope of the LFM-Barker coded signal. The following parameters are used: P = 13, f0 = 5 MHz, Tp = 0.6 ␮s and B = 3 MHz. The time–bandwidth product of LFM carrier is 1.8.

SNRout ST /N0 = = TB SNRin S/(N0 B)

(9)

where SNRout represents the SNR of matched filtered output, SNRin represents the SNR of the transmitted signal, S is the average power of the transmitted signal, N0 is the noise power spectrum density, T is the total duration of the transmitted signal, and B is the bandwidth of the transmitted signal. The TB product of the transmitted signal is often used in the literature to describe the SNRG of the matched filtered output [16]. Considering the Sinusoid-Barker coded excitation, let us substitute T = PTp into (9) as well as the approximation that the TB product of sinusoid carrier is on the order of one (Tp B ≈ 1), and the SNRG can be reduced to SNRG = PTp B ≈ P

(10)

which reflects that the matched filter SNRG of the Sinusoid-Barker coded signal can be approximated by the Barker code length [16].

J. Fu et al. / Biomedical Signal Processing and Control 13 (2014) 306–312

309

Fig. 4. The simulation block-diagram of an ultrasound coded excitation system.

It is well known that the SNRout of the matched filter is dependent on the energy of the transmitted signal [16]. In the Sinusoid-Barker coded excitation system, the sinusoid carrier contains one or multiple cycles of sinusoidal wave at the transducer central frequency. If the energy of one-cycle sinusoidal wave is fixed and the Barker code length is given, the energy of the SinusoidBarker coded signal is related to the chip duration of Barker code. When the chip duration of Barker code increases, the SNRout is improved. But the bandwidth of sinusoid carrier decreases and the axial resolution is degraded. It shows that the Sinusoid-Barker coded excitation system has the contradiction between the axial resolution and the SNRout . When considering the LFM-Barker coded excitation, however, the LFM carrier has the advantage of the TB product on the order of above one. As a result, the SNRG can be theoretically improved not only by an increase of the Barker code length but also by an increase of the TB product of LFM carrier. Moreover, the two parameters (i.e. the bandwidth of LFM carrier and the chip duration of Barker code) can be selected independently. When the bandwidth of LFM carrier increases, the axial resolution is improved. When the chip duration of Barker code is invariable, change in the bandwidth of LFM carrier hardly influences the transmitted energy. Moreover, the SNRout can be improved by increasing the chip duration of Barker code and the transmitted energy. 3. Simulation results To verify the performance of optimized LFM-Barker coded excitation/pulse compression scheme, ultrasound transmitter/receiver system was simulated using Matlab (Version 7.6, the MathWorks Inc, USA) software. Fig. 4 shows the simulation steps. The excitation sequences are sent through the transducer transfer function, then propagate in medium and finally pass back through the transducer transfer function again to form the received waveforms. The received waveforms are decoded by the pulse compression filter to obtain the compressed pulses. In order to simplify the simulation system, it is assumed that the medium is homogeneous and nonattenuating, and the reflectivity function is a ı-function. The two Barker coded excitations using the LFM carrier and sinusoid carrier, respectively, are considered. In the simulation experiments, the impulse response of the transducer can be approximated by a Gaussian shaped sinusoid with 5 MHz central frequency of 60% −6 dB fractional bandwidth (the −6 dB bandwidth is 3 MHz). Given the transducer, the central frequency of the sinusoid and LFM carriers is chosen with f0 = 5 MHz. The Barker-13 code [1 1 1 1 1 −1 −1 1 1 −1 1 −1 1] is used with P = 13. The chip duration of Barker code Tp must be integral times of T0 = 1/f0 = 0.2 ␮s because the coded signal needs consecutive phases between chips of Barker code. Both the LFM-Barker and Sinusoid-Barker coded excitation sequences used to drive the transducer have the same peak amplitude. For the Sinusoid-Barker coded excitation, the chip duration of Barker code can be flexibly selected to determine the bandwidth of sinusoid carrier. For the LFM-Barker coded excitation, the chip

Normalized amplitude (dB)

0

-20

-40

-60

-10

-5

0

Time (μs) Matched filter

5

10

Mismatched filter

Fig. 5. The envelopes of the matched and mismatched filtered outputs for the LFMBarker coded excitation.

duration of Barker code and the bandwidth of LFM carrier can be independently selected, but the TB product of LFM carrier cannot be large (<5.5) in order to avoid sidelobes inside the mainlobe of the compressed pulse. For the proper SNR comparison, the pulse compression filters are normalized to produce equal noise output power spectrum in the simulations. Therefore, the SNRout is calculated as the peak power of the compressed pulse in this section. In order to evaluate the proposed excitation/compression scheme, a set of computer simulations were performed to demonstrate the imaging quality in terms of the axial resolution, the PSL and the SNR. 3.1. Sidelobe suppression First, the mismatched filter for the LFM-Barker coded excitation is designed to suppress sidelobes of the compressed pulse. In a medical ultrasound imaging system, the sidelobe level of below −40 dB is commonly required to satisfy the contrast resolution of imaging. The mismatched filter for the LFM-Barker coded excitation is formed by the matched filter for the LFM pulse convoluted with the mismatched filter for the Barker-13 code. According to [17,21], the mismatched filter for Barker code needs to be three times as long as the length of Barker code to achieve sufficient sidelobe suppression. When using a longer mismatched filter, a further suppression of the sidelobes can be achieved. Considering the implementation complexity, the mismatched filter with shorter length is preferred, and hence the length of the Barker mismatched filter is chosen to be L = 39. In the simulation, the following parameters for the LFM-Barker coded excitation are used: Tp = 3T0 and B = 3 MHz. Fig. 5 gives the comparison of the compressed pulses for the LFM-Barker coded excitation with the matched and mismatched filters, respectively. The matched filter output is marked as a dashed line while the mismatched filter output is marked as a solid line. Table 1 presents the results of the −6 dB mainlobe width, the PSL and the SNRout . By using the mismatched filter, the sidelobe level is significantly suppressed from −22.3 dB to roughly −40 dB. But the SNRout of the mismatched filter is slightly degraded with less than 1 dB in Table 1 Results of the mismatched and matched filters for the LFM-Barker coded excitation. Filter

−6 dB mainlobe width (␮s)

PSL (dB)

SNRout (dB)

Mismatched Matched

0.69 0.69

−38.3 −22.3

22.7 22.9

310

J. Fu et al. / Biomedical Signal Processing and Control 13 (2014) 306–312

Table 2 Effect of the bandwidth of LFM carrier on the compressed pulse for the LFM-Barker coded excitation. B (MHz)

−6 dB mainlobe width (␮s)

PSL (dB)

SNRout (dB)

3T0 3T0 3T0 3T0

3 5 7 9

0.69 0.58 0.47 0.40

−38.3 −38.8 −39.3 −39.8

22.7 20.7 18.0 15.1

Normalized amplitude (dB)

Tp

0

Table 3 Effect of the chip duration of Barker code on the compressed pulse for the LFM-Barker coded excitation. Tp

B (MHz)

−6 dB mainlobe width (␮s)

PSL (dB)

SNRout (dB)

3T0 4T0 5T0 6T0

3 3 3 3

0.69 0.73 0.68 0.63

−38.3 −39.0 −39.1 −39.3

22.7 24.2 25.2 26.0

contrast to the matched one. Moreover, the numerical results show that the two compressed pulses have the same mainlobe width. Note that the mismatched filter for the Barker code does not compromise the axial resolution for sidelobe suppression. 3.2. Axial resolution and SNR improvements For the LFM-Barker coded excitation, the effect of the bandwidth of LFM carrier on the compressed pulse was simulated to demonstrate the improvement in the axial resolution. The results are shown in Table 2. The LFM-Barker coded signals with varying bandwidths of LFM carrier have the same chip duration of Barker code Tp = 3T0 . The LFM-Barker coded signal with the wider bandwidth of LFM carrier has the narrower −6 dB mainlobe width and better axial resolution. The axial resolution increases as the bandwidth of LFM carrier increases. However, it has a decrease in the SNRout , due to the fact that the coded signal of the wider bandwidth is attenuated greatly by the transducer, and the signals with various bandwidths have almost the same transmitted energy and average power. Moreover, the LFM carrier with wider bandwidth has larger TB product and as a result the PSL is reduced a little more. Similarly the effect of the chip duration of Barker code on the compressed pulse for the LFM-Barker coded excitation was simulated to demonstrate the improvement of the SNRout . Table 3 shows the simulation results. The LFM-Barker coded signals with varying chip durations of Barker code have the same bandwidth of LFM carrier B = 3 MHz. The longer coded signal leads to the larger SNRout . In other words, the SNRout increases as the chip duration of Barker code increases. Moreover, the −6 dB mainlobe width is slightly decreased except for Tp = 4T0 . The amplitude spectrum of the LFM pulse with small (<20) TB product is approximately bell-like shaped, and the −6 dB bandwidth of the LFM frequency spectrum increases as the LFM pulse duration (the same as the chip duration of Barker code) increases. But for Tp = 4T0 , the −6 dB bandwidth of the LFM-Barker coded signal may decrease because of its complex frequency spectrum, and as a result the −6 dB mainlobe width is increased compared to the case of Tp = 3T0 . In addition, the

-20

-40

-60

-10

-5

0 Time (μs) LFM-Barker

5

10

Sinusoid-Barker

Fig. 6. The compressed outputs for the LFM-Barker and Sinusoid-Barker coded excitations with the same chip duration of Barker code.

PSL is more reduced when the LFM carrier with the longer chip duration of Barker code has the larger TB product. In order to evaluate the improvement in the axial resolution, the LFM-Barker and Sinusoid-Barker coded excitations are compared. In the simulation, values of the chip duration of Barker code are the same for the two Barker coded excitations. Therefore, the transmitted energy and average power are almost the same. Given the chip duration of Barker code, the sinusoid carrier has the limited bandwidth of 1/Tp whereas the bandwidth of the LFM carrier can be set to be as large as possible in order to make the improvement in the axial resolution. Note that the TB product of LFM carrier is selected properly (<5.5) in order to avoid sidelobes inside the mainlobe of the matched filtered output. Fig. 6 gives the comparison of the compressed pulses between the two Barker coded excitations with the same chip duration of Barker code when the following parameters are used: Tp = 5T0 and B = 3.8 MHz. It shows that the axial resolution of the LFM-Barker coded excitation system is evidently improved. Table 4 summarizes the results for the LFM-Barker and SinusoidBarker coded excitations with the same chip durations of Barker code, and the results demonstrate the improvement in the axial resolution for the LFM-Barker coded excitation. As an example, the −6 dB mainlobe width is reduced from 0.94 ␮s to 0.50 ␮s, for Tp = 4T0 and B = 5 MHz. The −6 dB mainlobe width for the LFMBarker coded excitation is nearly doubly decreased because the LFM carrier has larger bandwidth in comparison with the SinusoidBarker coded excitation. However, the SNRout of the LFM-Barker coded excitation system is decreased as expected. The loss in SNR is relatively small (less than 4.2 dB). When the bandwidth of LFM carrier is larger, thereby resulting in better axial resolution, the loss in SNR is accordingly larger. The PSL is nearly −40 dB for all the cases tested. As discussed above, the SNRout of the LFM-Barker coded excitation system can be improved by increasing the chip duration of Barker code. Therefore, the comparison of the axial resolution of the

Table 4 Axial resolution improvement when the chip duration of Barker code of the LFM-Barker coded excitation is the same as that of the Sinusoid-Barker coded excitation, and the bandwidth of LFM carrier is set to be as large as possible. Tp

4T0 5T0 6T0 7T0

B (MHz)

5 3.8 2.8 2.3

Sinusoid-Barker

LFM-Barker

−6 dB mainlobe width (␮s)

PSL (dB)

SNRout (dB)

−6 dB mainlobe width (␮s)

PSL (dB)

SNRout (dB)

0.94 1.14 1.33 1.54

−38.5 −38.8 −39.0 −39.2

25.8 27.1 28.1 28.9

0.50 0.56 0.67 0.77

−39.3 −39.3 −39.4 −39.4

21.6 24.2 26.3 27.6

J. Fu et al. / Biomedical Signal Processing and Control 13 (2014) 306–312

311

Table 5 Axial resolution improvement when the SNR of the LFM-Barker coded excitation system is nearly the same as that of the Sinusoid-Barker coded excitation system, and the bandwidth of LFM carrier is set to be as large as possible. Tp

B (MHz)

Sinusoid

LFM

3T0 4T0 5T0

5T0 6T0 7T0

3.8 2.8 2.3

Sinusoid-Barker

LFM-Barker

−6 dB mainlobe width (␮s)

PSL (dB)

SNRout (dB)

−6 dB mainlobe width (␮s)

PSL (dB)

SNRout (dB)

0.75 0.94 1.14

−38.0 −38.5 −38.8

23.9 25.8 27.1

0.56 0.67 0.77

−39.3 −39.4 −39.4

24.2 26.3 27.6

Table 6 SNR improvement when the axial resolution of the LFM-Barker coded excitation system is nearly the same as that of the Sinusoid-Barker coded excitation system, and the chip duration of Baker code for the LFM-Baker coded excitation is set to be as large as possible. Tp

B (MHz)

Sinusoid

LFM

3T0 4T0 5T0 6T0

6T0 8T0 10T0 12T0

2.5 1.8 1.4 1.1

Sinusoid-Barker

LFM-Barker

−6 dB mainlobe width (␮s)

PSL (dB)

SNRout (dB)

−6 dB mainlobe width (␮s)

PSL (dB)

SNRout (dB)

0.75 0.94 1.14 1.33

−38.0 −38.5 −38.8 −39.0

23.9 25.8 27.1 28.1

0.75 0.91 1.09 1.32

−39.4 −39.4 −39.5 −39.6

26.6 28.7 30.2 31.3

two Barker coded excitation systems is considered when the LFMBarker coded excitation with longer chip duration of Barker code has nearly the same SNRout as the Sinusoid-Barker coded excitation. Table 5 shows the results. When the chip duration of Barker code for the sinusoid and LFM carriers is 3T0 and 5T0 , respectively, and B = 3.8 MHz for the LFM carrier, the SNRout of the Sinusoid-Barker and LFM-Barker coded excitation systems is 23.9 dB and 24.2 dB, respectively. The SNRout of the LFM-Barker coded excitation system is a little larger, and one can think that it is the same for both Barker coded excitation systems. In this case, the −6 dB mainlobe width is reduced from 0.75 ␮s to 0.56 ␮s. The simulation results reveal that the −6 dB mainlobe width for the LFM-Barker coded excitation is obviously improved because the bandwidth of LFM carrier is set to be as large as possible. Finally, the improvement in the SNRout of the LFM-Barker coded excitation system is evaluated when its axial resolution is the same as that of the Sinusoid-Barker coded excitation. When the chip duration of Barker code is given, the bandwidth of sinusoid carrier as well as the −6 dB mainlobe width of the compressed pulse can be determined. In order to have the same axial resolution as that of the Sinusoid-Barker coded excitation, the proper value of the bandwidth of LFM carrier can be selected for the LFM-Barker coded excitation. The chip duration of Barker code for the LFMBarker coded excitation can be set to be as large as possible for improving the SNRout . Table 6 summarizes the results. When the chip duration of Barker code for the sinusoid and LFM carriers is 3T0 and 6T0 , respectively, and B = 2.5 MHz for the LFM carrier, the −6 dB mainlobe width is almost the same for the two Barker coded excitations, and the SNRout is improved from 23.9 dB to 26.6 dB. It can be seen from Table 6 that the SNRout of the LFM-Barker coded excitation system can be improved by about 3 dB compared with the Sinusoid-Barker coded excitation when the axial resolution is nearly the same for the two Barker coded excitations.

bandwidth of LFM carrier is B = 3.8 MHz. Fig. 7 shows the B-mode images of the four point targets. The B-mode image as shown in Fig. 7(a) from the LFM-Barker coded excitation reveals that the four point targets can be resolved. The Sinusoid-Barker coded excitation cannot resolve the last two targets as shown in Fig. 7(b). The axial resolution of the LFM-Barker coded excitation system is improved from 0.7 mm to 0.4 mm. 4. Discussion and conclusions In this study, we propose a new LFM-Barker coded excitation for ultrasound imaging. The LFM-Barker coded excitation has two parameters, which are the bandwidth of LFM carrier and the chip duration of Barker code. The effects of the bandwidth of LFM carrier and the chip duration of Barker code on the compressed pulse are studied to improve the image quality of the axial resolution and the SNR, respectively. For conventional Sinusoid-Barker coded excitation, only one parameter (i.e. the chip duration of Barker code) can be adjusted. The bandwidth of sinusoid carrier is only determined by the chip duration of Barker code. When the chip duration of Barker code increases, the transmitted energy increases and the SNR is improved. However, the bandwidth of sinusoid carrier decreases, and the axial resolution is degraded. In comparison, the proposed LFM-Barker coded excitation can increase the

3.3. Simulation of a grayscale image The two Barker coded excitations using the LFM carrier and sinusoid carrier, respectively, are compared when used in B-mode imaging. B-mode grayscale images were simulated using the Field II program [22]. A linear scan of the phantom is performed by a 64-element transducer in both transmitting and receiving. The transmit focus is 30 mm. Within the phantom four point targets are defined. The point targets are spaced at 1, 1, 0.6 mm apart along the axial direction. The chip duration of Barker code is Tp = 5T0 . The

Fig. 7. B-mode images of four point targets with (a) the LFM-Barker coded excitation and (b) the Sinusoid-Barker coded excitation.

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chip duration of Barker code to improve the SNR, and increase the bandwidth of LFM carrier to improve the axial resolution at the same time. In the simulation experiments, in comparison with conventional Sinusoid-Barker coded excitation, the axial resolution of the LFM-Barker coded excitation system is doubly improved when its chip duration of Barker code is the same as that of the SinusoidBarker coded excitation and the bandwidth of LFM carrier is set to be as large as possible. It is worth noting that, when the bandwidth of LFM carrier increases for the improvement in the axial resolution, the transducer largely attenuates the coded signal, resulting in a loss in the SNR. When the SNR is almost ensured to be the same for both coded excitations, the axial resolution of the LFM-Barker coded excitation system is evidently improved. When the axial resolution is ensured to be the same for both coded excitations and the chip duration of Barker code for the LFM-Barker coded excitation is set to be as large as possible, the SNR of the LFM-Barker coded excitation system is improved by about 3 dB. Simulation of B-mode images with the Field II program demonstrates that the axial resolution is improved from 0.7 mm to 0.4 mm. When the chip duration of Barker code for conventional Sinusoid-Barker coded excitation is large enough to ensure the high SNR, the bandwidth of sinusoid carrier is accordingly decreased, thereby degrading the axial resolution. At this time the LFMBarker coded excitation has the advantage of improving the axial resolution. Likewise, when the bandwidth of sinusoid carrier is large enough to ensure good axial resolution, the chip duration of Barker code is accordingly decreased, thereby degrading the SNR. At this time the LFM-Barker coded excitation has the advantage of improving the SNR. Moreover because of the LFM frequency-shift tolerance, the LFM-Barker coded excitation can be applied in presence of frequency dependent attenuation. In conclusion, the new Barker coded excitation using the LFM pulse as the carrier instead of the sinusoid carrier is proposed in this paper. Pulse compression scheme of the LFM-Barker coded excitation that consists of the LFM matched filter and the Barker code mismatched filter is developed. In the simulations, the pulse compression filter is performed to suppress the sidelobes below −40 dB roughly, which is acceptable in medical imaging. In comparison with conventional Sinusoid-Barker coded excitation, the simulation results reveal that the LFM-Barker coded excitation can improve the axial resolution by increasing the bandwidth of LFM carrier, and can improve the SNR by increasing the chip duration of Barker code. The simulation of B-mode imaging was carried out to demonstrate the advantage of the proposed LFM-Barker coded excitation in improving the axial resolution. However, it requires a relatively complex pulser due to the complexity of LFM signal. As such, for the LFM carrier with a relatively broad bandwidth, it needs a relatively high operating frequency for both transmission and reception, which increases the computational complexity of signal processing and hardware cost of the imaging system. In an actual ultrasound imaging system, frequency-dependent attenuation and nonlinear propagation in tissue may degrade the LFM-Barker code performance particular to the SNR and sidelobe level. In our future work, the LFM-Barker coded excitation with relatively large (>5.5) TB product of LFM carrier will be further investigated.

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