A computationally efficient pulse compression method of Barker-coded excitation using a mismatched filter in medical ultrasound imaging

Article information

Ultrasonography. 2026;45(1):30-37

Publication date (electronic) : 2025 October 17

doi : https://doi.org/10.14366/usg.25135

Myeonghun Han¹, Hong Jin Choi², Changhan Yoon^,1,2

¹Department of Nanoscience and Engineering, Inje University, Gimhae, Korea

²Department of Biomedical Engineering, Inje University, Gimhae, Korea

Correspondence to: Changhan Yoon, PhD, Department of Nanoscience and Engineering, Inje University, 197 Inje-ro, Gimhae 50834, Korea Tel. +82-55-320-3301 E-mail: cyoon@inje.ac.kr

Received 2025 July 10; Revised 2025 October 10; Accepted 2025 October 17.

Abstract

Graphical abstract

Introduction

The image quality of medical ultrasound systems is primarily determined by their spatial resolution and signal-to-noise ratio (SNR). However, a well-known trade-off exists between resolution and SNR in ultrasound imaging. Short pulses are typically used to achieve high resolution but result in lower SNR or reduced pulse energy. Although increasing the excitation amplitude can improve SNR, it may induce unwanted bioeffects, such as heating or tissue damage. Using a longer transmit pulse offers an alternative means to increase SNR, but it does so at the expense of axial resolution.

Coded excitation was first introduced in radar applications and later extended to medical ultrasound imaging [1,2]. However, it attracted limited attention in the medical ultrasound community until the 1990s, largely due to the time–bandwidth limitation identified by Takeuchi [1] and the implementation challenges associated with performing pulse compression or correlation on every channel. In 1992, O’Donnell [3] reported that coded excitation could enhance SNR by approximately 15–20 dB. By using coded excitation, a longer transmit pulse can be employed without increasing the peak intensity, as pulse compression restores axial resolution while increasing total pulse energy. For practical implementation, pulse compression was performed after beamforming. Since then, extensive studies have explored coded excitation and pulse compression techniques.

Among various coded sequences, most studies have focused on the chirp, or linear frequency modulation signal, which provides excellent SNR improvement and robustness against attenuation [3–12]. However, chirp excitation requires an arbitrary waveform generator, making it feasible only for high-end ultrasound systems. Binary complementary Golay codes, in which range sidelobes can be perfectly canceled using Golay pairs, can be transmitted with conventional bipolar pulsers [13–15]. Nevertheless, Golay coding requires two sequential transmissions, resulting in a halved frame rate and potential motion-induced decoding errors.

For single-transmit binary codes, the Barker code provides the lowest range sidelobe level (RSLL) [16]. RSLL is defined as the ratio between the mainlobe and the sidelobe peak amplitudes. When a matched filter is used for pulse compression, the RSLL of Barker codes equals 1/N (where N is the code length). Unfortunately, only seven Barker codes exist, and the longest contains 13 chips. Consequently, the RSLL remains above −22.3 dB after compression with a matched filter. Given that the dynamic range of medical ultrasound imaging systems exceeds 60 dB [8], this RSLL is insufficient for high-quality imaging.

To address this issue, pulse compression using inverse filtering, pseudoinverse filtering, or mismatched filtering has been investigated [17–21]. Ideally, an inverse filter can flatten the spectral ripples of the transmitted code, yielding a completely uniform spectrum after compression. However, the inverse filter’s performance is highly sensitive to the system SNR [8,20]. Alternatively, mismatched filters—typically three to five times longer than matched filters—can effectively reduce RSLL [18,19]. Studies have shown that mismatched filters can improve SNR while suppressing RSLL to below −40 dB. However, because their coefficients are multilevel, mismatched filters require multipliers for compression. In contrast, matched filters for binary codes can be implemented using only adders, as their coefficients are limited to ±1. Moreover, mismatched filters are significantly longer: for example, a 13-chip Barker code with center and sampling frequencies of 10 MHz and 40 MHz requires a 156- or 260-tap filter for radiofrequency (RF)-domain pulse compression. This computational demand remains prohibitive for portable ultrasound systems.

This study presents a computationally efficient pulse compression method for Barker-coded excitation using a mismatched filter designed for portable ultrasound imaging. In the proposed approach, pulse compression is performed on in-phase and quadrature (IQ) data after decimation. Because both the IQ data and the compression filter coefficients are decimated, hardware complexity can be reduced by a factor of L² (where L is the decimation factor) using time-shared multipliers. The proposed method was implemented in a custom-built portable ultrasound imaging system, and its performance was evaluated through simulations, as well as in vitro and in vivo experiments.

Materials and Methods

Conventional and Proposed Pulse Compression

The binary code used in this paper is Barker code with a length of 13 (Barker-13); s(n) = [1, 1, 1, 1, 1, −1, −1, 1, 1, −1, 1, −1, 1]. To effectively transmit the signal through the transducer passband, the binary codes must be modulated by a modulation sequence m(n). This modulation sequence consists of one or more cycles of a bipolar pulse at the transducer’s center frequency. To achieve this, oversampling of the code sequence is first performed:

(1) s^n=s1, 0, 0, ⋯, s2, 0, ⋯, s13, 0, ⋯,

where the number of inserted zeros is M-1 (M=f_c/f_s, where fc and fs are the center and sampling frequencies, respectively). The modulated code sequence is then obtained by

(2) s^mn=s^n*mn,

where * denotes the convolution operator. In conventional pulse compression with RF data after beamforming, the receive data, r(n), can be compressed by correlating it with the modulated code sequence (Fig. 1A)

Fig. 1.

Block diagrams of the conventional and proposed pulse compression methods.

In the conventional method (A), pulse compression is performed after receive beamforming, whereas it is conducted with baseband in-phase and quadrature data after decimation in the proposed methods (B).

(3) rcn=rn*s^m−n.

In the proposed method, pulse compression is performed using IQ data after decimation, as shown in Fig. 1B. Since the sampling frequency is typically 40 MHz (≥4f_c), the data rate of IQ can be decimated to f_c; thus, at least 4-fold decimation can be performed. After demodulating the beamformed RF data, decimation is applied to produce the baseband IQ data: I^d(n) and Q^d(n). Then, pulse compression is performed as follows:

(4) Icdn=Idn*s−n,

(5) Qcdn=Qdn*s−n.

Although this method requires two convolution operations for pulse compression, it can be efficiently implemented using a single convolution through time-sharing, since both the IQ data and the filter coefficients are decimated.

Mismatched Filter

A mismatched filter is used to achieve a lower RSLL while maintaining the mainlobe width. For chirp-coded excitation, mismatched filters can be obtained by applying appropriate window functions to the excitation sequences [8,9]. However, for biphase codes, mismatched filters are optimized according to integrated sidelobe energy or peak sidelobe (PSL) criteria, defined as [18]:

(6) ISL=1R02∑k≠0Rk2,

(7) PSL=1R02maxk≠0Rk2,

where R_k is the cross-correlation between the coded sequence (s(n)) and the compression/sub filter. Previous studies have shown that a PSL-optimized mismatched filter with a length three times that of the original code can reduce RSLL to below −40 dB with only a marginal SNR loss [18]. Table 1 lists the RSLLs and SNR losses for PSL-optimized mismatched filters whose lengths are 3, 5, and 7 times the original code length.

Table 1.

RSLLs and SNR losses for mismatched filters with lengths 3, 5, and 7 times the Barker-13 code length

As shown in Table 1, increasing the filter length further suppresses RSLL with only a slight decrease in SNR. However, the difference in RSLL suppression between filters five and seven times the code length is minimal. Therefore, a mismatched filter length five times that of the code was selected for this study. Fig. 2 presents pulse compression results for the Barker-13 sequence using both matched and mismatched filters. Notably, the axial resolution remained consistent across all mismatched filter lengths, indicating that axial resolution is robust to filter length variations.

Fig. 2.

Results of pulse compression using the matched filter and the mismatched filter with a length 5 times that of the matched filter.

Overview of Custom-Built Portable Ultrasound Imaging System

Fig. 3 shows a block diagram and photograph of the custom-built portable ultrasound imaging system implemented on a field-programmable gate array (FPGA). The system included a 32-channel ultrasound imaging module and a power module. The imaging module comprised four 8-channel pulsers, eight 16-channel high-voltage multiplexers, a 32-channel analog front-end chip operating at 40 MHz with a low-voltage differential signaling interface, an Artix-7 FPGA, and a high-speed USB module. The sampling frequency was 40 MHz. The FPGA supported a 32-channel transmit/receive beamformer and mid-processing. To integrate all signal processing into a single FPGA, a pseudo-dynamic receive beamformer with a post-filtering method and look-up-table-based processing was used to minimize hardware complexity [22,23]. Mid-processing includes high-pass filtering, digital time-gain compensation, quadrature demodulation, and decimation. A real-time controller is integrated within the FPGA to synchronize all modules, including the transmit and receive subsystems. Baseband IQ data are transferred to an Android device via a USB 3.0 interface for back-end processing. The back-end was developed using Android Studio, and image processing was implemented using the OpenCV4Android library. Table 2 summarizes the FPGA resource utilization of the developed portable ultrasound imaging system, analyzed using Vivado 2024 (AMD, Santa Clara, CA, USA). As shown in Table 2, the 32-channel transmit/receive beamformer and mid-processing— including the proposed mismatched filtering for baseband compression—were successfully implemented on a single FPGA.

Fig. 3.

Overall block diagram and photography of developed prototype ultrasound system.

Overall block diagram of the portable ultrasound imaging system (A) and the photography of developed prototype ultrasound system (B) are shown. HV MUX, high-voltage multiplexer; FPGA, field-programmable gate array; LVDS, low-voltage differential signaling; USB, universal serial bus; Mid, mid-level processing.

Table 2.

Resource utilization of developed portable ultrasound imaging system

Results

Fig. 4 presents the simulated ultrasound B-mode images obtained with pulsed and Barker-coded excitation using matched and mismatched filters. For the mismatched filter, pulse compression was performed using both RF and baseband signals. The dynamic range for all images was set to 50 dB. As shown in Fig. 4, the B-mode image produced by the matched filter exhibited a high RSLL, whereas the images generated with the mismatched filters (Fig. 4C, D) closely resembled those produced by the pulsed excitation method. For quantitative comparison, the axial profiles at the transmit focal depth (20 mm) are plotted in Fig. 5. The −6 dB axial resolutions were 0.16 mm for all methods. The RSLL values were −21.40 dB for the matched filter and −45.39 dB for the mismatched filters. Without attenuation, the RSLL for the mismatched filter with a length five times the code length was −57.64 dB, as listed in Table 1. However, the performance of pulse compression degraded due to frequency-dependent attenuation (0.5 dB/cm/MHz), consistent with previous reports [9]. Although this degradation can be partially mitigated using depth-dependent compression filtering [24], such an approach may introduce challenges for real-time implementation. Overall, the simulation results indicate that pulse compression with a mismatched filter substantially reduces RSLL, and the performance of the proposed method (baseband compression) is comparable to that of conventional RF compression.

Fig. 4.

Field II simulated ultrasound images.

Field II simulated ultrasound images with pulsed and Barker-coded excitation (A) using matched filtering (B), mismatched filter using radiofrequency (C), and mismatched filter using baseband signals (D) are shown. The image was logarithmically compressed with a dynamic range of 50 dB.

Fig. 5.

Axial beam profiles at a focal depth (20 mm) from Fig. 4.

RF, radio-frequency.

Fig. 6 shows the ultrasound phantom images with a dynamic range of 50 dB obtained using pulsed and coded excitation. Because of system noise, speckle patterns at greater depths were not clearly visualized even after applying time-gain compensation. In addition, the phantom used in the experiments had a relatively high attenuation coefficient (0.6 dB/cm·MHz) compared with other tissue-mimicking phantoms, further limiting speckle visibility at depth. Nevertheless, the SNR improvement achieved by coded excitation is readily apparent in Fig. 6. Consistent with the simulation results, the ultrasound images obtained using the matched filter exhibited high RSLL, whereas this artifact was not observed in the images produced by the mismatched filters. Axial beam profiles at a depth of 20 mm are presented in Fig. 7. All methods produced identical −6 dB axial resolutions (0.36 mm). The RSLL measured for the matched filter was −14.36 dB. Similar beam profiles were observed for both RF and baseband signals after pulse compression using mismatched filters. In these cases, the RSLLs were comparable to or lower than the strength of the speckle signal, rendering them obscured by the speckle patterns. The SNR values computed using Eq. (8) from the region of interest in Fig. 6A were 23.76 dB for pulsed excitation, 34.72 dB for the matched filter, and 34.15 dB for the mismatched filter. The SNR improvement achieved by coded excitation with the matched filter was 10.96 dB, slightly lower than the theoretical value of 11.14 dB (=20 log₁₀√13) [25]. The SNR loss with the mismatched filter compared with the matched filter was 0.57 dB, marginally higher than the simulated value (Table 1). As previously reported, frequency-dependent attenuation and system noise modify the spectrum of the received signal [9]. Consequently, the pulse-compression output no longer represents the ideal auto-correlation (or cross-correlation) function of the coded signal, leading to degradation in both SNR improvement and RSLL.

Fig. 6.

Tissue mimicking phantom images.

Tissue mimicking phantom images with pulsed and Barker-coded excitation (A) using matched filtering (B), mismatched filter using radiofrequency (C), and mismatched filter using baseband signals (D) are shown. The image was logarithmically compressed with a dynamic range of 50 dB.

Fig. 7.

Axial beam profiles at a focal depth (20 mm) from Fig. 6.

RF, radio-frequency.

Fig. 8 shows in vivo ultrasound images of the carotid artery acquired using the custom-built portable ultrasound imaging system with pulsed and Barker-coded excitation (Video clip 1). The frames shown in Fig. 8 were selected from Video clip 1 to provide visually comparable appearances. As shown in the figure, improved SNR achieved with coded excitation is evident in the far field and can be more clearly observed in Video clip 1. Notably, only the proposed method (baseband compression) was implemented on the FPGA of the custom-built portable ultrasound imaging system. Although slight blurring artifacts caused by post-pulse-compression error were observed in the near field, these artifacts are unlikely to affect diagnostic interpretability, as the primary goal of coded excitation is to enhance SNR in the far field. The post-compression artifacts can be mitigated by using a larger F-number (e.g., >4), though this would come at the expense of lateral resolution. In terms of spatial resolution in the far field, the proposed method provides image quality comparable to that obtained with conventional pulsed excitation, including clear delineation of the carotid artery boundaries and consistent speckle representation.

Fig. 8.

In vivo images of carotid artery.

In vivo images of carotid artery captured by the custom-built portable ultrasound imaging system with pulsed (A) and Barker-coded excitation (B) with mismatched filter using baseband signal. The image was logarithmically compressed with a dynamic range of 50 dB.

Discussion

This study proposed a pulse compression method for Barker-coded excitation using a mismatched filter designed to reduce computational complexity in portable ultrasound imaging systems. In the proposed approach, pulse compression was performed on baseband IQ data after decimation, thereby reducing computational complexity by a factor of 1/L², since both the IQ data and the filter coefficients are decimated by L. The method was implemented on a custom-built portable ultrasound imaging system to demonstrate its feasibility and performance. Simulation, phantom, and in vivo experiments confirmed that the proposed method maintains image quality while significantly reducing computational complexity.

Supplementary Material

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Notes