Abstract

This paper presents the preliminary design of a mm-wave ultra-wideband (UWB) radar for breast cancer detection. A mass screening of women for breast cancer is essential, as the early diagnosis of the tumour allows best treatment outcomes. A mm-wave UWB radar could be an innovative solution to achieve the high imaging resolution required without risks for the patient. The 20–40 GHz frequency band used in the system proposed in this work guarantees high cross/range resolution performances. The developed preliminary architecture employs two monomodal truncated double-ridge waveguides that act as antennas; these radiators are shifted by microstep actuators to form a synthetic linear aperture. The minimum antenna-to-antenna distance achievable, the width of the synthetic aperture, and the minimum frequency step determine the performance of the 2D imaging system. Measures are performed with a mm-wave vector network analyzer driven by an automatic routine, which controls also the antennas shifts. The scattering matrix is then calibrated and the delay-multiply-and-sum (DMAS) algorithm is applied to elaborate a high-resolution 2D image of the targets. Experimental results show that 3 mm cross and 8 mm range resolutions were achieved, which is in line with theoretical expectations and promising for future developments.

本文介绍了用于乳腺癌检测的毫米波超宽带 (UWB) 雷达的初步设计。对女性进行大规模乳腺癌筛查至关重要，因为肿瘤的早期诊断可以实现最佳治疗效果。毫米波 UWB 雷达可能是一种创新的解决方案，可以在不给患者带来风险的情况下实现所需的高成像分辨率。在这项工作中提出的系统中使用的 20-40 GHz 频带保证了高交叉/范围分辨率性能。开发的初步架构采用两个单峰截断双脊波导作为天线；这些辐射器通过微步执行器移动以形成合成线性孔径。可实现的最小天线到天线距离、合成孔径的宽度和最小频率步长决定了 2D 成像系统的性能。测量是使用由自动程序驱动的毫米波矢量网络分析仪执行的，该程序还控制天线偏移。然后校准散射矩阵，并应用延迟乘加 (DMAS) 算法来制作目标的高分辨率 2D 图像。实验结果表明，实现了 3 mm 交叉和 8 mm 距离分辨率，符合理论预期，具有良好的未来发展前景。

1. Introduction

Breast cancer ranks fifth overall as a cause of death from cancer and remains the most frequent cause of death due to cancer in women [1]. In the United States, for example, almost 6% of the population aged between 50 and 69 is affected by breast cancer [2]. However, if the cancer is detected early enough (in stages known as I or IIA), surgery to completely remove the tumour mass has a consequent 5-year survival rate of more than 80% [2]. X-ray mammography is the most commonly used technique for breast screening because of its high resolution and good performance in tumor detection. Unfortunately, due to the use of ionizing radiations, it is not without risks, particularly for women younger than 50 years old; it is very uncomfortable because it involves breast compression [3], and it is not failsafe; 23.8% of women screened in [4] had at least one false positive mammogram.

A mm-wave breast imaging system is a very attractive alternative: it is risk-free and more comfortable and can provide a resolution in the range of a few millimeters, suitable for a basic breast cancer imaging. With a central operating frequency around 30 GHz, in fact, it is possible to provide an adequate resolution, not achievable with lower frequencies, while maintaining an acceptable penetration in the human tissues, not achievable at higher frequencies (in the mm-wave range).

Microwave and mm-wave radar techniques detect discontinuities in the dielectric constant  in the medium. In particular, a fraction of the power irradiated by the antenna system is reflected by the discontinuity back to the antenna system itself, and thus, the detection of the discontinuity position is possible. This methodology is also suitable for breast cancer detection; studies reported in [5] examined the electrical characteristic of human tissues. In particular, it is evident that in the microwave region the  of tumour tissue is approximately five times greater than that of fat.

The received signal is attenuated due to not only tissue propagation losses but also the limited backscattering of a target with small dimensions. Electronic circuitry requires strict constraints in terms of signal-to-noise ratio (SNR) in order to discern the scattered signal from the noise floor. Preliminary calculations [6], which take into account propagation losses within the human tissue and the expected ratio between incident and reflected power, indicate that the total signal power collected by a system composed of  antennas (Figure 1) can be estimated to be around −50 dBm, if 0 dBm is the power transmitted. Assuming a reasonable receiver noise figure (NF) of 10 dB and a receiver filter bandwidth  of 1 kHz, the total noise power  for a planar array of 49 antennas is given bywhere the first term is the noise floor at room temperature, the second is the noise collected within the filter bandwidth of 1 kHz, the third is the noise of each receiver, and the final term accounts for the integration of the noise along 20 frequency points for an array of 49 antennas. Therefore, a robust SNR of 37 dB is expected, and this is suitable for breast cancer detection.

Figure 1 A schematic  antenna array.

In the last few years, the lower frequencies of the microwave band have been exploited in several prototypes to produce three-dimensional breast images. The most widely employed band for breast cancer imaging has a central frequency of 7 GHz with an average span of 10 GHz [7–13]. This band involves wavelengths down to few centimeters, which guarantees significant penetration of the electromagnetic field in human tissues. While microwave circuitry is simpler at lower frequencies, it becomes bulky and thus inconvenient for system integration. In addition, the relatively low frequency poses limitation on the achievable resolution.

In the literature, mm-wave radar imaging systems have already been proposed, including a 3D holographic microwave imaging technique [14], which operates in the 30 GHz band and a K-band radar system for nondestructive concrete testing [15]. Also E-band imaging systems have been developed, but their use is best suited for the detection of concealed weapons. In fact, a prototype with a working frequency from 72 to 80 GHz has been designed and tested for the detection of guns or knives under passengers clothes [16, 17]. This latter shows very accurate cross resolution (resolution perpendicular to the direction of propagation of the transmitted signal), but at these frequencies there is no penetration within human tissues. In addition, the low bandwidth used (8 GHz) leads to a very poor range resolution (resolution along the direction of propagation of the transmitted signal). For these reasons, this type of system is not suited for breast cancer detection.

The novel contribution of this work is the development of a mm-wave radar imaging system with a 20 GHz bandwidth centered at 30 GHz, which can be potentially employed for breast imaging and cancer detection. This band makes it possible to pursue both high range and cross resolutions with respect to existing systems and at the same time to achieve adequate penetration in the human tissues. Compared to other works employing the 20–40 GHz frequency band, we have also developed a preliminary system prototype and tested it in a real experimental scenario, so as to evaluate its performance and target detection capability. Moreover, mm-waves favour the development of a compact, highly integrated system. This is fundamental to develop a cost-effective system for medical screening among a vast segment of the population.

In this paper, the design of a preliminary imaging system is presented. Instead of a complete system that includes a full planar array of antennas able to generate 3D images, this preliminary system is based on a synthetic aperture realized by two antennas for 2D imaging. Data collection used the reliable methodology of stepped frequency continuous wave (SFCW) radar. In particular, the data for image reconstruction were obtained by shifting the antennas along a predetermined line, parallel to the surface under investigation. In this way, an equivalent linear array of  radiators was investigated, and a 2D image (lateral displacement by vertical penetration) was obtained. Image reconstruction was based on the delay-multiply-and-sum (DMAS) algorithm, proposed in [18], which was selected for this application thanks to its good performance in terms of dynamic range.

For this preliminary system, the intended targets were synthetic objects in free space. This configuration allowed us to evaluate all the critical system aspects. In fact, a complete 3D imaging system, based on a planar array of  radiators, would only require larger computational resources and mechanical complexity. As said before, these aspects are expected to be solved thanks to the possibilities offered by mm-wave devices, which are suited to realizing a compact system in which the silicon-based integration between radiators, electronic front end, and data processing can be exploited.

This paper is organized in five sections: in Section 2 the design of the experimental setup of the antenna array is presented, in Section 3 the imaging algorithm is discussed, Section 4 presents the results and a high resolution 2D image of a two-target dielectric scenario, and Section 5 concludes the paper by presenting the next steps required to develop a complete mm-wave breast cancer imaging system.

2. Design of the Stepped Frequency Continuous Wave Radar

The SFCW approach considers the antenna-target-antenna electromagnetic system as a linear transfer function, by defining its behaviour according to the measured scattering parameters. All the information about the target is obtained from the magnitude and phase of the transfer function between two antennas. The architecture of the synthetic antenna array (in particular the central working frequency and the aperture width) sets the performance of the imaging system in terms of cross resolution, while the frequency bandwidth (BW) sets the range resolution. Range resolution has been well studied in previous works [11, 17, 19, 20] and is proportional to the inverse of BW. Another feature is the nonambiguous range; since the acquisition of the scattering parameters ( parameters) is based on a finite number of frequencies, the quantization step sets the distance in time (and consequently in space) between each signal replica, called the nonambiguous range (). This means that only the portion of space between the origin and  has a physical meaning.  is simply calculated as , where  is the propagation speed in the medium and  is the frequency step. The prototype architecture described in this paper, for the detection of targets in air, has an  of 300 mm.

The proposed 20 GHz bandwidth needs proper broadband antennas. In this preliminary design, the chosen radiators are two truncated double-ridge waveguides. Thanks to the double-ridge architecture, the cut-off frequency of the fundamental mode  is lower than that for standard waveguides, with a consequent widening of the bandwidth. Thus, the radiators reach the desired bandwidth, operating from 18 GHz to 40 GHz. On the other hand, this type of antenna does not offer optimal input matching, that is, approximately −6 dB. However, this is not a problem for this prototype because the power budget provides a large margin. Better matching could be achieved by designing a proper matching section, if required.

The main difference between a standard radar and this system for breast cancer detection is the distance between the target and the antenna array. Biomedical applications, in fact, usually need a range of view, which is well below one meter. In particular, breast cancer imaging is limited by breast depth, which is usually on the order of a few centimeters when the patient is lying supine during the screening. Furthermore, the high working frequency (more than 20 GHz in this case) and the overall array aperture (on the order of some tens of centimeters) impose a near field region that extends up to several meters or even tens of meters [21]. This means that this system operates in the deep near field. Therefore, a standard design approach does not guarantee an optimal performance of the antenna array. Nevertheless, a convenient point to start the design of the synthetic array is the antenna-to-antenna spacing and radiators number  [21]. As in far field approach, the radiators distance is related to the presence of (generally unwanted) grating lobes. On the other hand, the −3 dB beamwidth is directly controlled by the total aperture width.

The maximum aperture available, limited by the experimental setup dimensions, is 200 mm. A number of possible architectures were investigated, but the best performance was reached with a linear array of 35 antennas with variable reciprocal spacings. Physically adjacent antennas spacing is limited to 25 mm by flange transition hindrance. Subsequent spacings, achieved with the employment of linear actuators, are reduced to 5 mm. This architecture guarantees high performance both in terms of resolution, due to the large total aperture, and in terms of grating lobes, which are avoided across the entire field of view. The expected cross resolution is 3 mm, calculated as the third part of the central frequency wavelength, and the range resolution is down to 8 mm, thanks to the large bandwidth employed. Another benefit of this architecture based on a high number of antennas is the increasing of process gain and consequently a low noise floor in the resulting image.

In the experimental setup, four microstep linear actuators were used to shift the antennas. Each pair of shifters was crossed, as shown in Figure 2, to allow two-dimensional movement of the antennas. In this way, the experimental setup can be extended to generate 3D images, though for this prototype the antenna movements were limited to a single line and generated 2D images, as discussed in the previous section. The measurements are directed to a mm-wave vector network analyzer (VNA) that acquires the transmission S-parameters of the antenna-target-antenna system over the frequency band of interest. Radiators were fastened to the carriage of linear actuators using the holes of the flanges and connected to the VNA cables with coaxial K-1.85 mm male-female transitions. Antennas were directed towards the floor, and the measurement environment was totally surrounded by anechoic panels, as illustrated in Figures 3 and 4.

Schematic top view of the setup. The red dashed line identifies the total width of the synthetic array. The grey arrows sketch the RX antenna movements.

Lateral view of the setup.

Top view of the setup.