L1 Band Research Articles

Dual-resonance microwave probe for magnetic field mapping

This paper introduces a dual-resonance probe for mapping magnetic fields in electromagnetic compatibility (EMC) applications. The probe, consisting of a circular loop loaded with a 6-turn circular spiral, exhibits two resonant modes via capacitive coupling, resonating at 1.158 GHz and 1.582 GHz to cover L1 and parts of the L5 band. Designed for GPS applications, the presented equivalent circuit model of the probe simplifies its design. The probe maps the orthogonal magnetic field component at its resonant frequencies. Measurements, taken while scanning over a short-circuited microstrip line and a rat-race hybrid coupler, closely match their simulated orthogonal magnetic field component. The proposed probe offers advancements in sensitivity enhancing EMC in various electronic systems.

Dual-Band Low-Noise Amplifier for GNSS Applications

A new dual-band low-noise amplifier (LNA) operating at L1/E1 1.575 GHz and L5/E5 1.192 GHz center frequencies for global navigation satellite system receivers is proposed. A doubled common-source amplifier architecture is used with a single input, shared gate inductor, and two outputs to split the RF signal into separate RX channels. The main advantage of the proposed circuit is compatibility with widespread multi-band antennas with single RF connectors dedicated to high-precision applications, as well as the possibility to use cheap SAW filters with small footprints to build low-cost, highly accurate GNSS receiver modules. The input and both outputs are well matched to 50 Ω impedance. The LNA is designed with a 110 nm CMOS process, consuming 6.13 mA current from a 1.5 V supply. The measured noise figures and voltage gains of the dual-band LNA are, respectively, NF1/NF5 = 3.23/3.5 dB and G1/G5 = 21.22/18.2 dB in the band of interest for each channel. The measured impedance matching at the input (S11) and output (S22) of the dual-band low-frequency amplifier is as follows: S11_L1 = −23.89, S11_L5 = −8.42, S22_L1 = −12.65, S22_L5 = −15.08. The one-decibel compression points are L1 band PdB1 = −37.71 dBm and L5 band PdB5 = −34.72 dBm, respectively.

Compact Circularly Polarized Shared Aperture Antenna with Wide Axial Ratio Bandwidth for NavIC Receiver

A novel probe fed right hand circularly polarized (RHCP) shared aperture antenna with concentric configuration is designed for L5 and S-bands NavIC receiver application. The structure consists of a square loop-type patch antenna for the L5 band, serves as the top radiator, and a concentrically truncated corner patch antenna for the S-band is embedded in the non-radiating portion of the L5 band antenna. The square loop is orthogonally fed with electromagnetically coupled strips with equal power and quadrature phased shift through symmetric vias. These vias are connected to the feeding network, which consists of a Wilkinson power divider that is designed on opposite sides of the ground to mitigate spurious radiations. Furthermore, the S-band antenna, placed inside the L5 band substrate, achieves CP by corner truncation. This technique increases the aperture reuse efficiency and improves the isolation between both radiators. The overall profile of the antenna is 75×75×8mm3 and exhibits a wide impedance bandwidth of 25.5% for the L5 band and 6.5% for the S-band, with an isolation of better than 20dB for both bands. The axial ratio bandwidth achieved is 25.5% and 4.1% for the L5 and S bands, respectively, with boresight gain of 3.57 dBiC and 4.8 dBiC in the L5 band and S-band, respectively. The proposed antenna is based on a shared aperture technique, which has different feeding ports for both bands; thus, it improves the G/T performance and noise figure of the overall system. These characteristics make the proposed antenna suitable for use in NavIC application.

Study of Global Navigation Satellite System Receivers' Accuracy for Unmanned Vehicles.

The development of unmanned ground vehicles and unmanned aerial vehicles requires high-precision navigation due to the autonomous motion and higher traffic intensity. The existing L1 band GNSS receivers are a good and cheap decision for smartphones, vehicle navigation, fleet management systems, etc., but their accuracy is not good enough for many civilian purposes. At the same time, real-time kinematic (RTK) navigation allows for position precision in a sub-centimeter range, but the system cost significantly narrows this navigation to a very limited area of applications, such as geodesy. A practical solution includes the integration of dual-band GNSS receivers and inertial sensors to solve high-precision navigation tasks, but GNSS position accuracy may significantly affect IMU performance due to having a great impact on Kalman filter performance in unmanned vehicles. The estimation of dilution-of-precision (DOP) parameters is essential for the filter performance as the optimality of the estimation in the filter is closely connected to the quality of a priori information about the noise covariance matrix and measurement noise covariance. In this regard, the current paper analyzes the DOP parameters of the latest generation dual-band GNSS receivers and compares the results with the L1 ones. The study was accomplished using two types of antennas-L1/L5 band patch and wideband helix antennas, which were designed and assembled by the authors. In addition, the study is extended with a comparison of GNSS receivers from different generations but sold on the market by one of the world's leading GNSS manufacturers. The analyses of dilution-of-precision (DOP) parameters show that the introduction of dual-band receivers may significantly increase the navigation precision in a sub-meter range, in addition to multi-constellation signal reception. The fast advances in the performance of the integrated CPU in GNSS receivers allow the number of correlations and tracking satellites to be increased from 8-10 to 24-30, which also significantly improves the position accuracy even of L1-band receivers.

A deep learning GNSS spoofing and jamming detection method with dual-frequency C/N0 heatmap

Abstract The Global Navigation Satellite System (GNSS) is vulnerable to interference due to the open signal structure and low signal strength, posing a significant threat to the billions of terminals worldwide that rely on GNSS receivers for precise Positioning, Navigation, and Timing (PNT) services. In this paper, we propose a cloud-edge framwork for GNSS spoofing and jamming monitoring, comprising the data acquisition module, GNSS monitoring module, detecting and reporting module. In this framwork, we design a Deep Learning (DL) method for detecting GNSS interference through Dual-frequency Carrier-to-Noise density ratio (C/N0) heatmaps (DD-C/N0). This method involves extracting and correlating features from C/N0 heatmaps of visible navigation satellites operating in the GPS L1 and L2 frequency bands, allowing the identification of anomalous patterns. A U-BLOX receiver was utilized to capture the GNSS satellite signals, while commercial jammers and Software-Defined Radio (SDR) HackRF One kits were employed to simulate the interference sources. Experimental results demonstrate that the proposed method achieves significantly higher performance, with an accuracy of 99% and 98% on the public dataset and real-time testing data, compared to unsupervised, semi-supervised, and supervised detectors that rely solely on single-channel data (L1 frequency band). Integrated with the DD-C/N0 method, the online GNSS monitoring system will be improved and deployed to automate spoofing and jamming detection tasks in the next step.

Perspectives for Improvements on Real-Time GNSS Positioning with the Use of New Observables

The research aims to analyze Global Navigation Satellite System (GNSS) positioning solutions using the Precise Point Positioning (PPP) method in kinematic mode, in which the position is obtained epoch by epoch through data from only one GNSS receiver, precise ephemerides, and satellite clock corrections, both with high accuracy. In this context, the adopted methodology employs the open-source software RTKLIB, which, through its data post-processing capability, enables the evaluation of kinematic PPP performance by incorporating new observables such as L5 and E5a bands, crucial for enhancing positional accuracy and mitigating multipath effects. Additionally, for survey simulations, data from the UFPR and POVE stations of the Brazilian Network for Continuous Monitoring of GNSS (RBMC) were utilized. The selected stations are located in the Northern and Southern regions of Brazil. The GNSS data were processed with the same tracking duration for a 45-minute cold-start, aimed at observing solution convergence. Subsequently, the estimated outputs in RTKLIB were obtained based on station origins using coordinates provided by SIRGAS-CON. Moreover, by utilizing precise ephemerides data, it was possible to conclude that the addition of new observables for triple-frequency positioning led to an improvement in the accuracy of the obtained coordinates, particularly in the Vertical component. In this regard, the increase in accuracy in experiments using only triple-frequency data with a 15° elevation mask was approximately 25% at the UFPR station and about ~37% at the POVE station. Furthermore, it was observed that reducing the elevation mask from 15° to 10° had a positive impact on dual-frequency positioning at the UFPR station, resulting in gains of over 3% in the East component and around ~21% in the North component compared to values obtained with the 15° mask. Similarly, during triple-frequency positioning at the POVE station, gains exceedingly approximately 16% in the North component and around ~22% in the Vertical component were observed.

Antenna and attitude modeling of modernized GLONASS satellites

Next to the legacy frequency division multiple access (FDMA) signals in the L1 and L2 band, modernized GLONASS satellites of the M+, K1, and K2 generation also transmit new code division multiple access (CDMA) signals on L3, and, in part, the L1 and L2 frequencies. Depending on the specific satellite platform, either a common antenna or two distinct antennas are used for the individual signals. As a novel feature, the new CDMA navigation messages provide information on the antenna phase center locations as well as the spacecraft orientation during rate-limited noon and midnight turns. We establish a comprehensive set of phase center positions for the individual GLONASS antennas from manufacturer data and information in the CDMA navigation messages, inferred from the comparison of FDMA and CDMA broadcast ephemerides, and obtained from antenna baseline estimates using a triple-frequency carrier phase combination. Based on these, reference values for the signal-specific PCOs of each block of modernized GLONASS spacecraft are derived that may be used to extend the current antenna model of the International GNSS Service (IGS) to all frequency bands. Complementary to the analysis of antenna phase center information, the new CDMA attitude model for GLONASS-K satellites is reviewed. Algorithms for computing relevant parameters of the rate-limited yaw slews including the ramp-up and -down phase based on the Sun/orbit geometry are derived that enable a concise attitude modeling in GLONASS orbit determination and precise point positioning. The model is validated through comparison with yaw angle estimates derived from triple-frequency observations showing consistency at the 1° level for the K2 satellite. On the other hand, unexpected accelerations during noon turns of GLONASS-M+ are identified, which may cause short-term yaw angle deviations of up to 20° relative to attitude models in common use within the IGS.

A dynamic snow depth retrieval model based on time-series clustering optimization for GPS-IR

Due to the influence of environmental factors (i.e., terrain and surface coverage) around the GPS receivers, the snow depth retrieval results obtained by the existing global positioning system interferometric reflection (GPS-IR) method show significant variability. The resulting loss of reliability and accuracy limits the broad application of this technology. Therefore, this paper proposes a dynamic snow depth retrieval model based on time-series clustering optimization for GPS-IR to fully leverage multi-source satellite observation data for automatic and high-precision snow depth retrieval. The model employs Dynamic Time Warping distance measurement combined with the K-Medoids clustering algorithm to categorize frequency sequences obtained from various satellite trajectories, facilitating effective integration of multi-constellation data and acquisition of optimal datasets. Additionally, Long Short-Term Memory networks are integrated to capture and process the long-term dependencies in snow depth data, enhancing the model’s adaptability in handling time-series data. Validated against SNOTEL measured data and standard machine learning algorithms (such as BP Neural Networks, RBF, and SVM), the model’s retrieval capability is confirmed. For P351 and AB39 sites, the correlation coefficients for L1 band data retrieval were both 0.996, with RMSEs of 0.051 and 0.018 m, respectively. The experiment results show that the proposed model demonstrates superior precision and robustness in snow depth retrieval compared to the previous method. Then, we analyze the accuracy loss caused by sudden snowfall events. The proposed model and methodology offer new insights into the in-depth study of snow depth monitoring.

GLONASS-K2 signal analysis

K2 is a new generation of GLONASS satellites that provides code division multiple access (CDMA) signals in the L1, L2 and L3 frequency bands in addition to legacy L1 and L2 signals based on frequency division multiple access (FDMA) modulation. The first GLONASS-K2 satellite was launched in August 2023 and started signal transmission in early September 2023. Based on measurements with a 30-m high-gain antenna, spectral characteristics of the various signal components are described and relative power levels are identified. A 3 dB (L1) to 4 dB (L2) higher total power is determined for the CDMA signal compared to the legacy FDMA signal and an equal power of the open service and secured CDMA signal components is found. The ranging code of the L2 channel for service information, which has not been publicly disclosed so far, is identified as a Gold code sequence consistent with the data channel of the L1 open service CDMA signal. The high-gain antenna measurements are complemented by tracking data from terrestrial receivers that enable a first assessment of user performance. An up to 50% improvement in terms of noise and multipath performance is demonstrated for the new L1 and L2 CDMA signals in comparison with their legacy counterpart, but no obvious differences between the different binary phase-shift keying and binary offset carrier modulations of the data and pilot components of these signals could be identified for the test stations. Triple-frequency carrier phase observations from L1, L2, and L3 CDMA signals exhibit good consistency at the noise and multipath level, except for small variations that can be attributed to slightly different antenna phase patterns on the individual frequencies. Overall, the new CDMA signals are expected to notably improve and facilitate precise point positioning applications once fully deployed across the GLONASS constellation.

Multiband circularly-polarized stacked elliptical patch antenna with eye-shaped slot for GNSS applications

Abstract This paper introduces a tri-band stacked elliptical patch antenna featuring a right-handed circular polarized, designed to operate at the L2, L5, and L1 Global Navigation Satellite System bands. Initially, an elliptic patch is constructed and fed by a probe feed to generate TM110 and TM210 modes at resonance frequencies calculated using Mathieu functions. The probe position is precisely adjusted to excite the quasi-orthogonal mode of TM110 to generate circularly polarized (CP) waves at the L2 and L5 bands. Subsequently, an eye-shaped aperture is engraved into the elliptical patch to enhance the axial ratio (AR) beamwidth in the L2 and L5 bands and stimulate the orthogonal mode of TM210 to produce CP waves at the L1 band. Lastly, a stacked partially elliptical parasitic element is placed beneath the upper slotted elliptical patch to enhance the orthogonality of TM210 surface current versions and thus improve the AR beamwidth at the L1 band. The proposed antenna shows low reflection coefficient values at 1.12–1.33 (L2/L5), and 1.5–1.66 GHz (L1). The AR beamwidths are 133/213∘, 167/163∘, and 36/103∘ at two orthogonal cutplanes at L5, L2, and L1 bands, respectively. The antenna also has decent gains of 6–6.9 dBic across the three bands.

GNSS-R snow depth retrieval algorithm based on PSO-LSTM

The global navigation satellite system (GNSS)-interferometric reflectometry technique has been applied to retrieve snow depth, which has a high potential for application. The GNSS reflectometry classical algorithm retrieves the snow depth by extracting the frequency of the multipath signal and substituting it into an empirical formula. However, the retrieval errors of high and low snow depths are large due to the influence of factors such as surface vegetation and terrain environment. In this paper, we propose a snow depth retrieval algorithm based on a particle swarm optimized long short-term memory (PSO-LSTM) neural network. The algorithm extracted three characteristic parameters (frequency, amplitude, and phase) from the signal-to-noise ratio (SNR) data as inputs, and optimized the LSTM hyperparameters by the PSO algorithm to improve the retrieval accuracy for low snow depths and snow depths close to the antenna. The snow depth retrieval results of global positioning system L1 band SNR data collected from the P351 station in 2022 and AB33 station in 2017 were evaluated in this paper. The snow depth retrieval results of the PSO-LSTM algorithm for P351 station were in high agreement with the snow depth data provided by the snowpack telemetry network; the coefficient of determination ( R2 ) reached 0.986, and the root mean square error (RMSE) and mean absolute error (MAE) were 7.30 cm and 4.94 cm, respectively. Compared with the classical algorithm, the PSO-LSTM algorithm decreased the RMSE and MAE by 53.0% and 30.4% for the retrieval results of snow depths below 15 cm at the P351 station, and by 76.8% and 84.4% for the retrieval results of snow depths above 117 cm from the 1st day to the 137th day, respectively. Similarly, the RMSE, MAE, and R2 for the 2017 retrieval results at AB33 station were 5.90 cm, 4.25 cm, and 0.965, respectively. Compared with the classical algorithm, the PSO-LSTM algorithm decreased the RMSE and MAE by 47.9% and 33.0% for the retrieval results of snow depths below 15 cm at the AB33 station, and by 75.4% and 82.3% for the retrieval results of snow depths above 56 cm from the day 46 to day 120. In addition, the snow depth retrieval algorithm was proposed in this paper does not require antenna height and empirical formulas to realize snow depth retrieval, and at the same time, the algorithm effectively improved the retrieval accuracy for both high and low snow depths with strong robustness.

Dual-band circular polarized microstrip antenna for GNSS application

Abstract A dual-band circular polarized antenna with broad bandwidth is proposed. Two circular grooves with different radii are carved on the ground to generate two frequency bands. Two rectangular slots are engraved on the outside of the circular groove. By adjusting the length of the two slots, this antenna can radiate right-handed circularly polarized (RHCP) waves at two frequency bands, which can cover GPS L5 (1.176 GHz), L2 (1.227 GHz), L1 (1.575 GHz), BDS, GALILEO, and GLONASS bands. The measured −10 dB bandwidth is 46.3 % (1.13–1.81 GHz) and 3 dB axial ratio bandwidths are 15.6 % (1.11–1.30 GHz) and 17.8 % (1.38–1.65 GHz). The measured gains are 2.51 dBi and 2.67 dBi at 1.2 GHz and 1.56 GHz, respectively.

Use of microstrip antennas in aerospace applications: L5 band satellite communication example

Günümüzde mikroşerit antenler, yüksek performans gerektiren araçlarda, uçaklarda, askeri uçaklarda, İnsansız Hava Araçlarında (İHA), uzay araçlarında, radar sistemlerinde, uydu ve füze uygulamaları gibi pek çok havacılık alanında tercih edilmektedirler. Bu çalışmada, Mikro şerit yama antenlerin havacılık sektöründe kullanım alanları ve özellikle küresel konumlama sistemlerinde (GPS- Global Positioning System) kullanımı araştırılmış ve GPS L5 güvenlik bandında örnek bir mikroşerit yama anten tasarımı gerçekleştirilmiştir. Tasarımı gerçekleştirilen yüksek kazançlı ve dairesel polarizasyonlu anten High Frequency Structural Simulator (HFSS) program ile simüle edilerek sonuçlar incelenmiştir. Yapılan simülasyonların nümerik analizinde neticesinde 1176 MHz merkez frekansında, S11 değerinin -38.85 dB olan, band genişliğinin 54 MHz ve kazancının ise 6.07 dBm olduğu görülmüştür. Elde edilen bu değerler neticesinde küresel konum belirleme L5 güvenlik bandında kullanılabileceği sonucuna varılmıştır.

Tri-Band Circularly Polarized Annular Slot Antenna for GPS and CNSS Applications

A single-feed tri-band circularly polarized (CP) annular slot antenna is presented. The antenna structure is composed of two non-concentric annular slots that are fed by an L-shaped series step impedance microstrip line configuration. The proposed antenna is designed to operate at the L1 & L2 bands of the Global Positioning System (GPS) and the frequency band of the Compass Navigation Satellite System (CNSS). The measured results show that the impedance bandwidths are good for all bands. And the radiation patterns with good CP characteristics are obtained at the three resonant frequencies.

The Construction of Intelligent Platform in Ideological and Political Education in Colleges and Universities

Abstract Based on the feasibility of a personalized teaching platform and user requirements, this paper puts forward the overall architecture design and database design scheme of a personalized teaching platform in ideological and political education, which mainly consists of three functional modules, namely, the knowledge mapping module, ideological and political education course recommendation module, and learning effect evaluation module. After crawling the initial data based on the LTP model, the ideological and political education course resources were extracted and integrated to complete the construction of the knowledge graph module. The ideological and political education course recommendation module is created using the KGCNN algorithm, and then the learning effect evaluation module is constructed by combining the online behavior of students. After testing the system’s performance, the application effect of the teaching platform is assessed. The results show that KGCNN aggregation layer space in the interval of 10~100 can embed data with power law distribution more effectively, and the KGCNN algorithm also has certain advantages in the field of modeling personalized teaching platforms for ideological and political education. The number of experimental classes and ordinary classes with final grades in the L1 band increased by 21.90% and 7.17%, respectively, compared to the midterm, indicating that the personalized teaching platform for ideological and political education courses can effectively promote the improvement of student’s academic performance, and the enhancement effect of students with high levels is more significant.

Synthesized Binary Offset Carrier Modulation for Interoperable GNSS L1 Band Signals

Synthesized Binary Offset Carrier Modulation for Interoperable GNSS L1 Band Signals

Validation of GPS III transmit antenna calibrations

Accurate information about the satellite transmit antennas is essential for high-precision GNSS applications. Such metadata of the GPS III satellites were publicly made available by the manufacturer Lockheed Martin. They comprise phase center offsets (PCOs), phase patterns, and directivity patterns. These calibrations are validated with ground-based measurements of a global GPS tracking network and observations of a high-gain antenna. Phase center offsets and patterns are estimated from dual-frequency observations of a ground tracking network. The ionosphere-free L1/L2 z-PCOs show a 10 cm offset w.r.t. the manufacturer calibrations due to already known inconsistencies with the ITRF2020 scale fixed in the estimation. The standard deviation of the differences between estimated and calibrated z-PCOs is 2.7 cm. The estimated phase patterns have a 0.7 mm RMS consistency with the manufacturer calibrations after minimizing the raw patterns for nadir angles between 0° and 14°. The directivity patterns are validated with the effective isotropic radiated power (EIRP) measured with a 30 m high-gain antenna. The measured EIRP for the L1 and L2 band is affected by M-code transmission from a distinct antenna. When modeling the additional contribution of this antenna, the nadir-angle variation of the EIRP matches the calibrated directivity patterns with a precision of 0.1 dBW. Representative transmit power values of the main navigation antenna amount to 125 W, 30 W, and 85 W in the L1, L2, and L5 bands, while the L1 and L2 M-code signals are transmitted with about 30 W and 25 W, respectively.

Dual‐band pattern diversity liquid antenna with passive beam‐steering of the broadside modes

AbstractA dual‐band liquid cylindrical dielectric resonator antenna with pattern diversity at two different frequency bands is proposed using the lower order and higher order modes of the HEM and TM modes namely HEM11δ, HEM12δ+1, HEM31δ+1, HEM13δ, TM01δ, and TM02δ. The proposed antenna is designed to cover the GPS L2 band and the lower Wi‐Fi band at 1.227 and 2.4 GHz frequencies, respectively. The HEM modes which constitute the primary radiating modes achieved around 20.84% and 19.35% impedance bandwidth at lower and higher bands, respectively. In the later stage, beam‐steering is performed, whereby the realised broadside HEM modes at both lower and higher bands were passively steered with simple physical re‐orientation of the antenna structure. For this, the liquid's natural fluidic property of adhering to gravity is taken as an advantage which makes the proposed antenna adaptively steer its radiation pattern always towards the sky, irrespective of the tilt angle of the antenna. This concept of passively steering two modes at two different frequency bands without the use of any mechanical, electrical, or other associated components is presented for the first time.

Multi-Band Antenna Design by Reshaping Surface Currents of Higher Order Mode Using CMA Method

A multi-band antenna design by surface current reshaping of higher-order modes is presented. This method utilizes characteristic mode analysis to modify the conventional circular patch antenna in accordance with the surface current distribution of higher-order modes at the L5, S, and L1 bands using CMA. The antenna is evaluated up to four modes inducing fundamental mode. The S and L1 bands are obtained by exciting reshaped higher-order modes, while the L5 lower band is obtained by exciting the fundamental mode using full-wave analysis with 50 Ω coaxial feed. The measurement results are very similar to simulated antenna results. The measured operating frequencies of the proposed antenna are 1177.00 MHz (L5-band), 1575.00 (L1-band) MHz, and 2497.50 (S-band) MHz with associated impedance bandwidth (S11 ≤ −10 dB) are 25.30 MHz (1164.40–1189.70 MHz), 65.30 MHz (1535.50–1600.80 MHz), and 48.60 MHz (2464.10–2512.70 MHz) having desired gain with hemispherical radiation characteristics. These bands are used in Global Positioning Services (GPS) and in Indian Regional Navigation Satellite System (IRNSS) applications.

Robust Adaptive Beamformer Based on Constant Modulus Penalty Criteria

In this study, a robust adaptive beamformer based on constant modulus (CM) criteria is developed to improve the robustness of the array beamforming, which is a reconstructing minimal optimization for solving the mismatch problem of weight vector caused by steering vector mismatch. In the global positioning system (GPS) L1 band, firstly, a GPS array signal is modelled by designing a dual-polarized antenna array. Secondly, the distortion problem of beamforming is formulated in the traditional minimum variance distortionless response (MVDR) beamformer. For repairing the weight vector mismatch problem, a novel beamformer based on the CM envelope response is proposed to reconstruct MVDR beamforming in the array processing. Besides, min-max penalty criteria are used to enable the beamformer to allocate more degrees of freedom (DOFs) when penalizing the MVDR beamformer responses. Finally, an auxiliary two-element real variable is designed to plan the proposed beamformer. But it is still a nonconvex quadratic programming problem, so an alternating direction method of multipliers (ADMM) is employed to transform the objective function into several subproblems. Illustrative numerical simulation results are provided for validating the effectiveness of the proposed beamformer by comparing it with other existing approaches.