• Fabrication of hierarchical Ti6Al4V structures by hydrothermal treatment and laser interference lithography with enhanced ice resistance

      Liu, Ri; Wu, Xiaoming; Cao, Liang; Liu, Dongdong; Sun, Baishun; Weng, Zhankun; Wang, Zuobin; Changchun University of Science and Technology; University of Bedfordshire (IEEE, 2021-11-18)
      Icing widely exists in aerospace, transportation and electric power communication, causing great safety risks to people's production and life. Inhibiting icing is of great significance in practical engineering applications, and thus, employing an economical and efficient anti-icing method is a research hotspot. In this work, an anti-icing structured surface was fabricated by combining direct laser interference lithography (DLIL) with hydrothermal treatment. A micro-pillar array structure on the tc4 substrate was easily fabricated by DLIL, and a layer of nano-grass structure on the micro-pillar array was grown by hydrothermal treatment. These hierarchically textured surfaces exhibited low-temperature-adaptive water repellency (150° at −10°C, which delayed the frozen time (DT∼1h) and dropped frozen temperature. The above conditions were analyzed from the angle of wettability and heat conduction, and the influence of structure and wettability on ice resistance was discussed.
    • Fabrication of periodically micropatterned magnetite nanoparticles by laser-interference-controlled electrodeposition

      Wang, Lu; Dong, Litong; Li, Li; Weng, Zhankun; Xu, Hongmei; Yu, Miao; Wang, Zuobin; Changchun University of Science and Technology (Springer US, 2017-11-09)
      This paper introduces a laser-interference-controlled electrochemical deposition method for direct fabrication of periodically micropatterned magnetite (Fe3O4) nanoparticles (NPs). In this work, Fe3O4 NPs were controllably synthesized on the areas where the photoconductive electrode was exposed to the periodically patterned interferometric laser irradiation during the electrodeposition. Thus, the micropattern of Fe3O4 NPs was controlled by interferometric laser pattern, and the crystallization of the particles was controlled by laser interference intensity and electrochemical deposition conditions. The bottom-up electrochemical approach was combined with a top-down laser interference methodology. This maskless method allows for in situ fabrication of periodically patterned magnetite NPs on the microscale by electrodeposition under room temperature and atmospheric pressure conditions. In the experiment, Fe3O4 NPs with the mean grain size below 100 nm in the pattern of 5-lm line array were achieved within the deposition time of 100 s. The experiment results have shown that the proposed method is a one-step approach in fabricating large areas of periodically micropatterned magnetite NPs.
    • A feasibility study of implementation of oxy-fuel combustion on a practical diesel engine at the economical oxygen-fuel ratios by computer simulation

      Li, Xiang; Peng, Zhijun; Ajmal, Tahmina; Aitouche, Abdel; Mobasheri, Raouf; Pei, Yiqiang; Gao, Bo; Wellers, Matthias; University of Bedfordshire; Centre de Recherche en Informatique Signal et Automatique de Lille; et al. (SAGE Publications, 2020-12-09)
      To help achieve zero carbon emissions from inland waterway vessels, this implementation of oxy-fuel combustion on a practical diesel engine at the economical oxygen-fuel ratios were systematically studied and analysed in this paper. A 1-D simulation was used to explore the effect of various operating parameters for recovering the engine power when the engine is modified to the oxy-fuel combustion from conventional air combustion. The brake power of oxy-fuel combustion is only 26.7kW that has a noticeable decline compared with 40 kWof conventional air combustion with fixed consumption of fuel and oxygen. By optimising some valuable parameters, like fuel injection timing, intake charge temperature, intake components, engine compression ratio and water injection strategy, a benefit of 6.8kW has been acquired in the engine power. Afterwards, a remarkable benefit was obtained with the increase of lambdaO2 from 1.0 to 1.5, finally obtaining the same engine power with the conventional air combustion. Above all, taking advantage of various operating parameters, it is expected to further improve the value of the implement of oxy-fuel combustion on diesel engines at the economical oxygen-fuel ratios.
    • Fuzzy logic based intention recognition in STS processes

      Lu, Hang; Li, Dayou; Qiu, Renxi; University of Bedfordshire (Institute of Electrical and Electronics Engineers Inc., 2017-01-19)
      This paper represents a fuzzy logic based classifier that is able to recognise human users' intention of standing up from their behaviours in terms of the force they apply to the ground. The research reported focused on the selection of meaningful input data to the classifier and on the determination of fuzzy sets that best represent the intention information hidden in the force data. The classifier is a component of a robot chair which provides the users with assistance to stand up based on the recognised intention by the classifier.
    • Growth behavior of SHSY5Y cells on hybrid micro-pit and nano-pillar arrays

      Wu, Xiaomin; Li, Li; Liu, Ri; Weng, Zhankun; Wang, Zuobin; Changchun University of Science and Technology; University of Bedfordshire (IEEE, 2021-11-18)
      The directional arrangement and extension of cells is of great significance in the tissue engineering field. Great efforts have been made to study the effects of micro- or nano- structures on cell behaviors, but they are still poorly understood. In this work, hybrid micro/nano structures prepared by combining laser marking technology with metal assisted chemical etching (MACE) were introduced to study their effect on the growth behavior of SHSY5Y cells. It was found that the cells on the silicon micro-pit arrays (SiMP arrays, unetched substrate) were arranged orderly along the edge of the micro-pits, stretched and connected with each other, while the cells on the hybrid silicon micro-pit and silicon nano-pillar arrays (hybrid SiMP/SiNP arrays, etched substrates) were also arranged in an orderly manner with a relatively short cell stretch, but displayed a preference for independent growth. In addition, about 90% of cells showed a preference for growing on the area of nano-pillars (NPs), and only 10% of cells on the area of micro-pits (MPs) on the etched substrate. The results showed that the hybrid SiMP/SiNP arrays trapped cells and restricted the cell spreading. Thus, this approach is of great significance for the study of independent growth behavior of cells on the substrate in the field of single neuron research.
    • Highly birefringent nonlinear PCF for optical sensing of analytes in aqueous solutions

      Ademgil, Huseyin; Haxha, Shyqyri; European University of Lefke, Turkey; University of Bedfordshire (Elsevier, 2016-05-01)
      This paper presents a design of a nonlinear Photonic Crystal Fiber (PCF) based sensor exhibiting simultaneously high sensitivity, high birefringence and low confinement losses for liquid analyte sensing applications. We investigate the PCF sensor performance for the following analytes; Water, Ethanol and Benzyne. The impact of various design parameters of the highly nonlinear PCF on the relative sensitivity, the confinement losses and the birefringence features of the proposed PCF structure is numerically investigated by employing the full vectorial Finite Element Method (FEM). According to our FEM numerical results, a three ring nonlinear PCF based sensor is designed that simultaneously offers high birefringence of order 10-3 and high relative sensitivity at wide wavelength range.
    • A hybrid approach for image super-resolution of light field images

      Farag, Saber; Velisavljević, Vladan; Aggoun, Amar (IEEE, 2017-09-22)
      Recent advances in camera technologies has led to the design of plenoptic cameras. This camera type can capture multiple images of the same scene using arrays of microlenses, where each microlens has a shifted location providing a separate view of the scene. Such a design results in a superior performance as compared to traditional cameras, enabling multi-view or multi-focal imaging captured in a single shot. However, currently available plenoptic cameras are limited in spatial resolution, which makes it difficult to use them in applications where sharpness or high resolution is key, such as the film industry. Our paper presents a novel light field hybrid super-resolution method that combines two classical super-resolution techniques for efficient application to plenoptic images. After this combination, we first segment the output hybrid super-resolution image into the objects of interest. Afterward, we apply sparse representation to super resolve the segmented image. This technique helps to improve the quality by decrease computations for light field images and extract significant features from the objects of interest. We demonstrate the gain achieved by the novel method as compared to the current relevant approaches in terms of both PSNR and SSIM for various enhanced spatial resolutions.
    • Implantable antennas for bio-medical applications

      Malik, Nabeel A.; Sant, Paul; Ajmal, Tahmina; Ur-Rehman, Masood; University of Bedfordshire; University of Glasgow (Institute of Electrical and Electronics Engineers Inc., 2020-10-08)
      Biomedical telemetry has gained a lot of attention with the development in the healthcare industry. This technology has made it feasible to monitor the physiological signs of patient remotely without traditional hospital appointments and follow up routine check-ups. Implantable Medical Devices(IMDs) play an important role to monitor the patients through wireless telemetry. IMDs consist of nodes and implantable sensors in which antenna is a major component. The implantable sensors suffer a lot of limitations. Various factors need to be considered for the implantable sensors such as miniaturization, patient safety, bio-compatibility, low power consumption, lower frequency band of operation and dual-band operation to have a robust and continuous operation. The selection of the antenna is a challenging task in implantable sensor design as it dictates performance of the whole implant. In this paper a critical review on implantable antennas for biomedical applications is presented.
    • Implementation of oxy-fuel combustion (OFC) technology in a gasoline direct injection (GDI) engine fueled with gasoline–ethanol blends

      Li, Xiang; Pei, Yiqiang; Li, Dayou; Ajmal, Tahmina; Aitouche, Abdel; Mobasheri, Raouf; Peng, Zhijun (American Chemical Society, 2021-10-27)
      Nowadays, to mitigate the global warming problem, the requirement of carbon neutrality has become more urgent. Oxy-fuel combustion (OFC) has been proposed as a promising way of carbon capture and storage (CCS) to eliminate carbon dioxide (CO2) emissions. This article explores the implementation of OFC technology in a practical gasoline direct injection (GDI) engine fueled with gasoline–ethanol blends, including E0 (gasoline), E25 (25% ethanol, 75% is gasoline in mass fraction), and E50 (50% ethanol, 50% is gasoline in mass fraction). The results show that with a fixed spark timing, φCA50 (where 50% fuel is burned), of E50 and E25 is about 4.5 and 1.9° later than that of E0, respectively. Ignition delay (θF) and combustion duration (θC) can be extended with the increase of the ethanol fraction in the blended fuel. With the increase of the oxygen mass fraction (OMF) from 23.3 to 29%, equivalent brake-specific fuel consumption (BSFCE) has a benefit of 2.12, 1.65, and 1.51% for E0, E25, and E50, respectively. The corresponding increase in brake-specific oxygen consumption (BSOC) is 21.83, 22.42, and 22.58%, respectively. Meanwhile, θF, θC, and the heat release rate (HRR) are not strongly affected by the OMF. With the increase of the OMF, the increment of θF is 0.7, 1.8, and 2.2° for E0, E25, and E50, respectively. θC is only extended by 1, 1.1, and 1.4°, respectively. Besides, by increasing the intake temperature (TI) from 298 to 358 K under all of the fuel conditions, BSFCE and BSOC present slight growth trends; θF and θC are slightly reduced; in the meantime, φCA50, φPmax (crank angle of peak cylinder pressure), and the position of the HRR peak are advanced by nearly 1°.
    • Improved efficiency of microcrystalline silicon thin film solar cells with wide band-gap CdS buffer layer

      Jabeen, Maria; Haxha, Shyqyri; Charlton, Martin D.B.; University of Bedfordshire; University of Southampton (Institute of Electrical and Electronics Engineers (IEEE), 2017-12-01)
      In this paper, we have reported a new structure based upon an optical simulation of maximum light trapping and management in microcrystalline silicon thin film solar cells by using multi texture schemes and introducing an n-type cadmium sulphide (CdS) buffer layer with the goal of extreme light coupling and absorption in silicon absorber layer. Photon absorption was improved by optimising the front and back texturing of transparent conductive oxide (TCO) layers and variation in buffer layer thickness. We have demonstrated that light trapping can be improved with proposed geometry of 1μm thick crystalline silicon absorber layer below a thin layer of wide band gap material. We have improved the short circuit current densities by 1.35mA/cm2 resulting in a total short circuit current of 25 mA/cm2 and conversion efficiency of 9% with the addition of CdS buffer layer and multi textures, under global AM1.5 conditions. In this study, we have used 2 Dimensional Full Vectorial Finite Element (2DFVFEM) to design and optimize the proposed light propagation in solar cell structure configuration. Our simulation results show that interface morphology of CdS layer thickness and textures with different aspect and ratios have the most prominent influence on solar cell performance in terms of both short circuit current and quantum efficiency.
    • Interference mitigation in D2D communication underlaying LTE-A network

      Safdar, Ghazanfar Ali; Ur-Rehman, Masood; Muhammed, Mujahid; Imran, Muhammad Ali; Tafazolli, Rahim; University of Bedfordshire; Birmingham City University; University of Glasgow; University of Surrey (IEEE, 2016-10-25)
      The mobile data traffic has risen exponentially in recent days due to the emergence of data intensive applications, such as online gaming and video sharing. It is driving the telecommunication industry as well as the research community to come up with new paradigms that will support such high data rate requirements within the existing wireless access network, in an efficient and effective manner. To respond to this challenge, device-to-device (D2D) communication in cellular networks is viewed as a promising solution, which is expected to operate, either within the coverage area of the existing eNB and under the same cellular spectrum (in-band) or separate spectrum (out-band). D2D provides the opportunity for users located in close proximity of each other to communicate directly, without traversing data traffic through the eNB. It results in several transmission gains, such as improved throughput, energy gain, hop gain, and reuse gain. However, integration of D2D communication in cellular systems at the same time introduces new technical challenges that need to be addressed. Containment of the interference among D2D nodes and cellular users is one of the major problems. D2D transmission radiates in all directions, generating undesirable interference to primary cellular users and other D2D users sharing the same radio resources resulting in severe performance degradation. Efficient interference mitigation schemes are a principal requirement in order to optimize the system performance. This paper presents a comprehensive review of the existing interference mitigation schemes present in the open literature. Based on the subjective and objective analysis of the work available to date, it is also envisaged that adopting a multi-antenna beamforming mechanism with power control, such that the transmit power is maximized toward the direction of the intended D2D receiver node and limited in all other directions will minimize the interference in the network. This could maximize the sum throughput and hence, guarantees the reliability of both the D2D and cellular connections.
    • An investigation into in-cylinder tumble flow characteristics with variable valve lift in a gasoline engine

      Wang, Tianyou; Liu, Daming; Tan, Bingqian; Wang, Gangde; Peng, Zhijun; Tianjin University; University of Hertfordshire (Kluwer Academic Publishers, 2014-10-31)
      In this paper, the investigation into in-cylinder tumble flow characteristics with reduced Maximum Valve Lifts (MVL) is presented. The experimental work was conducted in a modified four-valve Spark-Ignition (SI) test engine, with optical accesses for measuring in-cylinder air motion in the vertical direction. Three different MVL of 6.8 mm, 4.0 mm and 1.7 mm were tested and Particle Image Velocimetry (PIV) was employed for those measurements. Measurement results were analysed by examining the tumble flow field, the tumble ratio variation and the fluctuating kinetic energy distribution. Meanwhile, a numerical analysis method for detecting the vortex centre was developed. From results of the vortex centre distribution, the cyclic variation of the in-cylinder flow was explored. The phase-averaged flow fields show that higher MVLs could produce stronger vertical flows which turn more toward to the piston top and finally are possible to form big scale tumble flow structure. Although lower MVLs create a higher tumble ratio when the piston is close to the Bottom Dead Centre (BDC), higher MVLs substantially produce higher tumble ratios when the piston is moving close to the Top Dead Centre (TDC). In terms of kinetic energy, lower MVLs result in higher values including higher total kinetic energy and higher fluctuating energy. Finally, the vortex centres results demonstrate lower MVLs could enhance cycle-to-cycle variation due to the weakened tumble vortex.
    • Investigation of oxyfuel combustion on engine performance and emissions in a DI diesel HCCI engine

      Mobasheri, Raouf; Izza, Nadia; Aitouche, Abdel; Peng, Jun; Bakir, Boualem (IEEE, 2020-01-09)
      Due to stronger environmental standard aims, the European Union (EU) has recently adopted more stringent limits for emissions from inland waterway vessels. The objective of “RIVER” project is to apply an oxyfuel combustion technology for diesel engines that eliminates NOx emissions, and captures and stores all carbon dioxide emissions in order to achieve zero-carbon and zero other pollutant emissions. As part of this project, a 3-D computational fluid dynamics model coupled with detailed chemical kinetics has been used to evaluate the influence of oxyfuel combustion on engine operating conditions and combustion characteristic in a high speed direct injection (HSDI) diesel engine under homogenous charge compression ignition (HCCI) mode. In this work, a reduced chemical n-heptane-n-butanol-PAH mechanism which consists 76 species and 349 reactions has been applied to simulate the combustion process. The mechanism has been initially validated by experiments under HCCI combustion mode and then, it has been used to examine the oxyfuel combustion using different diluent strategies over a range of air-fuel equivalence ratio (lambda). The simulation results indicate that increasing the inlet carbon dioxide concentration, as a diluent gas, under constant fueling rate does not bring any serious change to the amount of brake mean effective pressure (BMEP) in the relatively rich mixtures regions. However, by decreasing the fuel rate (higher lambda) the difference between different diluent strategies become more obvious as the minimum amount of BMEP is achieved when 83% of carbon dioxide is used. In addition, the results show a considerable reduction of PM emissions while the NOx emission have been completely eliminated using oxyfuel combustion.
    • Large Eddy Simulation analysis on confined swirling flows in a gas turbine swirl burner

      Liu, Tao; Bai, Fuqiang; Zhao, Zixuan; Lin, Yuzhen; Du, Qing; Peng, Zhijun; Tianjin University; University of Ottawa; University of Bedfordshire; Beihang University (MDPI, 2017-12-07)
      This paper describes a Large Eddy Simulation (LES) investigation into flow fields in a model gas turbine combustor equipped with a swirl burner. A probability density function was used to describe the interaction physics of chemical reaction and turbulent flow as liquid fuel was directly injected into the combustion chamber and rapidly mixed with the swirling air. Simulation results showed that heat release during combustion accelerated the axial velocity motion and made the recirculation zone more compact. As the combustion was taking place under lean burn conditions, NO emissions was less than 10 ppm. Finally, the effects of outlet contraction on swirling flows and combustion instability were investigated. Results suggest that contracted outlet can enhance the generation of a Central Vortex Core (CVC) flow structure. As peak RMS of velocity fluctuation profiles at center-line suggested the turbulent instability can be enhanced by CVC motion, the Power Spectrum Density (PSD) amplitude also explained that the oscillation at CVC position was greater than other places. Both evidences demonstrated that outlet contraction can increase the instability of the central field.  [m1]Is’t right? Yes.
    • Laser interference field induced re-distribution of Ag nanoparticle arrays

      Yue, Ming; Liu, Mengnan; Li, Li; Liang, Xiubo; Wang, Lu; Wang, Zuobin; Changchun University of Science and Technology; University of Bedfordshire (IEEE, 2021-11-18)
      The wide application of metal nanoparticle arrays has attracted much attention in the field of nanotechnology. Such as quantum dots, structural colors, sensors, metamaterials. In this work, we fabricated periodic micro-and nanostructures through the interference of two beams with the same frequency and vibration direction. By controlling the spot energy and light field energy distribution of Gaussian interference lithography, the various surface characteristics of Ag-Si material system (Ag@Si) are optimized, and the mass transfer brought by Oswald ripening is used to control the Rayleigh instability in the thermal dewetting process. To achieve the purpose of the periodic gradient Ag nanoparticle arrays (AgNPs) pattern can be controlled. The experimental results show that the periodic micro-and nanostructures can be obtained by optimizing the spot energy and the number of pulses.
    • Life Cycle Assessment (LCA) of BEV's environmental benefits for meeting the challenge of ICExit (Internal Combustion Engine Exit)

      Zheng, Ge; Peng, Zhijun; University of Essex; University of Bedfordshire (Elsevier Ltd, 2021-02-19)
      Based on necessary literature review, LC (Life Cycle) emissions, in particular LCCO2 (Life Cycle CO2) emissions, of BEVs (Battery Electric Vehicles) have been assessed and compared with the most efficient ICEVs (Internal Combustion Engine Vehicles), such as non-plug-in HEVs (Hybrid Electric Vehicles) and diesel cars. By considering CO2 emissions from vehicle production, vehicle recycle and the entire process of energy flow (from the mining of the energy source to a vehicle being driven), LCCO2 emission models of BEVs and ICEVs were built. For comparing between BEVs and ICEVs in terms of their LC emissions, a new measure named SRPR (Square Root of Power and Range) has been proposed for correctly reflecting the powertrain's main performance. Results show that, although BEVs have much lower ECR (Energy Consumption Rate) than non-plug-in HEV and diesel cars, their LCCO2 are very variable, and are very dependent on LCCO2 of power generation mix of specific country. In some countries where thermal power generation, in particular coal power generation, is still dominant, BEVs’ LCCO2 are apparently higher than ICEVs. If a country would like to have their BEVs operating lower LCCO2 than ICEVs, the overall average LCCO2 from their power generation mix should be at least at the level about 320 g/kWh. As a case study, by analysing the power generation development trend and the BEV development trend in China, it suggests that their aim for developing BEVs to have lower LCCO2 than ICEVs in next two or three decades would be very difficult to meet. If they like to put priority on the reduction of LCCO2 of ground vehicles, BEVs could not be widely promoted in China until they made their power generation clean enough, probably at least in next 20 even 30 years. Finally, BEVs’ other LC pollutant emissions, such as NOx (Nitrogen Oxides), PM (Particulate Matters), SOx (Sulphur Oxides) would not be a very serious problem if those thermal power generations are equipped with adequate exhaust aftertreatment for removing those pollutant emissions.
    • Light-switching-light optical transistor based on metallic nanoparticle cross-chains geometry incorporating Kerr nonlinearity

      AbdelMalek, Fathi; Aroua, Walid; Haxha, Shyqyri; Flint, Ian; National Institute of Applied Science and Technology, Tunisia; University of Bedfordshire; 3Selex ES Ltd, Luton (Wiley-VCH Verlag, 2016-06-13)
      In this research work, we propose all-optical transistor based on metallic nanoparticle cross-chains geometry. The geometry of the proposed device consists of two silver nanoparticle chains arranged along the x- and z-axis. The x-chain contains a Kerr nonlinearity, the source beam is set at the left side of the later, while the control beam is located at the top side of the z-chain. The control beam can turn ON and OFF the light transmission of an incoming light. We report a theoretical model of a very small all-optical transistor proof-of-conceptmade of optical ‘light switching light’concept. We show that the transmission efficiency strongly depends on the control beam and polarization of the incoming light. We investigate the influence of a perfect reflector and reflecting substrate on the transmission of the optical signal when the control beam is turned ON and OFF. These new findings make our unique design a potential candidate for future highly-integrated optical information processing chips.
    • A low profile antenna for millimetre-wave body-centric applications

      Ur-Rehman, Masood; Malik, Nabeel A.; Yang, Xiaodong; Abbasi, Qammer Hussain; Xidian University (IEEE, 2017-09-27)
      Millimetre-Wave frequencies are a front runner contender for the next generation body-centric wireless communications. In this paper, design of a very low profile antenna is presented for body-centric applications operating in the millimetre-wave frequency band centred at 60 GHz. The antenna has an overall size of 14£10.5£1.15 mm3 and is printed on a flexible printed circuit board. The performance of the antenna is evaluated in off-body, on-body and body-to-body communication scenarios using a realistic numerical phantom and verified through measurements. The antenna has a bandwidth of 9.8 GHz and offers a gain of 10.6 dBi in off-body (free space) configuration while 12.1 dBi in on-body configuration. It also acheives an efficiency of 74% in off-body and 63% in on-body scenario. The small and flexible structure of the antenna along with excellent impedance matching, broad bandwidth, high gain and good efficiency makes it a suitable candidate to attain simultaneous data transmission/reception at millimetre-wave frequencies for the 5G body-centric applications.
    • Millimetre-wave antennas and systems for the future 5G

      Ur-Rehman, Masood; Abbasi, Qammer Hussain; Rahman, Atiqur; Khan, Imdad; Chattha, Hassan Tariq; Abdul Matin, Mohammad; University of Bedfordshire; Texas A & M University at Qatar; University of Glasgow; North South University, Dhaka; et al. (Hindawi, 2017-04-10)
      Editorial of the special issue on Millimetre-Wave Antennas and Systems for the Future 5G
    • Minimal mean-square error for 3D MIMO beamforming weighting

      Xu, C.; Cosmas, John; Zhang, Yue; Brunel University; University of Bedfordshire (Institution of Engineering and Technology, 2016-11-24)
      The 3D MIMO beamforming system needs a weighting method to determine the direction of beam whist reducing the interference for other beam areas operating at the same carrier frequency. The challenge is to determine the weights of the 3D MIMO beams to direct each beam towards its cluster of user terminals while placing its nulls at undesired user directions to minimise undesired interference. Therefore, the signal-to-interference-plus-noise ratio should be increased while the interference from the side lobes of the other beams reduced. A weight determining method is presented that constructs horizontal and vertical array weights, respectively, by minimising the mean-square error between the array pattern vector and the unit vector, where the unit vector expresses the desired direction for the array pattern and zero vector expresses the undesired direction. Since the rectangular planar array can be viewed as M linear arrays of N elements, the weight of the M–Nth element can be obtained based on the horizontal and vertical array weights.