In this paper, the problem of how to optimally and precisely control array response levels is addressed. By using the concept of the optimal weight vector from the adaptive array theory and adding virtual interferences one by one, the change rule of the optimal weight vector is found and a new formulation of the weight vector update is thus devised. Then, the issue of how to precisely control the response level of one single direction is investigated. More specifically, we assign a virtual interference to a direction such that the response level can be precisely controlled. Moreover, the parameters, such as, the interference-to-noise ratio (INR), can be figured out according to the desired level. Additionally, the parameter optimization is carried out to obtain the maximal array gain. The resulting scheme is called optimal and precise array response control (OPARC) in this paper. To understand it better, its properties are given, and its comparison with the existing accurate array response control ( ${\textrm {A}}^2\textrm{RC}$ ) algorithm is provided. Finally, simulation results are presented to verify the effectiveness and superiority of the proposed OPARC.

This paper presents a novel strategy to simultaneously estimate the direction-of-arrival (DOA) of a source signal and the phase error of a partly calibrated array with arbitrary geometry. We add up the snapshot data of two different sensors, and then extract a knowledge associated with the DOA and phase errors of these two elements by using singular value decomposition (SVD). In such a manner, we can establish a series of linear equations with respect to the unknown DOA and phase error, by simply conducting the procedure on any two sensor elements. On this basis, it can be shown that the problem of jointly estimating DOA and phase error is equivalent to a least square (LS) problem with a quadratic equality constraint. To solve this LS problem (so that the DOA and phase error can be obtained), an effective convex-concave procedure (CCP) is employed. Different from the conventional algorithms that are limited to specific array geometries, the proposed one is suitable for arrays with arbitrary geometries. More importantly, the devised method only requires one extra calibrated sensor, which is not necessarily adjacently located with the reference one. Several simulations are carried out in this paper and the effectiveness of the devised method can be clearly observed.

This paper presents a new method to synthesize high-performance beampatterns, with the aid of linear fractional semidefinite relaxation (LFSDR) technique and quasiconvex optimization approach. We consider two beampattern synthesis problems. The first one is how to determine the weight vector to maximize the array gain (or equivalently, to minimize the gain loss in mainlobe), under the condition that the amplitude response satisfies specific requirements. The second one is how to minimize the notch level at a given region, on the premise of a permissible gain loss in mainlobe. To these ends, two non-convex optimization problems are first formulated and then relaxed to their quasiconvex forms, by using the LFSDR technique. To further solve the resultant problems, the bisection method, which is commonly used in quasiconvex optimization, is adopted. Suboptimal solutions to the original non-convex problems are finally obtained through eigenvalue decomposition (EVD) or randomization manipulations. The proposed method performs well in both cases described above. Moreover, our method is not limited to the array configurations and/or noise environments. Representative simulations are presented to demonstrate the effectiveness of the proposed method in high-performance beampattern synthesis.

This paper presents a flexible array response control algorithm via oblique projection, abbreviated as FARCOP, and its application to array pattern synthesis. The proposed FARCOP algorithm stems from the adaptive array theory, and it can flexibly, precisely and simultaneously adjust the array response levels at multiple angles based on an arbitrarily given weight vector. Different from the existing approaches, the proposed FARCOP algorithm controls multi-point responses by linearly transferring the given weight vector, with a transformation matrix containing a set of parameters, each of which can be very easily determined by the desired response level (at the control angle). Owing to the fact that those parameters are independent of each other, the response levels at the control angles can be either individually or jointly and, therefore, flexibly adjusted. Since the parameter phases can be arbitrary, we take the beampattern into account and propose to uniquely choose the optimal parameters under the typical criterion of maximum white noise gain (WNG). Accordingly, a gradient projection (GP) algorithm is devised to achieve the optimal solution. Moreover, a closed-form solution is derived for the centro-symmetric array. In addition, the application of the FARCOP algorithm to pattern synthesis is discussed. Comparing to the state-of-the-art methods like multi-point accurate array response control (MA ² RC), the proposed FARCOP algorithm controls the array responses more flexibly with lower computational complexity. Representative examples are presented to demonstrate the effectiveness and superiority of the FARCOP algorithm under various situations.

This paper presents two secure transmission algorithms for millimeter-wave wireless communication, which are computationally attractive and offer analytical solutions. In the proposed algorithms, we employ phased-array transmission structure and consider phase shift keying (PSK) modulation. It is found that the traditional constellation synthesis problem can be solved with the aid of polygon construction in the complex plane. A detailed analysis is then carried out and an analytical procedure is developed to obtain a qualified phase solution. For a given synthesis task, it is derived that there exist infinite weight vector solutions under a mild condition. Based on this result, we propose the first secure transmission algorithm by varying the transmit weight vector at symbol rate, thus resulting exact phases at the intended receiver and producing randomnesses at the undesired eavesdroppers. To improve the security without significantly degrading the symbol detection reliability for target receiver, the second secure transmission algorithm is devised by allowing a relaxed symbol region for the intended receiver. Compared to the first algorithm, the second one incorporates an additional random phase rotation operator to the transmit weight vector and brings extra disturbance for the undesired eavesdroppers. Different from the existing works that are only feasible for the case of single-path mmWave channels, our proposed algorithms are applicable to more general multi-path channels. Moreover, all the antennas are active in the proposed algorithms and the on-off switching circuit is not needed. Simulations are presented to demonstrate the effectivenesses of the proposed algorithms under various situations.