Robust Capon beamforming with weighted sparse constraint

Abstract

Adaptive beamforming is widely used in the fields such as radar, sonar, wireless communication to estimate the parameters of the signal of interest (SOI) at the output of a sensor array by data-adaptive spatial filtering and interference suppression. The standard Capon beamformer (SCB) is a typical adaptive beamforming approach which provides a superior performance by minimizing the array output power while simultaneously maintaining the array response under the assumption of distortionless direction of arrival (DOA). However, the advantages in performance of SCB are obtainable only when the number of snapshots available for the sample covariance matrix estimation is large enough and the direction of the SOI is known accurately. When applied to practical situations where the aforementioned two requirements are not satisfied, SCB will suffer high sidelobe levels and performance degradation in the parameter estimates due to lack of measurements and mismatch in the steering vector.A sparsity-constrained Capon beamformer (SCCB) arises to alleviate these problems. Unlike SCB, the constraint in SCCB is composed of two parts: the original array output power constraint part and the sparse constraint part (?1 norm constraint, encouraging sparse distribution in the array responses). However, if the sparse constraint in SCCB is set too large compared with the array output power constraint part, the responses in the directions of interferences will be influenced, and a tradeoff between the ability to reduce the sidelobe levels and the ability to reject the interferences must be made. Thus, based on the SCCB, a new robust Capon beamformer utilizing a weighted sparse constraint is proposed in this paper. In the proposed method, the sparse constraint part is replaced by a weighted sparse constraint, which is applied only to the sidelobe regions of the beampattern. By doing so, the number of the non-zero elements in the sidelobe response is minimized, resulting in an enhanced mainlobe region and suppressed sidelobe ones.In sparse recovery, the sparse constraint (the l1 norm constraint) does not necessarily enforce democratic penalization, which means that larger coefficients are penalized more heavily than smaller coefficients. Based on such a consideration, a weighting matrix can be constructed to put larger weights in the interferences directions to discourage their responses, and put smaller weights to maintain the responses in the remaining parts of the sidelobe regions. In this paper, the weighting matrix is obtained by utilizing the orthogonality between the signal subspace and the noise subspace. Since the steering vectors corresponding to the interferences and the SOI span the same space as the signal subspace, the inner products between the steering vectors in the interference directions and the noise subspace will produce zeroes ideally. By taking the reciprocals of these inner products, large values will yield in the interference directions while small values are obtained in other directions in the sidelobe regions. Using these values as the weights to the sparse constraint, a beampattern with deeper nulls, lower sidelobes, and better robustness to steering vector mismatch is obtainable as compared with SCB and SCCB. Besides, the output SINR is also effectively improved. Numerical simulations and a water-tank experiment are conducted to demonstrate the effectiveness of the proposed method.

Presheath formation and area design limit satellite-based Langmuir probes

“…On satellites, Langmuir probes are designed to measure space plasmas with plasma density ranging from 10 2 -10 7 cm −3 . Increasing the size of the probe tip is often the most direct way to ensure sufficient signal strength, as in the case of the semi-spherical Langmuir probe, with a diameter of 5 cm, used on the China Seismological Electromagnetic Satellite (CSES) [10,11]. This probe size is orders of magnitude larger than that of probes used in almost all other lowtemperature plasmas (usually on the order of millimeters).…”

“…In the past, the size of spacecraft, such as satellites and sounding rockets, was relatively large. Therefore, even Langmuir probes with centimeter-level diameters could meet the criterion where the probe area was less than 1/1000 of the spacecraft's surface conductivity area, providing a sufficient design margin to obtain complete probe data [10]. On the other hand, the recent promotion of low-cost micro/nanosatellites, such as CubeSats, has made the use of micro/nanosatellites for space plasma exploration increasingly popular [15][16][17].…”

Robust Beamforming Based on Weighted Vector Norm Regularization

“…However, these methods can hardly realize spatial filtering when the SNR is not high enough or the number of the desired signal plus interferences is extremely high [12]. With the wide application of sparse representation in statistical signal processing and parameter estimation [19], [20], [21], [22], some sparse-constraint-based beamforming methods have emerged [23], [24]. Given the sparse distribution of interferences in the sidelobe region, the array response in the sidelobe region is sparsely constrained in these methods.…”